An Inexpensive Laser Interferometer-Based Precision Measurement System

Version 1.51 (21-Sep-2018)

Copyright © 1994-2018
Sam Goldwasser
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Reproduction of this document in whole or in part is permitted if both of the following conditions are satisfied:
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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 © 1994-2018
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 wafer FAB you picked up 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. ;-)

ACKOWLEDGEMENT

Thanks to Jan Beck for getting me interested in microcomputer development. If anyone had told me six months ago that I'd be writing code in C, MIPS assembly language, and Visual Basic - and enjoying it (sort of) - I would have suggested they were certifiably nuts. ;-) Links to his Web information may be found under References.


Abstract

A complete system is described which provides all the functions required for precision measurement of displacement or other movement based on two frequency (heterodyne) laser interferometry. The stabilized HeNe laser, interferometer optics, and signal processing are built up from readily available low cost components with readout of displacement or velocity, angle, and straightness, including frequency analysis via a Windows-based PC. Performance should be similar to that of commercial systems costing 100 times as much. Complete documentation is available including circuit schematics and software/firmare source code. Any portion or its entirety can be easily replicated for educational purposes or to be used in an actual application.


Introduction

Precision measurement of displacement (change in position) using laser interferometry is a well established enabling technology for wafer positioning in lithography steppers, programming of profiles in diamond turning optical lathes, and numerous other metrology applications. These systems use the wavelength of laser light as the "yard stick" to provide resolution down to the nm-scale. Most such systems are based on heterodyne interferometry using a a special low power two frequency Helium-Neon (HeNe) laser, various interferometer optics configurations, and electronic processing for measurement display or closed-loop motion control. The vast majority of commercial systems in use are from HP/Agilent (now Keysight), followed by Zygo, Excel, and a few others. Systems employing single frequency lasers are also available. Both types use very similar interferometer optics and have advantages and disadvantages. The hardware for the single frequency laser is somewhat simpler. However, the two-frequency approach is less sensitive to changes in laser (optical) power and alignment, which eases the burden on the processing electronics.

Such technology doesn't come cheaply, at least not if a turn-key solution is desired. The typical price of a basic commercial system can easily exceed $20,000. While there is a great deal of surplus equipment availaible on eBay and elsewhere, putting together a usable system is still typically several thousand dollars. In this article, we describe an implementation that can be assembled by a dedicated hobbyist or researcher for less than $200 depending on skill level and the desire to use as few commercial (or at least interferometer-specific) parts as possible. It is based on a common HeNe laser tube similar to those that used to be found in grocery store barcode scanners, and are still widely available on the surplus market. Permanent magnets converts it into a two-frequency Zeeman laser, and some optics and an Arduino-compatible microprocessor board stabilizes the laser to produce the required F1 and F2 optical frequency components. Multiple interferometer configurations may be constructed from a few basic types of new or surplus low cost general purpose optics in place of those inteended for commercial interferometers. The measurement electronics are implemented using a second higher performance microprocessor development board with custom firmware and a Windows-based Graphical User Interface (GUI) for readout, plotting, and logging. Absolute displacement (change in position) accuracy down to better than 1/20th wavelength at 633 nm and a detectable displacement change below 1 nm is readily achievable. Measurement of angle and straightness are also possible with appopriate interferometer optics. If properly calibrated, the performance should be comparable to that of commercial metrology systems.

While not currently "open-source", technical support including electronic schematics and source code for the firmware is available to all users, and source code for the Windows GUIs can be made available at little to no cost for non-commercial users. The development environments are freely available from their respective suppliers.

The system consists of several distinct and essentially independent subsystems and may be built up in several stages with complete testing at each stage:

  1. Two frequency HeNe Zeeman laser: This consists of a common 5 or 6 inch barcode scanner HeNe laser tube and power supply, several strong magnets, and its associated feedback and controller called µSLC1 implemented using an Arduino-compatible microprocessor and a handful of discrete electronic components. The controller includes a Windows GUI but that is only required for initial setup and tuning of the feedback loop parameters. Alternative control schemes are also possible.

  2. Interferometer optics:. A small number of component types can be configured in a variety of ways for displacement, angle, and straightness measurements and assembled on a breadboard, rail, or cage, along with a moving stage so that actual measurements can be made.

  3. Measurement display: Once the laser and optics are assembled, the µMD1 Micro Measurement Display based on a microchip chipKit DP32 development board can be add to read out, plot, and log displacement or velocity data.

  4. Basic instrumentation: While not essential, being able to measure laser power with a laser power meter, and to display the polarized mode sweep as well as the actual longitudinal modes via a Scanning Fabre-Perot Interferometer (SFPI) are desirable. However, µSLC1 will plot the mode sweep via a plot in the Windows GUI and can be used to estimate laser power. Viewing the longitudinal modes is more of academic interest as long as the laser tube has been selected based on criteria outlined below.

Either of the three major subsystems - laser, optics, display - can be swapped out for a commercial implementation should that ever be desired (or if the builder doesn't want to construct that particular subsystem).

However, this is NOT an inexpensive solution to repairing your wafer Fab. ;-) The effort required at each stage makes it extremely NOT cost effective for a commercial effort, especially if engineers' time has any value. Furthermore, the reliability of a system constructed in this manner could be questionable unless a major effort is made in the design and construction. It is intended as a challenge and learning experience.

This article begins with background material on interferometers for metrology applications starting with the basic Michelson interferometer and progressing through those typically used with single and two-frequency lasers. Then each of the subsystems above are covered in more detail.


Interferometers for Metrology Applications

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 as 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, 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 design such that changes in the measured variable are detectable by 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 "line width" from a laser that ideally produces 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. A two frequency laser (the type that will be relevant in the remainder of this article) produces a pair of narrow linewidth components typically separated by a few MHz, and has similar properties.

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.

The first enhancement 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, 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 their relative angle isn't affected.

The second enhancement is to use a polarizing beam-splitter in place of the 45 degree partially reflecting mirror (used as a beam-splitter). The beams reflected to the two arms of the interferometer then have orthogonal polarization which effectively makes them independent until they are combined at the detectors and means the maximum amount of the laser optical power is available - nothing exits out the bottom of the beam-splitter as it would in the basic Michelson setup. (However, about half the power is lost in the detection scheme that is typically used.)

This arrangement with a single frequency laser, polarizing optics, and cube-corner retro-reflectors is used in some applications but has limitations. The signal amplitude depends critically on the returned optical power, which can vary based on the age of the laser, alignment, and dirt on the optics. That is why there is generally an "Intensity" detector to keep track of the signal strength and adjust the processing accordingly. Electronic and optical noise is also an issue.

For these reasons, the approach based on a two-frequency laser is much more common in critical applications, especially where a large amount of movement (change in displacement) is involved. The optics including the polarizing beam-splitter and retro-reflectors are similar, but instead of a laser producing a single optical frequency, the laser produces two closely spaced optical frequencies, F1 and F2 typically between 1 and 20 MHz apart. These have orthogonal polarization and are separated by the polarizing beam-splitter in the same way as with the single frequency laser. This approach is virtually immune to changes in beam power due to laser aging or contamination along the optical paths and less sensitive to changes in alignment. The difference or "split" frequency is in essense a carrier so that electronic processing can be done in the AC domain. Even though the laser output is no longer a single line, as a result of the way the processing is done, the effective PLD and change in PLD can still be hundreds of meters and is not directly affected by their difference, but only the line-width of each component, which is still very narrow..

There are several ways of implementing a two-frequency laser. A single frequency laser can have part of its beam shifted in optical frequency by an Acousto-Optic Modulator (AOM). This is used in several Zygo lasers. Or two single frequency lasers can be "offset locked" to each-other opto-electronically, though this approach is not to be the best of our knowledge used in any commercial systems due to its complexity and cost. However, the most common technique is also perhaps the most clever and elegant: By applying an axial magnetic field of up to a few hundred Gauss to a short HeNe laser tube meeting certain criteria, the neon gain curve is split into two parts separated in optical frequency by approximately 2.8 MHz/Gauss. When a lasing line is centered between the gain curves, it is split into left and right circular polarized components with a separation of up to a few MHz. Since these come from the same laser tube, they inherently have identical beam characteristics and are perfectly aligned with each-other. A Quarter WavePlate (QWP) converts the left and right circular polarization to orthogonal linear polarization resulting in the required F1/F2 frequency components aligned with the horizontal and vertical axes of the laser. The axial Zeeman HeNe laser is found in all HP/Agilent/Keysight 55xx lasers as well as lasers from several other companies, and is by far the most common approach in use today and for the past 30+ years. Nearly every microchip is made in a Fab using multiple lithography steppers controlled by interferometers using two frequency lasers. Many precision and custom optical components are produced on diamond turning lathes guided by similar devices. And there are numerous other similar applications.

One frequency component is typically bounced off a fixed or "Reference" retro-reflector (REF) while the other bounces off the "Tool" or target whose position is to be measured (MEAS). They return after passing through a polarizer at 45 degrees to a photodiode in the optical receiver which converts the difference in optical frequency between F1 and F2 to an electrical signal. When the Tool retro-reflector is stationary, REF is equal to MEAS. When the Tool retro-reflector moves, the difference frequency changes due to the Dopplar effect. Comparing the phase of the fixed REF signal (F2-F1) derived from the beam out of the laser to the changing MEAS signal (F2-F1+deltaF) results in the displacement.

In addition to the configuration with the PBS and RRs shown above called a Linear Interferometers (LI), there are two other common ones for displacement measurements that are widely used.

The "Single Beam Interferometer" (SBI) reduces the space required while still maintaining the same beam size using a pair of Quarter WavePlates (QWPs) to minimize back-reflections to the laser. The "Plane Mirror Interferometer" (PMI) enables the remote reflector to be a mirror rather than a cube-corner, thus permitting translation perpendicular to the measurement axis. As far as the measurements are concerned, there are no changes for the SBI, and a factor of 2X in resolution for the PMI because of the double pass. And there are a variety of more complex configurations including those for higher stability or higher reoslution displacement, or to support multiple axes in one interferometer block.

Other configurations exist for measuring angle, straightness, flatness, squareness, and more. And by allowing the Reference retro-reflector to move, differential measurements can be made as well. But they are all variations on the Michelson interferometer. Most only result in changes in calibration factor except for angle where a slightly more complex calculation is involved. Any type of physical movement that can be converted into a change in the PLD can be measured or controlled using these techniques.


The Zeeman-Split Two Frequency HeNe Laser

The heart of these systems is the Zeeman-split two frequency HeNe laser. It must provide a stable output consisting of a pair of optical frequencies separated by a few MHz, known as the "split frequency". The two optical frequencies (henceforth denoted F1 and F2) must be stable as they are in effect the "yardstick" on which all measurements are based. The split frequency is in essense a carrier used by the processing electronics, but it's precise value - or even long term stability - isn't critical.

It turns out that the red (633 nm) HeNe has several characteristics that make it the ideal laser for these metrology applications even more than 50 years after its invention. The principle one is that because the gain bandwidth of neon is only around 1.6 GHz, the absolute location of a lasing mode is never more than around 1 GHz either way, even without doing anything special, and the wavelength would already be good to 1 part in 180,000. And by specifying the isotope of mix of Ne, the approximately temperature and pressure inside the tube, and electronically locking the lasing modes relative to the Ne gain curve, this can be easily improved by a factor of 50 or more. So the optical frequency is locked to an intrinsic characteristic of the HeNe lasing process which is absolute and doesn't change much over the life of the tube. This could not be done with anywhere similar precision for diode or solid state lasers due to their orders of magnitude wider gain bandwidth. And while locking a diode or soid state laser to a reference frequency like a spectral line in a gas cell is possible, the cost of such an implementation is so much higher that it is simply not practical.

Including even a brief introduction to the principles of the HeNe laser would require too much space, and understanding how the thing works is really not essential for a metrology user. But if interested, refer to the Laser FAQ chapter on Stabilized HeNe Lasers, and specifically, the sections starting with Hewlett-Packard/Agilent/Keysight Stabilized HeNe Lasers.

The instant explanation is that when an axial magnetic field is applied to a short HeNe laser tube, under certain conditions, the usual single lasing mode will split into two lasing modes with left and right circular polarization separated by up to a few MHz. Refer to the above links to find out why this happens. But to construct a useful system, all that is needed is to know the relavant parameters for the tube and magnetic field strength, and how to implement the stabilization and conversion to the F1/F2 frequency components needed by the interferometer.

Laser Implementation

For a two-frequency laser to be suitable for metrology applications, it must provide a stable F1/F2 frequency output without additional "rogue modes". These are achieved through a combination of the physical design of the laser tube, strength of the Zeeman magnet, and control electronics.


Laser Tube:

The requirements for the HeNe laser tube for a two-frequency Zeeman laser are:

HeNe laser tubes that satisfy these requirements were used in many applications. Hand-held and in-counter barcode scanners were perhaps the most common with 100s of thousands of units deployed annually during their peak. Others include alignment, positioning, and document scanning. It's mostly a coincidence that they are suitable to be used as Zeeman lasers, a byproduct of low power (under 1 mW) making most of them 150 mm in total length or less and no requirement for a polarized output (which increases cost).


Typical HeNe Laser Tube from a Barcode Scanner

Fortunately, most of these tubes are so-called "hard-sealed" so that they don't leak over any time scale that matters and thus a laser that was unused or healthy and put on the shelf in the 1980s will be perfectly good in 2017 or later.

Beam Expander:

For the beam to be useful in an interferometer, it needs to be well collimated. The divergence of a diffraction limited beam from a single spatial mode laser like this is inversely proportional to diameter so a larger diameter beam can be better in this regard. It is also easier to align and provides more area minimizing the effect of the edges in cube corner where hitting them is unavoidable.

The raw beam from the typical small tubes to be used in this system has a diameter of only around 0.5 mm with a theoretical minimum divergence of around 1.7 mR. But many are wider - as much as 8 mR by design from the original barcode scanner application. Thus, additional optics are required to collimate the beam. The most common arrangement is a Galilean or Kepler telescope consisting of a pair of lenses. The one closest to the laser has a short focal length and expands the beam while the second one has a longer focal length and collmates it. The expansion factor is the ratio of the focal lengths. The difference between the two types is that the Gallilean telescope uses a negative lens while the Kepler telescope uses a positive lens for the beam expander. The only practical differences are that the Galilean telescope is slightly more compact and the beam doesn't focus anywhere (which is really only relevant for high power lasers).

Based on the physical size of the interferometer optics that will be used that are NOT single beam configurations, a 2.5-3 mm beam is optimal so that a pair of lenses of 9 and 54 mm or thereabouts will be suitable. However, the single beam configurations would be better using a 5-6 mm beam since they will be hitting the cube corner where the edge converge. Thus 9 and 108 mm lenses could be used.

Based on the ultimate divergence, a 3 mm beam will have a usful range of around 1 meter while a 6 mm beam is good to 10 meters or more.

Tube Heater:>

To generate the F1/F2 components requires that the lasing mode be centered between the split neon gain curve. This is done by controlling the distance between the tube's mirrors down to a fraction of 1 µm. The first HP Zeeman lasers used a PieZo Transduceer (PZT) behind the rear mirror inside the tube. [PZT actually derives from the chemical formulation of most of these materisla - lead zirconate titanate (Pb[Zr(x)Ti(1-x)]O3), but it's easier to remember the acronym based on the device name! ;-)] This is not possible with a barcode scanner tube. While a PZT could be attached to one of the mirror mounts pushing and pulling on it externally, this would be rather complex.

Later HP lasers switched to an electric resistance heater (also inside the tube). While the response isn't as fast, it is adequate and eliminates the high voltage required by the PZT. A heater can also be wrapped around the outside of the tube with acceptable performance. In fact, these lasers are often rebuilt by independent facilities using a conventional tube and external heater since genuine HP/Agilent/Keysight tubes are not available - they will only repair lasers, not sell new tubes.

The heater is used to control the cavity length of the laser tube so that a stable split frequency is generated. A variety of schemes can be used but the simplest is either an (expensive) thin-film Kapton/Polyimide heater or a wound heter using insulated copper "magnet" wire. The latter is perfectly satisfactory but somewhat tedious to wind.

Conventional HeNe Laser Tube with Heater, Ballast, and Cables Added

The general scheme is that the heater is designed to raise the temperature of the tube assembly comfortably above where it would be simply from the heating of the electrical discharge insidee the HeNe laser tube so that a modest amount of power can maintain the temperature constant (using a feedback loop). Typically, this is around one third to one half of the electrical power to the laser tube with the heater driver running at 1/2 of its maximum power. The thermal design is such that there is a controlled amount of heat loss through conduction and convection so that this balance can be maintained over an acceptable range of ambient conditions via the feedback loop.

Zeeman Magnet:>

Commercial Zeeman-split lasers generlaly utilize a cylindrical Alnico magnet in which the tube is mounted. Typical dimensions are: length of 4 inches, outside diameter of 2 inches, and inside diameter of 1.5 inches. The field strength measured near the center inside may be anywhere from around 150 to 400 Gauss depending on the laser model (e.g., 5517A, B, C, D). The magnetic field along with the tube length and output mirror reflectivity determines the REF frequency. However, if the parameters are not selected carefully, one can end up with no beat at all or "rogue" modes in addition to the desired split mode. And for these reasons, using onee of these magnets as-is could result in poor performance, particularly with the barcode scanner tube. It is trivial to reduce the magnetic field to any arbitrary value, and possible to increase it to beyond 500 G with an easy to construct magnetic pulser. So, using a commercial cylinder magnet is always an option but it's field may need to be adjusted.

However, a variety of other approaches to the magnet are possible. A series of strong bar magnets about 4 inches in length is the approach that was used by Teletrac. They are simply mounted surrounding the tube. Another option, which is probably the least expensive is to purchase a pile of small rare earth magnets and configure then in a similar way. It was possible to buy 50 magnets 10 x 6 mm for around $6 delivered. When 49 of them were arranged in 7 stacks (like bar magnets), a sufficiently strong field was created to result in an acceptable split frequency using a barcode scanner tube. Mounting the magnet with N-S or S-N flips the sign of the displacement versus direction of motion for any given interferometer configuration. So, it's not really even necessary to know this when constructing the tube assembly unless one is a stickler for consistency. :)


Melles Griot 05-LHR-007 HeNe Laser Tube with Heater and Axial Zeeman Magnets


This shows the 49 magnets simply taped in place on a plastic pill bottle that slips over the laser tube/heater combination. The length and number of stacks can be traded off to optimize the performance, usually to achieve the highest split frequency. Where a tube is not cooperating and there is no beat at all, additional magnets can be added. Using this approach it's not likely the field will be too strong. For an experimental system, the split frequency is not critical as it only affects the maximum velocity that can have displacement unambiguously determined in the direction that reduces the MEAS frequency. However, too weak a magnetic field will result in no splitting at all, or an unstable output. Around 1 MHz is a comfortable minimum which should be achievable with readily available magnets. But something somewhat lower is fine. Not all tubes will work with this relatively weak magnetic field though most will work with a genuine HP/Agilent cylindrical magnet. But that would be cheating. :) So, the best option is to be able to select among several short tubes to determine which is best.

In order to test for the split frequency, the tube must be powered inside the magnet while monitoring its output with a high speed photodetector behind a polarizer. A suitable detector can be constructed using almost any small silicon photodiode, a 9 volt battery (or power supply) to back bias it, and a load resistor of a few k ohms, with the vertical input to an oscilloscope across the resistor. As the tube warms up and the cavity expands, the lasing mode will drift through the neon gain curve which is split by the magnetic field. When it is in the region where the split gain curves overlap, there will be a beat. Generally, it will not be present for must of the mode sweep cycle, but then appear and vary in frequency. Determining what exact frequency will correspond to the usable split frequency can be tricky for the barcode scanner tubes with relatively weak magnetic fields, but it will probably be where the amplitude of the beat signal is highest.

Once the split frequency has been confirmed, the magnets should be secured with RTV silicone or other moderately high temperature adhesive. (Hot-melt glue may be problematic since the temperature near the heater may exceed 70 °C.) For my prototype, groups of 7 of these magnets were wrapped with 1 inch wide Kapton tape to make stacks that would not fall apart and these will held in place against the tube with elastic bands made of strips from a bicycle inner tube.

Note that rare earth magnets may lose their magnetic properties in an irreversible way if they get too hot. The specific temperature depends on so-called "N Grade". Therefore, it may be desireable to insulate them from the actual tube and heater by a small amount. Alnico does not have this issue (at least not at any temperature that matters.)

Feedback Beam Sampler and Photodiodes:

To lock the laser tube using the heater to control cavity length at the optimal location to generate a stable two frequency output requires optical feedback. The raw output of the axial Zeeman laser is not linearly polarized but a pair of left and right circularly polarized components for F1 and F2. A Quarter WavePlate (QWP) is required to convert these to linear polarization and align them with the horizontal and vertical axes of the laser assembly. Most of the resulting beam can then be sent out of the laser for use by the interferometer. But a portion (typically 5-10 percent) is sampled by a non-polarizing beam-splitter like a piece of uncoated glass and used for the feedback. This is then sent through a polarizing beam-splitter to a pair of photodiodes as shown in the diagram above. The control loop then adjusts the cavity length using the heater to force their amplitudes to be equal. When the slope of the error signal is correct, this will assure that the lock point is where the Zeeman beat occurs.

In addition, the REF signal needs to be generated for use by the measurement electronics. This can be done by splitting off another portion of the main beam and putting it through a polarizer with a sensitive optical receiver to convert that to an electrical signal. There will be more on this later. Alternatively, the small waste beam out the back of the laser tube can be used for this purpose. The difficulty with that is the relatively low power makes it more of a challenge to construct an optical receiver with sufficiennt sensitivity. An HP 10780 (A, B, or C) would work well, but some might consider it cheating to use a commercial module. Cost-wise, these can be really inexpensive on eBay, so a pair of them could be used initially (REF and MEAS) and then a photodiode and electronic circuit could be substituted later for each in the interest of purity. :)

Micro Stabilized Laser Controller

The function of the axial Zeeman HeNe laser controller is to lock the laser such that the Zeeman split longitudinal mode is centered between the split gain curve resulting in equal amplitudes for F1 and F2. As noted above, this is done by controlling the laser tube's cavity length with a heater to an accuracy of a few nm. In order for this to be effective, both heating and cooling are required. Heating is implemented by driving the heater surrounding the tube with a variable source of power; cooling is by allowing convection and conduction to the environment. The tube must be preheated to a temperature significantly higher than ambient where the rate of temperature rise due to maximum power into the heater, and cooling with no power are similar, where the steady state is maintained with approximately 50 percent heater power. The controller therefore must preheat the tube and then maintain the lock point with feedback using the beam sampler and photodiodes by adjusting the heater power. Heating and cooling near ambient temperature using a Thermo-Electric Cooler (TEC) is possible but generally more complex both physically and in terms of electronics, and thus more expensive. And not needed.

Laser controllers can be implemented in many ways. In fact, locking as a proof of concept can be achieved with as few as 3 discrete electronic parts costing under $1. ;-) A more practical controller providing the required functionality can be implemented with a few dozen discrete electronic components and op-amps, but requires some skill to design, assemble, and test. And aside from some minor adjustments, these are not very flexible. Most modern systems are based on microprocessors with firmware (low level software) in charge of all functions. For this system, a controller based on an Arduino compatible microprocessor board is used. It provides the following funtions:

In addition, a bidirectional communications link with a Windows PC (laptop, tablet, etc.) enables both monitoring of laser operation, and adjustment of almost every parameter affecting locking behavior.


Two Frequency Axial Zeeman HeNe Laser using µSLC1

The actual control loop runs at around 1 kHz using a timer interrupt. Three are 8 "states" based on the list of functions, above, which determine exactly what is done on each pass through the loop.

However, the controller will run independent of the PC so that once the optimal locking parameters have been set up and stored in non-volatire memory, the PC is not needed.

The photo below shows an Axial Zeeman laser built almost totally from scratch. It doesn't even incorporate any HP/Agilent parts except for the recycled 5501A baseplate, but that doesn't count. :) The feedback for stabilization utlizes the waste beam from the back of the tube rather than the front (shown in the diagrams, above).

Sam's Home-Built Axial Zeeman Two Frequency HeNe Laser using µSLC1

Note that for the resulting lock point to be centered between the split gain curves to produce a beat, the sign of the error signal matters. It would be quite challenging to predict this ahead of time, so if it locks at the wrong location and there is no beat, the outputs of the photodiodes in the beam sampler should be swapped. ;-)

The same setup could be configured as a (non-Zeeman) single or dual mode stabilized HeNe laser (assuming the tube is satisfactory for those) by removing the stacks of magnets surrounding the tube cylinder and Quarter WavePlates (QWPs) mounted in the blue sleeves at the rear and front (not visible).

The µSLC1 Main Window is shown below:


µSLC1 Main Window Near End of Locking Process

Complete information on µSLC1 can be found at Micro Stablized Laser Controller 1 (µSLC1) Installation and Operation Manual.


Practical Interferometer Optics

All of these are variations on the Michelson Interferometer modifed as described above to eliminate or minimize undesirable side effects (like back-reflections directly into the laser) and convert the measured variable into a change in path length.

Most of the configurations are similar to common widely used implementations, though, a few do not have any commercial counterparts. However, they can all be constructed from generic optical components like those shown below. Of course, providing a stable mounting is more challenging than bolting together HP parts.


Generic Interferometer Optics: 1/2" PBS, 1/2" CCs, 1/2" QWPs, Mirrors

The mirrors are first surface aluminum while the cube corners are metal-coated on their back surface, which is protected with paint. Metal coating of the CCs is required to minimize their effect on polarization. (These are copper-coated, but silver would be slightly more efficient.) The QWPs are optical grade mica.

Due to the relatively low cost and availability of 1/2" (12.7 mm) PBS cubes, all of these use them along with 1/2" cube corner trihedral prism retroreflectors. For those that are NOT single beam configurations, this requires a beam diameter of 3 mm or less and the working distance is limited to approximately 1 meter based on beam divergence considerations. (For the first configuration - with no retroreflectors - the practical distance and displacement range is much smaller.) And most are designated "Compact" since they are about half the size of most of their commercial counterparts.. Due the small size, an angled mirror may be needed to pick off the return beam to a standard optical receiver like the HP/Agilent 10780. And the Single Beam versions could also be arguably called "Compact" since without the metal block, they, too, could be even smaller.

Note that in the diagrams below for the single beam versions, where a ray is drawn centered on a cube corner, the beam should be as wide as possible to minimize the signal loss from the apex or corners of the prism. In addition, the optical quality in terms of angle and polishing of the prism must be high enough to minimize wavefront distortion and signal degradation. The relative performance of genuine HP/Agilent, name brands like Thorlabs or Newport, or inexpensive Far East imports, is not known in this regard, though the general specifications are quite similar.

For our purposes using the heterodyne approach, the "Laser" is assumed to be a two frequency Zeeman HeNe and there is a linear polarizer at 45 degrees in front of the Optical Receiver. However, these configurations are generally equally applicable to the homodyne approach but with a single frequency laser and quad-sin-cos detector.

And while most of these configurations are not as critical in terms of alignment as the classic Michelson configuration, alignment is still important. In general, whereever beams interact in the interformeter, they should be as parallel as possible and overlap of the REF and MEAS beams should be maximized at the optical receiver.

Construction doesn't require fancy costly Newport-quality opto-mechanical parts. A 3-D printer can be used to create miniature mounts that will be more than precise and stable enough for experimental use. For more permament installation, 5 minute Epoxy or UV-cure optical cement will suffice. (UV-cure optical cement is now inexpensively available for smartphone screen repair and can be cured using a 365 nm LED, resistor, and battery.) Where adjustable alignment is required, shims or split washers can provide the compliance needed.

Interferometer Configurations:

The first group are for displacement measurements (change in linear position). Any of these can be modified for differential displacement measurements by mounting the reference mirror or cube corner (above the cube) on a second moving stage or whatever, possibly with the addition of suitable beam turning optics.

The next two are intended for angular measurements but could also be used for differential measurements if the retroreflectors are mounted separately.

The Straightness Interferometer is more specialized and probably not something that a typical hobbyist/experimenter type would care about. If is included here for completeness should one have particular massochistic tendencies as these are very challenging to construct and align.

Finally, to create equivalent non-Single Beam configurations using a larger beam with longer range, it is possible to use a pair of small PBS cubes to create the equivalent of the standard 1 inch PBS. They can be any size that comfortably accomodates the desired beam diameter. 1/2 inch (12.7 mm) PBSs will work with beams up to 9 mm. A slightly smaller 2/5 inch (10 mm) PBS will be satisfactory for 6 mm beams. The cube corners would also double in size to 1 inch. The QWPs (if any) would need to either increase in size or could be implemented with a pair of smaller ones. The following is an example for the Linear Interferometer; others should be self evident.


Micro Measurement Display (µMD1)

In a heterodyne interferometer system, the displacement information is contained in the phase difference between the REF and MEAS signals. In a typical configuration where the remote reflector is stationary, this difference is 0. When its position changes, there will be more or less wavelengths between the interferometer and moving stage. This is what needs to be determined and converted to a displacement in common units like mm or inches.

A variety of techniques can be used to extract this information but virtually all are ultimately based on digital counters for REF and MEAS, or a single up/down counter with suitable logic to deal with race conditions. These result in a basic resolution of 1/2, 1/4, or 1/8 wavelength depending on the type of interfermeter. Additional hardware, software, or firmware are then (optionally) used to extend the resolution down to the nm range. A variety of techniques can be used including Phase Locked Loops (PLLs) to multiply the REF and MEAS frequencies by 16 or 32 or more before applying them to the counters, or digital estimation of the phase difference between the REF and MEAS signals. PLLs are used in commercial systems like the HP 5508A while phase estimation is used in the system here - µMD1 - since it can be done entirely in firmware.

Early measurement displays like the HP 5505A were based on SSI-MSI TTL and occupied 5-1/4" high rack mounted units. Modern ones are typically implemented with a combination of microprocessors, FPLDs, and custom LSI parts.

LIPM is intended to use µMD1 which runs on an inexpensive chipKit DP32 development board with a PIC32 microprocessor which includes all the required hardware except for the line receivers for REF and MEAS. On-board counters implement the basic measurement computation with high performance firmware to estimate the phase difference between REF and MEAS to extend the resolution. The firmware is written in C and the source code is available.

The µMD1 Graphical User Interface (GUI) runs on PC or laptop under Windows (XP/Vista/7/10 or later). Raw measurement data from the chipKit board can also be input directly to a user-developed analysis application.


µMD1 Main Window Typical Display

Complete information on µMD1 can be found at Micro Measuremnt Display 1 (µMD1) Installation and Operation Manual.

µMD1 Firmware Architecture:

The µMD1 Firmware is primarily divided into two parts:

The only other routine is for initial setup.

Everything is written in C except for the low level phase estimation to extend the resolution which is in MIPS assembly code. The firmware source may be found via the µMD1 link, above.

The key feature of the Microchip PIC32MX250F128B processor that facilitates the µMD1 are its five 16 bit high speed hardware counters (or "Timers" as they are called). While there are numerous versions of the PIC32, many of them - even those that have many more features or greater performance - do not provide the same required timer capabilities. Timer 1 is driven by the CPU clock (default of 40 MHz) and triggers an interrupt when it overflows. This is essentially the master clock for computation and data communications sending packets of data at several hundred Hz to the host. Timers 2-5 are clocked by the REF input signal (Timer 3) and MEAS input signals for up to 3 axes (Timers 5, 4, and 2). Firmware extends the length of the counters from 16 to 64 bits so there is never a possibility of overflow within the life of the Universe (or at least before this thing becomes obsolete!). These values are sent to the host and are what all measurements are based down to 1/2, 1/4, or 1/8 wavelength depending on the type of interferometer.

Code written in MIPS assembly language captures 31 samples of the peripheral word containing the REF and MEAS signal bits simultaneously at the full CPU clock rate into CPU registers, and saves them to memory. This is done multiple times during each interrupt and the resulting "waveforms" are then analyzed in C and averaged to compute a phase shift between REF and each of the MEAS signals. This Phase is sent as a fractional value along with the REF and MEAS counts.

The µMD1 firmware comes up in single axis mode. If activity is detected on MEAS2 or MEAS3, it will switch to multiple axis mode. The primary difference is in the size of the data packet. A hardware reset is required to return to single axis mode. For most purposes this doesn't matter and is handled automatically by the GUI which will then display all the axes. However, it will affect the format for data capture in a user application.

There is support for environmental sensors in the firmware but by default it is disabled due to issues with reliability due to bugs in some C libraries. Therefore, entering temperature, pressure, and humidity values manually is highly recommended. :( :)


Conclusions

This article has presented a description of a precision laser interferometer-based measurement system with nanometer precision that can be constructed using parts about as close to stone knives and bear skins as is reasonably practical.

Such a undertaking is not for the lazy. For someone who has little or no experience with lasers and electronics, it may take several months to a year or more. For a tinkerer-scrounger type with some basic experience, it could be as little as a few days. Construction will require the fabrication of some mechanical parts, wiring up of electronics, and testing of the laser and controller. But this could make a nice college-level Senior Project if combined with some real application for precision measurement.

It is basically a combination of a stabilized Zeeman laser, generic interferometer optics, and microprocessor-based measurement display, and each can be done separately and then combined, or commercial alternatives can be subtituted for selected ones if desired.

The result will be similar in performance to that of a $20,000 metrology system and the entire experience could be quite rewarding.

However, where enthusiasm is lacking, a half-hearted attempt will result in the parts ending up piled in a box in your attic next to the unfinished telescope mirror. :( Trust me, I know about unfinished telescope mirrors. :)


Specifications


Parts List

The following includes the major components of this system excluding wire, cable, mounting hardware, etc.

HeNe Zeeman Laser:

Stabilized Laser Controller (µSLC1):

Interferometer optics:

Micro Measurement Display (µMD1):