Sam's Educational Michelson Homodyne Interferometer Project Manual V2.1

Abstract

An experimental setup is presented which allows for several types of interferometers to be easily implemented without requiring any special tools or test equipment. The behavior of various interferometer configurations will be explored as well as how the characteristics of the laser impact performance. Various enhancements are also described for both the laser and detector, as well as extensions to actual measurements like displacement (change in position) down to nm precision. The set of parts may be easily duplicated and/or modified for specific interests.

Introduction

IMPORTANT: If the interferometer is from Excel, it will be necessary to confirm that the Polarizing Beam Splitter (PBS) cube (labeled 1011A or 1012A) functions correctly. I have recently come across a small number of Excel PBSs - even new/NOS ones - where the coating on the diagonal is defective even though it looks pristine by eye. At the normal angle of incidence they are either marginal or totally ineffective at behaving like a PBS.

The simplest way to test the PBS uses the linear polarized laser that comes with most of these kits. Its polarization axis should be oriented vertically. For a random polarized laser, a linear polarizer (LP) will be required to create a linearly polarized beam that is oriented vertically. It can be a piece of LP film from this kit or one for a camera but NOT a circular polarizer. Remove everything from the interferometer - cube corner(s) and quarter wave plate(s) and place it in the beam with the label at the top and an edge parallel to the beam. If the PBS is good, there will be almost no light coming out the front with most being reflected to one side. Rotate the PBS a few degrees either way around the vertical axis and very little light should still get through. Rotate the PBS 90 degrees around the vertical axis and repeat. The behavior should be similar except that the reflected beam will exit from the opposite face. If either test behaves strangely, contact me for a replacement. I will pay shipping for the replacement and to return the original. Sorry about that. These have been included in the Hobby Special kits for several years but just recently, someone found a defective one. It had never occurred to me to even test high quality PBS cubes as they should not go bad, or be bad from the factory.

IMPORTANT: This manual applies to version 2.1 of Sam's Educational Michelson Homodyne Interferometer Kit. Here are links to all of them:

• Sam's Educational Michelson Homodyne Interferometer Project Manual V1.x: Original versions developed for a local college.

• Sam's Educational Michelson Homodyne Interferometer Project Manual V2.0: Versions for sale prior to 2022.

• Sam's Educational Michelson Homodyne Interferometer Project Manual V2.1: This manual. Differences compared to V2.0 are minor. Versions available starting in 2022.

• Sam's Educational Michelson Heterodyne Interferometer Project Manual V2.1: There is no V1.x or V2.0. Kits will be available soon.

For the combined kit (heterodyne + homodyne), both of the relevant manuals will need to be referred to, though there is a lot of overlap.

Detailed information and instructions on using and constructing most of the sub components of these kits like the various custom PCBs may be found at Sam's Electronics and Laser Kit Information and Manuals. There will also be links to them throughout this manual.

Homodyne interferometers employ a laser which nominally produces a single optical frequency ("laser line") while heterodyne interferometers employ a laser that generates two closely spaced optical frequencies. They each have their advantages and drawbacks. Much more on this below.

The photo below shows the Basic version configured for the LI. There are minor variations in the actual kits depending on version and whether they are the "Basic", "Deluxe", or "Deluxe+" versions, though this layout will work for all of them. Differences will be noted below. Where the total path length and PLD is small, no beam expander is needed for the laser as in the Basic version. This may result in a larger signal since the entire beam hits the detector. But the smaller beam makes it more sensitive to alignment.

Typical Linear Interferometer Setup with Quadrature Decoder and µMD0

Interferometers are the key technology is numerous applications in manufacturing and testing where the very minute wavelength of light is the "yardstick" providing non-contact measurements down to nanometer precision. In short, a light source is split into two parts that may travel different paths and then recombined at some type of detector. Where the path lengths differ by an integer number of wavelengths, the result will be constructive interference and the output of the detector will be high; where it differs by an integer number of wavelengths plus one half wavelength, the result will be destructive interference and the output of the detector will be low. In between, the output will vary sinusoidally. With suitable detectors and electronics, remarkably precise measurements can be performed. For example, nearly every microchip manufactured in the explored universe has been done with wafer steppers whose stages were positioned using interferometry based on HeNe lasers.

While interferometers are employed in a wide array of applications, the general emphasis for these experiments relate to the use of interferometery in metrology - precision measuremens of physical characteristics like displacement, velocity, angle, straightness, and more. Therefore unlike numerous interferometer experiments that may be found via a Web search, the emphasis here is on the signals that the setup provides, not so much on the interference patterns. (Though nothing precludes the observation of these.

The experimental setups will enable various interferometer configuration to be easily implemented and then tested with one arm being on a micrometer linear stage and/or with some other device or material that can vary the path length precisely.

The light source is a Class II 633 nm Helium-Neon laser (HeNe for short) with an output power of between 0.4 and just over 1 mW. The basic detector is a biased photodiode connected to a dual channel digital oscilloscope. Variations and enhancements to these will be offered as options.

Among the areas that can be explored with the Basic setups are:

• Techniques for aligning the interferometer.
• Impact on performance of the coherence length of the laser source.
• Inserting optics in one of the beam paths.
• Using the interferometer as a pressure and/or temperature sensor.

There is no need to construct all of the interferometer configurations described below. Doing the Linear Interferometer (LI) first makes sense since there are detailed instructions on its construction, alignment, testing. Building the High Stability Plane Mirror Interferometer (HSPMI) would be the logical next step moving from cube corners to plane mirrors. It also permits the loudspeaker and/or PZT actuators to be added. Then after that one of the others. Perhaps coordinate with the other project students using this same kit so that each of you do different ones.

This minimal set of experiments can all be done using parts in the Basic Kit:

• Construction of Linear Interferometer (LI).
• Evaluating and explaining fringe response for various path length differences with respect to lasing modes.
• Interferometer as air pressure or index of refraction of air sensor.
• Interferometer as temperature sensor.
• Construction of Quad-Sin-Cos detector for displacement measurements.
• Homodyne measurement display using µMD0.

The following additional projects can be done using parts in the Deluxe kit:

• Construction and testing of other types of interferometers including the PMI, HSPMI, and SBI.
• Construction of Original Michelson Interferometer (BMI) and comparison with the LI.
• Resolution of the various interferometer configurations.
• Sensitivity to alignment based on configuration.
• PZT actuator for sub-wavelength-scale movement.
• Loudspeaker actuator for wavelength scale movement and "interferometer microphone".
• Interferometer as earthquake and/or vibration detector.
• Analysis of interferometer behavior as a function of the laser modes.

The following are more advanced projects, but they may require additional parts and/or different parts including the laser that are not included in the either kit:

• Interferometer as gas partial pressure sensor.
• Substitution of random polarized HeNe laser for the linearly polarized laser.
• Construction of the laser itself using a bare laser tube, power supply, and mounts.
• Stabilizing the laser for single frequency operation using analog circuits or µSLC1.
• Implementation of stabilized two frequency Zeeman HeNe laser. (Requires suitable random polarized laser.)
• Heterodyne measurement display using µMD1 or µMD2.

There is some information on these in this manual and links will be provided to learn more.

As of Winter 2022, there are 3 versions of the setups. Around 5 each of V1.0 and V1.5 (which differ in minor details) have been built and are being used for in-person and remote project labs at a local college; V2.1 is the one for sale going forward and comes in several flavors. The detailed asseembly instructions in this manual are for V2.1.

Various configurations of V2.1 are or will be available on eBay under my user ID siliconsam or by searching for "Sam's Educational Michelson Interferometer Interferometer Experimental Setups for Education-Signal Oriented". Or directly from me with more options and slightly lower cost. If interested, contact me via Sci.Electronics.Repair FAQ Email Links Page.

Some of the photos here are of the original prototype on a custom aluminum optical breadboard. They are only for reference (and because I'm too lazy to reshoot them!).

Note: Off-page links (including any clickable graphics) open in a single new window or tab depending on your browser's settings. A suitable fixed width or monospace font like "Courier New" must be specified in your browser to make sense of the simple ASCII diagrams. For Firefox, go to: "Settings", "General", "Fonts", "Advanced", "Monospace", and confirm that it is "Default (Courier New)".

Interferometers for Metrology Applications

Classic Michelson Interferometer

The textbook version is shown below:

In short, a light beam is split into two parts which are bounced off of a pair of reflectors and recombined at a detector. Any change in the relative path lengths of the two "arms" formed by the reflectors results in a phase shift between the waves in the two beams resulting in constructive or destructive interference which can be measured and converted to displacement (change in position) down to nanometer precision. All other types of measurements made by these systems are based on opto-mechanical configurations designed such that changes in the measured variable are detectable by what is in essense a Michelson interferometer.

Where the Path Length Difference (PLD) between the two arms is small, the requirements for the laser are not very stringent. In fact, for very small PLDs, an LED or even a totally incoherent source like an incandescent lamp may be substituted for the laser. However, to be useful for the PLDs necessary for most applications (millimeters to 10s of meters or more), the light source must be a laser. And not just any laser, but one that has a narrow "linewidth". While the popular concept of a laser is of a light source that is monochromatic (single color or wavelength), in reality most lasers do not even come close. It takes careful design and implementation to achieve that. For these metrology applications using the so-called "homodyne" interferometer, the laser should ideally produce an output that is a single optical frequency with a linewidth approaching zero. In practice, it isn't that narrow but can still result in a linewidth of much less than 1 MHz, resulting in a usable PLD of 100s of meters. This is usually a low power stabilized HeNe laser. However, for PLDs of a few inches, a common (much less expensive) unstabilized HeNe laser will be adequate. Within this range, all the modes will be sufficiently correlated and the fringe contrast/signal amplitude will be acceptable.

For a heterodyne interferometer, instead of a single optical frequency, there are two generated within the laser spaced by up to 20 MHz. The split frequency only limits the maximum slew rate of the remote reflector. The PLD can be very large. More on this later.

Engrave PLD on your brain. It will be used throughout this manual. :)

Cube Corner Retroreflectors

Near the end of this manual is an experimental setup similar to the original Michelson Interferometer configuration adapted for the Polarizing Beam-Splitter. So you can experience these issues for yourself.

The diagrams below show some variations on the angles of the Beam-Splitter (BS) and Mirrors (M1, M2).

The first one is essentially the same as the diagram, above. The "Single Angled" one does nothing to prevent back-reflections. And while the "Double Angled" version does eliminate back-reflections, the two beams are angled at the detector which means their relative phase will vary across the detector. That is undesirable for our experiments in at least two ways: First, it will mean that the detector won't see a clean fringe signal. In fact there may be little or no signal depending on how the fringes average across its face. Second, alignment will change as either mirror is moved making testing with respect to PLD very tricky. But can you suggest an application where it may be useful?

The first enhancement of the Michelson interferometer is to add a means of separating the outgoing and return beams so that there is vitrually no optical power returned to the laser. The simplest way to do this is to replace the mirrors with Retro-Reflectors (RRs), typically cube-corner (trihedral) prisms, which have the property of returning the beam directly back parallel with the outgoing beam, but which may have an offset. In this way, virtually none of the reflected light ends up back at the laser. The use of the RRs also greatly reduces the sensitivity to alignment as any change in their angle is converted to a small change in the distance between the outgoing and return beams, but they remain parallel.

All of the practical interferometer configurations include at least one cube corner retro-reflector.

Polarizing Beam-Splitter

The beams reflected to the two arms of the interferometer then have orthogonal polarization which effectively makes them independent until they are combined at the detectors.

The result is then one of the most widely used configurations - the Linear Interferometer (LI), which was the first one used by HP in their original 5500A laser interferometer displacement measuring system. (As an aside, I do NOT know where that name "Linear Interferometer" comes from except perhaps that the inital configuration was in-line with the laser and thus "linear".) In practice, Arm 1 is used as the reference and is made as short as possible with the Cube Corner (CC) attached directly to the PBS cube. Both arms can move where differential measurements are required.

With the use of the PBS, the maximum amount of the laser optical power is available - virtually nothing exits out the unused side of the beam-splitter as it would in the original Michelson setup, above. However, at least half the power is lost in the detection scheme that is typically used so it would end up being similar. In principle, this wasted power can be diverted to a second detector. Their difference will then have twice the amplitude and the signal-to-noise ratio will nearly double (but with opposite phase). This is rarely, if ever, done though. But for the more complex multi-pass interferometer configurations described later as well as for use with two frequency lasers, the use of the PBS is essential to avoid incurring very large losses, or for the more complex schemes to work at all.

Common Interferometer Configurations for Displacement Measurements

• Linear Interferometer (LI): Simplest, cube corner for remote reflector, single pass: resolution X1.

• Plane Mirror Interferometer (PMI): Plane mirror for remote reflector, double pass: resolution X2.

• Single Beam Interferometer (SBI): Compact, small cube corner for remote reflector, single pass: resolution X1.

• High Stability Plane Mirror Interferometer (HSPMI): Plane mirror for remote reflector, sensitivity to temperature changes <1/10th that of PMI, double pass: resolution X2.

• Modified Linear Interferometer (MLI): Same architecture as SBI but beam paths separated, cube corner for remote reflector, single pass: resolution X1. It really only has "linear" in its name because it uses cube corners like the basic LI.

• Double Pass Linear Interferometer (DPLI): Similar to the HSPMI but with cube corners for the arm reflectors, double pass, resolution X2. Like the MLI, it really only has "linear" in its name because it uses cube corners like the basic LI.

• Single Pass Plane Mirror Interferometer (SPPMI): Uses NO cube corners, single pass: resolution X1. The SPPMI may also be called the "No Cube Corner" interferometer. It is most similar to the original Michelson interferometer but uses QWPs to avoid back-reflections. However, it is similarly very sensitive to misalignment and useful only over short changes in PLD.

• High Resolution Plane Mirror Interferometer (HRPMI): Doubles the resolution compared to the PMI or HSPMI but is much more complex and tricky to align. Quadruple pass, resolution x4. A few additional parts and much determination may be required to construct this.

When used in a displacement measuring system with a 633 nm HeNe laser, 1X represents a full cycle resolution of 1/2 wavelength or ~316 nm; 2X of ~158 nm, and 4X of ~79 nm. For a homodyne system with a Quad-A-B deterctor, there are 4 counts per cycle so that gets multiplied by up to 4. For a heterodyne system using µMD2, there are 2 counts per cycle so that gets multiplied by up to 2. The very commonly used PMI or HSPMI will then have a heterodyne resolution of ~79 nm and interpolation techniques can extend it down to under 1 nm. However, if the signals are noisy or asymmetric, the benefits may not be achievable. Suggested Demonstration Setup This is a configuration that can be used to demonstrate behavior with a well random polarized HeNe laser using either the LI or PMI, and an oscilloscope in X-Y mode. It consists of:

• Standard layout with linear rail (ball bearing preferred) but with the Interferometer Mount positioned to enable maximum range for the rail. This may require placing the Interferometer (PBS) mount one or more holes to the left of the default position depending on version.

• JDSU 1107 or 1108 random polarized HeNe laser tested to confirm that it is not a flipper. These have a cavity length of 5.417 inches for a longitudinal mode spacing of 1.09 GHz. Other similar short random polarized HeNes may also be used. The polarization axes should be oriented at ±45 degrees for use as a random polarized laser (1) and at 0/90 degrees with a linear polarizer at 45 degrees to use it as the more conventional linear polarized laser (2). No beam expander is required. The random polarized setup (1) is much more exciting and challenging. But if assembling this for the first time, the linear polarized setup (2) will be easier figure out . ;-)

• Linear Interferometer (LI) or High Stability Plane Mirror Interferometer Interferometer (HSPMI) are the most straightforward since the REF and MEAS path lengths are the same for equal reflector (cube corner or plane mirro) spacing. The Plane Mirror Interferometer (PMI) may also be used but the MEAS path length is double the REF path length. The path length difference will be critical in being able to unscramble how the interferometer behaves with respect to the laser longitudinal modes as a function of cavity length which changes due to temperature resulting in mode sweep. Other interferometer configurations can of course be used, but the LI and HSPMI are easy to set up and align, switching between them can be done in under 5 minutes including optimization of alignment.

• Loudspeaker to be used as linear actuator in Arm 1 with a cube corner or planar mirror attached to the cone without restricting movement. A PZT can also be used with a mirror for the HSPMI, though mounting a cube corner on a PZT may be problematic for the LI. The actuator is placed in Arm 1 to allow for the maximum travel of the stage in Arm 2.

• Electronic function generator. One of the function generator kits on eBay for under $10 would be perfectly adequate.

• Quadrature Decoder with sin/cos analog outputs.

• Oscilloscope set up for X-Y (Lissajous) display. This can be almost any analog scope - even one more than 50 years old - or some specific DSOs. But since DSOs do not usually do an actual vector display, they may not have a fast enough refresh rate for changing signals even if there is an X-Y mode. So even a Quad-Sin-Cos signal changing at even 1 Hz (1 rotation per second) may show up as discrete spots. Thus your mileage may vary.

• Micro Measurement Display 0 (µMD0) with PC to provide a readout of displacement (optional). Alternatives are a Quad-Sin-Cos (analog) to Quad-A-B (digital) interface with µMD2 and in-line interpolator from a company like Renishaw. Or, designing such an interpolator could be a nice student project in itself implemented within the Teensy 4.0 of µMD2 using its A/Ds or stand-alone with an interpolator chip from iCHaus.

All of these are discussed below. The benefit of the suggested set of components and setup is that it allows for a variety of principles to be demonstrated without major modifications. Using the HSPMI, one complete rotation of the Lissajous (X-Y) display represents approximately 158 nm - 2.65 degrees per nm. It is hard to overemphasize the impact of being able to easily view displacements of less than 1 nm on the oscilloscope! ;-) For a "Rube Goldberg" solution to computing displacement with video capture and fast pattern analysis, it would even be possible to provide a readout of displacement down to a fraction of 1 nm using the scope display alone - at least for very slowly changing displacement. To be unambiguous, the displacement would need to change by less than 79 nm (one half rotation of the X-Y display) between frames. For something more conventional, a Teensy 4.0 using two of the analog inputs set up for 12 bit resolution and some Trigonometry. ;-) This appears capable of at least 100K samples per second on two inputs which works out to around 1 cm/s unambiguous movement. Details are left as an exercise for the student. ;-)

A parts list for the demo version may be found at Parts in Homodyne DEMO VERSION Kit ONLY. There may be a kit of parts in the future with everything except the oscilloscope and PC, and wires, etc.

Detectors - Optical to Electrical Conversion

Biased Photodiode (BPD1)

The most basic circuit is shown below:

           Silicon 
          Photodiode
   +---------|<|-------+-------o Output to scope or DMM
   |  Cathode   Anode  |
   |                   /
   |                   \ R-Load
   |                   /
   |     Bias Supply   \
   |       +| | -      |
   +--------||||-------+-------o GND / Common / Return
            | |

Note the polarity of the PD with its cathode connected to the positive of the power supply and thus reverse biased. With no light incident on the PD, only the so-called "dark current" will flow, which is generally small enough to be ignored (nanoamps or less). Actual usable detectors are almost identical to this simple circuit.

Single Channel Detectors

• Thorlabs DET110: This is typical of a commercial biased detector without amplification. More information may be found at Thorlabs DET110 Spec Sheet.

           R-Protect            PD          BNC Center
     +-------/\/\----------+----|<|------<<-----------------+------o Scope or DMM
     |        1K           |           +-<<-------------+   |
     o                     |           |    BNC Shield  |   /
      \ Power             _|_ C-Bypass |                |   \ R-Load
     o                    ---          |                |   /
     |    12 V Battery     |           |                |   \
     |        +| |-        |           |                |   |
     +---------||||--------+-----------+                +---+------o GND
               | |
  
     |<--------- Thorlabs DET110 -------->|<---- Output Wiring ---->
    

  R-Protect limits current should the battery be installed backwards or should the PD fail shorted. C-Bypass improves the high frequency response by eliminating the other components from the AC signal path.

  The DET110 mounts on a standard post using an 8-32 setscrew. Threads on the front allow accessories to be easily attached.

  The primary advantage of a detector like the DET110 is that it is in a nice shielded case with a BNC coax connector.

• Custom single channel detector: For the purposes of these kits, a much lower cost approach will have similar performance and more flexibility, being easily extended to two channels for the Quad-Sin-Cos decoder. And it will be educationally more rewarding. ;-) The circuit is virtually identical to that of the DET110:

         R-Protect    PD        Yellow
     +-----/\/\-------|<|----<<----------------------+---------o Scope Channel 1
     |                                               |
     |                                               /
     |                                               \ R-Load
     |                                               /
     |                                DC Power       \
     |                          Red    +| |-   Black |
     +-----------------------<<---------||||---------+---------o Scope Ground
                                        | |
  
     |<--- SBB or QDx PCB --->|<---- Scope / Power Wiring ---->
  

  PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.

  R-Protect: 250-1K ohms typical. R-Load: 10K-1M ohms typical.

  DC power comes from either a wall adapter or USB +5 V, so no power switch is needed. And for the low signal bandwidth here, no C-Bypass is shown, though there is a spot on the detector PCBs for one.

  Initial construction is most easily done using a small Solderless BreadBoard (SBB). This has 17 columns of two sets of 5 bussed holes. Short #20 to #24 AWG wires are used as jumpers where the busses aren't convenient. The SBB has a double-sided sticky pad on the bottom which enables it to be attached to a standard post using the "Detector adapter plate" and an 8-32 setscrew. A couple of small detector PCBs that mount directly on Thorlabs posts are also included. These accomodate either 1 or 2 PD chennels.

  For the single channel detector, only two wires need to attach to the SBB: +DC power and the signal output. The load resistor can be external, or on the SBB with an additional wire to scope GND and -DC. The wire colors are suggestions, the electrons won't care. ;-)

Testing of either detector can be done using the laser or even a flashlight to confirm sensitivity to light. However, even a super-bright flashlight will likely result in only a small signal compared to the laser.

Dual Channel Detectors

       R-Protect    PD1      Yellow
   +-----/\/\----+--|<|---<<-----------------------+----------o Scope Channel 1
   |             |                                 |
   |             |  PD2      Blue                  |
   |             +--|<|---<<---------------------------+------o Scope Channel 2
   |                                               |   |
   |                                               /   /
   |                                       R-Load1 \   \ R-Load2
   |                                               /   /
   |                                DC Power       \   \
   |                          Red    +| |-   Black |   |
   +-----------------------<<---------||||---------+---+------o Scope Ground
                                      | |

   |<--- SBB or QDx PCB --->|<----- Scope / Power Wiring ------>
  

PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.

R-Protect: 250-1K ohms typical. R-Load: 10K-1M ohms typical.

The same PCBs may be used for this circuit.

What is done with the light before it hits the photodiodes is the interesting part, which will be described where relevant. ;-)

Dual Channel Quad A B Preamp (AB2)

The purpose of the Quad-A-B Preamp (henceforth referred to as QAB2 or simply AB2) is to provide a simple solution that accepts photodiode inputs and generates differential RS422 A and B signals that can be input to µMD0, µMD1, µMD2, or another compatible displacement measuring system.

QAB2 is on a 1.6 inch by 2.25 inch PCB and runs on 12 to 15 VDC. (The PCB itself is called SG-AB2.) The optical input is a beam up to ~3 mm in diameter (using the default photodiode) with an optical power from <25 µW to >1 mW. QAB2 has >3 MHz bandwidth (full cycle) which is more than adequate for systems using the kit lasers as well as for many real applications. With a Linear Interferometer which has a full cycle of ~316 nm, the slew rate can be greater than 1 meter per second, which is a fairly nutty velocity. ;-). And it is expected that the bandwidth limit can be extended with trivial changes to only a few part values. This is left as an exercise for the student. ;-)

Populated AB2 V1.00 PCB

Although shown with photodiodes plugged into the PCB, in actual use, they would probably be on the detector PCB with short twisted wire cables to connect them to the SG-AB2 PCB.

Parts to construct AB2 will eventually be included as part of the homodyne setups. More information on AB2 including complete "Heathkit™-style" assembly instructions may be found at Quad-A-B Preamp 2 (QAB2) Assembly and Operation Manual.

Linear Interferometer

The designations m-n show the paths taken by the Arm 1 and Arm 2 beams where "m" is the Arm and "n" is the sequence number.

Linear Interferometer Setup

Linear Interferometer Diagram and Suggested Breadboard Layout

The other configurations will have a few additional or substitute parts and small variations in the horizonatal position of the laser and placement of the detector but are otherwise similar. Therefore the LI setup will be described in more detail.

• Baseplate: This is a 6x18x0.5 inch aluminum optical "breadboard" with an array of 108 1/4-20 tapped holes on one inch centers to which all the components are attached with cap-head screws or set-screws. (We may use the terms "baseplate" and "breadboard" interchangeably.)

• HeNe laser: This is a ~1.25" cylindrical laser "head" mounted within a pair of aluminum rings each with 4 screws to allow for its position and alignment to be easily adjusted. A separate high voltage power supply which plugs into the AC line drives the laser tube safely enclosed in the aluminum cylinder. The laser is of very high quality from JDS Uniphase or Melles Griot. It is the only somewhat fragile item so please don't drop it or use it to hammer nails. Your instructor (and I), and perhaps your grades won't like that. :( :)

  The photo shows a laser without a beam expander but the laser in the kit will either come with a beam expander already attached to convert the ~0.5 mm beam from the laser tube into a ~4 mm beam with low divergence, or the expander which can be attached and centered with 3 screws.

  The raw beam is a bit trickier to align and to maintain alignment as the stage in Arm 2 is moved, but it is quite adequate for a small range of PLD. But where the PLD is large (e.g., for use as an earthquake sensor), the beam expander eases the alignment and is required so that the divergence of the beam doesn't affect the detector response (e.g., the fringe contrast). Since the beam expander is secured by 3 screws (see below) it can be removed to explore how the raw beam behaves. However, two cautions: (1) Do NOT remove the plastic bezel of the laser head as that will expose the high voltage connected to the laser tube and (2) careful lateral adjustment of the beam expander will be required when reattached to center the beam.

  If using the beam expander, the posts/rings for the laser should probably be mounted one hole to the left of where they are in the photo to provide more clearance.

• Installing the optional beam expander: The black beam expander itself attaches to the "Beam Expander Adapter" which is a circular plate around 1-1/4". The threaded end of the beam expander will need to be glued to the adapter ring unless it is a tight enough fit to stay in place. If too loose, use a small amount of 5-Minute Epoxy attach it. Make sure it is centered and straight.

  Once cured (give it 15 minutes to be safe), it attached to the front of the laesr head using three M2.5 capscrews, which may already be installed. If not, they will be in one of the hardware bags or with the beam expander or adapter ring. The holes in the adapter ring are large enough so that there is (hopefully) enough adjustment range to center the beam, which must be done "live" - with the laser powered. Thread the M2.5 screws in just snug and adjust the centering until the beam is nice and round - this can also be confirmed by looked at the scatter off the front lens of the beam expander and centering there. Then tighten the screws just enough so it won't move around but it is metal in plastic so overtightening may strip the threads.

• The heart of the setup is an assembly using optical components from Hewlett Packard (HP), Agilent, or Keysight. These may be configured in a variety of ways to create several types of interferometers:
  • HP/Agilent 10702A or 10706A Polarizing Beam Splitter Cube (PBSC). (The two part numbers are physically and functionally identical except for the label.) It is a high quality 1 inch PBSC mounted in a precision stainless steel frame.

  • HP/Agilent 10703A Cube Corner (CC) retro-reflector. This is a glass trihedral prism installed in a stainless steel cylidrical case. It can be attached directly to the PBSC. Not in basic kit.

  • A pair of HP/Agilent 10722A or equivalent Quarter WavePlates (QWPs) can also be attached to the PBSC. Not in basic kit.

  As a point of interest (or trivia), these parts cost something like $4,000 if purchased new. Fortunately for us, eBay is much less expensive. :-)

  This assembly attaches to an aluminum "PBS Mount Adapter Plate" which itself secured to the breadboard with optical posts and spacers.

• Two unmounted glass cube corner retro reflector trihedral prisms: These can be secured in the one inch Thorlabs KM100 kinematic mirror mounts with the KM100s rotated 180 degrees so the knobs face the PBSC.

  For some of the other interferometer configurations, these will be replaced either with 1" planar mirrors installed in the KM100s, or with a thinner mirror glued to a loudspeaker or PZT. (More on these later.)

• The turning mirror: is simply a small rectangular high quality planar first surface aluminized mirror that redirects the output beam to the detector if needed. The exit direction of the beam depends on the specific interferometer configuration but most of them direct the output to the left so to get it to the detector requires a right angle reflection.

• The single channel detector shown in the photo is a Thorlabs DET110 biased photodiode which generates a current proportional to the amount of light (i.e., optical power). It's in a nice shielded case feeding a nice shielded BNC cable for the output and has its own own battery. It also costs a fortune. ;-) At 633 nm, the relationship is approximately 0.3 mA / mW of laser power. An external load resistor sets the sensitivity in terms of V/mW. For example, with a 10K ohm load resistor, the effective sensitivity is approximately 3 V / mW. Other commercial detectors may be substituted for the DET110. But parts are included in the kit to construct a detector that will serve the same purpose with essentially the same performance (for our needs) and can be modified for two channels to generate both amplitdue and position signals (Quad-Sin-Cos) outputs for displacement measurements. It just doesn't look as cool unless perhaps you choose to install it in a 3-D-printed case. :)

  Going forward, only parts for this home-built single or two channel detector will be included in the kits. At the very least, building the thing is more educational. ;-)

• There are either one or two types of Polarizers:
  • All kits include one or more pieces of Circular Polarizer (CP) which is a Linear Polarizer (LP) combined with a Quarter WavePlate (QWP). The LP axis is at 45 degrees to the sides.

  • Some kits also include a square piece of Linear Polarizer (LP) sheet with its polarization axis lined up with one of the sides.

  The CP type can be used for most purposes in place of an LP. Specifically here for placing in front of the detector and/or photodiodes. And if using a random polarized HeNe laser, the CP can be used to force it to be linearly polarized with the circular polarized output sent to the PBSC, which works fine. That's why some kits may not have an LP at all. But where an LP is present, it will probably be larger since the LP is used for most experiments. Only a very small piece of CP is required for the Quadrature Detector. For everything else, the LP is simpler to deal with since which side is the input doesn't matter.

  Do NOT remove the protective film until ready to use. Also note that the CP sheet has a weak adhesive on the QWP surface and it will attract dust and debris (including grubby fingerprints!) Cleaning can be done with isopropyl alcohol but the adhesive will still be there when it evaporates.

  Only small pieces of these are required for any given purpose so they can be cut as desired. Four or 9 equal pieces of each is probably a decent choice. Use masking tape to stick them whever they need to be stuck to. ;-)

A variety of mounting schemes are used:

• Laser: As noted above, the laser head cylinder is secured in a pair of 4-screw adjustable ring mounts so that it can be moved horizontally and vertically, and have its alignment fine tuned. For the interferometers, it will need to be positioned at a height of 4-1/4 inches above the baseplate and either centered or offset approximately 1/4 inch toward the back of the setup (as shown above) depending on the specific interferometer being implemented.

• PBSC assembly and turning mirror: The mount for this is the "PBS Mount Adapter Plate" attached to a pair of 3 inch Thorlabs posts with 1/4" spacers. This replaces the funky wood block in the really early versions of these kits. ;-)

• Interferometer Arm 1: This would normally be the "Reference Arm" in the basic Linear Interferometer. A Cube corner (CC) or one inch first surface mirror is installed in a one inch Thorlabs KM100 adjustable mount on a post in a post holder which allows for height and rotation about the vertical axis, and also fine adjustment pan and tilt of the CC itself via the knobs on the KM100.

• Interferometer Arm 2: This is what the "Tool" of a displacement measureing system (for example) would mount on. It has a similar KM100 for a mirror or CC, but mounted on a micrometer controlled linear stage so that its position can be adjusted very precisely. A loudspeaker with a mirror glued to its cone to be used as an electrically driven actuator or as a laser microphone can also be installed in the KM100.

• Custom detector: For the kits, this is a small solderless breadboard (though a prototyping board or even a custom PCB may be used instead). For the single channel version, a photodiode and its protection resistor to the bisa supply are installed, along with an LP (or CP used as an LP) at 45 degrees in front of the PD. For the interferometer setup, the performance is more than adequate and indistinguishable from the DET110. And the ~100:1 cost advantage :) makes it likely to be the default going forward. This same platform will also be used for the quadrature decoder.

Setting the Heights

Required Optical Components and their Suggested Heights.

The heights of any Retro-Reflectors (RRs) in the setup will be what most affect the beam height. This is true of the Linear Interferometer (LI). Where there is an RR attached to the PBS cube like the Plane Mirror Interferometer (PMI), the alignment of the laser will need to be used. However, there is a wide tolerance and enough degrees of freedom so in the end, it should not really be much of a problem to set it up.

Here is an annotated photo of the Deluxe version configured for the HSPMI:

Deluxe Version Configured for the High Stability Plane Mirror Interferometer with µMD0

The Deluxe+ version would be similar except for the larger breadboard and longer rail; The Basic version does not include the beam expander, mounted CC, QWPs, or planar mirrors.

Assembly and Alignment of the Linear Interferometer

It is assumed that nothing has been mounted, but depending on the previous use, some of these steps have already been completed. Refer to the layout diagrams, above, parts locations that are known to work.

Parts attached with fasteners should be snug but don't overtighten.

It is also assumed that the laser is linearly polarized. Slight changes are required if it is random polarized.

1. Laser mount posts: Attach two 3 inch posts to the breadboard using 1/4-20 set screws.

   If the laser head has a beam expander, or it is anticipated that one will be added later, it is recommended that the posts be mounts 1 hole to the left of where the are in the photo.

   Note: To assure that there are ample threads engaged in both parts here and in subsequent steps with set-screws, the set-screw should be installed approximately half-way into the baseplate or mounting plate and then a thin tool or even the edge of a metal plate or stiff cardboard can be used to keep the set-screw from turning as the post or post holder is threaded onto it before tightening.

2. Laser mount rings: Secure through to the top of the posts with 8-32 1/2 inch cap-head screws. If the mounting hole in the rings is threaded, there should be plastic washers to go between the rings and the spacers to provide compliance so the rings can be tightened with the correct alignment.

3. Laser head: These steps secure and align the laser head cylinder.
   • Install the Nylon thumbscrews in the ring mounts if not already present. If there are two different lengths of thumbscrews (e.g., 1 and 1-1/4 inch), the longer ones should be in the front side of the rings. If the thumbscrews are much longer than needed, they can be trimmed. However, since not all interferometer configurations have the laser head in the same position, make sure not to cut them too short!

   • Slip the laser head into the rings. Initially set it to approximately centered horizontally and vertically. Then shift it 1/4 inch toward the back of the baseplate.

   • Plug the big white male "Alden" connector of the laser head into the female Alden connector of the power supply. Make sure it is seated fully, usually against the shoulder with no part of the prongs visible.
     • If the power supply is "lab style" - a chessy plastic box with keylock switch and power indicator - then it plugs into the AC line. An IEC type line cord will be included if in the USA; you will have to provide the approriate like cord if elsewhere. If there is a voltage switch on the back of the supply, confirm that it is set corretly for your location. If set wrong, the power supply may be damaged.

     • If the power supply is a bare "brick", it requires 12, 15, or 24 VDC from a matching wall adapter that should be included. Confirm that the voltage ratings match. There may be more than one wall adapter in the kit that appear similar. Check the labels! Using the wrong one may damage the brick and/or wall adapter. The wiring is probably already done via a barrel to screw terminal adapter, but confirm that the wires are secure and attached to the correct terminals. Positive is red and negative is black. If there is a yellow wire, it should be attached to the black wire and thus negative as well.

   • Power up the laser by turning the keylock switch or plugging in the wall adapter. It may take a few seconds or even up to a minute to light. If it doesn't light in a reaosnable length of time, check the wiring. Shining a flashlight in the front of the laser will sometimes help it along. DO NOT stare into the beam with your remaining good eye. :-)

   • Confirm that the laser is polarized: The model number should be 1107P, 1108P, or 05-LHP-211. There should be an alignment mark near the front of the laser. If not or just to confirm, rotate an LP or LP/CP in front of the laser. If the laser is polarized, there will be orientations where virtually no light gets through at all times. The polarization axis is then at 90 degrees to this. Add an alignment mark if there is none. (If it is random polarized, this orientation will swap by 90 degrees over a few seconds as the laser warms up. More on this below in the section on linear versus randon polarized lasers.) DO NOT assume the yellow arrow of the safety sticker (if present) identifies the polarization orientation (though it probably does if there is no other mark). But check it anyhow!

   • Orient the laser head so the polarization axis is at -45 degrees (counterclockwise) from vertical when viewed from the front. What differences will there be if it is at +45 degrees?

   • Using the thumbscrews, adjust the position so that the beam is at a height of exactly 3-3/4 inches (which should be centered vertically in the rings) and perfectly horizontal, and 1/4 inch toward the back of the setup. DO NOT overtighten the thumbscrews - just enough so the laser head won't move on its own.

     Doing this accurately is critical to the ease with which the subsequent alignnment can be performed since not all mounts have sufficient degrees of freedom to accomodate an arbitrary beam location and direction. Fabricating an "alignment aid" out of carboard may be useful. This would have a hole at the optimal height offest 1/4" toward one side from a mark at the bottom.

4. Interferometer assembly: This consists of the Polarizing Beam-splitter cube, mounting plate, 2x 3" posts. 2x 1/2" 1/4-20 setscrews, 2x 1/4" spacers, 2x 8-32 x 1/2" cap-head screws.
   1. Attach a pair of 3" posts to the breadboard with 1/4-20 x 1/2" setscrews in the locations shown above. Thread the setscrews about half-way into the breadboard. Then with something thin pressing on their sides to prevent them from turning, thread the posts onto the setscrews until they contact the breadboard. Use a thin rod (e.g., hex wrench) through the hole in the post to tighten them.

   2. Attach the "PBS Mount Adapter Plate" to the posts with a pair of 8-32 x 1" or 1-1/8" cap-head screws with 3/4" spacers between the plate and post. The screw on the right should be made fairly tight as it won't be accessible once the PBSC is installed.

   3. Remove any optics that may be attached to the PBSC. They will not be required for the LI. Store them wrapped in soft paper towels, bubble wrap, etc., to protect the optical surfaces.

   4. Place the PBSC on the PBS Mount Adapter Plate so that the diagnonal marking is front-left to back-right with the "In" arrow pointing left-to-right.

   5. Use four 4-40 x 1-3/4" cap-head screws to secure the PBSC to the plate from the top if the adapter plate holes are tapped or four 6-32 x 1/2" cap-head screws from the bottom if they not tapped.

   The laser beam should pass through the PBSC centered vertically and 1/4 inch toward the back. It should be at the same location relative to the breadboard at the far end. If not, fine tune alignment. :) Getting this dialed in via the nuts on the studs will greatly simplifiy alignment later.

5. Turning mirror: Use tape or a *tiny* bit of adhesive to attach the turning mirror to the right angle "Turning Mirror Bracket" centered vertically with respect to the PBSC and flush with the right edge. Attach the bracket to the PBS Mount Adapter Plate with a 3/8" 4-40 cap-head screw and #4 washer. Center the screw in the elongated hole for now.

6. Arm 2: These steps assemble the components of Arm 2. Arm 2 is assembled first because the lateral position of the CC cannot be adjusted relative to the laser.
   1. Thorlabs rail, ball bearing rail, or motion control platform: This assumes an initial installation, not swap.
      • Thorlabs rail (Homodyne only):
        1. Attach the Thorlabs RLA0600 6 inch rail (Basic and Deluxe) or Thorlabs RLA1200 12 inch rail (Deluxe+ version) to the breadboard. The recommended location is shown in the diagram above.

        2. Add 8-32 screws and #10 washers to the ends of the rail to act as stops.

        3. Attach the linear stage to the RC1 carrier using a 4-40 cap-head screw and washer.

        4. Install the stage/carrier assembly onto the RLA rail.

      • Ball bearing rail (Heterodyne or combined):
        1. Attach the MGN15-150mm rail with MGN15C carriage to the breadboard. Try to avoid removing the carriage from the rail as it is then easy for some ball bearings to attempt to escape. :( ;-) Since the holes in the MGN15-150mm rail do not line up with breadboard holes, it is attached to the breadboard with either a pair of 6-32 cap-head screws installed in special tapped holes, or one of these along with a 6-32 screw with nut and lockwasher through a 1/4-20 hole. The recommended location is shown in the diagram above.

        2. Attach the linear stage adapter plate to the MGN15C carrier using four M3-6mm flat-head screws. Tighten these securely as they won't be accessible after the other parts are installed.

        3. Attach the linear stage to the MGN15 adapter plate using four 4-40 1/4 inch cap-head screws at the corners.

        4. Add stops at both ends of the rail using the rubber bumpers (150 mm rail) or screws, spacers, and nuts (300 mm rail) provided. ;-)

      • Motion Control Platforms: These instructions will differ slightly depending on whether the MCP is Type 1 or TYpe 2, and on the length.
        1. If purchased at the same time as the interferometer, holes will already have been drilled in the breadboard for the stepper motor rig, with the motor on the right. These locations will enable the maximum usable travel. Else holes wlil need to be added.

           Secure the platform on the breadboard using four 4-40 1/2" cap-head screws if the holes are tapped, or 4-40 3/4" screws and nuts if not. Take care to assure that it is aligned.

        2. Attach the linear stage adapter plate to the platform using four M3-6 flat-head screws. To maximize travel, the plate should extend to the left (toward the PBS).

        3. Attach the linear stage to the linear stage adapter plate using four 4-40 1/4 inch cap-head screws at the corners.

        For more on setting up and using the MCP, see the section: Motion Control Platform

   2. Refer to the "Suggested Heights" diagram and attach a 2" post holder (rail or slide) or 1" post holder (MCPs) to the linear stage with an M3-12mm cap-head screws and #4 washer through the hole in the bottom of the post holder. Orient it so the knob on the post holder is easily accessible. Center the screw as best as possible and tighten it securely. Note: The hole may be tapped 4-40, in which case the screw should be 4-40 1/2".

      CAUTION: Make sure the tip of the screw does NOT contact the fixed part of the linear stage. If it does, an addition washer may need to be added. Or the screw can be shortened slightly with a metal file or grinding wheel.

   3. Adjust the micrometer so the stage is approximately in the center of its travel range.

   4. KM100 or similar mirror mount: Secure to a 1" post (rail or slide or MCP Type 1) or 3/4" post (MCP Type 2) with an 8-32 3/8" cap-head screw. Slip the post into the Arm 2 post holder and hand tighten its htumbscrew. Adjust the two alignment knobs so that the mounting plate is parallel to the base in both directions. If the adjustments are too tight, check that any locking screws are not tightened. Else, total removal, cleaning, and lubricating with a tiny amount of light grease or machine oil will be required.

   5. Cube Corner (CC) trihedral prism: Install the CC in the KM100 with its apex facing out and oriented to that a flat is at the top or bottom. (This reduces the chance of the beams hitting an edge of the prism.) It should be secured with either a soft-tipped set-screw or Nylon wide-head screw. DO NOT overtighten - it should be snug enough not to fall out (these are fragile!) but not so tight as to smash the CC! Note that the CCs mount backwards from what might be expected so that their edge can be secured properly. It's flat surface is facing through the mount.

   6. Set the knobs of the adjustable mount so its fixed and moving plates are approximately parallel and orthogonal to the beam axis as in the diagrams.

   7. The horizontal and vertical position (not orientation) of the CC relative to the incident beam adjusts the corresponding coarse position of the return beam.
      • Since the adjustable mount on Arm 2 and thus its CC cannot be moved laterally relative to the laser, the laser alignment should be double checked and fine tuned via its mounts if necessary so the incident beam is offset 1/4" toward the back of the setup from the center of the CC and aligned with the holes, and thus the return beam will be offset 1/4" toward the front of the setup and parallel to the incident beam.

      • The vertical position of the CC is adjusted by loosening the post holder's thumb-screw and should be set so the incident and return beams are at the same height.

   8. Place a piece of paper where the detector would be for the beam from the turning mirror. Fine tune the orientation and height of the mirror mount so there is a bright return beam there from Arm 2.

1. Attach a 2" post holder to a BA1S holddown with a 1/4-20 3/8" cap-head screw. Orient it so the thumbscrew (knob) is accessible.

2. Attach this assembly to the baseplate using a 1/4-20 1/2" cap-head-screw.

3. KM100 or similar mirror mount: Secure to a 2" post with an 8-32 3/8" cap-head screw. Slip the post into the Arm 1 post holder and hand tighten its thumbscrew. Adjust the two alignment knobs so that the mounting plate is parallel to the backplate in both directions. If the adjustments are hard to turn, check that any locking screws are not tightened. Else, total removal, cleaning, and lubricating with a tiny amount of light grease or machine oil will be required.

4. Cube Corner (CC) trihedral prism: Install a CC in the mount with its apex facing out and oriented so that a flat is at the top or bottom. This is to orient the prism so that the beams do not hit an edge. It should be secured with either a soft-tipped set-screw or Nylon wide-head screw. DO NOT overtighten - it should be snug enough not to fall out (these are fragile!) but not so tight as to smash the CC! Note that the CCs mount backwards from what might be expected so that their edge can be secured securely. :) They thus face through the mount.

5. Start with the knobs of the adjustable mount set so its fixed and moving plates are approximately parallel and orthogonal to the beam axis as in the diagrams. The BA1S can be moved to adjust the coarse horizontal position of the return beam. The post holder's thumb-screw may be loosened to move the adjustable mount up or down to adjust coarse vertical position of the return beam. The return beam should hit the PBSC at the same height as the incident beam, and offset 1/4" to the left of center. The spacing between the centers of the incident and returns beams should then be 1/2".

6. Using your piece of paper with the Arm 2 return beam unblocked, there should now be two spots reflected from the turning mirror corresponding to the returns from Arms 1 and 2. (Unless, that is, you're very lucky and they are already superimposed perfectly!)

7. Adjust the position and orientation of the CCs to superimpose the return beams from Arm 1 and Arm 2. This can be fine tuned with the adjustable mount knobs initially by eye. Then later once the oscilloscope is set up, it can be further optimized by maximizing signal amplitude from the detector.

• Attach a BA1S Holddown to a 2 inch post holder with a 1/4-20 3/8 inch cap-head screw.

• Install a 3 inch post into the post holder with the small (8-32) tapped hole at the top with the lock screw just snug.

• Clamp the assembly down loosely with a 1/4-20 1/2 inch cap-head screw.
  • Custom detector: Install a photodiode, 1K ohm resistor, and male-male jumper wires to the solderless breadboard or detector PCB based on the circuis in the section: Single Channel Detectors and mount it on the post.

  • Thorlabs DET110: Mount the DET110 on the post and attach a BNC cable for the signal.

• install a 10K ohm resistor for R-Load. 10K is probably an acceptable value but depending on laser power and alignment, a higher (most likely) or lower resistance may be desirable. R-Load can be located at the detector or scope, whichever is more convenient.

• Tape or place a piece of LP or LP/CP to the front of the sensor with its polarizaiton axis at 45 degrees (edges at 0/90 degrees). If using the CP, remove the protective film from both sides. The sticky side can be stuck directly to the DET110 or PD when used as an LP.

• Apply power to the home-built detector from the 12 VDC adapter or switch on the DET110.

And for those new to interferometers, to reiterate, the optimal alignment will also be where the signal instability is maximized. ;-) Almost ANYTHING will affect it from touching the apparatus or table on which it is on, to just walking across the floor. The wavelength of light is really really small. ;-) To put this in some perspective, a full cycle of the signal with the Linear Interfemeter is a change in PLD of 316.4 µm (1/2 wavelength of 632.8 nm or 1/3,160th of a mm). That's about 1/158th the diameter of an average human hair (~50 µm) or 1/22th the diameter of a human red blood cell (7 µm). Street traffic will be detectable, as will drafts from the A/C, changes in temperature, and siesmic events. Some of these effects can be further explored using parts in these kits.

Observing the Effects of PLD on Fringe Contrast

The tests above were done with the PLD near 0. What happens otherwise? If the laser operated with a Single Longidudinal Mode (SLM), the PLD would not matter up to a very large number in the 100s of meters or more. (Such lasers are also called "single frequency".) However, the laser used here is NOT SLM but has 1 or 2 modes depending on its cavity length, which changes due to thermal expansion during warmup as the modes sweep through the neon gain curve. (There is much more on this in the section: Linear polarized versus random polarized laser.)

For the first of the following tests, the lasing modes must all have the same polarization. And the (single pass) Linear Interferometer should be used.

• For a linearly polarized laser (most commonly used here), the polarization axis (indicated by the alignment line near the front) should be oriented at 45 degrees. What will be the effect if it is at +45 degrees or -45 degrees?

• If your laser is random polarized, it should be oriented so the two outer lines near the front are aligned horizontally and vertically. A CP should be mounted in the beam with its LP side facing the laser and its polarization axis at 45 degrees. If the CP is stuck to a microscope cover slip, this means the LP (shiny) side of the sandwich is facing the laser and the cover slip is out. *Gently* tape it in place, cover slips are fragile. While the resulting beam is actually circularly polarized (why?), the effect will be similar to that of a linearly polarized beam at 45 degrees.

For all these tests, it will be better to shut off the laser for a few minutes before starting. Then when it is turned on, the mode sweep due to cavity expansion will be fastest.

1. Check behavior with the PLD set as close to 0 as possible by measurements of the distance from the PBSC to the CCs in each arm. ±1 mm will be acceptable. Monitor the behavior of the detected signal over time by twiddling the micrometer periodically over a few minutes. Note any significant change in signal amplitude. A change of 10 or 15 percent can be attributable to the normal variation in total power during mode sweep and warmup, but anything more will be due to the interferometer.

The cavity length of the tube in the 1107 and 1108 lasers is around 137.6 mm or 5.417 inches. One half of this is 68.8 mm or 2.7085 inches.

2. Change the location of the mirror in Arm 2 so the PLD is within ±1 mm of one half the cavity length by relocating the stage and/or adjusting its position using the micrometer. Now observe the fringe signal again and describe what you see over the course of a few minutes. (Turn off the laser again and allow it to cool for a few minutes as above.) Check alignment to confirm that a change in alignment is not the cause of the effects being seen.

3. Try intermediate locations for the Arm 2 mirror.

4. If the Arm 1 adjustable mount is positioned as close as possible to the PBS cube using the BA1S holddown, it will be possible to achieve a PLD of at least the tube cavity length. See how the signal amplitude there compares with the one with a PLD of 0. If it's noticeably lower, why might that be? There are several factors involved.

Now explain the behevior in each case. And what are special about a PLD of zero and one half the cavity length?

How might these results differ if the HSPMI were used instead of the LI?

If your laser is random polarized, it is possible to perform the following additional tests with the CP removed from the front of the laser:

4. Repeat the above tests with the laser oriented so the outer lines are aligned with the horizontal and vertical axes.

5. Repeat with the lines on the laser oriented at ±45 degrees.

Explain your results with respect to the longitudinal mode behavior.

What would happen if the PLD could be extended to more than the cavity length of the laser as would be possible with the 12 inch rail in Deluxe+ kit?

All of these tests can also be done with the other interferometer configurations. Predict how the results would change, if at all. What about the HRPMI?

High Stability Plane Mirror Interferometer (HSPMI)

The HSPMI on the other hand is perfectly symmetric: The beam paths for both Arms 1 and 2 are double pass and go through the CC. However, the change in PLD is double the change in position of the mirror in either arm. Thus it could also be used as a differential HSPMI where the relative displacement of Arms 1 and 2 is to be measured.

Normally, the Arm 1 mirror would be mounted along with the QWP on the PBSC as the reference since absolute PLD doesn't matter with the single frequency or two frequency lasers used in metrology applications. But as with the LI, we need the PLD to be close to zero or ohter specific value for experiments using a multi-longitudinal mode laser. (The "other specific value" would normally be a small integer multiple of the laser's internal cavity length. Why?)

As with the LI, above, the designations m-n show the paths taken by the Arm 1 and Arm 2 beams where "m" is the Arm and "n" is the sequence number.

High Stability Plane Mirror Interferometer Setup

1. Install the HP retro-reflector (10703A) on the PBSC face closest to the detector. The orientation should be such that the beam doesn't hit an apex. This usually means the serial number (if present) runs up and down.

2. Install QWPs (HP 10722A or unmarked) on the faces toward the Arms. Their orientation does not matter as long as the screw slots are used.

3. Replace the unmounted cube corner retro-reflectors with circular 1" planar mirrors. The mirror mounts can be rotated 180 degrees to make them easier to adjust.

Adjust the location of the Arm 2 planar mirror so that the PLD is close to zero. Since the Arm 1 and Arm 2 beam paths are identical, distances from the mirrors to the faces of the PBSC block can be used.

Alignment will be similar to that for the LI, differ in some respects due to the planar mirrors and double pass architecture:

• Adjustment will be more finicky. This includes setup at a PLD of 0 as well as with respect to changes in PLD. While grabbing and manipulating the entire mirror mounts may be acceptable for the LI, the knobs should probably be used for the HSPMI. Why?

• The signal level will be lower by as much as a factor of 2 or more. Trace the beam paths and compare them to those of the LI.

• How will the fringes frequency change?

Monitoring the PLD

Direct Observation

1. Using the DSO to directly view REF and MEAS: This is simplest. Display the waveforms for REF from the laser head cable and MEAS from BPD1 or OR3 above the one-another on the scope. Trigger on REF. Then the MEAS waveform will move back and forth relative to REF as the PLD changes. Almost any type of oscilloscope with a bandwidth of at least a few MHz would be adequate.

   With care, both the gross change of the PLD in integer wavelengths as well as the subtle variation in rate of change at sub-wavelength resolution can be observed either directly or by recording the display and playing it back in slow motion. Since the change is analog - not quantized into bits - more subtle behavior can be easily seen at a resolution down to a few nm. And the extreme sensitivity of the interferometer to any disturbance will be obvious.

2. REF-MEAS difference: Another method that would provide a display that might be useful is to combine the REF and MEAS signals using a simple resistor network. However, this does lose the direction information. A 10K ohm pot wired with terminals 1 and 3 connected to REF and MEAS, and the wiper connected to a DSO with a 10K ohm resistor to GND would provide a voltage at the split frequency with an amplitude that would vary based on their phase relationship - maximum when in phase and minimum when 180 degrees out of phase. The pot would be used to maximize the variation to account for any difference in amplitude of the REF and MEAS signals. The envelope of the combined signal can then be displayed on the DSO.

Using a Measurement Display

• Displacement readout: Although nothing is moving for an interferometer sensor like the gas cell, the displacement readout and graph will correlate with a change in the index of refraction of what's inside, which can thus be calculated. In effect, the value will represent by how much the number of wavelengths that fit in Arm 1 is changing. This is subject to a scale factor, which will be affected by the "Interferometer Type" and "Wavelength" settings. It may be possible to finagle the scaling to display an index of refraction offset, but probably not an actual index of refraction. If the graph "Displacement Range" for the GUI is locked, then the display will appear similar to that of a scope, scrolling continuously right-to-left rather than sweeping repetitively from left-to-right.

• Firmware-only enhancements to generate analog output: The addition of some simple C code to generate a voltage proportional to displacement and a means to reset it would result in a display on a DSO similar to the Homodyne version, above. Any additional circuitry can be wired to the pad array on the PCBs or installed on a separate solderless breadboard or prototyping board Two simple additions are required:
  • Analog voltage: This is easily generated in C code based on the value of DISP(lacement) in the firmware. It is sent one of the microprocessor's WPM-capable output pins. A simple RC filter can be used to remove the PWM switching noise.

  • Reset to zero voltage: This is necessary because the µMD GUI "Reset Display" button only zeros the value used by the GUI and there is currently no means of sending information from the µMD GUI to the firmware - and that's not likely to change. An SPST momentary switch can be added between an IO pin and GND. Firmware would simply look for a LOW and clear the REF and MEAS counters. If this was done at the same time the "Reset Display" button was "pressed" on the GUI, they would track.

Source code for the GUI can be made available, but changing anything is highly discouraged! Hacking the firmware for µMD0 (Homodyne only) is straightforward. For µMD2 (Homodyne and Heterodyne versions), it is more dicey but shouldn't explode the Universe if care is taken to limit additions to the code just before the values are sent to the USB port - and not messing with any values that impact what is sent! However, there is no - zero - tech support for unauthorized changes, even to a single bit in a comment fields. I've lost too many brain cells in the creation of the GUI and firmware to want to revisit them. And after overloading my brain, many of the relevant memories have been off-loaded to long term storage. ;( :-)

Controlling the PLD

Before proceeding with any of these, please read the sections on Monitoring the PLD since changing the PLD without measuring it is like a tree falling in a forest with no one around. ;-)

Thorlabs or Ball Bearing Rail

Micrometer Linear Stage

The micrometer stages permit µm-scale displacement to be manually set, though as a practical matter doing *anything* at that resolution manually is a challenge. And even just touching the knob introduces a displacement shift and vibrations which are easily detectable and jitter in the fringe display or measured displacement.

Motion Control Platform

It would replace the Thorlabs or ball bearing rail and carrier with a stepper motor-driven platform and an Arduino-compatible board to drive it. Among other things, this will enable the characterization of non-linearity, backlash and displacement scaling error. These are critical parameters in CNC machine calibration. In addition, controlling Arm 2 motion electronically should introduce far lower vibration than actually touching the micrometer knob.

However, these are not super precision rigs. Their selection was based on the small size to fit the interferometer setup - and cost. So they may have significant free-play, backlash, and other errors. But that's exactly the sort of thing that experiments can aim to characterize. The main issue is that they use a lead screw (not a ball screw) into a threaded brass block. And aside from a setup like that being inherently imprecise, the machining is sometimes, well, not so great as well. :(

(Doing something similar using a servo motor rather than stepper motor is possible and theoretically superior, but likely much more expensive and complex.)

The basic components are:

• Mini stepper motor driven platform: The Arm 2 reflector and micrometer stage will be mounted on this in place of the ball bearing rail.

  There are currently 2 variations designated Type 1 and Type 2. Type 1 is smaller (height and width), but is not as precise as Type 2, which is also slightly more expensive. But both are quite compact. Other types could be used but they quickly become massive and just a wee bit overkill to move a mirror mount. ;( :-)

  The default models that have been selected have a travel length of either 100 or 200 mm. The screw pitch for Type 1 is 1 mm resulting in 200 full steps per 1 mm of linear movement. For Type 2 the pitch may be 2, 4, 6, or 8 mm resulting in 100, 50, 37.5, or 25 full steps per 1 mm of linear movement. The default will either be 2 mm or 8 mm (my choice).

• Stepper motor controller: The default will be a a STEPPERONLINE DM320T NEMA micro-step controller. It is capable of generating up to 32 micro-steps per for each basic motor step, though how linear they will be is not known. For the coarsest setting, 1 input pulse moves the platform by 1/2 the basic step or 1 mm / 400 = 2.5 µm. When set for 32 micro-steps, the resolution becomes 0.078125 µm. Funny how that works out to be close to 1/8th of 633 nm. ;-) Of course, backlash and free play in the system means achieving anything close to this is probably a total fantasy, but characterizing the various errors is part of the goal here using the interferometer as the reference.

  For more of a DIY approach, an Arduino A3967 EasyDriver or something similar may be used, but their maximum current and micro-step resolution are usually much more limited. An even more rudimentary approach using an H-bridge driver shield and suitable Arduino sketch could also be used. But doing something like either of these is not really worth it unless what you really want to do is explore the finer points of motor control rather than interferometers. ;-)

• Arduino or PC software to issue commands to the motor controller. These would mostly be in the form of direction and pulses to move the stepper motor. For stand-alone control, an Arduino NANO or UNO would probably have enough capabilities. Or the motion control functions could be integrated into µMD2 since the Teensy 4.0 should have more than enough horsepower.

• A PC or MAC (GASP) Graphical User Interface (GUI) to implement the top-level motion control and comparison via data from µMD2 of the error between the issued commands and actual displacement.

The setup below was used for the initial implementation and is similar to what will be included in the kit, (currently an option). This rail with a travel of 200 mm would fit easily fully on the "Extended" version of the interferometer. In fact, rails with a 250 mm travel would also fit and they may be available in the future. For the shorter setups, a rail with a travel of 100 mm would be used. Putting the motor on the left enables a micrometer stage with the knob on the end to be used without hitting the motor housing, which is at a greater height than the platform. However, to minimize the PLD for the homodyne setups, the motor should be on the right using a micrometer stage with side-mounted knob. For Heterodyne, the absolute PLD doesn't make any difference so there's no real need for the reflector to be able to move as close as possible to the interferometer.

Holes will need to be drilled or drilled and tapped on the breadboard to mate with the Metric hole spacing of the rail. BA-type hold-down clamps or even industrial strength double sticky tape would also work, if a bit clunky.

To mount the micrometer stage on the stepper platform, an adapter plate is needed unless one is willing to simply use glue. It's the same one used with the ball bearing rail, so that can be transferred if available. 5-Minute Epoxy would be satisfactory, and could be removed if necessary. (If installed on a V2.0 setup, the optical centerline increases by 1/2 inch so some parts change, mostly Thorlabs posts and spacers.)

The Atmega 328P Nano runs the firmware in the link, below. This is for testing only or if all that's desired is a manually-controlled motorized stage. ;-) It has no error checking so twiddling the knob faster than the motor can move so it just whines is very easy, and there are no limit switches so the flaform can smack into the end plates. But as can be seen, there are many extraneous useless LEDs. ;-) The DM320T controller is set for 400 pulses/mm and the lowest motor current of 0.3 A. Higher current will increase the maximum speed to some extent, but don't go above a sustained current of more than 0.6 A. CAUTION: I you decide to play with a rig like this, make sure the DC to the DM320T is clean and comes on quickly. Else the DM320T may get into a funky state which among other things can send lots of current through the motor, as well as not respond to drive pulses. At least, that's what appeared to have happened on more than one occasion when ramping up the input voltage manually. A 12 VDC wall adapter solved that. I don't know if the red Fault LED on the DM320T being off is sufficient to guarantee correct operation.

              

Test of 200 mm Travel MCP (left), on Extended Heterodyne Setup (Left-Center), Test of 100 mm Travel MCP (Right-Center), and on Basic Homodyne Setup (Right)

The photos show samples of the 100 and 200 mm travel MCPs along with typical installation on the optical breadboards. The electronic Solderless BreadBoard (SBB) with the Nano driving the 200 mm versions is my original rig for testing the quad decoder sketch; the one with the 100 mm versions is all that's needed and is what will be included in the kit. Feel free to add decorative LEDs. ;-) And yes, if you look closely, the tip of the micrometer is not touching the bracket in one of the pics. That's because the stage can be locked in place and wasn't unlocked for the photo. ;-)

The hardware is the easy part and a mock-up has been constructed as shown above. For V2.1, the motion control platform can be substituted for either the Thorlabs or ball bearing rail with virtually no changes to anything else. But for V2.0, it will not quite be a drop-in as the heights have increased by 1/2 inch. So some opto-mechanical components will need to change - mostly Thorlabs posts and spacers, but there would be negligible additional cost involved.

The software to make this educational and useful is the challenge.

An Arduino sketch for an initial version that simply enables the platform to move based on Quad-A-B encoder signals - NOT from the interferometer! - can be found at:

NEMA Motor Driver Demo Firmware: NEMA_Test1_fw_v01, implemented in an Atmega 328P Nano 3.0 (although almost Arduino-compatible could be used). The input is an encoder that provides TTL-compatible Quad-A-B signals; The outputs are Motor Direction (both polarities) and Motor Drive Pulse with a resolution of 1 step or microstep for each transition of either A or B (4 per cycle). This firmware is based on a general quad-pulse demo sketch so there's a bunch of other stuff in there, mainly to drive useless but pretty LEDs. ;-) While currently implemented on a solderless breadboard as shown, there will be an SG-µMC1 PCB in the near future as part of the motion control option providing this function - along with all the useless LEDs. ;-)

The SG-µMD0, SG-µMD1, or SG-µMD2 PCBs can have firmware added for motor control in addition to their other duties. Or another microcomputer could be used.

Suggestions for actual challenging applications (and coding volunteers) are welcome. :( :-)

Mechanical installation

1. Motion control platform: If purchased at the same time as the interferometer, holes will already have been drilled in the breadboard for the stepper motor rig, with the motor on the right. These locations will enable the maximum usable travel.

   Secure the platform on the breadboard using four 6-32 1/2" cap-head screws if the holes are tapped, or 6-32 3/4" screws and nuts if not. Take care to assure that it is aligned.

2. Adapter plate and stage: These are the same as used for the ball bearing rail. If transferring them, first remove the stage and then the flat head M3 screws securing it to the ball bearing rail carriage Reinstall in the opposite order on the MCP using the appropriate set of holes. To maximize range, have the plate extend on the side away from where the knob is located.

Electrical installation

Please refer to the connection diagram below.

Typical Connection Diagram for Motion Control Platform Testing

(To reverse direction, do only ONE of the following: Swap A and B, Mov DIR from D16 to D14, swap A+ and A-, swap B+ and B-.)

1. Motor wiring: These may vary. Two schemes are known:
   1. Red/blue, green/black.
   2. Yellow/blue, red/green.

   There could be others, so confirm with a multimeter. The coil resistance should be no more than a few ohms. Connect them to the A+/A- and B+/B- terminals of the DM320T. As a practical matter, it doesn't much matter which motor winding goes to A or B, or even the polarity as long as they aren't cross-connected (which should not damage anything but the motor won't move). Direction of motion is reversed by swapping any single pair of wires going to a specific winding. The DM320T connector blocks may be removed by grasping them and pulling straight ou if that is more convenient to secure the connections.

2. DM320T power: 12 to 15 VDC is recommended. For the homodyne systems, a 12 VDC power pack is included for this purpose. For the heterodyne system, DM320T power can come from the +15 VDC power supply for the laser.

3. Control signals: These are opto-isolated logic level signals. OPTO should be connected to +5 VDC from the Nano. DIR(ection) and PUL(se) can be driven from a Nano digital output as in the sample sketch. ENA(ble) defaults to active if left open. PUL triggers the motor to move on the negative edge of the electrical signal (logical rising edge).

4. DM320T DIP switches: For the NEMA11 stepper motor, set "PK Current" to 0.3 A. If there are problems with vibration, go to 0.5 A but not more. A higher current will simply cause the motor to get hotter even at idle. Initially set the "Pulse/rev" to 400 (which is the coarsest resolution). Rotating the encoder will result in fairly fast movement of the platform. For these settings, all the switches should be ON (down). You can play with the Pulse/rev settings later. ;-)

5. Arduino wiring: Carefully plug the Nano into the solderless breadboard with its USB connector at one end. Power can come from a USB port or USB charger cube, 5 VDC to 5V, or a 7-12 VDC power supply to VIN and GND. (A USB backup battery pack is not recommended as these may shut down after a few seconds due to insuffient current.) If using VIN, adding a zener diode, three-terminal regulator (e.g., 7808), or some other means to drop the voltage to between 7 and 8 V is recommended to reduce the power dissipation in the Nano's on-board regulator. For example, if using 12 VDC for the DM320T, a 1N4732 (4.7 V) will drop the input voltage to around 7.3 V. 5V from the Nano then powers the encoder and OPTO for the DM320T.

   Here are the required connections. Referring to the sample sketch, there are other pins that may be used to monitor up/down pulses and PWM signals to drive various flavored LEDs for your own amusement. ;-)

     Arduino Pin   Nano Pin   Name   Function
    ----------------------------------------------------------------------------
          D2           5       A     Encoder input
          D3           6       B     Encoder input
         D14          19      DIR-R  Direction reverse to DM320T*
         D15          20      Pul    Motor drive pulse (low) to DM320T
         D16          21      DIR-F  Direction forward to DM320T*
         GND          29      GND    Ground/common for optical encoder+
          5V          27      +5V    +5 VDC for DM320T OPTO and optical encoder
         VIN          30      VIN    +7 to +12 VDC input power (optional)
   

   * Only one of the Direction signals should go to the DM320T. They are complements of one-another. So if the platform moves the wrong way, use the other one.

   + Since the control signals to the DM320T are opto-isolated, the DM320T GND does not need to connect to the Arduino or encoder GND.

6. Encoder wiring: The typical wire colors/functions are:

      Color   Function
    -------------------------------------
       Red    Vcc (+5 to +24 VDC)
      Black   GND/Common
      Green   Output A (open collector)
      White   Output B (open collector)
   

   Double check with the labeling on the encoder. Tin the wire ends or solder them to #24 AWG solid wire to insert into the SBB. The required pullup resistors are provided by the Nano so no other components are required.

   The encoder can also be used to drive µMD0 or µMD2 with Homodyne firmware. For that, pullups will need to be added to the A and B signals and a reference voltage will be required on the A- and B- inputs at about 1/2 the signal swing.

When power is applied to the DM320T, the green LED should come on but NOT the red one. If it does, check connections and that power is clean and being applied quickly (not ramping up). The motor should not get more than slightly warm even after being on for a while at the 0.3 or 0.5 A current setting. The motor may make a hissing noise when stationary due to the DM320T's drive. I assume it is some sort of dither to overcome stiction (or something). It is not known yet how much the resulting vibrations will be seen by the interferometer. That may be an interesting thing to quantify. Ears and interferometers are very sensitive. ;-)

The typical rotary encoder included in the kits has a resolution of 400-600 cycles per 360 degree rotation. So turning the shaft should get the platform moving at a reasonable clip and it is easily possible to exceed the pulse rate where the motor responds. In that case, the motor will stall and whine with the platform remaining stationary. This is a mechanical limitation, not the Nano firmware. The lead screw has a small pitch (1 mm) which is desirable to maximize resolution for interferometer testing. But it also means the motor has to exert itself to produce fast movement. At the DP320T's coarsest Pulse/rev setting, the maximum platform speed is about 1 cm/second corresponding to 6,000 steps/second, or an encoder rotation rate of 2.5 revs/second. (6,000 steps/second / (600 cycles/rev * 4 pulses/cycle). If the DM320T DIP switch Pulse/rev setting is increased, the rate of movement will decrease proportionally and the maximum (input) pulse rate before the motor stalls will increase proportionally. Mounting a massive knob or wheel (not included) on the encoder would enable the friction and imbalance of the shaft to be measured by the interferometer. ;-)

Voice Coil Linear Actuator

The mini loudspeaker 4 ohm woofer can move its cone a couple of mm with 1.5 V at 0.375 A. But for these tests, it only needs to move a few µm.

One of the interferometer configurations using planar mirrors is simpler to use for this since it's more difficult to attach a cube corner to the loudspeaker. The HSPMI is recommended. To use it:

1. The 1" diameter 1/4" thick "Speaker Mounting Disk" should be glued to the back of the loudspeaker with Epoxy. This will permit it to be installed in a KM100 mount just like a 1" diameter mirror.

2. One of the small mirrors should be attached to the front of the loudspeaker with the tiniest of tiny dots of Epoxy at the corners. as shown below. Position it to be as parallel as possible to the loudspeaker frame.

However, a cube corner can be atteched to the loudspeaker with the aid of a 1 inch ID x ~3/4 inch tall ring. This provides the needed support and can be glued to the loudspeaker cone. Then the Linear Interferometer and others requiring CCs in the moving arm can be used.

For seeing how its movement will affect the interferometer, the loudspeaker can be driven with a 1.5 V battery (not included) and series resistor. Even with a fairly high resistor value like 10K ohms, the mirror will move decent amount, probably much more than one fringe cycle. Or it can be driven through a resistor via the 10K ohm potentiometer and 10K ohm series resistor from a 9 V battery or 12 VDC power supply. One of these should be included in the kits.

       + o--------+
                  |
     Battery      /     10K
    or Power  10K \<---/\/\---> +
      Supply      /
                  \       Loudspeaker
                  |
       - o--------+-----------> -

Calculate the sensitivity of movement in nm with respect to loudspeaker voice coil current.

DO NOT connect the loudspeaker directly to the 12 VDC power supply or 9 V battery as they both may be damaged or destroyed. No more than 1.5 V should ever be applied to the speaker. This can be done using a series resistor between it and the power supply or battery or with the potentiometer and series resistor as shown above. Only a very small current will be needed to move the mirror enough to be readily detected and it won't be visible by eye.

An electronic function generator with simple buffer amplifier can also be used to drive the loudspeaker over a larger range as long as the voltage to the loudspeaker doesn't exceed around 1.5 V. For a small range of travel, a current limiting resistor is that would be needed. With a triangle wave and µMD0, it should be possible to demonstrate the linearity (or non-linearity) of the loudspeaker cone with respect to voltage.

There are all sorts of electronic function generators. For this application, something very basic like an antique Wavetek would be acceptable. Function generator kits are available on eBay for under $10. With minor modifications, those based on the XR2206 chip would be more than adequate. The modifications would be to extend the range down below 0.05 Hz by replacing the capacitor for the highest range with 100 µF and to provide a constant (0 Hz) output by replacing the capacitor for the next highest range with a jumper wire. Unfortunately, there is no offset control but the amplitude knob will then change the output over a few tenths of a volt. Alternatively or in addition, and external amplitude control may be desirable since the kit knob does not go to 0. An offset adjust could be added at the same time. ;-)

The loudspeaker will also be sensitive as a microphone so monitoring the detector output on the scope should result in a fairly sensitive response to voice and music, though the frequency response will be poor due to the large mass of the mirror. Send that to the line input of a stereo system and listen to it on headphones. Why? The quality will be terrible but it will demonstrate possibly the most complex way of going from acoustic sound to electronic sound. ;-)

Why might any of these NOT behave as expected? Think of not only issues with the interferometer but other causes.

Piezo Transducer

The PZT beeper element in the kit is 27 mm in diameter with an active area of around 20 mm in diameter. It is what's called a "drum head" PZT because the surface moves in and out at its center when a voltage is applied. It can move a few µm with 15 V at essentially no current - it has some capacitance but an infinite resistance, which for slow movement is all that matters.

Since the PZT must be free to change shape so the center can move in and out, it must ONLY be secured around its perimeter. One approach is to attach it to the 1 inch mirror mount with 3 or 4 dabs of 5 Minute Epoxy. But almost any technique that doesn't interfere with the area of the disk beneath the white Piezo material should be satisfactory. Further as shown in the diagram above, the mirror must be attached only at its center with something like a small washer.

As with the loudspeaker, one of the interferometer configurations using planar mirrors must be used for this since it's not practical to attach a cube corner to the PZT. The HSPMI is recommended.

1. A small platform should be fashioned from a washer or something similar so that one of the small mirrors can be glued to the center ONLY of the PZT. This is necessary because a large mounting area may impede its movement.

2. The PZT can be mounted directly on one of the KM100s with three tiny dots of Epoxy around the edges, or taped in place. Take care attaching the wires as the solder connections are fragile. Putting a small amount of Epoxy over them (but only in their vicinity so as not to impede movement) would be useful.

3. A 9 V battery or the 12 VDC power supply can be used along with the 10K ohm potentiometer to vary its voltage:

          + o--------+
                     |
        Battery      /     10K
       or Power  10K \<---/\/\/\---> +
         Supply      /
                     \              PZT
                     |
          - o--------+-------------> -
   

   (The 10K ohm series resistor is not required for the PZT but using it makes the circuit identical and safe for the speaker.)

Calculate the sensitivity of mirror movement in nm with respect to PZT voltage.

As with the speaker, an electronic function generator can be used to drive the PZT. With a typical output voltage swing of 20 V peak-peak, the change in position will be several wavelengths. By using a triangle wave and µMD0, it should be possible to observe how good the linearity of movement of the PZT is with respect to voltage, though there will be fewer full cycles compared to the speaker.

Or it can driven from the loudspeaker output of an audio amplifier through a step-up transformer.

The PZT may be sensitive enough to act as a microphone as well.

Gas Cell Compensator

It may be done using any of the interferometer configurations, though the sensitivity will depend on which one is used.

The concept is that an increase in air pressure will change its index of refraction, and while this is totally invisible to the human eye, the interferometer should be able to easily detect it as a shift in the fringe signal. In fact many fringe cycles even for a space of a couple inches. With some simple calculations, it is possible to corelate the pressure reading on the gauge with the phase change of the fringe signal. If it's sealed well enough, even warming the gas cell by holding it tightly should result in a detectable fringe shift. However, doing that without introducing vibrations that totally swamp any change due to the expansion would be a challenge.

The Gas Cell Compensator (GCC) consists of a ~2" length of 1" OD Acrylic tube, a pair of planar windows sealed to the ends, the pressure bulb and gauge for a blood pressure cuff (sphygmomanometer), and some simple plumbing. It can mount on a Thorlabs post and post holder using a BA1S hold-down.

GCC Assembly:

The Acrylic tube will already be cut to length and drilled and tapped for the 10/32 hose barb and 8-32 set-screw to attach it to a Thorlabs post. The ends will have been ground to be close enough for government work. :) They don't need to be perfectly perpendicular to the tube or parallel to each-other. Nor do they need be polished - the rough cut surface is better for gluing. Only that they can seal to the windows.

The windows are 1-1/8" in diameter and made of either glass or Acrylic. The Acrylic will have paper protective brown paper on both sides.

1. If there is more than one hose barb with threads, one of them may have the threads shortened so as not to protrude inside the Acrylic cylinder. Partially thread it into its 10-32 hole. Mix the tiniest amount of 5 minute Epoxy and apply it to the exposed threads. Then rotate it clockwise until fully seated. Wipe off any excess Epoxy and allow time to cure.

2. Apply a small amount of the remaining Epoxy to the threads of a 8-32 1/2" set-screw. Intstall it in the 8-32 tapped hole so that no more 3/8" is exposed. Apply some more Epoxy at the threads where they meet the tube. (Since this one is vertical and can't interfere with the beams, some portion of it protruding inside the Acrylic tube is OK. Add an 8-32 nut as shown in the diagram for added strength with the Epoxy joining the nut to the cylinder.

3. Clean one window end one end of the 2" tube with alcohol if available. Soap and water is also acceptable. DO NOT use anything stronger. Make sure it is completely dry and dust-free by shining a bright light through it before proceeding. Repeat as needed.

4. Carefully place the tube on top of the cleaned window. Put a weight on top of it or use some other means to prevent it from moving accidentally.

5. Prepare a small amount of 5 minute Epoxy and apply the tiniest bead all around the outside of the joint between the 2" tube and window.

   Avoid getting any Epoxy inside the tube, especially on the windows, as much of their area may need to be unobstructed depending on the type of interferometer and/or whether the laser has a beam expander.

   If it gets messed up before curing, the Epoxy can be careully wiped off and then the glass and/or Acrylic can be cleaned with alcohol (but nothing stronger!). After curing, a single edge razor blade can be used to remove Epoxy, then cleaned with alcohol. Take care to avoid scratching the window(s).

6. Repeat the previous three steps for the other end. A cotton swab can still be used to clean the previously attached window if necessary. It's especially important that the inner surfaces of both windows be clean as they will be inaccessible once the second window is installed.

7. Wait an hour or so before proceeding to allow the Epoxy to fully cure.

8. Connect the hose barb on the tube with the pressure gauge and bulb using the rubber tubing. Test to confirm the connections are reasonably gas-tight and correct if necessary. For this experiment, a small leak may be preferred as it will allow for a controlled pressure decline which can be used to correlate with the fringe signal.

The photos show the Basic homodyne version with the GCC installed in Arm 1 of the interferometer. The mirror mount post holder is moved further out to make room for it. The arrengement is identical for the heterodyne setups except for the substitution of the laser and optical receiver.

For more details on the setup to view the signal, refer to the section: Monitoring the PLD.

     

This photo shows the complete setup with the prototype of the GCC and a scope trace of the photodetector out showing the GCC loosing some of its pressure over 20 seconds or so. Hands-off bleed-down is better for visualizing what's happening as any vibrations - which are inevitable during pump-up - will show in the display.

Closeup of GCC Assembly using a Piece of PVC Pipe (left), Overall Setup Showing the Fringe Signal as the Pressure Declines

Note: If doing this using one of the plane mirror interferometers, the Arm 1 mirror mount may need to face away from the PBSC (with the mirror installed backwards) as with the CCs in the LI to provide enough clearance for the GCC. Then adjust the Arm 2 mirror position so the PLD is 0.

The blood pressure gauge reads up to 300 mm/Hg (almost 6 psi), but there should be no need to go anywhere near the extreme hypertension region for these tests! :) 100 mm/Hg will be more than enough.

The gas cell can be mounted in either arm of the interferometer, though using Arm 1 is probably better as it has nothing else. It can be positioned so that either one or both beams (where present) pass through it. (How will this change the calculations?) Avoid aligning the gas cell so that the windows are perfectly perpendicular to the beam paths - angle it slightly so the reflections from the surfaces of the windows do not coincide with the main beams.

The Arm 1 and Arm 2 path lengths do not need to be the same so that at least is simpler than for the homodyne setup with unstabilized laser.

Fine tune the alignment of the interferometer to maximize signal amplitude. Close the bleeder valve and slowly pump up the bulb while watching the scope display and pressure gauge. The index of refraction, n, will be approximately equal to 1 + P * k. By measuring the number of cycles and partial cycles as the pressure is changed, it is possible to calculate k. Check it against a value found in a search. Why might it not be the same? Knowing k, an arbitrary pressure can be measured with the interferometer.

Based on the NIST Refractive Index of Air Calculator using Ciddor Equation, the index of refraction of air at 1 atm (760 mm/Hg), 20°C, and 50%RH, is 1.000271372. As an example, at a pressure above 1 atm of 100 mm/Hg, it is 1.00030715. What is the value of "k"? Over the 3 inches (76.2 mm) inside the GCC, the change in path length is approximately 2.73 µm or 4.31 full wavelengths at 633 nm. You can complete the calculations. ;-) Perform the test with 100 mm/Hg and your favorite interferometer configuration. Explain your results. What are the possible sources of error? Hint: What effect will reflections from the parallel surfaces of the windows have on transmission?

You might be wondering if it would be possible for the interferometer to act as a microphone using only the change in air pressure from sound waves in one arm. This could be done in principle, but the sensitivity would be extremely poor. In fact to get a detectable response due only to the air pressure variations would require sound levels similar to what might be found a few feet from a jet engine or directly in front of the loudspeaker array at a rock concert. Of course the entire interferometer would be vibrating (assuming it didn't totally disintegrate) and that would dominate any response. Original equipment human ears are extremely sensitive. ;-) See, for example: Engineering Toolbox: Sound Pressure.

Thermal Expansion

This shows how a change in temperature of an object undetectable by eye can produce a noticeable effect if in one arm of the interferometer. A glass block with two polished surfaces actually called a "compensator plate" is included in the kit, along with 1 or 2 power resistors to heat it.

It may be done using any of the interferometer configurations, though the sensitivity will depend on which one is used.

Thermal Assembly Assembly:

1. Thread the ~1x1-1/4x1/4" block with 8-32 stud into a Thorlabs post and install it in a post holder attached to the breadboard for convenience in mounting the other parts.

2. Use a drop of Epoxy to secure the 25 ohm 5 watt resistor to the block using one of its flat faces. Wait at least 15 minutes for the Epoxy to cure.

3. Use a drop of Epoxy to secure a long frosted surface of the compensator plate to the top (labeled side) of the power resistor. Wait at least 15 minutes for the Epoxy to cure.

4. This assembly can then be installed in Arm 1 of the interferometer using a Thorlabs 1.5" post, post holder, and BA1S Holddown. Angle the broad polished faces of the compensator plate very slightly to avoid back-reflections into the beam paths.

The 12 VDC power pack is used to do the heating. DO NOT use a 9 V battery, it won't last very long. The power into the resistor(s) is 12*12/R - 5.76 watts for the 25 ohm resistor.

 

The Coefficient of Thermal Expansion (CTE) for optical glass is around 8x10^-6/°C. (It varies slightly depending on the specific type, which is not known for the compensator block.) That means a 1 °C change in temperature will result in its length changing by 8 ppm (parts per million or 0.000008 x its length). Assume that the index of refraction of optical glass, n_g, is approximately 1.5. (Again not precisely known .) Calculate the expected number of full cycles from the detector for a 10 °C change in block temperature. Don't forget that it's the net change in PLD that matters.

Monitor the signal using your choice of method as the block heats or cools and use the results above to estimate the temperature of the glass block based on its length. Without actually knowing the temperature of the block throughout its volume, and knowing it actual CTE and n_g. it is not possible to be precise. That's OK.

The effect will not be as dramatic as with the GCC, above, but with care, should be easily detectable.

CAUTION: Do NOT leave the resistors plugged into the power pack continuously for too long as bad things may happen.

What else may be impacting the PLD change besides the block itself? For example, is there any detectable response to the heating if the block is rotated and/or offset so it just misses both beams?

Index of Refraction of Air

The index of refraction of air, n, varies by just under -1 ppm/°C. Or more precisely, according to the same NIST Web site, -9.517x10^-7. So heated air in one of the interferometer arms should change the path length due to its change in n.

This can be tested with the same Gas Cell Compensator assembly and interferometer configuration used for the air pressure measurements. Heat it with a blow dryer with the inlet port unplugged from the hose so that the pressure won't be affected. Do this well away from in the interferometer to avoid heating other components. Then quickly install it in Arm 1 and wait a few seconds for the vibrations to die away. Watch the signal as its temperature (and that of the air inside) declines. The heating could also be put into an oven on LOW. Just don't get it so hot that the Epoxy decomposes (which could be as low as 160 °C). :( :) While the sensitivity of n with respect to temperature compared to the effect on the glass block is around 1/10th as great, the GCC is ~5 times as long, so it should still produce an easily detectable signal.

Note that the expansion of the Acrylic cylinder itself is not a significant factor for these measurements. Why?

Gas Partial Pressure Measurement (Advanced)

Engineering Toolbox - Refractive Index for some common Liquids, Solids and Gases lists the values for many common substances.

Parts to do these tests are not included in the kits, but with a bit of resourcefulness, it should be possible to provide a suitable vessel either for a gas or liquid (with its vapors actually being what's measured). The Gas Cell Compensator, above, can also be used for this purpose if a way is devised to fill it with the test gas, for example by adding a second hose barb so there are entry and exit ports.

Inexpensive glass cuvettes with polished parallel sides would make suitable containers to introduce liquids, or with an improvised cover, gases, without the need for additional plumbing. Cuvettes are typically 1 cm wide but may be up to 5 cm or more in length. 1 cm is not enough width for both beams in an arm to fit and the length is desirable to maximize the sensitivity. So, two cuvettes side-by-side may be needed. Or a custom cuvette could be constructed from pieces of microscope slides sealed with RTV Silicone.

As a simple test, start with the cuvette(s) being empty and allow the interferometer to come to thermal equilibrium. Then carefully add some alcohol (at the same temperature and filled to below the level of the beam) and watch the fringe signal as vapors come off the liquid.

Mounting the cuvette(s) on the power resistor heater could allow the effects of temperature to be explored either with a liquid or gas. But interpreting the results may be more complex than it appears at first.

More on this is left as an exercise for the student's imagination. ;-)

Earthquake or Vibration Detector

For these experiments where one of the arms is of considerable length, the 6 mm beam (up to around 5 meters) or 9 mm beam (up to at least 10 meters) will need to be needed. A narrower beam would expand too much to be useful. But don't get carried away putting the reflector 25 meters away. Remote alignment will be a large challenge at the very least.

Start with perhaps 0.5 meter. Then extend it gradually, tweeking alignment at each step.

The remote reflector should preferably be mounted on a separate structure, not the same table as the rest of the setup. Another table or wall, for example. Or even suspended by springs or wires. Either arm can be extended but using Arm 2 with the linear stage may be simpler for mounting to a slab of wood or aluminum.

The use of µMD2 would be best as it would be possible to record data and (with some simple formatting in Excel) then display it like a seismograph. But just watching the REF/MEAS signal on the scope should provide some valuable insight into what's going on. Not only vibrations, but temperature changes and even air convection should be detectable.

Variations on the basic interferometers can be used to sense tilt (angle), lateral movement (straightness), deviation from right angle (squareness), and others. See Optics for Interferometers Using Two-Frequency Lasers. The same optics can be used with single frequency lasers.

Other Interferometer Configurations

Original Michelson Interferometer (BMI)

Without the cube corners and/or QWPs to separate the outgoing and return beams, everything will be jumbled together and there will be back-reflections directly to the laser. This won't cause damage but there could be serious instability in the resulting behavior. However, with a polarized HeNe, the effects may not be detectable either visually or even in the fringe signal. But for a random polarized laser, the result would be mode polarization switching, which could reak havoc with the signal.

No Retro-Reflector Plane Mirror Interferometer (NRRPMI)

The NRRPMI minimizes the required size of the optical components but with no retro-reflector, will require very precise in alignment during setup to maintain a usable signal with any significant movement. It is most similar to the original Michelson interferometer but the addition of the QWPs avoids (most) back-reflections to the laser.

Plane Mirror Interferometer (PMI)

However, it is asymmetric in terms of the beam paths. The reference (Arm 1) is single pass while the measurement (Arm 2) is double pass. To achieve a PLD close to 0 - required for the non-single mode laser - the positions of the two reflectors must differ significantly. Note how close the mirror on the stage is to the PBSC in the diagram - and that may not even be close enough for the paths to be equal!

For this reason, while the PMI is widely used, the HSPMI is recommended as the one to be built after the LI.

Single Beam Interferometer (SBI)

This is commonly used where space is tight since it doesn't require two offset beams. Normally, much smaller PBSC and CCs could and would be used. As with the NRRPMI, above, the use of the QWPs avoids most back-reflections to the laser.

Modified Linear Interferometer (MLI)

Double Pass Linear Interferometer (DPLI)

The signal level may be even lower than with the PMI since the CCs are slightly lossier than planar mirrors. A single pass through the silver coated CCs is ~86% resulting in a net transmission of ~74% since there are two passes. For the planar mirrors these values are closer to 90% and 81%, respectively. The CCs also mess slightly with the polarization. With linearly polarized light, the plane of polarization is rotated by ~±10 degrees depending on which set of internal surfaces are involved. What the effect is on the circularly polarized light is not known.

What would be the effect if only one of the QWPs were present in Arm 1 or Arm 2? Try it!

High Resolution Plane Mirror Interferometer (HRPMI)

The HRPMI is essentially an HSPMI in which instead of the return beam going to the detector, it is reflected back into the interferometer, but offset in position by an additional cube corner and traverses all of the optics a second time. So instead of 2 passes, it becomes 4 passes, and the losses will more than double reducing the signal level significantly. In principle, this could be extended to 6 or more passes using a similar approach, but as you will undoubtedly see if you're crazy enough to attempt to implement the HRPMI, it's already tough enough to align.

Drawing the detailed beam paths for the HRPMI showing how the photons are routed would be more work than it's worth. But since it is equivalent to the HP/Agilent/Keysight 10716A, a Web search will find information, but no need to bother Google, get it at HP/Agilent/Keysight 10716A High Resolution Plane Mirror Interferometer. However, the 10716A is normally used with a two frequency laser for heterodyne interferometry. So, wherever it refers to "ΔF", replace that with "ΔΦ" since we are changing the phase rather than the frequency.

The HRPMI setup requires some additional optics (another turning mirror and adjustable mount for an unmounted cube corner). The laser may also need to be positioned further to the left to make space. The only way to really test it without a measurement display would be with one of the methods of fine tuning path length - loudspeaker, PZT, air pressure, tmperature, etc. The micrometer stage will simply not have fine enough control to reliably detect a difference between X1 or X4. Thus the setup is shown with the loudspeaker.

Although drawn with all the beam paths in a plane, it is possible to implement it in 3-D as a 2x2 array within the PBSC by carefully offsetting the cube corners (as is done in the actual 10716A). Consider everything about the HRPMI to be a challenge. :-)

Displacement Measurement

The output from an interferometer using a single frequency or two frequency laser may be processed to yield displacement information in digital form.

In their simplest form, the measurement electronics for a homodyne system is just a quadrature decoder circuit driving an up-down counter; for the heterodyne system it is a pair of accumulators and a subtractor. The interferometer optics are identical. In practice, the electronics is considerably more complex, in part to provide sub-wavelength interpolation and extend the range down to nm resolution. And yes, kits are available for these as well.

        

However, a basic implementation of a homodyne interferometer displacement measurement system for demonstration purposes can be done with a $3 microprocessor board and a few inexpensive parts as shown below. Where the path length difference is limited to be less than a few cm, a multi-longitudinal mode (not strictly single frequency) laser like the one in these kits may be used.

Quadrature Decodor

This shows a rotary optical encoder which uses a pair of LEDs and photodiodes physically offset by 90 degrees to generate Quad-Sin-Cos analog signals which are then thresholded to yield Quad-A-B digital signals. The specific type of sequence is called a "Gray" code (not based on color but attibutable to someone named Frank Gray) and has the property that any possible allowable change in value is a change in only a single bit. This eliminates the ambiguity with sensors using the normal binary order where two bits can change at not quite the same time.

(The animated encoder graphic seems to be all over the Web. If anyone knows who the original copyright holder is, I will acknowledge them.)

Many other types of encoders produce similar signals. They may use optical, mechanical, or magnetic sensing, among others.

A Web search for "Quadrature Decoder" or something aimilar will turn up all sorts of overly complex implementations which may or may not even be applicable to the type of application being discussed here.

An interferometer with angled paths for the two interfering beams produces fringes similar to the pattern of an optical encoder so a quad detector could be built with offset photodiodes. But this complicates the optical paths and detector driving up the cost and complicating assembly and alignment. I am aware of only one commercial stabilized HeNe laser that was designed like this, but it has been used in HeNe ring laser gyros since the angled beams are inherent in their construction. More commonly, the 90 degree phase shift is done optically using a single combined beam as shown below. The detected analog output is Quad-Sin-Cos and if thresholded and converted to digital form, the output is Quad-A-B.

Below are several implementations of basic quadrature decoders found in a variety of devices with interferometers. Types 1 and 2 are optically equivalent and have the desirable attribute that the relative phase between the outputs can be fine tuned without a reduction in sensitivity by adjusting the angle of one of the linear polarizers. But Type 3 is recommended here due to its simplicity, especially by using bits of inexpensive Circular Polarizer (CP) sheet for both the QWP and LP as described below. The resulting phase is typically so close to 90 degrees that no adjustment is needed. If it's too large, adjustment is possible by rotating it the CP. While the phase cannot be increased, a true QWP (or even a piece of the protective film or other clear plastic which is typically highly birefringent) can be added in front of the CP for the B Channel and oriented for optimal phase. Even without doing this, the phase will still probably not be off by more than 10 degrees. That sort of error would only matter if attempting to achieve perfect equality of the 4 counts per full cycle. In fact, it is possible to use ONLY the protective film in place of the QWP, adjusting it for 90 degree phase, and substituting an LP for the CP! And even a range of common common materials are highly birefringent including clear packing tape, polystyrene packaging, and plastic bag material. Any of these can be oriented for optimum phase and stuck to one of the LPs in the Quad Decoder with performance that is indistinguishable from that using a real QWP. For the Type 3 Decoder, it appears as though the behavior is identical with the QWP at any orientation (and not only the zero degrees shown) as long as the adjacent LP is offset 45 degrees from it as it is using the CP. An example using the Type 3 Decoder is shown later.

Constructing the Type 1 decoder will require an actual waveplate (a QWP or immitation stand-in like those described above, but NOT a CP) oriented in the incident beam. Pieces of CP can then be glued to the two PDs at 0 and 45 degrees (for the two LPs, their QWPs being ignored). Then the phase can be fine tuned by slightly tilting one of the PDs (if they are installed in sockets as is recommended) or the input WP.

Concentrating on the Type 3 decoder, the NPBS can be replaced with a plate beam-splitter (left) or with an "Attenuator Plate" set at an angle to reduce the effects of the reflection on polarization (center, right) as shown in the diagrams below:

As noted, this is what I call "Type 3" and is among the simplest. It can be implemented with pieces of inexpensive CP sheet for the QWP and LP. In most instances, the photodiodes should be reverse biased to provide a linear response. It may be possible to get away without that for initial testing but it will be needed if doing anything useful with the outputs. In addition, a third "Intensity" channel is almost always included to accommodate variations in detected power due to the laser aging, changes in alignment, and contamination over time. The Intensity channel can be implemented electronically or optically with a non-polarizing beam-splitter at the input and additional photodiode. But for educational purposes, the intensity channel will be omitted.

Simply reverse biasing the PDs provides adequate signal quality and bandwidth to 10s of kHz. But for many real applications, a pair of transimpedance amplifiers would be added to reduce noise and extend the bandwidth into the MHz range.

The output signals from these will be close to sinusoidal with a relative phase close to plus or minus 90 degrees depending on the direction of motion of the remote reflector or ring laser gyro.

The purpose of the angled arrangement is to minimize the difference between the amplitudes of the two polarizations. Otherwise, with 45 degrees being close to the Brewster angle (around 57 degrees), one will be much larger than the other. Even so-called 50:50 beam-splitters may be subject to this, so using the angled arrangement for either one may be beneficial. The parts for the version using the Attenuator Plate (AP) are what are in the kit, which simplifies construction. Using the AP also permits the relative amplitudes of the Channel A and B signals to be changed somewhat without electronic adjustments.

Some resourcefulness will be required to mount the parts in this kit to put together a Quad-Sin-Cos decoder. A variable attenuator plate is included that may be used as the NPBS. Pieces of CP will be satisfactory for both the combination of the LP+QWP (since that's exactly what the CP is), as well as the LP (flipped) since the output polarization doesn't affect PD behavior. See the information on polarization, below.

This would be a great excuse to finally make good use of that 3-D printer sitting idle. ;-) A simple frame could be designed to mount the AP via its spring and screw so its position, and thus reflection and transmission, would be adjustable in the beam. Slots and/or faces would be used to attach the pieces of CP and the PDs. Be creative! But this is probably gross overkill. The most likely location for the beam to hit the AP is where its density (and thus reflectivitly) is maximum and one the photodiodes are in place, the location and angle of the AP will be fixed. The parts can then just be glued in place.

        
Quadrature Detector using Variable Attenuator Plate and Circular Polarizer Sheets. Optical Layout, Parts), Constructed on Solderless Breadboard, Protoboard, and PCB Assembly

Before finally attaching the QWP, the interferometer should be running so the outputs can be monitored. Doing this with the scope set up in X-Y mode is the simplest way to confirm the phase shift is set for 90 degrees. The result is called a "Lissajous Figure", "Lissajous Display", or simply X-Y display if you can't spell Lissajous ;-) and will be a perfect circle when the phase difference between the A and B signals is 90 degrees and the amplitudes on the screen are equal. A smaller or larger phase difference will produce a tilted ellipse. Short videos of this may be found further down.

These photos show a diagram for the preferred implementation of the Quad decoder itself, the typical parts, and 3 perfectly workable construction options, the first of which uses a small solderless breadboard and doesn't require any soldering. For that one, the AP and pieces of CP sheet could be glued to wires that would be stuck in holes. Or U-shaped pieces of wire could simply be stuck in holes to keep the CPs and AP in place. ;-) The benefit of this primitive approach is that adjustments can always be made.

Before constructing the prototype or PCB versions, it was desirable to to conclusively prove that the simple Type 3 scheme with CPs for the polarization optics actually worked as advertised as it was not certain that such a simple setup could actually work. So a prototype version was installed on the Michelson Interferometer test-bed:

In the interest of expediency, I cheated and used an NPBS cube rather than a plate beam-splitter or variable attenuator and two Thorlabs DET110s rather than bare photodiodes, but the QWP+LP for Channel B is a piece of CP (as in the diagram on the right, above) stuck to a microscope cover slip that is glued to a platter clamping ring from an ancient defunct harddrive. Got that? :)

The ugly scope screen shots below were taken using this setup:

   

Displacement Positive (Left) and Negative (Right)

Capturing a decent photo while twiddling the micrometer screw is quite challenging. ;-) But the conclusions are clear: This simple Quad decoder does its job well with a phase shift of ±90 degrees. If the Arm 2 mirror or retro-reflector were on an electronically controlled positioner like a loudspeaker voice coil or linear motor driven with a ramp, the waveforms would be textbook quality. ;-) But with only a small stretch of the imagination, it can be seen that the screenshots agree with the expected behavior based on the diagrams, above.

The circuit was then constructed on a prototyping board to confirm similar behavior, and then the simple PCB was made so that mounting of the photodiodes and other electrical components would be simplified. There is nothing to really secure the AP/BS but that could be done with double-sided tape.

Constructing the Quad-Sin-Cos Detector

The mounting scheme doesn't need to be fancy or pretty but should hold the pieces securely while maintaining alignment. This can use bits of tape and Epoxy or other adhesive. The CPs, QWPs, and NPBS plate are expendible so feel free to chop them up if necessary for them to fit. :)

The photos above show various possibilities not involving a 3-D printer :), including a simple PCB (which is available), but some soldering is required for that. The simplest approach is to use the same Solderless Breadboard (SB) as the Single Channel Detector, attached to the post using the Detector Adapter Plate as in this closeup:

1. Set up the HeNe laser so that there is a linearly polarized beam. Orient the polarization to be at 45 degrees or preferably, the output of the interferometer as well.

2. Mount the AP at an angle as close to normal to the incident beam as is convenient to still be able to locate the Channel B CP and PD in the reflected beam. The rational for this is to minimize the effect of the angled plate on the polarization of the reflected and transmitted beams. Why? If you're into fancy 3-D-printed mounts, it can be arranged to use the screw/spring combination to adjust it's position, and thus attenuation (or transmission and reflection). But that certainly is not required and the screw and spring can be relegated to your junk drawer. ;-)

3. Mount one PD to intercept the transmitted beam. (This will be designated Channel A or 1.) Trim the leads if necessary so that in conjunction with adjusting the height of the platform, the beam can be approximately centered vertically in the AP. Higher rather than lower is best since the PD for Channel B or 2 must be slightly lower due to the tilt of the AP.

4. Adjust the position of the AP so that the transmitted and reflected beam intensities are approximately equal. This will be near or at the higher-density end of the AP. Perfect balance may not be possible since the maximum reflectance of the AP is not 50 percent, so the remaining adjustment will need to be done with the Gain trim-pots (substituting for the fixed resistors, or later when the interface circuit is built).

5. Install the second PD (Channel B or 2) to intercept the reflected beam. Note that the AP glass is slightly tilted so it may be necessary to trim the PD's leads or bend them over so its heights will be correct.

6. The PDs should be reverse biased with 5 to 15 VDC (+ to cathode, the right leg facing front). A load resistor of approximately 100K ohms should result in a decent signal amplitude for a ~1 mW laser. If too high or too low using only the laser, no need to change until using the actual interferometer output. To accomodate lower power lasers and/or losses in the interferometer optics, 1M ohm trim-pots are included in the kits for this purpose. The typical wiring is shown below.

          R-Protect    PD1      Yellow
      +-----/\/\----+--|<|---<<-----------------------+----------o Scope Channel 1
      |             |                                 |
      |             |  PD2      Blue                  |
      |             +--|<|---<<---------------------------+------o Scope Channel 2
      |                                               |   |
      |                                               /   /
      |                                       R-Load1 \   \ R-Load2
      |                                               /   /
      |                                DC Power       \   \
      |                          Red    +| |-   Black |   |
      +-----------------------<<---------||||---------+---+-------o Scope Ground
                                         | |
   
      |<--- SBB or QDx PCB --->|<----- Scope / Power Wiring ------>
     

PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.

R-Protect: 250-1K ohms typical. R-Load: 10K-1M ohms typical.

In the photo, above, one piece of CP sheet is stuck directly to the channel 1. PD. The other piece of CP sheet is simply propped in front of the channel 2 PD with the sticky side facing out. Long term, that side should be protected with some 5 Minute Epoxy or a microscope cover slip. The AP is just sitting on the SB. Dabs of 5 Minute Epoxy, wire loops, or other means can be used to secure them more permanently. If using wire loops, take care not to short out anything that shouldn't be connected. ;)

The following must be done using the output of the interferometer that has been properly aligned so that interference can be seen on a white screen if a linear polarizer is placed in the output beam at 45 degrees.

Make sure your hands are clean or use a pair of latex surgical gloves when handling the pieces of CP.

5. Cut a pair of 0.5x0.5cm or larger pieces of the CP sheet aligned with the original edges.

6. Carefully remove the protective film from both sides of the cut pieces. One side is simply bare plastic; the other side has a sticky adhesive.

7. The adhesive-side of the CP is the QWP with its optical axis at 0/90 degrees (aligned) with the edges; the other side is the LP with its axis at 45 degrees. This can be confirmed by testing with a linearly polarized laser or a random polarized laser with a separate linear polarizer in front of it:
   • When the CP's LP-side faces the laser, rotating it will result in the transmitted intensity going very close to 0.

   • With the CP-side facing the laser, there will be little or no change in intensity.

8. Channel A: Attach the adhesive side of one of the pieces of CP directly to the front of the Channel A PD making sure to keep it aligned with the horizontal and vertical axes. This will result in its LP-side facing the AP oriented so the polarization axis is at 45 degrees (edges aligned with the X and Y axes). The result should be a strong signal as the micrometer stage is moved or whatever is convenient to change the PLD.

9. Channel B: Attach the other piece of CP in the reflected beam so that its QWP-side faces the AP and is oriented at 0/90 degrees (edges also aligned with the X and Y axes). This is best done by using a drop of 5 Minute Epoxy to stick it directly to the Channel B PD, but if large enough, it can just be placed in front of the PD with a wire loop or something similar to stabilize it. Just make sure that the wire loop doesn't short out something important. ;) The result should be a strong signal as the micrometer stage is moved or whatever is convenient to change the PLD. Once correct behavior is confirmed, coat the adhesive-side with a thin layer of 5 Minute Epoxy to prevent it from attracting contamination like dirt and dust, or stick it to a microscope cover slip.

   Remarkably, the orientation of the CP in front of PD-B makes almost no difference in the phase angle or amplitude of the quadrature signals. Initially, this seemed to make no sense at all and a complete mathematical derivation is above my pay grade, ;-) But a couple of special cases can be analyzed without the hairy math:

   • QWP at 0 or 90 degrees: The X and Y signals are shifted by 90 degrees with respect to each other. When combined by the LP at 45 degrees, the result is the quadrature signal with a 90 degree phase shift.

   • QWP at ±45 degrees: The X and Y signals are converted to left and right (or right and left) circular polarization by the QWP. When combined by the PD at 45 degrees (though it could really be any value in this case), the result is also the quadrature signal with a 90 degree phase shift.

   For a QWP at any other angle the result is elliptical polarization but that can be decomposed into a linear combination of those above so the result is the same regardless of orientation as long as the 45 degree relationship with the LP is maintained..

   Murphy must have been on vacation when these were invented. ;-) This behavior has been confirmed with a piece of CP stuck to a microscope cover slip and rotated in front of PD-B as shown below. Its orientation indeed makes no difference in the orthogonality or amplitude of the signals beyond what can be accounted for by imperfections in the CP. I had to repeat the test several times to be convinced it wasn't an illusion.

      

   Type 3 Quadrature Decoder Test to Confirm Orientation Independence of CP in Front of PD-B

   So rotation of the CP on PD-B won't do much, but tilting it should be able to fine tune orthogonality if necessary.

   With an LP in place of the CP, the X-Y display is just a diagonal line; with the CP - regardless of orientation - it is nearly a perfect circle. The angle of the CP/cover slip in the photo above is totally arbitrary. I was contemplating putting the CP on a ball bearing mount for the test but that would have been way too much work. ;-) The center photo of the montage below shows the normal version with a bit of CP stuck to PD-A with its adhesive on the QWP side creating an LP at 45 degrees, and another bit of CP implementing the QWP+LP combination) stuck to PD-B with 5 Minute Epoxy and also coated with it to prevent dust build-up on the exposed adhesive.

   A piece of packaging plastic (e.g., cut from a used salad container) inserted in one of the beam paths can very dramatically affect the orthogonality and amplitude since it is birefringent but not pure quarter wave and probably something that is largely beyond analysis. ;-)

10. Fine tune interferometer alignment to maximize signal amplitude and adjust the values of the PD load resistors so that the signal amplitudes are between 3 and 5 V p-p.

11. Observe the Channel A and B signals on the oscilloscope. They should be in quadrature (or very close). And the phase shift between them should flip from +90 to -90 degrees depending on the direction of motion as in the photos, above. The best way to visualize the quadrature behavior is using the scope's X-Y mode to display a "Lissajous Figure". This works well with almost any analog scope or a pricey "digital Phosphor" scope. The typical inexpensive DSO may not work well in X-Y mode, though probably acceptable for slowly changing signals at least.

    One full rotation on the scope screen is 316 nm for the single pass Linear Interferometer and 158 nm for the double pass High Stability Plane Mirror Interferometer. Even with this simple implementation, the Signal to Noise Ratio (SNR) is so good that the error uncertainty of the display if there are no vibrations or extraneous light on the PDs can be smaller than the CRT spot diameter, much less than 1 nm.

    Note: Even if the peak-peak amplitudes are made equal, it may not be possible to avoid an offset on one channel. In that case, the scope vertical position can be set to superimpose them on the screen, and later, the Threshold trim-pots can be set appropriately.

    There can be a number of reasons for this offset. What might they be? Hint: Think polarization.

Now for the good stuff. ;-)

A voice coil actuator similar to the one described above was driven with a sine wave from a function generator. Two implementations of the Quad-Sin-Cos decoder along with the scope display of the Sin and Cos outputs is shown below:

And to actually visualize the phase difference, here are two short videos showing the Lissajous X-Y display on my "Continuum Laser Zapped Oscilloscope" ;-) of the two outputs of a Quad-Sin-Cos decoder:

How easily the phase can be fine tuned will depend on the design of the Quad-Sin-Cos decoder but is usuallly not even necessary.

The simplest way to put these together with bits of the CP sheet using the adhesive already present on the QWP-side that is to be stuck to the PD. For the LP-side where there is no adhesive, 5 minute Epoxy or UV-cure index matching optical cement can be used. The UV-cure stuff ends up being less messy to apply. I use Norland 65 UV-cure cement and a $1 1W 365 nm LED to cure it or $25 for a beautifully machined UV LED flashlight. No need to spend $2,583 for the UV cure gizmo they sell - or an even much higher cost for the same thing that dentists buy, but perhaps with a DMD certified label. ;-) Similar UV-cure cement is also available for replacing smart phone screens and is less expensive. But depending on the type, it may not cure to a tack-free surface (or mine may just be past its "use by" date. ;-) But 5 minute Epoxy is just fine and neither significantly messes with the polarization. And either type can also be used to coat the sticky side of the CP that faces out so it doesn't collect dust.

Or an alternative:

This shows the Type 3 Quad Decoder with pieces of CP sheet used as LPs stuck to the PDs and a piece of clear plastic for the QWP positioned in front of one of the PDs. In fact the simplest implementation might be to use bits of LP sheet at 45 degrees stuck to both PDs along with packaging cellopane carefully oriented for the most circular X-Y display. An expensive QWP is definitely not required. ;-)

Micro Measurement Display 0 (µMD0)

For the purposes of these interferometer kits, µMD0 consists of three parts:

1. Interface from Quad-Sin-Cos analog signals to Quad-A-B digital signals, consisting of very simple circuitry to provide gain and thresholding.
2. Atmega 328 Nano 3.0 (or similar Arduino-compatible) microcomputer board, which runs the µMD0 firmware.
3. Micro Measurement Display (µMD) Graphical User Interface which typically runs on a Windows PC or laptop.

The general organization of a typical system is shown below (though the one implemented in this kit differs in some subtle details):

Typical Homodyne Interferometer Measurement Setup using µMD0

To convert the analog sin and cos signals to something for a low cost microprocessor with adequate performance requires a simple interface which provides gain and threshold adjustments. (While it has analog inputs, their conversion rate is way too slow.)

Referring to the schematic, the trim-pots on the left are the load resistors for the quadrature detector. The 100K value should be satisfactory to resultin a signal of a few volts p-p using a laser with an output power of around 1 mW and no beam expander. (The expanded beam may slightly exceeds the dimensions of the photodiodes so the sensitivity will be reduced.) For a lower power laser or a laser with a beam expander, larger values may be required. Or for finer control, fixed resistors can be added in series with the trim-pots. The trim-pots on the right adjust the comparator threshold for the Sin and Cos signals from the Quad decoder, with the feedback resistors providing some hysteresis. The Atmega 328P Nano 3.0 board runs firmware that is compatible with the µMD GUI. Of course, no high tech system would be complete without indicator lights, so LEDs are added to monitor the A and B inputs. ;-)

The minimal implementation is shown below along with a shot of the laptop screen while twiddling the linear stage micrometer:

   

µMD0 and Interface Schematic (left), Impementation on Solderless Breadboard (Middle), µMD GUI Display while changing Displacemet (right)

A schematic with slightly more detail like pin numbers may be found at: µMD0 Sin-Cos Analog and RS422 Digital Interfaces.

A simple assembled PCB for quad decoder is included. Blank PCBs are available for the µMD0 and interface, but should not be required for a student project. ;-)

The ptototype setup is shown below, but with the dual Thorlabs DET110 detectors and interface without gain adjustments, sorry. ;-)

Overall Setup showing Interferometer, Scope, µMD0 with Interface, and µMD GUI Display

The bandwidth of the photodiode + resistor combination is quite limited, probably a few thousand counts/second, if that. But it is sufficient to track the movement of the micrometer stage, though not if it's pushed back and forth by hand without the micrometer or being moved on the rail. That would require a proper transimpedance pre-amp circuit. µMD0 has a maximum slew rate believed to be above 125,000 counts/second, or around 1 cm/s with the Linear Interferometer.

For more information, see the Laser FAQ chapter Laser Instruments and Applications, sections starting with "Interferometers for Precision Measurement in Metrology Applications". And the Micro Measurement Display 0 (µMD0) Installation and Operation Manual.

Miscellaneous

Where Does the Missing Light Go?

The analog with the signal is that it can be high or low. But since the laser is still lasing and with no polarizer in front of the detector, the detected signal is more or less constant. So when the signal is low (or the spot is dark), where is the missing power? I'll save you some of your brain cycles and state that with the LP film, it's lost in the plastic and actually increases its temperature a miniscule amount.

But what about a Polarizing Beam-Splitter (PBS) like the large one that is the heart of this setup? They have negligible losses and it would be simple in principle to use one in place of the LP film. To do that, either the PBSC would need to be rotated 45 degrees or the polarization of the beam would need to be rotated 45 degrees so that the PBS can generate the two polarized outputs. Rotating the polarization of the beam can be done with a Half WavePlate, but there is none in the kit, believe it or not. ;-) However, it can be simulated using two pieces of LP film and the Attenuator Plate (AP) as a Non-Polarizing Beam-Splitter (NPBS). This isn't quite identical because there will still be losses in the LPs, but if oriented at ±45 degrees, the effect will be the same.

Dual Polarization Detector using LPs at ±45 Degrees

This uses the same CP as the quad decoder but for these experiments, the QWP portion is totally irrelevant and the QWP (sticky) side goes toward the photodiodes for both.

It should be pretty obvious what is going to happen, but seeing it is not quite the same as theory. ;-)

Exploration using a Random Polarized Laser

The High Stability Plane Mirror Interferometer (HSPMI) configuration is recommended but any of the others can be used possibly with slightly different behavior. However, if using the PMI, keep in mind that it is single pass for Arm 1 and double pass for Arm 2, making initial setup more challenging, but the arm length can still be changed by moving the mirror on Arm 2.

For the most dramatic demonstration, a setup like the one in the diagram below may be used:

It uses the Voice Coil actuator to move Arm 2 by a small amount driven with a function generator with the Quad-Sin-Cos decoder which allows the dynamic behavior to be easily observed on an oscilloscope set up for the Lissajous display in X-Y mode. The PZT could also be used though its maximum excursion is smaller.

For the HSPMI and other two-pass interferometers, changing the position of Arm 2 by x will result in a path length change of 4x. Why?

The JDSU 1107/8 HeNe lasers have a cavity length of 5.417 inches (13.76 cm); 1/4 cavity length of 1.354 inches (3.44 cm), and lase with 1 or 2 longitudinal modes (which changes during mode sweep). With some other similar short laser, the results of the various tests below should be able to determine its cavity length. How?

If the laser is being used for the first time, its polarization axes need to be determined: Set the laser up with a linear polarizer in the output. Rotate the polarizer until an orientation is found where the transmitted beam intensity goes to 0 or nearly to 0 periodically as its warming up. This is the variation in longitudinal mode amplitude due to mode sweep. Mark the laser head (or tube if you're so brave as to risk being zapped!) at that orientation and put another mark at 90 degrees to it, and then one at precisely 45 degrees between them. If the brightness changes suddenly at any point, the laser is a flipper and cannot be used here because it will result in strange and unpredictable behavior of the interferometer.

The linear polarizer can be a piece of either the CP or LP sheet with the protective film removed on the non-adhesive side and that side used as the input. The output polarization will be unpredictable with the adhesive-side protective film in place but for the laser set up, that doesn't matter. However, note that for the CP sheet, the polarization is at 45 degrees to one of the original edges; for the LP sheet it is parallel to one of the original edges. How would the exact orientation be determined for each if unmarked?

The first test will be set up this random polarized laser so it behaves like one that is linear polarized. Attach a piece of Linear Polarizer (LP) with its non-adhesive side facing the laser with the protective film removed. This must be a pure LP, but CP sheet can be used for "extra credit" to see how it behaves. ;-) The LP should be aligned with the intermediate mark (at 45 degrees) put on the laser in the step above; the CP should be aligned with the 0 or 90 degree marks (which puts its LP at 45 degrees). The effect of this is to create an output that is virtually identical to that of a linear polarized laser at the orientation of the LP. If installed in the interferometer with its polarization axis at 45 degrees, it will behave like a linear polarized laser (though the power will have been cut by more than half due to the LP). Where does the missing light go? ;-)

Now for some experiments. If using the HSPMI, the path length difference is precisely the difference in spacing from each mirror to the PBS. This is also true of most other configurations but NOT the PMI? Why?

What follows does not include the expected results - that is for you to determine. (A suitable search of the Laser FAQ and possibly elsewhere will find them but that would be cheating. "Variation" means how both the fringe signal and DC level changes during the laser's mode sweep:

1. JDSU 1107 or 1108 set up as linearly polarized laser:
   • Orient the laser's polarization axis (after the LP) at +45 or -45 degrees. (Can you predict how the +45 or -45 degree orientation will change the behavior, if at all?

     Test for the variation in signal amplitude for arm length differences of 0, 1/4, and 1/2 cavity length (PLDs of 0, 1, and 2 cavity lengths) as well as intermediate values like 1/8 and 3/8 (PLDs of 1/2 and 1-1/2 cavity lengths), and larger ones if your setup permits.

   • Orient the laser's polarization axis at 0 or 90 degrees:

     What is expected for the signal amplitude?

2. JDSU 1107 or 1108 random polarized laser. Remove the LP in front of the laser.
   • Orient the laser's polarization axes (the outer marks) at +/-45 degrees:

     Test for the variation in signal amplitude for arm length differences of 0, 1/4, and 1/2 cavity length (PLDs of 0, 1, and 2 cavity lengths) as well as intermediate values like 1/8 and 3/8 (1/2 and 1-1/2 PLDs), and larger ones if your setup permits.

     What happens if one of the +/-45 degree polarization axes is blocked by putting an LP in the beam path? Do it at the minimum, approximate mid-point, and maximum of the signal, and for both orientations.

   • Orient the laser's polarization axes at 0/90 degrees:

     What is expected for the signal amplitude?

Notes:

1. For some cass, there will be a wide variation in signal amplitude meaning the range may go from very close to 0 to the maximum available with clean optics and careful alignment.

2. For some cass, there will be a minimum variation in signal amplitude meaning the only change will be due to normal power fluctuations during mode sweep.

3. Intermediate spacings will result in some variation in signal amplitude.

More to come.

More Advanced Options

Other (non-Displacement) Interferometers

But many other parameters can be measured using interferometry including angle, straightness, and flatness. The layouts for these are not particularly complex but would require creativity in mounting and some optics and mechanical parts not included in the standard kits. See the information at Optics for Interferometers Using Two-Frequency Lasers.

DIY Single Frequency (SF) HeNe Laser

With an SF laser and the Quadrature Detector, the signal output from any of these interferometer configurations will provide complete displacement information that can be used with a measurement display or for closed-loop control. Systems using SF lasers are called homodyne interferometers.

SF HeNe lasers are available for order of $5,000 from a few laser companies (though this number has been dwindling). But fortunately, it is possible to construct one from readily available parts for less than 1/20th as much. The laser tube can be identical to the one used in the JDSU 1107 or 1108 random polarized HeNe laser head that comes with some of these interferometer kits. Adding a heater to control cavity length along with a simple controller using discrete analog components or an Arduino turns it into an SLM laser with performance similar to that of the high priced ones. If interested, a kit of parts along with detailed assembly instructions is available. For the manuals, go to Sam's Electronics and Laser Kit Information and Manuals.

Modifying the Output of a Two Frequency Laser for use in a Homodyne Interferometer

There are a couple of ways of doing this without actually rebuilding the laser itself. ;-) But unfortunately, both lose at least 1/2 the optical power. There's no easy way around that for a single axis as is the case here. (For two axes, a PBS could be used to separate the H and V polarized components with each one rotated to the desired polarization orientation or converted to circular polarization with waveplates. Each axis could then use 1/2 the total power and nothing would be inherently wasted.)

1. Linear polarizer at 45 degrees: This is simplest but strictly doesn't create a single frequency output. In fact, the output is similar to that of a multi-longitudinal mode laser like those used in the other kits, but the mode spacing is at the split frequency rather than close to the ~1 GHz of a short linearly polarized HeNe. If the detector is "blind" at or above the 1.5 to 2.0 MHz split frequency of the two frequency laser, this scheme will work fine. But that cannot be guaranteed even for the basic detection schemes used here. And the soon-to-be-released AB2 Quad-A-B preamp has a response exceeding 3 MHz. In fact, as should be recalled, an LP at 45 degrees is exactly the scheme used to combine the F1 and F2 components for the optical receiver. The only reason this isn't an issue with the other kits is that none of the electronics responds at ~1 GHz.

2. Linear polarizer at 0 or 90 degrees with Half WavePlate (HWP) to orient the beam at 45 degrees: This one is "pure". It blocks F1 or F2 (which one doesn't much matter) and then rotates the single frequency beam to 45 degrees.

In the interest of efficiency (since as noted, the theoretical best that can be done is to only cut the power in half), a small PBS cube is used rather than LP sheet. The HWP has only a 5-10 percent loss and will be attached to its output-side. (Or vice-versa as the operations are symmetric). The detailed mechanics are yet to be worked out but any special parts will be provided with the combined kit and the "Single Frequency Converter" will mount on the faceplate of the laser.

DIY Two Frequency Zeeman HeNe Frequency Laser

Where a random polarized HeNe laser tube meets certain requirements, applying an axial magnetic field will result in the normal single longitudinal mode splitting into two components that are left and right circular polarized, which are converted to orthogonal linear polarization with a QWP. It turns out that many of the HeNe laser tubes that used to be used in 100s of thousands of supermarket checkout barcode scanners satisfy these requirements, and the laser tube found in a $10,000 metrology laser is essentially the same. ;-) Stabilization is then similar to that of SF laser, above, and a kit is also available. Since the SF and TF lasers are very similar, it may be possible to use the same tube and controller. But while a homodyne interferometer can work using an unstabilized laser with restrictions on PLD, a two frequency Zeeman HeNe must be stabilized because the beat frequency actually appears for only a portion of mode sweep. So it must be locked to the center of that range.

Kits are available to construct stabilized Zeeman HeNe lasers that would perform well for use with the interferometer. They include a bare HeNe laser tube, power supply, heater, magnets, optional parts to construct an Arduino-based controller, and more. So if you really want to be able to claim that this was built from parts closer to stone tools and bear skins than HP/Agilent lasers, see the manual at: Stabilized Zeeman HeNe Laser Kit 1 with or without Arduino.

Future Options

Transparent Laser Enclosure with Heater

 

HeNe Laser Tube in Transparent Acrylic Cylinder with Heater (left), Scope Display of Fringe Signal while Heating Glass Block in Arm 1 (right)

Something like this would be used to house the single frequency or two frequency lasers described above. The heater would also be useful to accelerate mode sweep for experiments dealing with the interferometer response particularly for random polarized lasers.

Information

Required Tools, Equipment, and Supplies

• Hand tools:
  1. Hex driver set: 0.05 inch to 1/4 inch. The "ball-driver" variety are generally preferred if available.

  2. adjustable ("Crescent" wrench): One with a maximum opening of 3/4 to 1 inch should be acceptable.

  3. Screwdrivers: Small flat blade and Philips, jewelers screwdriver set.

  4. Needlenose pliers, flush-cutters, wire strippers:

  5. Assorted small metal files:

• Soldering equipment:
  1. Soldering iron: While it is possible to get away without soldering for the opto-mechanical construction and basic experiments, it will be required to assemble tne various PCBs - AB2, OR3, µMD0, µMD2, etc. A small temperature-controlled soldering iron is preferred. It doesn't need to be fancy or expensive. A usable setup can be purchased for under $25. A propane torch or Weller soldering gun is NOT suitable. ;-)

  2. Desoldering tool: This also doesn't need to be fancy or expensive. A hand desoldering pump like a full size "SoldaPullt™" is quite satisfactory. The smaller ones or other brands never have seemed to work as well. And yes, there will always be a need to remove components either because the wrong part was installed or was damaged.

  3. Solder: Rosin core solder, #20 typical. 60:40 tin:lead solder is close to the easiest to work with. There are lead-free solders now but they generally do not seem to work as well. DO NOT even think about using that old spool you found with your plumbing supplies!

  Just as important are the skills to do fine soldering. If you are not proficient, find someone who is or practice on scrap PCBs. Correcting sloppy work on a PCB is much more difficult than doing it right in the first place and may not even be possible.

• Supplies:
  1. Hookup wire: This is insulated wire for connecting various discrete components like the potentiometer used for the PZT or loudspeaker. #22-24 AWG stranded hookup wire is optimal.

  2. Male-male Arduino jumpers: These are typically used for attaching the solderless breadboard(s) to screw terminal blocks.

  3. 5-Minute Epoxy: Epoxy is for securing various parts like the gas cell end-plates and PZT mirrors. the 5-Minute variety is soft enough that it can be removed if necessary. DO NOT use Cyanoacrylate-based adhesives like Crazy Glue™! Aside from accidentally sticking your fingers together, it may ruin optics.

     TWo-part 5-Minute Epoxy is included in all the kits.

• Test equipment:
  1. Digital Multimeter (DMM): A DMM is always handy to have and one that costs under $20 will be more than adequate.

  2. Digital Storage Oscilloscope (DSO): While one can spend 10s of thousands of dollars on a DSO, the type needed here are under $150. Two suggestions are the Owon VDS1022I USB scope (around $110) or FNIRSI ADS1013D DSO (around $175). The Owon works in conjuction with a PC or MAC while the FNIRSI has a touch screen and is stand-alone. These are both color two channel scopes with a real bandwidth of 20-25 MHz. But if you're serious about electronics or photonics, consider something more capable. Spending under $500 will get you a scope with a bandwidth of 100-200 MHz and many features similar to those of the professional scopes. ;-)

     While it is possible to use an analog scope for some of the experiments, being able to capture a trace at 1 Hz or 10 MHz is nearly essential. Analog storage scopes were never very good and are almost as rare now as raw dinosaur eggs.

  3. Laser power meter: This can be constructed with one of the kit PDs using the biased photodiode circuit and a DMM.

Parts Identification

Polarization Control Optics

• Linear Polarizer (LP): A linear polarizer only passes light that is aligned with its polarization axis. More precisely, it obeys Malus's law whereby the optical power of the light passed is equal to:

  I_o = I * cos²(Θ_i)

  where:

  • I_o is the output power.
  • I is the input power.
  • Θ_i is the angle between the input and polarizer's axis.

  Where the input light has multiple polarized components with differing polarization orientations, the result is the sum of Malus's law applied to each one.

  One use of an LP in this interferometer is to combine the two orthogonally polarized components from the PBSC at 45 degrees so they line up and can interfere at the detector.

• Quarter WavePlate (QWP): A QWP is a part of the Circular Polarizer (CP) and are used in the quadrature-sin-cos detector. The effect of a QWP is summarized below. For the following, "θ" is the angle with respect to the fast axis of the waveplate.

            Input                      Output
    ------------------------------------------------
      Linear, θ = 0° or 90°       Unchanged
      Linear, θ = +45°            Right circular
      Linear, θ = -45°            Left circular
      Linear, θ ≠ ±45°, 0°, 90°   Elliptical
      Right circular              Linear, θ = -45°
      Left circular               Linear, θ = +45°
      Elliptical, θ = 0 or 90°    Linear at angle
  

  "Elliptical, θ = 0 or 90°" means its major and minor axes are aligned with the waveplate optic axes. This case can be easily decomposed into the vector sum of a linear component (which is unchanged) and a circular component which gets transformed into a linear component at 45°.

  QWPs are used in several of the interferometers. Their optical axes are always at ±45 degrees. (The handedness of the circular polarization will be swapped but that doesn't matter here - they are unmarked and can be mounted either way.) Thus when light polarized at 0 or 90 degrees passes through the QWP, it is converted to circular polarization. When that is reflected from a CC or plane mirror, the handedness flips and when it passes back through the QWP, the polarization axis is rotated 90 degrees. This allows the PBSC to redirect it resulting in the various beam paths required by the interferometers.

• Circular Polarizer (CP): The CP is a combination of an LP and QWP:
  

Some specific applications:

• For the basic detectors, the CP would be used like an LP since the output polarization doesn't matter to a photodiode.

• For the Type 3 quadrature decoder, one CP is used like an LP (PD Channel A) and the other is used as a QWP with an LP (PD Channel B). Much more on this in the sections on the Quad decoder.

• A CP may be used like an LP in front of a linear polarized laser (with its LP-side facing the laser) to convert it to circular polarization and to adjust the usable output power. However, the behavior of the interferometer will be subtly different than with linear polarization at 45 degrees. That will be something to analyze.

• A CP may be used like an LP in front of a random polarized laser (with its LP-side facing the laser) to convert it to circular polarization. (1) A single polarized component may be selected if lined up with it or (2) both of its linearly polarized components may be combined so it behaves like a linearly polarized laser with the same cavity length (though with reduced output power). As above, the behavior of the interferometer will be subtly different than with linear polarization at 45 degrees.

• A pair of CPs may also be used to select a single polarized component of a two frequency laser and orient it as desired. The first CP blocks one of the polarized components and converts the other to circular polarization. The second CP then takes that and produces a linearly polarized output aligned with its optical axis. The sticky sides of the two CPs will even be what gets stuck together after determining the correct orientations. ;-) This is the simplest and least expensive way to convert a two frequency laser to a single frequency laser. But there is a downside compared to using a true PBS and HWP or even some of the other schemes: The output power will likely be cut by 50 percent or more (in addition to blocking the unwanted polarized component) due to losses from the two CPs.

• A CP and QWP may be used in a way similar to a pair of CPs. The CP blocks one of the polarized components and converts the other to circular polarization. The QWP then takes that and produces a linearly polarized output aligned with its optical axis. The benefit is that the losses will be lower - only from the CP and reflections from the QWP's surfaces if not AR-coated. So the output power could be nearly double.

And as a point of interest CPs are used in front of LCD displays to increase their contrast under ambient illumination: With the LP side toward the viewer, ambient light will pass through it and the QWP, and be reflected by the display itself. But when CP light is reflected, the "handedness" flips and the result is linear polarization at 90 degrees to what it was originally, and thus blocked by the LP. That is part of the reason your smart phone screen looks dark when nothing is displayed on it.

However, while circular polarizers intended for use with cameras are constructed as shown above, the "polarizing films" sold for smart phones and the like may or may not be true CPs. Some are just linear polarizers or linear polarizers coated with a weak neutral density filter. And it's not clear how one can select the proper type since the sellers are typically clueless. The only actual CPs consistent with the above diagram I've found so far were listed as something like: "New Backlit Screen Modify Part Polarizing film For GBA GBC GBA SP N_ES". Those listed as "LCD Polarizer Film Polarization film Polarized Light Film For ip.ccHHH" may also be CPs but with (1) the adhesive and non-adhesive sides swapped and (2) the axes of the LP and QWP rotated 45 degrees. They may also have a weak ND filter. Sometime a faint colored line can be seen which is at the orientation of the LP or 90 degrees from it. But that doesn't help with whether there is a QWP, though sometimes there are also a series of small circles, presumably to indicate CP, though they tend to be on the opposite side from the QWP. Those listed specifically for iPhones were of the simple LP type (usually with a faint line at 90 degrees to the LP axis parallel to the short side). Interestingly though, the protective film that normally gets discarded is birefringent and may even be a QWP. Which of course makes little sense. :( :) A further issue is that some of these may be diffuse, not trasparent. That doesn't make much difference for use on the PDs, but means they won't work elsewhere in the beam path. Confirm if possible. Confused yet? I sure am. :( :)

This same scheme is also used in what is sometimes called a "poor man's optical isolator", whose purpose is to minimize back-reflections from an optical setup into the laser, which may destabilize it or worse. The combination of a linear polarizer (or PBSC) and QWP acts as a "diode" for polarized light. It's called "poor man's" because it is much less expensive than a Faraday isolator, and adequate for many purposes. But for it to work well, any reflective surfaces in the optical setup must not mess with the polarizaton.

The piece of CP provided in these kits is intended for such an application. It can be cut into smaller pieces since they only need to be slightly larger than the beam, which even if expanded is only ~4 mm. As noted shown in the diagram above, the optical axes of the QWP are at 0 degrees with respect to the edges of the CP and the axis of the LP is at 45 degrees.

The CP comes with protective film on both sides which MUST be removed because it acts like some type of waveplate and messes with the polarization. The side of the CP with the QWP is sticky since that was intended to go against the screen. To prevent it from collecting dirt and fingerprints, the smaller pieces to be actually used in the detector(s) should be stuck to microscope cover slips (included) or glass windows. CAUTION: Microscope cover slips are thin and fragile - don't press too hard.

Adjusting the Micrometer Stage

• Generic stage: There are 4 setscrews located on the side of the stage. Depending on the version, these may be on either side. It may also be necessary to loosen screws on the top which secure the inner track(s). If there is a locking knob, some may be concealed under the lock-plate.

• Parker stage: There are 3 setscrews located on the side opposite the lock knob (if present) which may be concealed by a sticker.

A 1/16" hex driver may be used to tighten or loosen them the smallest amount which should not be more than 1/10th of a turn.

The micrometer can be lubricated with light grease if it seems rough or tight. The ball bearings for the stage itself should not need lubrication unless serious dust or other contamination has gotten into the tracks.

Adjusting the Motion Control Platform

1. Move the platform to the motor-end of the rail by rotating the lead screw manually or with power applied temporarily to the DM320T controller using the Arduino MCP test sketch and encoder. If the lead screw appears to bind there and is more difficult to rotate or the platform gets stuck, loosen the two screws securing the motor and adjust the lateral position of the motor so that the rotation requires the least torque.

2. Move the platform to the far end of the rail in a similar manner and repeat by adjusting the lateral position of the bearing end-plate.

3. Move the platform to approximately the center of travel.

4. Loosen the 4 screws securing the platform to the carriage and then set them so they are just snug.

5. Gently twist the platform while testing the axial free play and set it so the free play is just barely detectable. Tighten the 4 screws and confirm that it hasn't changed. If the free play is set to exactly zero, then the the lead screw may be too tight. This is basically compensating for imprecise machine work in cutting the threads.

6. Run the platform fron end-to-end using a low current setting of the DM320T (e.g., 0.3 or 0.5 A) to confirm it doesn't bind anywhere.

7. Repeat all these steps as necessary to optimize.

It still won't be a $20,000 rig but should be quite acceptable.

Removing 5 Minute Epoxy

Where the adhesive is accessible, a single-edge razor blade can often be used to slice it or get underneath and peel it off. But that may not be possible if the turning mirror were attached in the wrong location with bits of Epoxy underneath it. Or reusing the mirror stuck to the PZT. Attempting to pry the thin mirrors off would likely result in bits of glass.

The easiest method where the parts can withstand it is to use a common heat gun. The exact temperature at which the typical Devcon 5 Minute Epoxy decomposes is not known. The datasheet only states that the "Operating Temperature" range is -40 °F to +200 °F but not what happens at +201 °F. ;-) It may exceed +500 °F. However, from experience, a sufficient temperature can be reached in a couple minutes to soften the Epoxy without damaging parts made of glass or metal. However, some plastics might melt. ;( As the critical temperature is reached, the Epoxy will soften, so work over a non-flammable surface that won't damage the part to be removed and gently prod it with a popsicle stick or something similar until it falls off. After cooling, the residue can be removed by scraping or with isopropyl alcohol. Since the Epoxy at least partially decomposes, this method should not be used for repositioning, only removal. Clean the two surfaces and then start fresh. ;)

CAUTION: Don't try this with the gas cell or loudspeaker, they would likely get damaged. "INFORMATION1.htm">

Linear Polarized versus Random Polarized HeNe Laser

Although the experiments are described with a linear polarized HeNe laser, it is possible to use a random polarized laser instead if one is more readily available. However, its output will need to be converted to linear polarization in a very specific way with a linear polarizer to behave the same. But a random polarized laser can also demonstrate some interesting interferometer behavior not available with a linear polarized laser.

Most random polarized lasers do not actually have polarization varying, well, at random. :) The term "random polarized" with respect to to HeNe laser simply means that nothing special is done to control the polarization. (I.e., no Brewster plate.) In the case of many red (633 nm) HeNe lasers, that means:

1. There are two polarization axes instead of one.
2. They are orthogonal to each-other.
3. Their orientation cannot be predicted without testing but remains fixed for the life of the tube.
4. Adjacent longitudinal modes have orthogonal polarization.
5. Adjacent longitudinal modes differ in wavelength by 1/(2 x total the number of wavelengths that fit in the laser tube cavity).

Murphy must have taken a day off when the HeNe laser was invented because these attributes end up being quite useful - in fact fundamentally important - for many applications and especially the stabilized HeNe laser. Most of this applies to any laser, but one characteristic that is quite critical is the bit about adjacent modes having orthogonal polarization. This applies only to red HeNes and not even to "other color" HeNes, let alone most other common lasers. Specifically, it facilitates the use of the modes for stabilization feedback.

A laser tube with these characteristics would be considered "well behaved". if the longitudinal modes move smoothly through the neon gain curve without abrupt changes in amplitude. Not all are like this. :( :) A "flipper" will have "polarization switching" whereby at some point or points during mode sweep, the two sets of longitudinal modes will swap their polarization axes, usually instantly. For some truly nasty tubes, this will happen continuously, somewhat well, at random. Flippers are often not suitable for an interferometer because in the region of the flip, there may be excessive optical noise, possibly due to even the smallest amount of back-reflection, which will show up as large oscillations in the fringe signal. (While that in itself may be interesting, it will also be confusing.) More fundamentally, the effect of PLD on the interferometer depends in part to the relative intensity of the modes in each arm and that would be unpredictable for a flipper.

The simplest way to test for a well behaved random polarized laser is to put the output through a linear polarizer and monitor it on a graphing laser power meter or photodiode and data acquisition system. Adjust the orientation of the polarizer for the maximum amplitude of the mode sweep variation. That aligns it with one of the polarization axes. Then inspect the plot over a couple minutes (from a cold start to get the fastest mode sweep) for abrup changes in amplitude. There should be none. A tube that flips when cold may calm down once it warms up. The opposite is also possible but appears to be less common.

The following animation shows the mode sweep of a random polarized HeNe laser similar to the JDSU 1107 or 1108. The red and blue lines represent the amplitudes of the orthogonal polarized outputs. To actually view these live with a similar display requires an instrument called a Scanning Fabry-Perot Interferometer (SFPI) with a dual polarization detector. While commercial SFPIs cost several thousand dollars, an SFPI with these capabilities can be built as a nice student project at modest cost. It's all done with mirrors. ;-)

Mode Sweep of Short Random Polarized HeNe Laser

A linearly polarized HeNe laser of similar length would have both modes be the same polarization and same color. :)

The rate at which the modes pass through the neon gain curve will depend on how fast the tube is expanding from heating of the gas discharge, so it will slow down as it reaches thermal equilibrium from a cold start.

Plots of the two polarized modes for a well behaved tube (non-flipper) would look something like:

Mode Amplitude Plots of Well Behaved Short Random Polarized HeNe Laser

The plots cover the time range from a cold start to close to thermal equilibrium. Note how both the red and blue plots are continuous. A full mode sweep cycle at the start is a few seconds while at the end it is a few minutes. After that it would be irregular as just ambient air moving around will have an effect.

(For a linearly polarized tube with similar physical characteristics, the amplitude of the output would be the sum of the red and blue plots.)

Some possible options for a random polarized laser:

1. Polarization axes at 0 and 90 degrees.

2. Polarization axes at 0 and 90 degrees with linear polarizer at 45 or -45 degrees. (This is most like the linear polarized laser.)

3. Polarization axes at &plmn;45 degrees.

4. Effects of the PLD on detected fringe signal for all the above cases with the specific cases of 0, 1/2, 1, and 2 times the laser tube cavity length (5.41 inches / 13.4 cm for the JDSU 1007/8) usually being the most interesting.

The plots of a typical flipper might look like the following (zoomed in to a few mode sweep cycles to show details):

Mode Amplitude of Short Random Polarized "Flipper" HeNe Laser

(The shape of the curves differ due to the tube not being the same model.) The vertical green line is the instant of the flip, which occurs quite close to the same location during each mode sweep cycle. However, experience shows that in the interferometer, there may be nasty stuff going on around that region and it won't be confined to an instantaneous event. The detected signal may be very noisy.

For an academic challenge, a random polarized flipper is probably the most interesting type of tube to study. But a good understanding of what's going on is necessary to not to go insane attempting to decipher the behavior. This is not recommended. Even for us so-called experts that can be a problem. ;-( A random polarized flipper may be available in place of or in addition to the linear polarized or random polarized well behaved tube if interested. :-)

The next most interesting tube would be one that is random polarized and well behaved. One or two of the kits put together to date includes that type of laser and it may be an option going forward pending availability of suitable tubes since it can be used as a linear polarized laser with the addition of a linear polarizer at 45 degrees with respect to its principal polarization axes.

Homodyne V2.1 Summary of Features and Options

There are three versions of the V2.1 Homodyne setups, though customization is possible.

• The Basic version uses a 6x18" breadboard and will be able to do the linear interferometer using cube corners, the pressure and temperature sensors, and displacement measurement using uMD0. The smaller width breadboard compared to V1.0 and V1.5 only affects the mounting of the Arm 1 post holder.

• The Deluxe version also uses a 6x18" breadboard and in addition to everything in the Basic version, it will be able to do the interferometers using planar mirrors, actuators using planar mirrors, and more on laser coherence and effect of mode sweep.

• The Deluxe+ version uses an 8x24" breadboard to facilite more experiments on coherence length and mode sweeep, as well as being able to add other optics in Arm 2.

The Basic version really has enough for an introduction to interferometry and can be upgraded to the Deluxe version by adding the appropriate parts from me or elsewhere.

Other changes compared to V1.0 and V1.5 include:

1. V2.1 (and V2.0) use an aluminum plate on Thorlab posts rather than a wood block for the PBS and turning mirror mount as in V1.0 and V1.5. Both are very stable, but the plate affair is more in keeping with optical setups and doesn't contribute to the demise of trees. ;-) The wood block also had issues of degradation with multiple cycles of assembly and disassembly.

2. A custom detector made from discrete parts replaces the Thorlabs DET110 in V1.0 and V1.5. The performance for the purposes of these kits is identical. And it facilitates adding a second channel for the quad-sin-cos decoder or X/Y detector and also simplifies the wiring with a terminal block and/or jumper wires instead of requiring BNC cables and clip leads. Both a solderless breadboard and assembled PCB version will be included.

   However, for the die-hard, a few DET110s are available at a lower cost than the current version of a biased photodiode from Thorlabs.

3. The adjustable mounts will be either Thorlabs KM100s or Newport U100s. For the purposes of these kits, they are functionally equivalent and the Thorlabs are smaller and sleeker. ;-) The U100s are more precise (and a lot pricier if bought new!), though these versions lack knobs, requiring the use of a 5/64" ball driver, which may be less convenient. But never fear, appropriate Thorlabs knobs will be included in the kit.

4. The QWPS and mounted CC in the Deluxe and Deluxe+ versions may be custom parts rather than from HP/Agilent. They will be functionally equivalent without issues of availability.

5. A generic linear stage will be used, though a Parker 3902 may be an option. The generic stage is equally good for positioning here, possibly even more stable due to its wider track spacing.

6. All versions will have either a Thorlabs RC carrier with RLA rail, or MR15 rail with MGN15-C block.

Photos of each of the three versions with typical interferometers are shown below. The first is the Basic version with the 6x18" the breadboard, configured with Linear Interferometer and quad decoder PCB attached to the SG-µMD0 PCB:

The next one is the Deluxe version configured for the High Stability Plane Mirror Interferometer. The laser includes a beam expander but it is otherwise configured the same way.

The next is the Deluxe+ "Stretch" version on the 8x24" breadboard.

Sam's Educational Michelson Interferometer Interferometer Kit Parts List

Replicating it should be straightforward

The 8x18" optical breadboard for V1.0 and V1.5 is custom with the dimensions selected to be convenient for the projects while being able to easily ship Worldwide. The 6x18" and 8x24" breadboards for V2.0 and V2.1 are standard. If machining one, fewer than half the standard holes are enough based on all reasonable mounting locations, but that's only worth it if you're paying by the hole. ;-)

Most other standard opto-mechanical parts are from Thorlabs. The major exceptions are the HP/Agilent PBS cube, QWPs, and mounted CCs (via eBay). But low cost substitutes for those are in the works.

The JDSU 1107P and 1108P, or similar laser heads from Melles Griot/Pacific Lasertec like the 05-LHR/P-211 are ideal for these experiments. The criteria include being linearly polarized, eye-safe output power, and physical size. Optics companies like Edmunds, Newport, and Thorlabs have suitable lasers (though most are made by JDSU and PLT), but eBay is often a good source at a fraction of the cost. The laser could also be a bare tube safely enclosed, though the preferred linearly polarized variety is not that common at the low power of 0.5 to 1 mW. Random polarized heads and tubes can be used (and actually add some interesting areas to study) if certain criteria are met, primarily that they are not "flippers". See section: Linear Polarized versus Random Polarized HeNe Laser.

Parts List for V2.1

Differences between the versions will be noted.

Parts in Homodyne Kits ONLY

 Quantity Description               
------------------------------------------------------------------------------
 Baseplate/Optical breadboard:

    1x Aluminum optical breadboard 6x18" (Basic and Deluxe versions, BASE Lab
       Tools SAB0618) or 8x24" (Deluxe+ version, BASE Lab Tools SAB0824).

 Laser Assembly: 

    1x Laser consisting of 0.5-1 mW JDSU 1107/P or 1108/P laser head
       and power supply with DC input brick and universal wall adapter,
       which may be used Worldwide.  Minimum power 0.4 mW.
       A lab-style HeNe laser power supply may be an option.

    1x (Random polarized lasers only): ~1x1" piece of circular polarizer.
       Consists of linear polarizer (+/-45 degrees) with QWP (0/90 degrees).
       Cut up as needed.

    1x Beam Expander (Deluxe/Deluxe+ only) consisting of:

      1x Beam Expander Adapter Plate.  The front bezel of the laser has
         had 3 tapped holes added for this.

      1x HP/Agilent 6 mm beam expander, modified, must be glued or
         press-fit into Beam Expander Adapter Plate.  Resulting beam
         is 3-4 mm in diameter.

      3x M2.5 x 5 mm cap-head screws to secure adapter plate.

    2x Laser Mounts each consisting of:

      1x Small Ring Mount with two 8-32 x 1.5" and two 8-32 x 1" thumbscrews.

      1x Thorlabs TR3 post with 8-32 x 1/2" cap-head screw to secure the ring
         mounts and optional #8 plastic washer to provide compliance if the
         mounting hole in the rings is threaded (some are) so the orientation
         can be set correctly.  In the latter case, an 8-32 x 1/2" setscrew
         can substitute for the cap-head screw so as not to impinge on the
         available space within the rings for the laser head.

 Custom Single Channel Detector and Quadrature Decoder:

    1x Variable attenuator plate to be used as NPBS.
    1x 1/2-1" piece of CP sheet (may be used as CP or LP), cut to size.
    2x Silicon photodiodes + spare.
    1x 1K ohm resistor (PD protection).

    2X Load resistors, 100K to 1M typical, or 1M trim-pot

    1x Set of jumper wires, etc.

    1x Solderless breadboard with adhesive back, 170 tie points.
    1x Detector adapter plate with 8-32 or 1/4-20 1/2" setscrew. 

    1x QD1 PCB (option) with  8-32 1/2" cap-head screw and 1/4" x 1/4" #8
       spacer.

       2x 4 pole screw terminal block.
       1x 1K ohm resistor.
       1x 0.1 µF capacitor.
       2x Photodiode.
       2x 2 pin male to female socket strip.

  AB2 quadrature decoder parts kit. 

  Common to all detectors:

    1x Thorlabs PH2 post holder.
    1x Thorlabs TR3 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and
       1/4-20 5/8" cap-head setscrew to attach to base. 

 Micro Measurement Display 0 (µMD0):

    1x Atmega 328 Nano 3.0 microcomputer board with pins soldered.
    1x Homodyne firmware for Nano (may be preloaded or download from
        µMD0 Manual).

    1x µMD Graphics User Interface (download from
        µMD0 Manual).

    1x Solderless breadboard 3-1/4" x 2-1/4", 25 columns, 400 tie points.
    1x LM393P dual voltage comparator.
    1x 3 mm Red LED and 1-2K ohm resistor.
    1x 3 mm green LED and 27-47K ohm resistor.
    2x 100K to 1M ohm resistors or trim-pots.
    2x 10K ohm trim-pots.
    2x 100K ohm resistor.
    2x 470K ohm resistors.

    1x SG-µMD0 PCB (option).

       1x 30 pin Socket for Nano (may need trimming).
       2x 8 pin sockets for LM393 and UA9637.
       1x 3 mm blue LED.
       1x 10K ohm resistor.

 Support (Deluxe and Deluxe+):

    1x  10K ohm potentiometer wired with 10K ohm current limiting resistor.
    -   Hookup wire and jumper wires.

Parts Common to both Heterodyne and Homodyne Kits

  Biased Photodiode Detector (BPD1):

    1x 1/2x1/2" piece of CP polarizer sheet (may be used as CP or LP with
       LP axis at 45 degrees), to be cut to size.

    1x 1/2x1/2" piece of LP polarizer sheet (LP axis XY), cut to size.
 
    1x BPD1 PCB with 8-32 1/2" cap-head screw and 1/4" #8 spacer.
    1x Silicon photodiodes + spare.
    1x 2 pin male to female socket strip for photodiode.
    1x 1K ohm resistor (PD protection).
    1x 0.1 µF capacitor.
    1X Load resistors, 2-3K ohms typical, or 10K trim-pot
    1x 4 pole screw terminal block.
    1x Solderless breadboard with adhesive back, 170 tie points.
    1x Set of jumper wires, etc.

  Common to BPD1, OR3, and AB2:

    1x Thorlabs PH2 post holder.
    1x Thorlabs TR3 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and
       1/4-20 1/2" cap-head setscrew to attach to base. 

  Interferometer Assembly. (HP part numbers are used here; The actual parts
   may be the physically and functionally equivalent from Excel or Zygo.)

    1x HP/Agilent 10702A or 10706A PBS cube in frame with 4x 4-40 x 1-3/4"
       cap-head screws.

    1x HP/Agilent 10703A Cube Corner or mounted equivalent with 2 4-40 cap
       head screws.

    2x HP/Agilent 10722A Quarter WavePlate or custom equivalent each with two
       4-40 cap-head screws.

    1x Turning mirror (Approximately 1/2" x 1"). 

    1x Turning Mirror Bracket V2.0 with 4-40 x 5/16" cap-head screw and washer.

    1x PBS Mount Adapter Plate V2.1 with 2x Thorlabs TR3 post, 2x 3/4" spacer,
       and 2x 8-32 x 1" or 1-1/8" cap-head screw.

  Arm 1:

    1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap-head
        screw to secure it to post.

    1x 1" bare Cube Corner.
    1x 1" diameter planar mirror.
    1x Thorlabs PH2 post holder.
    1x Thorlabs TR2 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and
       1/4-20 1/2" cap-head sscrew to attach to base.

  Arm 2:

    1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap
       screw to secure it to post.

    1x 1" bare Cube Corner.
    1x 1" diameter planar mirror.
    1x Thorlabs PH2 post holder (rail or slide) and/or PH1 (MCPs).
    1x Thorlabs TR1 post (rail or slide or MCP Type 1) or TR075 (MCP Type 2).

    1x Generic 40x40 mm linear stage, end or side micrometer adjuster,
       maximum of 20 mm thick.  A 4-40 or M3 screw into a tapped hole is
       used to secure the post holder the top of the stage.

  Thorlabs rail assembly (Homodyne only):

    1x Thorlabs RC1 carrier with screw and washer to secure it to the
       bottom of the stage.

    1x Thorlabs RLA0600 6 inch rail (Basic or Deluxe version) or RLA1200
       12 inch rail (Deluxe+ version).

  Ball bearing rail assembly (Heterodyne):

    1x MGN15C carriage block.

    1x MGN15 stage adapter plate with 4x 4-40-3/16" cap-head screws to
       secure generic stage to plate and 4x M3-8 flathead screws to
       secure plate to MGN15C carriage block.
 
    1x Locking bracket with 2x M2.5x16 mm screws to secure bracket to
       MGN15C carriage block and 4-40 1/2" Nylon thumbscrew.

    1x Rail:

       1x MR15-150 150 mm rail with 2x 6-32 3/8" cap-head screws to secure
          rail to breadboard and rubber bumpers to be used as end-stops.
          Breadboard requires addition of two 6-32 tapped holes. (Compact
          version.)

       1x MR15-200 200 mm rail with 2x 6-32 7/8" cap-head screws and nuts to
          secure rail to breadboard.  The screws with spacers also can act
          as the end-stops (Mid-Size version.)

       1x MR15-300 300 mm rail with 2x 6-32 7/8" cap-head screws and nuts to
          secure rail to breadboard.  The screws with spacers also can act
          as the end-stops (Extended version.)

  Motion Control Platform (Option):

    1x Mini-stepper driven platform, 100 mm, 150 mm or 200 mm travel, with
       4x 4-40 1/2" cap head screws or 4x 4-40 3/4" cap-head screws
       and nuts to secure it to the breadboard.  Each of these will nearly
       entirely fit on the breadboard for the Compact, Mid-Size,
       and Extended Versions, respectively.  The hole pattern may differ
       for the Type 1 and Type 2 MCPs.

    1x MCP adapter plate (if not already present with the generic stage, they
       are the same.

    1x STEPPERONLINE DM320T micro-step stepper motor controller.

    1x Atmega 328P Nano 3.0 microcomputer board with solderless breadboard.

    1x Optical high resolution rotary encoder to move the platform via
       the Nano at least for testing.

  Voice Coil Actuator:

    1x 1-1/2" to 2" loudspeaker. 
    1x 1" D x 1/4" T aluminum or Acrylic Speaker mounting Disk.
    1x Speaker mirror (Approximately 1/2"x 1", may be same as turning mirror).
    1x Optional: Cube corner mounting ring.

  Piezo Transducer (Deluxe):

    1x 27 mm PZT beeper element.
    1x #2 washer to use as spacer.
    1x PZT mirror (Approximately 1/2"x 1", similar to turning mirror).

  Gas Cell Compensator (Air Pressure and Temperature):
    
    1x 1" OD, 7/8" ID, 2" L Acrylic tube.
    2x 1-1/8" D glass or Acrylic window.
    1x 10-32 to hose barb adapter.
    1x 8-32 3/8" or 1/2" set-screw.
    1x Blood pressure bulb with valve.
    1x Blood pressure gauge.
    1x 3-3.5 mm (or 1/8") ID Rubbor tubing to connect.
    1x Hose barb "T" for 3 to 4 mm tubing.

  Thermal Expansion:

    1x  ~1x1x2 cm compensator plate or other glass block with polished sides.
    1x  25 ohm, 10 W power resistor.
    1x  12 VDC 1 A power pack (PD bias, voice coil, PZT, thermal expansion).
    1x  Screw terminal to 5.5/2.1 female barrel connector adapter.
    1x  ~1" x 1-1/4" x 1/4" Delrin "chip" with 8-32 set-screw.

  Parts common to Gas Cell Compensator and Thermal Expansion:

    1x Thorlabs PH2 post holder.
    1x Thorlabs TR3 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and 1/4-20
       1/2" cap-head setscrew to attach to base. 

    1x Two part 5 minute Epoxy.

Parts in Homodyne DEMO VERSION Kit ONLY

 Quantity Description               
------------------------------------------------------------------------------
 Baseplate/Optical breadboard:

    1x Aluminum optical breadboard 6x18" (BASE Lab Tools SAB0618).

 Laser Assembly: 

    1x Laser consisting of 0.5-1 mW JDSU 1107 or 1108 random polarized laser
       head and power supply with DC input brick and universal wall adapter,
       which may be used Worldwide.  Minimum power 0.4 mW.
       A lab-style HeNe laser power supply may be an option.

    1x ~1x1" pieces of circular polarizer (linear polarizer at ±45
       degrees with QWP at 0/90 degrees AND linear polarizer.  Cut up as
       needed.

    2x Laser Mounts each consisting of:

      1x Small Ring Mount with two 8-32 x 1.5" and two 8-32 x 1" thumbscrews.

      1x Thorlabs TR3 post with 8-32 x 1/2" cap-head screw to secure the ring
         mounts and optional #8 plastic washer to provide compliance if the
         mounting hole in the rings is threaded (some are) so the orientation
         can be set correctly.  In the latter case, an 8-32 x 1/2" setscrew
         can substitute for the cap-head screw so as not to impinge on the
         available space within the rings for the laser head.

 Custom Single Channel Detector and Quadrature Decoder:

    1x QD1 PCB with  8-32 1/2" cap-head screw and 1/4" x 1/4" #8 spacer.

       1x 4 pole screw terminal block.
       1x 1K ohm resistor.
       1x 0.1 µF capacitor.
       2x Photodiode.
       2x 2 pin male to female socket strip.
       1x Variable attenuator plate to be used as NPBS.
       1x 1/2-1" CP sheet to be cut to size.
       2X Load resistors, 100K to 1M typical, or 1M trim-pot
 
    1x Thorlabs PH2 post holder.
    1x Thorlabs TR3 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and
       1/4-20 5/8" cap-head setscrew to attach to base. 

 Micro Measurement Display 0 (µMD0):

    1x µMD0 kit.
    1x Homodyne firmware for Nano (may be preloaded or download from
        µMD0 Manual).
    1x µMD Graphics User Interface (download from
        µMD0 Manual).

  Interferometer Assembly. (HP part numbers are used here; The actual parts
   may be the physically and functionally equivalent from Excel or Zygo.)

    1x HP/Agilent 10702A or 10706A PBS cube in frame with 4x 4-40 x 1-3/4"
       cap-head screws.

    1x HP/Agilent 10703A Cube Corner or mounted equivalent with 2 4-40 cap
       head screws.

    2x HP/Agilent 10722A Quarter WavePlate or custom equivalent each with two
       4-40 cap-head screws.

    1x Turning mirror (Approximately 1/2" x 1"). 

    1x Turning Mirror Bracket V2.0 with 4-40 x 5/16" cap-head screw and washer.

    1x PBS Mount Adapter Plate V2.1 with 2x Thorlabs TR3 post, 2x 3/4" spacer,
       and 2x 8-32 x 1" or 1-1/8" cap-head screw.

  Arm 1:

    1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap-head
        screw to secure it to post.

    1x 1" bare Cube Corner.
    1x 1" diameter planar mirror.
    1x Thorlabs PH2 post holder.
    1x Thorlabs TR2 post.

    1x BA1 or BA1S with 1/4-20 3/8" cap-head screw to attach to PH2 and
       1/4-20 1/2" cap-head sscrew to attach to base.

  Arm 2:

    1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap
       screw to secure it to post.

    1x 1" bare Cube Corner.
    1x 1" diameter planar mirror.
    1x Thorlabs PH2 post holder for rail or slide.
    1x Thorlabs TR1 post for rail or slide.

    1x Generic 40x40 mm linear stage, end or side micrometer adjuster,
       maximum of 20 mm thick.  A 4-40 or M3 screw into a tapped hole is
       used to secure the post holder the top of the stage.

  Thorlabs rail assembly:

    1x Thorlabs RC1 carrier with screw and washer to secure it to the
       bottom of the stage.

    1x Thorlabs RLA0600 6 inch rail (Basic or Deluxe version) or RLA1200
       12 inch rail (Deluxe+ version).

  Ball bearing rail assembly (option):

    1x MGN15C carriage block.

    1x MGN15 stage adapter plate with 4x 4-40-3/16" cap-head screws to
       secure generic stage to plate and 4x M3-8 flathead screws to
       secure plate to MGN15C carriage block.
 
    1x Locking bracket with 2x M2.5x16 mm screws to secure bracket to
       MGN15C carriage block and 4-40 1/2" Nylon thumbscrew.

    1x Rail:

       1x MR15-150 150 mm rail with 2x 6-32 3/8" cap-head screws to secure
          rail to breadboard and rubber bumpers to be used as end-stops.
          Breadboard requires addition of two 6-32 tapped holes. (Compact
          version.)

       1x MR15-200 200 mm rail with 2x 6-32 7/8" cap-head screws and nuts to
          secure rail to breadboard.  The screws with spacers also can act
          as the end-stops (Mid-Size version.)

       1x MR15-300 300 mm rail with 2x 6-32 7/8" cap-head screws and nuts to
          secure rail to breadboard.  The screws with spacers also can act
          as the end-stops (Extended version.)

  Voice Coil Actuator:

    1x 1-1/2" to 2" loudspeaker. 
    1x 1" D x 1/4" T aluminum or Acrylic Speaker mounting Disk.
    1x Speaker mirror (Approximately 1/2"x 1", may be same as turning mirror).
    1x Cube corner mounting ring.

  Bare Bones Function Generator:

    1x XR2206-based function generator kit (eBay, a search will fine these).
    1x 1K ohm trim-pot.
    1x 1K 1/4 W resistor.

-- end V2.25 --