quad-decoder1.jpg Michelson Interferometer Project Manual

Michelson Interferometer Project Manual

Assembly and Experiments

Version 1.12 (19-Apr-2021)

Copyright © 1994-2021
Sam Goldwasser
--- All Rights Reserved ---

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Reproduction of this document in whole or in part is permitted if both of the following conditions are satisfied:
  1. This notice is included in its entirety at the beginning.
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Table of Contents


Preface

Author and Copyright

Author: Samuel M. Goldwasser

For contact info, please see the Sci.Electronics.Repair FAQ Email Links Page.

Copyright © 1994-2020
All Rights Reserved

Reproduction of this document in whole or in part is permitted if both of the following conditions are satisfied:

1. This notice is included in its entirety at the beginning.
2. There is no charge except to cover the costs of copying.

DISCLAIMER

The information in this document is intended for use in hobbyist, experimental, research, and other applications where a bug in the hardware, firmware, or software, will not have a significant impact on the future of the Universe or anything else. We will not be responsible for any consequences of such bugs including but not limited to damage to the $100,000,000 wafer FAB that was purchased on eBay for $1.98 + shipping, financial loss from the waste of 28 spools of ABS due to the office 3-D printer fabricating a part with random dimensions due to loss of lock, or bruising to your pet's ego from any number of causes directly or indirectly related to the implementation and use of this system. ;-)

ACKNOWLEDGMENT

This experimental setup was originally developed for Engineering student projects at Swarthmore College, Pennsylvania.

SAFETY

The only safety issues with the experiments to be performed using this kit are with respect to the low power Helium-Neon (HeNe) laser. Sure, you could drop the breadboard on your foot, but that's outside our control. :( :-)

Even though this laser is not likely to cause any harm, one should always take laser safety seriously. Someday you may be working with one that is truly dangerous.



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    Abstract

    The Michelson interferometer is one of the most widely used configurations in a variety of applications including metrology (precision measurement). An experimental setup is presented which allows for several types of interferometers to be easily implemented and 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.



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    Introduction

    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 1A 633 nm Helium-Neon laser (HeNe for short) with an output power of between 0.5 and just over 1 mW. The basic detector is a biased photodiode connected to a dual channel USB oscilloscope. Variations and enhancements to these will be offered as options.

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

    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:

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

    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:

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

    As of Spring 2021, there are three versions of these setups which differ in very minor details. For the two in the field (V1.0 and V1.5), the differences will be identified where needed.

    Note: Off-page links (including any clickable graphics) open in a single new window or tab depending on your browser's settings.



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    Interferometers for Metrology Applications

    Classic Michelson Interferometer

    All of the measurements performed by these systems are based on variations of the Michelson interferometer, invented over 100 years ago by Albert Michelson. This is one of the simplest interferometer configurations but also one of the most widely used. 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), 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 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 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.

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

    Cube Corner Retroreflectors

    The simple Michelson interferometer setup can be used in a metrology system, but it has severe limitations which make it impractical for most applications. Alignment is extremely critical. Even the slightest deviation from perfect alignment will result in a reduction or loss of signal. Yet when perfectly aligned, one half of the optical power from the laser reflects directly back into the laser - which may destabilize it resulting in erratic fluctuations of its output in amplitude, optical phase, optical frequency, and polarization.

    Near the end of this manual is an experimental setup using this Basic Michelson Interferometer configuration. So you can see these various 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 second enhancement is to use a Polarizing Beam-Splitter Cube (PBSC) in place of the 45 degree partially reflecting mirror. While a plate beam-splitter could be used, the PBSC is much more common.

    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 basic 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. This is rarely, if ever, done though. But for the more complex 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 schemes to work at all.

    However, since the laser used in these experimental setups are not single frequency, the PLD between Arm 1 and Arm 2 should be minimized for the initial setup. The effects of larger PFDs may be explored once "first signal" is achieved. Alternatively, a single mode laser can be built. Much more on all this below.

    Common Interferometer Configurations for Displacement Measurements

    Here are several interferometers that may be used for measuring displacement (change in position). The first 4 are the most common.

    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 4. The very commonly used PMI will have a resolution of 40 nm and interpolation techniques can extend it down to under 1 nm.



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    Linear Interferometer

    Although HP called the combination of the PBSC and reference CC attached to it, the "Linear Interferometer", the term "LI" here will refer to the entire setup. And to enable the PLD to be set to zero, the CC normally attached to the PBSC will be mounted a few inches away.

    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

    The diagram below shows the general arrangement of the laser, beam splitter, cube corners, and detector used for all the interferometer configurations.

    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.

    The photo below shows the actual setup used for initial testing. There are minor variations in the actual kits depending on version and whether they are the "Basic" or "Deluxe" versions. These will be noted below.

    A variety of mounting schemes are used:

    Setting the Heights

    The following diagram shows the relationships of the various mounts for setting the heights during assembly. The specific heights used aren't critical but 3-1/4 inches places the laser in the center of the rings vertically:


    Original Version 1.0 (Left) and Version 1.5 using Block with Pedestal and Arm 2 on Rail (Right)

    Clicking on this diagram will open a high resolution version in the other window or tab. The heights of any retro-reflectors in the setup will be what really determines the beam height. For most configurations, the critical RR will be the one installed on the PBSC since its height is not adjustable. So everything will be aligned to that.

    Assembly and Alignment of the Linear Interferometer

    The following procedure may be used to install each of the parts and then get to the point of "first signal" using the oscilloscope. The procedure for the other interferometers will be virtually identical in most respects, but may be trickier depending on the type.

    It is assumed that nothing has been mounted, but depending on the previous use, some of these steps have already been completed.

    Parts attached with fasterners 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.

    There are minor differences in the assembly procedure depending on the version of the kit; specifically the mounting of the PBS and whether Arm 2 uses a rail. These will be address below. The use of a detector other than the Thorlabs DET110 or equivalent will be dealt with separately.

    1. Laser mount posts: Attach the two 2 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 to the top of the posts with 8-32 cap head screws.

    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 (1 and 1-1/4 inch), the longer ones should be at the front side of the rings.

      • Slip the laser head into the rings. Initially set it to approximately centered. 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 sticking out.

      • Power up the laser. It may take a few seconds to light. 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 a 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. 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.)

      • Orient the laser head so the alignment mark and polarization axis is at 45 degrees counterclockwise from vertical when viewed from the front.

      • Using the thumbscrews, adjust the position so that the beam is at a height of exactly 3-1/4 inches (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 rotate on its own.

    4. Wood block (plain or with pedestral: Secure the wood block using a 1 inch 1/4-20 cap-head screw. The location should have the laser beam passing over it 1/4 inch back of center with the wider part to the left. Carefully align it parallel to the X-Y axis before tighening the screw. It won't be accessible once the PBSC is installed.

    5. One inch Polarizing Beam Splitter Cube (PBSC) in stainless steel frame: This will be labeled 10702A or 10706A.

      • Remove any optics (10703A and 10722As) 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.

      • There are two variations on the PBSC mounting depending on the design of the wood block:

        1. Simple rectangular block: The PBSC may be attached to an HP 10711A mount or a 1/2" adapter plate. If not, locate the 10711A or adapter and secure the PBSC to it with four 4-40 ~1-5/8 Philips head screws and washers.

          Attach the PBSC to the wood block using two 3/4" wood screws. Center them in the slots with the PBSC aligned with the X-Y axes. The diagonal of the PBSC should be facing front-left to back-right with the arrow pointing left-to-right. If it cannot be mounted this way, rotate the PBSC on its mount.

        2. Block with pedestal: The PBSC should be attached with four #4 2 inch wood screws. The diagonal of the PBSC should be facing front-left to back-right with the arrow pointing left-to-right.

      • The laser beam should pass through the PBSC centered vertically and 1/4 inch toward the back. If not, fine tune alignment. :)

      • Turning mirror: Use tape or a tiny bit of adhesive to attach the turning mirror to the right angle bracket centered vertically with respect to the PBSC. Attach the bracket to the Wood Block with a single 3/4 inch #5 wood screw in the pilot hole already drilled. If the bracket has an elongated hole, center the screw for now.

    6. Arm 1: These steps assemble the components of Arm 1.

      • Attach a 2 inch post holder to the baseplate using a 1/4-20 set-screw.

      • KM100 mirror mount: Secure the KM100 to a 2 inch post with an 8-32 3/8 inch cap-head screw. Slip the post into the Arm 1 post holder and hand tighten the its thumbscrew. Adjust the two alignment knobs so that the mounting plate is parallel to the base in both directions.

      • 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. 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. :)

      • Adjust the height and orientation of the KM100 so that the return beam hits the PBSC at the same height as the incident beam, and offset approximately 1/4 inch to the left of center. The spacing between the centers of the two beams should then be approximately 1/2 inch.

      • Place a piece of paper where the detector would be for the beam from the turning mirror. There should be a bright return beam there from Arm 1.

    7. Arm 2: These steps assemble the components of Arm 2.

      The first part of the procedure differs slightly for the original version with the linear slide and adapter plates, and the upgraded version with the six inch Thorlabe rail:

      Orignal version with linear stage and adapter plates:

      • Attach a 1 inch post holder to the linear slide adapter top plate using a short 1/4-20 set-screw. The set-screw must not protrude through the plate.

      • Attach the top plate with post holder to the linear slide via the slots with two M3x8mm cap head screws.

      • Attach the linear slide to the bottom 0adapter plate using four 4-40 1/4 inch screws. It will be necessary to push or adjust the moving part of the slide to access the corner holes.

      • Secure the bottom adapter plate of the Arm 2 assembly to the baseplate, lining it up with a set of holes such that the PLD between the CCs in the two arms can be adjusted to be zero using the micrometer. Two 1/2 inch 1/4-20 cap-screws are required at diagonal corners, four may be used if desired.

      • Adjust the micrometer so the distance to the center of the PBS cube is the same ±0.1 inch (2.5 mm) for Arms 1 and 2 for a PLD near 0. (2.5 mm).

      Version with rail:

      • Attach a 1 inch post holder to the Parker linear slide with a 4-40 3/8" screw and large washer through the hole in the bottom of the post holder. CAUTION: Make sure the screw does NOT contact the fixed part of the slide. 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.

      • Attach the Parker linear slide to the Thorlabs RC1 rail carrier with a 4-40 3/8" or 1/2" cap head screw slipped through the base of the slide secured with a large #4 washer and nut.

      • Add stops at both ends using a 8-32 3/8" cap head screw and #10 washer positioned as high as possible.

      • Secure the rail to the baseplate / breadboard with 1/4x20 3/8" cap head screws in the end holes.

      • Install the RC1 carrier with Parker stage and post holder onto the rail.

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

      • Position the RC1 carrier so the distance to the center of the PBS cube is the same ±0.1 inch (~±2.5 mm) for Arms 1 and 2 for a PLD near 0.

      Common to both:

      • KM100 mirror mount: Secure the KM100 to a 3/4 inch post with an 8-32 3/8 inch cap-head screw. Slip the post into the Arm 2 post holder and hand tighten its thumbscrew. Adjust the two alignment knobs so that the mounting plate is parallel to the base in both directions.

      • 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. 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.

      • Adjust the height and orientation of the KM100 so that the return beam hits the PBSC at the same height as the incident beam, and offset approximately 1/4 inch to the left of center. The spacing between the centers of the two beams should then be approximately 1/2 inch.

        With the rail setup, this may occur a slight distance below the lowest possible height of the mirror mount. In that case, raise the laser and Arm 1 mount by approximatley double that distance. It should be less than 0.1" so will be well within the height adjustment range of the laser and the clear aperture of the PBSC. If you'd prefer to raise the laser mounting rings in the interest of purity :), add a few washers between the rings and posts.

      • Using your piece of paper, there should now be two spots corresponding to the returns from Arms 1 and 2.

      • Adjust the height and orientation of the KM100s to superimpose the return beams from Arm 1 and Arm 2. Fine tuning can be done with the KM100 knobs.

      • As a quick test, place a linear polarizer (LP or LP/CP with the non-adhesive facing the beam) with the polarization axis at 45 degrees in the combined return beam. If the alignment is close, very slight rotation of the linear slide micrometer should result in the intensity varying dramatically. Further fine tuning of the alignment may be required to maximize the variation. Of course, much more more can be done using these simple observations including effects of alignment, expansion using a lens, display using a Web cam, etc.

    8. Basic Detector: These steps assemble the components of the fringe detector using the Thorlabs DET110 or equivalent.

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

      • Install the DET110 to a 2 inch post with an 8-32 3/8 inch cap-head screw and slip it into the post holder.

      • Clamp the assembly down with a 1/4-20 1/2" cap head screw.

    9. Set up the oscilloscope: (If using a USB scope, this assumes that the required software and device drivers have already been installed on your PC or MAC.)

      • Attach a BNC cable to the DET110 and the other end with BNC "T" and screw terminal adapter to Channel 1 of the scope.

      • install a 10K ohm load resistor across the terminals. 10K is probably an acceptable value but depending on laser power and alignment, a higher or lower resistance may be desirable. See the resistor color chart below if you are not familiar with reading the bands on the resistors.

      • Tape a piece of LP or LP/CP to the front of the DET110 with its polarizaiton axis at 45 degrees.

    10. Observing "First Signal":

      • Flip the toggle switch on the DET110 to On (up).

      • Adjust the position of the DET110 so that the combined return beams are centered on the area of the sensor.

      • If alignment is close, the amplitude of the signal on the scope should vary dramatically as the micrometer is rotated by the smallest amount. The wavelengths of light are TINY! Each full cycle is 1/2 wavelength or around 316.5 nm. The micrometer moves the stage by 0.5 mm per full rotation, or around 1,389 nm/degree.

      • The amplitude can be maximized using the knobs on the KM100s. The signal amplitude may vary slightly (up to ~20 percent) in a periodic cycle over a time scale of seconds to minutes in addition to it probably increasing slightly as the laser warms up. The time scale will depend on how long the HeNe has been on. Why? There can be several causes.



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    Observing the Effects of PLD on Fringe Contrast

    The tests above were done with the PLD near 0. What happens otherwise? If the laser were Single Longidudinal Mode (SLM), the PLD would not matter up to a very large number in the 100s of meters or more. However, the laser used in the 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 laser must be linearly polarized with its polarization axis (indicated by the alignment line near the front) oriented at 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.

    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 laser tube is around 137.6 mm or 5.417 inches. One half of this is 68.8 mm or 2.7085 inches.

    1. 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.)

    2. Try intermediate locations for the Arm 2 mirror.

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

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

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

    2. 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?

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



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    High Stability Plane Mirror Interferometer (HSPMI)

    The basic Plane Mirror Interferometer (PMI) as its name implies uses a plane mirror instead of a cube corner for the remote reflector. It has a double pass architecture which halves the distance for a full fringe cycle at the detector. However, it is not desirable to use a PMI here because it is double-pass only for the remote reflector (Arm 2) but single pass for the reference (Arm 1). Thus while the PLD can be set to zero, the spacings or lengths of the two arms are not the same, which at the very least is confusing. (More on this in the section on the PMI.)

    The HSPMI on the other hand is perfectly symmetric: The beam paths for both Arm 1 and Arm 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.

    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 specified for experiments using a multi-longitudinal mode laser.

    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

    Assuming the LI was already built, not many changes/additions are required:

    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 runs up and down.

    2. Install HP QWPs (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 Thorlabs LM100s 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, but more critical due to the planar mirrors and double pass architecture.



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    Controlling the PLD

    These are various methods of fine adjusting the PLD without moving the linear stage as well as using the interferometer as a precision sensor.

    Voice Coil Linear Actuator

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

    To use it:

    1. The 1 inch diameter 1/4 inch thick aluminum "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 like a 1 inch 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 speaker frame.

    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.

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

    Calculate the sensitivity of movement in nm with respect to speaker current.

    DO NOT connect the speaker 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.

    The speaker 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 terrible due to the large mass of the mirror.

    Piezo Transducer

    A PieZo Transducer (PZT) can be used to move a mrror where only a small displacement is required. (The acronym PZT is actually based on the active material, an inorganic compound of Lead (Pb), Zirconium (Zr), Titanium (Ti), and oxygen). Look it up. But our abbrebiation is easier to remember. ;-)

    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.

    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.

    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.

    A 9 V battery or DC power supply can be used along with the 10K ohm potentiometer to vary its voltage, or it can driven from the line or speaker output of an audio amplifier.

           + 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 loudspeaker.)

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

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

    Gas Cell Compensator

    This may be the niftiest experiment and demonstrates the sensitivity of the interferometer to changes in the index of refraction of air.

    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. 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 inch length of 1" inch 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. :) There's no need for them to be perpendicular to the tube or parallel to each-other. Only that they can seal to the windows.

    1. If there is more than one hose barb with threads, one of them may have the threads shortened so as not 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.

    2. Apply a small amount of the remaining Epoxy to the threads of an 8-32 3/8" or 1/2" set-screw. Intstall it in the 8-32 tapped hole so that no more 1/4" 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.

    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 before proceeding.

    4. Prepare a small amount of the two-part Epoxy and apply the smallest bead all around the outside of one end of the 2" tube.

    5. Carefully place the tube on top of the cleaned window. DO NOT move it laterally as that will spread adhesive insde the tube. Wait for the Epoxy to cure (15 minutes)

      As noted, 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. 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.

    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.

    The photo on the left shows the prototype using a 3/4" OD PVC tube installed in Arm 1 of the interferometer. The ends are covered with pieces of heat shrink to hide the ugly cut microscope slide windows. Yours will be (1) shorter, (2) made of 1" OD clear Acrylic (Plexiglas) instead of PVC, (3) use circular windows, and (4) hopefully nicer looking when completed. ;-)

    The photo on the right shows the complete setup (with the extended PLD rail option) and a scope trace with showing the GCC loosing presure some of its pressure over 20 seconds or so.

     

    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 should be set as close to equal as possible for these experiments taking into consideration the increase in optical path length due to the 1 mm glass microscope slide windows. How much does this affect the total path length?

    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?

    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 from the Thorlabs DET110 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

    Or interferometer thermometer. ;-)

    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.

    Thermal Assembly Assembly:

    1. Thread the wood chip (~1x2x3/16" 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. There are either two 10 ohm power resistors or one 25 ohm power resistor. Use a drop of Epoxy to secure one of the resistors to the wood chip using its flat unlabeled surface. There may be some Epoxy residue from a previous life but this shouldn't affect anything. 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. If there is a second resistor, attach its flat unlabeled side to the top of the compensator plate with another drop of Epoxy. Wait at least 15 minutes for the Epoxy to cure.

    5. This stack can then be installed in Arm 1 of the interferometer using a Thorlabs 1" or 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 - 7.2 or 5.76 watts for the 2x10 ohm or 25 ohm resistors, respectively.

     

    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, ng, 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 fringe signal 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 ng. 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

    This one may be a bit more challenging but no additional special parts are required. (And it's related to the last question, above.)

    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 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 (around 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)

    In addition to temperature and pressure, other gases mixed in with air. or in pure form affect the index of refraction. A variety of common substances have a significantly higher index of refraction than air and thus could result in a detectable effect even at low percentages of partial pressure. These include carbon dioxide, acetone, alcohol, chloroform, and ether. Thus, if one of these is introduced into an arm of the interferometer, there should be a detectable change in PLD. It's probably not a good idea to be messing with chloroform or ether, and even acetone has its risks (both to bodily internal organs and to plastics including acrylic), but certainly CO2 (from carbonated beverages, a CO2 gas canister, or even exhaled breath) and isopropyl (rubbing or medicinal) alcohol or ethyl alcohol (wine, whiskey) can be suitable for tests.

    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).

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

    Inexpensive glass cuvettes with polished parallel sides would make suitable containers to introduce liquids, or with an improvised cover, gases. 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

    If you have successfully constructed any of the interferometers, it will have been obvious that avoiding generating a varying fringe signal due to vibrations is a challenge even if the entire setup is on a stone counter-top. :) But what about actually enhancing this effect? The mirror on the loudspeaker does that to some extent. However, by mounting one of the reflectors (cube corner or mirror) remotely, it will be possible to easily detect someone walking across the room or a truck going down the street a block away. Or an earthquake.

    For these experiments where one of the arms is of considerable length, the beam expander will need to be mounted on the laser. Without it, the beam would expand too much to be useful. Also, rather than making the PLD zero, it will need to be a multiple of the laser tube cavity length, around 137.6 mm or 5.417 inches for the JDSU 1107/P or 1108/P. 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 plus or minus whatever is needed for the PLD to be 0 mod(137.6 mm). 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. 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.

    A displacement measuring system would be ideal. Using µMD0, it would be possible to record data and (with some simple formatting in Excel) then display it like a seismograph. But just watching the fringe 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.

    For the unstabilized HeNe laser, the PLD mod(tube cavity length) should be adjusted to be close to 0. This may best be done by maximizing the fringe amplitude. Unless a major earthquake strikes, any motion should be compared to the tube cavity length - but not relative to wavelengths of 633 nm light!

    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.



  • Back to Michelson Project Manual Table of Contents.

    Other Interferometer Configurations

    There are some other variations on the Michelson interferometer that may be put together using parts in this kit, starting with the original form of the Michelson Interferometer.

    Basic Michelson Interferometer (BMI)

    This is identical to the original except that it uses the polarized laser and PBS cube as the beam-splitter. But note that the linearly polarizer located in front of the detector has been removed. The PBS in effect acts as a pair of beam-splitters, for the vertically and horizonatlly polarized portion of the input beam. Without the cube corners and/or QWPs to separate the outgoing and return beams, everything will be jumpled 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.

    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 basic Michelson interferometer but the addition of the QWPs avoids (most) back-reflections to the laser.

    Plane Mirror Interferometer (PMI)

    The PMI is probably the most common of the interferometers that use a planar mirror.

    Note how close the mirror on the stage is to the PBSC - and that may not even be close enough for the paths to be equal!

    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.

    Modified Linear Interferometer (MLI)

    The MLI adds a pair of QWPs to direct the beam to the detector out the side of the PBSC and is achitecturally similar to the SBI but with offset beam paths that have two advantages: (1) retro-reflections back to the laser are reduced further and (2) the beams don't hit the apex or edges of the cube corner trihedral prisms.

    Double Pass Linear Interferometer (DPLI)

    The remote reflector is a cube corner which is better for long distances yet it has double the resolution of the normal LI, same as the PMI.

    High Resolution Plane Mirror Interferometer (HRPMI)

    This doubles the resolution over the PMI or HSPMI. The HRPMI is also high stability because the two beam paths have the same length through the optics, and a PLD of 0 if the distance in Arm 1 and Arm 2 are the matched. This will be much more complext to align and may require additional parts and determination. ;-)

    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, so it traverses all of the optics a second time. So instead of 2 passes, it becomes 4 passes. 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, that will be 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 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. :-)



  • Back to Michelson Project Manual Table of Contents.

    Extensions (Advanced)

    Quadrature Detector

    The basic detector using a single photodiode like the DET110 can generate a signal corresponding to light and dark fringes, but cannot provide direction information, essential for using an interferometer in metrology applications. The Quad-Sin-Cos decoder provides a pair of outputs that are 90 degrees offset from each-other in position, similar to the outputs of a rotary or linear encoder:

    This show 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.

    (These graphics seem 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.

    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. However, more commonly, the 90 degree phase shift is done optically using a single combined beam as shown below. If thresholded and converted to digital form, the result would be a Quad-A-B format.

    This shows variations on one of several common implementations for a Quad-Sin-Cos decoder that provides Sine and Cosine outputs for use in a displacement measuring system. This is among the simplest. In most instances, the photodiodes would be reverse biased to provide a linear response. It may be possible to get away without that for initial testing but it will probably 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.

    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 on the right 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 balanced without electronic adjustments.

    Some resourcefullness 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 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! This is probably overkill though.

        >   
    Quadrature Detector using Variable Attenuator Plate and Circular Polarizer Sheets. Optical Layout, Parts), Prototype, and Partially Constructed PCB Assembly

    Before constructing the prototype or PCB versions, it was dedirable to to conclusively prove that the simple Type 3 scheme with CPs for the polarization optics actually worked as advertised, so a prototype version was installed on the Michelson Interferometer test-bed:

    In the interest of expediency, it cheats and used an NPBS rather than a plate beam-splitter or variable attenuator, 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. ;-)

    The prototype on a prototyping board was then constructed and tested 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.

    A couple resistors will be required which are included so here is info on reading the color codes:


    Resistor Color Code Chart (from the Digikey Web site)

    Initially, connect the PDs directly to the scope input with a high value load resistor across their leads. As a test, place one of the PDs in the laser beam to determine if there is enough response on the scope. Since there is a 50-70 percent loss in the CP and more than 50 percent in the NPBS, this may prove inadequate and back biasing will be needed. Even then, with the laser power available, the response may still be quite low. But it's just an experiment!

           R-Protect          PD1
       +-----/\/\-------------|<|---+---o Scope Channel 1 (direct) or X1 probe
       |    1K ohms                 | 
       |               Common       /
       |           <-- to both      \ R-Load1
       |               Channels     / 30K typical
       |   9 V Battery              \
       |     +| | -                 |
       +------||||------------------+---o Gnd
              | |
    
    (Except for part values, this circuit is similar to what's inside the DET110 and can be constructed on a 3-D-printed mount.)

    To confirm PD polarity, wire up this circuit and test it with no light: There should be minimal voltage across the load resistor. If it goes to close to the battery voltage, the PD is backwards (or broken!).

    The Sin and Cos channels can share the Battery and R-Protect resistor with only the photodiode and load resistors/scope inputs being separate.

    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. :) However, as noted above, this would be a great excuse to put that 3-D printer to a practical use. The photo above shows one possibility (and a simple PCB will be available eventually), but some soldering is required for that. Its behavior is virtually identical to that of the PBSC and Thorlabs DET110s, at less than 1/100th the cost. But a cover would be worthwhile to block ambient light from hitting the PDs. The A Channel PD can be used alone as the sensor for other experiments (with or without the AP installed). More details on the Quad decoders and associated electronics may be found at Construction Guidelines for Basic Quadrature-Sin-Cos Decoder and Quad-A-B Interface Kits>.

    1. Set up the HeNe laser so that there is a linearly polarized beam. Orient the polarization to be vertical for the initial tests. This (can and probably should) be done using 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 possible, arrange it to use the screw/spring combination to adjust it's position, and thus attenuation (or transmission and reflection).

    3. Adjust the position of the AP (using the screw/spring if mounted that way) so that the transmitted and reflected beam intensities are approximately equal.

    4. Mount the PDs to intercept the transmitted and reflecteed beams. They should be reverse biased with 5 to 15 VDC (+ to cathode). 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. 100K ohm trim-pots are included in the kits for this purpose.

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

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

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

    3. 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.

    4. Channel A: Attach one of the piece 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.

    5. 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. 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.

    6. 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.

    7. Observe the Channel A and B signals on the oscillscope. They should be in quadrature (or very close). The phase shift between them should flip from +90 to -90 degrees depending on the direction of motion as in the photos, above.

      Note: Even if the peak-peak amplitudes are made equal, it may not be possible to avoid an offset on one channel. This may be due to the effects of the Epoxy coating on polarization. In that case, the scope vertical position can be set to superimpose them.

    More on all this below in the section on displacement measurement.

    Stabilized Single Frequency (SF) Laser

    By replacing the common HeNe laser head with a stabilized single frequency laser, PLDs of up to 10s to 100s of meters would be supported with essentially no other changes. They would become very boring. :) But that's exactly what is needed for most metrology applications. (Strictly speaking, no laser is truly single frequency but rather Single Longitudinal Mode or SLM, which is pretty darn close to SF for all practical purposes. But whatever it's called, HeNes are close to ideal in this respect.)

    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.

    Stabilized Two Frequency (TF) Laser

    Another approach to displacement measurement uses heterodyne interferometers, which are based on lasers producing a beam with two orthogonally components at slightly different optical frequencies (typically between 1 MHz and 20 MHz). Rather than measuring the amplitudes of sin and cos signals from a Quad detector, these systems measure the phase difference between a "REF" signal direct from the laser and a "MEAS" signal that is the Dopplar-shifted return from the "Tool" - the part that moves. The vast majority of systems in use in the Universe today are heterodyne. This has been confirmed by at least one totally non-scientific study counting the number of surplus SF and TF lasers that show up on eBay. ;-) The heterodyne approach has several advantages including signal processing being in the AC domain, superior immunity to noise, and not as sensitive to misalignment or contamination of optics

    Most of the interferometer optics for homodyne and heterodyne systems are identical and in fact, the PBSC, housed CCs, and QWPs in this kit are actually intended for heterodyne systems.

    Where a random polarized laser tubes meets certain requirements (which turn out to be present in many of the HeNe laser tubes that used to be used in 100s of thousands of supermarket checkout barcode scanners), 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. 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.

    However, the detector also needs to change and it becomes more complex. Rather than a pair of photodiodes as in the Quad detector, two optical receivers must be used. These convert the difference frequency to an electrical signal. There is one for the difference frequency direct from the laser called "REF" and another for the return beam through the interferometer call "MEAS". The difference in their phase is what the measurement electronics utilizes to complete displacement. The optical receiver for REF can be relatively simple since it monitors the output of the laser directly which doesn't vary much. But the one ofr MEAS is usually more elaborate with automatic gain control built-in so that it can accomodate changes in signal amplitude and be able to deal with the output of the laser being split n-ways for multiple axes.

    Displacement Measurement Display

    Finally, 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. In practice, they are 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 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.

    The trim-pots on the left are the load resistors for the quadrature detector and 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 can be 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:

            

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

    Simple PCBs for the quad detector and interface will be available, but should not be required for a student project. ;-)

    And the complete Michelson interferometer setup interfaced to µMD0 below:

    While 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. 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.



  • Back to Michelson Project Manual Table of Contents.

    Future Options

    Easily Adjustable Path Length Difference

    This modifies Arm 2 so that the optic can be easily moved over a ~5 inch distance to cover the range of PLDs of interest for the HeNe laser being used. It's more a matter of convenience than a requirement since the other setups can do this, but it requires physically remounting the linear stage assembly and/or adjusting the micrometer. However, adding this option is not just a matter of adding the rail as the linear stage has to be swapped as well to minimize impact on the height, and thus other components. Here is the version for the LI:

    The others would be similar.

    The addition of the Thorlabs rail and carrier and substitution of the Parker linear stage is shown in the lower right. The only other change (which is independent of this) is to add a pedestal to the Wood Block which eliminate the HP mount for the PBS cube since it served no purpose and added cost.

    Future versions of this kit will probably include a short rail as the default, though the exact details may differ.

    Transparent Laser Enclosure with Heater

    Modified laser head cylinders may be available made of transparent aluminum (a.k.a., acrylic or Plexiglas). While there isn't a huge amount of action that would be visible, it would add a cheery glow to the setup. And at the same time (and more importantly), a thin-film heater can be added to the laser tube to control cavity length. The photo on the left is a closeup of the laser while the one on the right is the rail setup with Thermal Expandsion experiment using the glowing laser.

     

    (Click on images for high resolution versions.)

    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

    Polarization Control Optics

    Three types of optics that affect the polarization are used in various parts of the interferometer:

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

    However, if placed in front of a linearly polarized laser, or used to modify the polarization of a random polarized laser, the circular polarized output make a subtle difference to how the interferometer behaves. That will be something to analyze.

    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 I've found so far were called something like: "New Backlit Screen Modify Part Polarizing film For GBA GBC GBA SP N_ES". Those listed for iPhones were of the simple LP type, although interestingly, the protective film that normally gets discarded is birefringent and may even be a QwP. Which of course makes little sense. :( :)

    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.

    Linear Polarized versus Random Polarized HeNe Laser

    There are two basic types of HeNe lasers with respect to polarization of the output beam: Random polarized and linearly polarized. With just a pair of mirrors and HeNe gas, the result will usually random polarized. To construct a linearly polarized HeNe laser, a Brewster-angle plate is added inside the laser cavity. (Search for: "Brewster Angle".) This introduces an orientation dependent loss with respect to polarization and virtually 100 percent of the photons will then be linearly polarized with the orientation with minimal loss. The Brewster plate on the types of HeNe laser tubes used here are buried within one of the mirror mount stems and are thus not readily visible.

    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.

    And note that this only applies to red HeNes, not even other color HeNes, let alone most other lasers. 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.

    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 and 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.)

    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.

    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 a significant 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.)

    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.

    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. A random polarized flipper can be provided in place of or in addition to the linear polarized or random polarized well behaved tube if interested. :-)



  • Back to Michelson Project Manual Table of Contents.

    Michelson Interferometer Kit Parts List

    These are the parts for each setup except as noted.

    Replicating it should be straightforward. But if doing so, consider doing the "Rail Option" if possible depending on availability of the required parts at reasonable cost (usually on eBay). It is simpler, requires no machining for the linear stage, only at most single tapped hole, and is more flexible. The original setup was designed based on the availability of certain parts.

    The optical breadboard is custom but its size was selected to be convenient for the projects including being able to easily ship them Worldwide. Anything larger would be acceptable. If machining it, fewer than half the holes specified are enough based on all reasonable mounting locations, but that's only worth it if you're paying by the hole. ;-)

    Most other opto-mechanical parts are from Thorlabs (direct or via eBay).

    The JDSU 1107/8/P or Melles Griot/Pacific Lasertec 05-LHR/P-211 laser heads are ideal for these experiments, but other red HeNe lasers of similar length (so there are at most two longitudinal modes) would work equally well. Optics companies like Edmunds, Newport, and Thorlabs would have suitable lasers, but eBay is often a good source at a fraction of the cost. The laser could also be a bare tube safely enclosed.

     Quantity Description               
    ------------------------------------------------------------------------------
     Baseplate/Optical breadboard:
    
        1     Aluminum plate 18x8x1/2" tapped 1/4-20 144 places on 1" centers.
               (A 24x8" version to extend the maximum PLD may be desirable.   And
               future versions with fewer holes (3x3 rows) to simplify machining
               may be acceptable.
    
     Laser Assembly: 
    
        1     Laser consisting of 0.5-1 mW JDSU 1107/P or 1108/P laser head
               and power supply.  Some kits have a JDSU 1205 lab-style
               power supply but this only runs on 115 VAC.  Others will have,
               a Laser Power 103-23 brick and universal wall adapter is
               provided which may be used Worldwide.
    
        1     ~1x1" piece of circular polarizer.  Consists of linear polarizer
               (+/-45 degrees) with QWP (0/90 degrees).  Cut up as needed.
               This is only required for random polarized lasers.
    
        1     Beam Expander Adapter Plate.  The front bezel of the laser has
               had 3 tapped holes added for this.
    
        1     HP/Agilent beam expander, modified (sam), must be glued into Beam
               Expander Adapter Plate.
    
        3     M2.5 x 5 mm cap-head screws (sam)
    
        2     Small Ring Mount with four 8-32 x 1.5" thumbscrews     
        1     8-32 x 1/2" Philips screw to attach ring mounts to posts
        2     Thorlabs TR2 post with 1/2" 1/4-20 setscrew to attach to baseplate
      
     Interferometer Assembly:
    
        1     HP/Agilent 10702A or 10706A PBS.  This is either on an adjustable
               base or only a frame.
        1     HP/Agilent 10703A Cube Corner 
        2     HP/Agilent 10722A Quarter WavePlate
        6     4-40 cap head screws to attach 10703s and 10722 (should be already
               installed in PBS cube frame).
        1     PBS Mounting Block with 3/4" 1/4-20 cap screw to attach to baseplate
               or PBS Mounting Block with pedestal and 4 #4 x 2" wood screws to
               attach PBS assembly directly to block.
        1     Turning mirror (Approximately 1/2" x 1". 
        1     Turning mirror bracket
        1     #5x3/4" round head wood screw for turning mirror bracket (sam)
        2     #5x3/4" round head wood screws (sam, only for PBS mount if used) 
      
     Arm 1:
    
        1     Thorlabs LM100 or Newport U100 mirror mount with 3/8" 8-32 cap
               screw to secure it to post.
        1     1 inch bare Cube Corner 
        1     1 inch diameter planar mirror. (Installed or to be installed in
               mirror mount.)
        1     Thorlabs TR1 or TR1.5 post 
        1     Thorlabs PH2 post holder with 1/2" 1/4-20 setscrew 
    
     Arm 2:
    
        1     Thorlabs LM100 or Newport U100 mirror mount with 3/8" 8-32 cap
               screw to secure it to post. 
        1     1 inch Cube Corner 
        1     1 inch diameter planar mirror. (Installed or to be installed in
               mirror mount.)
    
        1     Thorlabs PH1 post holder 
    
     Linear Stage Assembly (original version only):
    
        1     Linear Stage Top Adapter Plate 
        2     M3 x 8 mm cap-head screws 
        1     40 x 40 mm linear stage
        1     Linear Stage Bottom Adapter Plate with 1/2" 1/4-20 setscrew
        4     4-40 x 1/4" Philips head screws 
        4     1/4-20 1/2" cap screws 
      
     Rail Option for studying the effects of limited coherence length (replaces
      linear stage assembly, above, and will be standard going forward).
    
        1     Parker 3902 or 3902M micrometer linear stage (modified)
        1     4-40 Philips head screw to secure post holder to stage 
        1     4-40 3/8" screw, washer, and nut to secure RC1 to stage 
        1     Thorlabs RC1 dovetail rail carrier 
        1     Thorlabs RLA0600 dovetail 6" optical rail 
        2     #10 washer and 8-32 3/8" cap head screw for end-stops.
    
     Basic Detector:
    
        1     Thorlabs DET110 biased photodiode with SM1 threaded ring.
               (Alternate constructed with bare photodiode on protyping board,
               PCB board, 3-D-printed mount.)
        1     Thorlabs PH2 post holder with 1/2" 1/4-20 setscrew 
        1     Thorlabs TR1 or TR1.5 post with 1/2" 8-32 setscrew for DET110
               and 8-32 3/8" cap head screw for prototyping or PCB.
        1     Thorlabs BA1S (preferred) or BA1 holddown 
        1     1/4-20 1/2" cap screw for holddown
        1     BNC cable with banana jack/screw terminals (M-M cable,
               BNC FMF "T", BNC M-to-terminals) 
        1     Set of assorted resistors for termination 1K-1M 
      
     Quadrature Decoder:
    
        1     Variable attenuator plate to be used as NPBS 
        2     Piece of circular polarizer to cut into suitable size pieces
        3     Cover slips to which pieces of CP can be attached
        2     Silicon photodiodes 
        1     9V battery with leads 
        1     1K ohm resistor 
        -     Load resistors including 100K and 1M (from the assortement, above)
        1     Jumper wires, etc. 
        1     Mountng scheme for all this (Student's creativity possibly involving a 3-D printer) 
    
     Micro Measurement Display 0 (µMD0):
    
        1     Atmega 328 Nano 3.0 microcomputer board with pins soldered
        1     Homodyne firmware for Nano (may be preloaded or download from µMD0 Manual)
        1     µMD Graphics User Interface (download from µMD0 Manual)
        1     Solderless breadboard 3-1/4" x 2-1/4", 25 columns
        1     LM393P dual voltage comparator
        1     3 mm Red LED and 1K ohm resistor
        1     3 mm green LED and 47K ohm resistor
        2     100K ohm resistors or 100K ohm trim-pot
        2     10K ohm trim-pots
        2     100K ohm resistor
        2     470K ohm resistors
      
     Voice Coil Actuator:
    
        1     1-1/2" to 2" loudspeaker 
        1     Speaker mounting Disk
        1     Speaker mirror (Approximately 1/2"x 1", same as turning mirror) 
    
     Piezo Transducer:
    
        1     27 mm PZT beeper element
        1     PZT mirror (Approximately 1/2"x 1", same as turning mirror)
    
     Gas Cell Compensator (Air Pressure and Temperature):
        
        1     1" OD, 7/8" ID, 2" PVC or Acrylic tube
        2     1" round or square window (cut microscope slide)
        1     10-32 to hose barb adapter (sam)
        1     8-32 3/8" or 1/2" set-screw
        1     Blood pressure bulb with valve
        1     Blood pressure gauge
        1     Rubbor tubing to connect
        1     Hose barb "T"
        1     Thorlabs PH2 post holder
        1     Thorlabs TR1 or TR1.5 post
        1     Thorlabs BA1 (preferred) or BA1S holddown
        2     1/4-20 1/2" cap-screw for holddown
    
     Thermal Expansion (Glass Block Temperature):
    
        1     ~1x1x2 cm compensator plate
        1     Power resistor(s) - 2x10 ohm or 1x25 ohm
        1     Screw terminal to 5.5/2.5 female barrel connector adapter
        1     Wood chip with 8-32 Nylon set-screw
    
     Test Equipment / Tools / Supplies:
    
        1     Scope (USB or stand-alone) with two probes
        2     3 foot BNC cable with Banana jack adapter and BNC "T". 
        1     DMM
        1     10K ohm potentiometer wired with 10K ohm current limiting resistor
        1     12 VDC 1 A power pack
        1     Screw terminal to 5.5/2.5 female barrel connector adapter
        1     Screwdriver set 
        1     Hex wrench set 
        1     Two part Epoxy
        -     Hookup wire and jumper wires
       10     Wire nuts
    

    Here is a separate parts list covering only the fasteners (screws, washers, etc.) for the version with the rail. This should be redundant.

     Laser Assembly	
    
        8     8-32 1-1/4" to 1-1/2" Nylon thumbscrews for rings
        2     8-32 1/2" caphead screws, join posts to rings
        2     1/4-20 1/2", set screw; join posts to breadboard
    	
     PBS Assembly	
    
        1     #5, 1/2" or 3/4" round head wood screws; join mirror bracket to wood block
        4     #4, 2" round head wood screws; join PBS to wood block (version without HP mount)
        1     1/4-20  1" caphead screw; join wood block to breadboard
        6     4-40 3/8" caphead screw, optics to PBS cube (should already be attached to PBS cube)
    	
     Mirror Mounts	
    
        2     8-32 3/8" caphead screw; join mirror mount to post (Thorlabs LM100 or Newport U100?)
        1     1/4-20 1/2" setscrew; join Arm 1 post holder to breadboard
    	
     Detector and Sensor	
    
        2     1/4-20 3/8", caphead screw; join BA to PH
        2     1/4-20 1/2", caphead screw; join BA to breadboard
    	
        1     8-32 3/8" caphead screw; join detector board to post (if using detector board)
        1     8-32 1/2" setscrew; join DET110 to post (if using DET110)
    	
        1    	8-32 1/2" setscrew; join pressure sensor acrylic cylinder to post
        1     8-32 nut; spacer/strengthener for setscrew above
    	
        1     8-32 1/2" Nylon setscrew, join temperature sensor wood "chip" to post
    	
     Parker Stage and Rail Assembly	
    	
        1   	4-40 1/2" caphead screw, Parker stage to RC1 carrier
        1     4-40 nut; Parker stage to RC1 carrier
        1     #4 washer (large preferred if available); 1" post holder to Parker stage
    	
        1     4-40 3/8" Philips head; 1" post holder to Parker stage (length critical to not extend too far into Parker stage)
    	
        2     1/4-20 1/2" setscrew; attach rail to breadboard
        2     8-32, 3/8" or 1/4"; caphead screw; stops on rail
        2	    Large #10 washers for stops on rail
    


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