In this blog we explore the camera array size required to accurately measure Zernike polynomials in a laser Fizeau interferometer, and thus determine when a zoom system is important. (Hint: Zoom is a historical artifact)
Is a Zoom System Required?
Recently we were asked to provide a system with 4X zoom imaging to accommodate a 25 mm part in a 100 mm system. The thinking being to accurately measure a small part a zoom system is required. It is important to first understand what is the measurand, the quantity measured. In this case the customer wanted to measure and correct alignment errors as indicated by Zernike polynomial terms.
A zoom system adds complexity and cost, plus it can make calibrating the aperture size (pixel size) more complicated. A zoom also matches the image size to the camera, maximizing the pixel count active in a measurement. This raised the question, “How important is pixel count for measuring 36 Zernike terms accurately?” In this case accurate meant up to λ/10 P-V.
Camera Array Size Simulation
Using ÄPRE’s REVEAL software we simulated a measurement by building an artificial surface in the Zernike surface generator. The generator can be set for any pixel array size. Three pixel array sizes were simulated: 512 X 512 (1X zoom), 128 X 128 (4X zoom), and 64 X 64 (8X zoom). See figure 1 for examples of the 64 X 64 and 512 x 512 array data.
figure 1: Simulated data and represented in a 54 x 64 array (left) and 512 x 512 array (right)
The input values of the 36 Zernike coefficients were compared to the calculated results for the three array sizes. These differences indicate the measurement uncertainty simply due to array size influences on the calculation of the Zernike polynomials.
As can be seen in figure 2 the 64 X 64 array deviated up to 0.08 fringe (0.04 wave = λ/25). The 256 X 256 and 512 X 512 never induced errors no greater than 0.006 fringe! Indicating arrays larger than 128 x 128 have no influence on the results.
figure 2: Reported result subtracted from input for up to 36 Zernike coefficients
Aperture Converter
To measure a part smaller than 25% of the aperture add an aperture converter to decrease the output aperture to match the smaller part. Caution: Adding an aperture converter can make the interferometer more sensitive to retrace errors in high slope measurements
Why Zooms?
Zoom systems were introduced in the late 1970’s when vidicon cameras were 64 X 64 or at best 128 X 128 effective array resolution. Beyond 2X zoom the Zernike terms started to fail and thus a zoom was needed. Continuous zoom systems were commercially available at 6X and thus 6X became the standard. After 35 years of use it is easy to assume a zoom imaging system is needed.
Conclusions
A zoom system (up to 8X zoom) is not required to “fill the camera array” to achieve results accurate to λ/25 when measuring up to 36 Zernike polynomial terms. The best configuration in this case is a fixed magnification system, optimized for the camera array to pass the maximum spatial frequencies.
The new S100|HR laser Fizeau interferometer was introduced at the Optatec tradeshow in Frankfurt Germany this past week. We are excited by the industry’s response to a high-performance system offered at a fair price, and the continued interest in interferometer upgrades. The S100|HR was displayed measuring in the vibration insensitive mode and performed flawlessly.
This year we co-exhibited with the PTB working group for precision optical metrology. Thank you to Heiko and his team for coordinating the booth set up and the great catering! Everyone was very supportive.
OptoTech GmbH displayed our S100|HR integrated into their new OWI 150 Inverse workstation. This high performance workstation measures radius of curvature over 1 meter and surface figure while using ÄPRE’s REVEAL software in an OEM configuration. This is a great example of the power of REVEAL to automatically read the Z position to measure radius of curvature and to be modified to a specific customers requirement. OptoTech favors a more classic appearance including a dark blue background to be more familiar to users.
Again thank you to all who visited us at Optatec this year.
Our next show is Optics and Photonics in San Diego California. See you there!
This blog post discusses improvements in phase shifting algorithms for increased accuracy.
From the earliest days of phase shifting interferometry (PSI) phase ripple has been a problem. Ripple in the phase data follows the live fringe pattern but with twice the fringe frequency (ripple with the same frequency as the fringes can also appear and will be discuss at the end of the article). Ripple is an increase in measurement uncertainty (lower accuracy) and thus needs to be minimized. Further ripple can mimic mid-spatial frequency errors confusing the control feedback when spot polishing. Thus its minimization is important to good quality control.
Correcting Phase Ripple
In the late 1970’s Phase Ripple was called the “ripple bug” and its origin was unknown. The primary source was found to be vibration in the interferometer cavity during the data acquisition, and later other sources were identified such as nonlinearities in cameras and the phase shifting mechanisms. Any deviation from equally spaced phase shifts during acquisition or non-linearities that distorted the shape of the fringes cause ripple to form. Cameras became more linear with the advent of the then new CCD’s, and control of phase shifting mechanics improved, yet vibration is always present.
Nulling the Fizeau Cavity to Minimize
The first technique to minimize ripple was simply to null the cavity. By minimizing the visible fringes, the ripple is spread across the data. If perfectly nulled the ripple is insignificant when the test surface is a perfect sphere. This is still good practice as a nulled cavity exhibits the least errors in a Fizeau interferometer. Yet it is not always possible to null the fringes and so ultimately a better approach was needed.
Improved Phase Shifting Algorithms
In the early 1980’s the standard phase algorithm was four camera frames (buckets) spaced by 90°. Jim Wyant pointed out that only three frames were required to find phase, but this algorithm is particularly vibration sensitive. Four frame PSI, initiated by John Bruning’s group1, was less sensitive and in the late 1980’s Hariharan2 introduced a five frame PSI algorithm that was better than both. In 1988 Kathy Creath3 investigated numerous algorithms with varying sensitivity to ripple and in 1997 Peter Degroot4 wrote a “definitive” paper on phase shifting algorithms. These approaches made PSI less sensitive to phase shift spacing and the jitter between phase frames, but did not directly address the unequally spaced fringes due to vibration.
New Approach: Post Acquisition Correction
Ripple in Phase Data and Corrected with Äpre Universal Phase Algorithm
In 1982 Morgan5 investigated applying a post acquisition least squares correction to PSI. In the 1990’s a parallel line of investigation became active. This approach corrects the acquired data to the expected phase shifts through mathematical optimization. I.Kong and S. Kim 6,7 created a least squares PSI algorithm and an algorithm to “automatically suppress phase shift errors”, followed by C.Wei, M. Chen, & Z. Wang 8 with a “General Algorithm for phase-shifting interferometry by iterative least squares fitting”. Over the next 10 years a flurry of work 9,10,11,12,13,14,15 developed algorithms immune to translational and in some cases tilt shift error using iterative optimization. These works established the methodologies for vibration tolerant algorithms and demonstrated that with fast computers phase shifting errors could be minimized algorithmically, and practically.
Commercially Available Today
Vibration tolerant PSI, based on 35 years of development, are now commercially available as found in ÄPRE’s “Universal Phase Algorithm”6 in REVEAL™. The universal phase algorithm effectively minimizes phase ripple, as long as the vibration does not exceed ~150 nm P-V (λ/2 fringe). If the vibration exceeds 150 nm P-V then phase shifting interferometry breaks down and simultaneous PSI (Multi-Camera or Carrier Fringe) is required.
Vibration is not the only source of phase ripple
Intensity Variations
When phase ripple appears at the same frequency as the fringes illumination intensity variation during measurement is a likely cause. This can occur due to a laser or light level control failing. Interestingly, in interferometers equipped with rotating diffusers, variations in light level may occur due to differences of transmissivity in different areas of the diffuser rotating disk or simply by dirt on the diffuser disk.
Fringe Contrast Variations
Fringe contrast (modulation) is generally defined by the coherency of the source and is usually quite stable. However a laser can exhibit variations when the source is not properly stabilized. Also laser instability can be caused by mechanical vibrations when combined with long exposure times (usually longer then 10 ms.). In the later case the moving fringes will “average out” over a small area causing a loss of modulation that may be different for each recorded fringe image. The combination will create phase ripple in the data.
Tilt Variations
Vibration is considered a “piston” term – equal for every pixel across the aperture. If the phase shifting mechanics do not move straight the phase shifts will vary across the aperture, causing uncorrected ripple even with a correction algorithm. Recent work9,14 has attempted to address this error. This tilt induced ripple can also occur if the test or reference is not rigidly mounted.
Test or Reference with High Reflectivity
When one of the test parts has a high reflectivity fringes are detected that have reflected several times within the cavity. These multiple reflections distort the fringe shape. PSI algorithms, including vibration tolerant algorithms expect sinusoidal fringes. The distorted fringes are non-sinusoidal and induce phase ripple. To suppress the multiple reflections special coatings are applied to the reference or a thin pellicle is placed between the test and reference to suppress the multiple reflections.
References:
J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses”, Appl. Opt. 13, 11, 2693-2703 (1974)
P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm”, Appl. Opt. 26, 13 2504 – 2506 (1987)
K. Creath, “Phase-shifting interferometry techniques,” Progress in Optics, E. Wolf, ed. (Elsevier, 1988), Vol. 26, 349-393
C.J.Morgan, “Least-squares estimation in phase-measurement interferometry”, Opt. Lett. 7, 368-370 (1982)
I.B.Kong & S.W.Kim, “General Algorithm for phase-shifting interferometry by iterative least squares fitting”, Opt. Eng. 34, 183-187 (1995)
I.B.Kong & S.W.Kim, “Portable inspection of precision surface by phase-shifting interferometry with automatic suppression of phase shift errors”, Opt. Eng. 34, 1400-1404 (1995)
C.Wei, M. Chen, & Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357-1360 (1999)
Chen, Guo and Wei, “Algorithm immune to tilt phase-shift error for phase-shifting interferometers”, Appl. Opt, 39, 22, 3894 – 3898 (2000)
K.G.Larkin & B.F.Oreb, “Design and assessment of symmetrical phase-shifting algorithms”, J. Opt.Soc.AM. A 9, 1740-1748 (1992)
K.G.Larkin, “A self-calibrating phase-shifting algorithm based on natural demodulation of two-dimensional fringe patterns”, Opt. Expr.9, 236-253 (2001)
H.Guo & Z.Zhang, “Phase shift estimation from variances of fringe pattern differences”, Appl. Opt. 52, 26, 65726578 (2013)
Y-C Chen, P-C Lin, C-M Lee, & C-W Liang, “Iterative phase-shifting algorithm immune to random phase shifts and tilt”, Appl. Opt. 52, 14, 3381-3386 (2013)
M.Wielgus, Z. Sunderland, K. Patorski “Two-frame tilt-shift error estimation and phase demodulation algorithm”, Opt. Letters 40, 3460-3463, August 1 2015
L. Deck, “Model-based phase shifting interferometry”, Appl. Opt. 53, 4628-4636, July 2014
P. Szwaykowski, “Minimization of vibration induced errors using a geometrical approach to phase shifting interferometry”, ASPE Summer Conference on Interferometry, July 2015
This blog is about the performance and price options for laser Fizeau interferometers
Up to this point we have been discussing how various applications require specific interferometer sensor configurations and features. Now comes the key point when you need to do something. Do you need increased production capacity? Has a new process been introduced that requires better feedback? Is the IT department concerned about an old operating system? Has the computer failed, or the system has become unreliable but meets your production needs? Do you have a new program that requires a dedicated system? Or your customer is pushing for a result your system does not produce. What do you do? Do you buy a new interferometer? What are the options?
Buy New, Upgrade or Buy Refurbished?
Asking some questions can lead you to the purchasing options to consider.
Is the system to support a spot polishing process where slopes and mid-spatial frequencies are important?
Yes – indicates a high performance imaging interferometer with a 2K X 2K level camera, low distortion and low ray-trace errors.
Is the environment harsh, with vibration and air turbulence present?
Yes – indicates a SPMI (Multi-detector or Carrier Fringe acquisition) system
Does your application require custom fixturing, a special wavelength or non-standard aperture?
A custom system is required – talk to the various providers regarding your best option
Does the system support a standard lap polishing process where form is the key measurand?
Yes – indicates a classic interferometer
High Performance Imaging System laser Fizeau
These are the latest technology and will meet all the requirements for most situations, the problem is they tend to be expensive. Not only do they image mid-spatial frequencies well, the associated low ray trace errors mean they are suitable for carrier fringe data acquisition for operation in harsh environments. The major drawback is price. Most systems are 1.5X to 2X more expensive than a classic interferometer. If they were the same price everyone would probably buy one of these interferometers.
Harsh Environment laser Fizeau or laser Twyman-Green
There are several interferometers available that meet this need using both carrier fringe and multi-camera or multi-pixel configurations, Many of these applications have specific specifications that dictate size, weight, and result output. It is best to discuss these with the manufacturer to arrive the best choice.
Classic laser Fizeau Interferometer
With the classic Fizeau there are the most choices.
Refurbished miniFIZ interferometer
Buy New or Refurbished: Increase Production Capacity
If increased production capacity is required there are two choices: Buy new or refurbished. There are a few choices for new systems that have the same optical system as produced for the last 30 years – with extensively upgraded software! These new system are priced between $60,000 and $75,000 (USD).
Also available from time to time are refurbished interferometers with the same/similar classical optical design. These refurbished systems have the latest data acquisition and analysis software like a new system and are priced between $33,000 and $37,000.
Upgrade: Failed System, Old Operating System, New Acquisition and Analysis Software Required
There are thousands of interferometers installed worldwide that can be renewed by upgrading the electro-optics and software. These systems can operate as well as a new system, with the latest software, cameras and computer systems. Upgrading is cost effective and is priced between $22,000 and $27,000. Upgrading is usually the best choice when production capacity is not an issue, but systems are down. A side benefit is the increased efficiency of new electronics can also increase the throughput and therefore production capacity of existing systems.
Summary
There are several purchasing options available regarding laser Fizeau interferometers. Applications often drive the decision but price is also important.
In this blog the measurement of thin parallel plates with a Fizeau interferometer is discussed.
Filters, etalons and plane parallel components exhibit reflections from the front and back surface rendering them impossible to measure in a standard laser Fizeau interferometer. A standard interferometer uses a laser, making interference easy to create, no matter the interferometer cavity length. With parallel plates additional interferometer cavities are created adding confusing fringes: 1) Reference surface to the plate front surface, 2) reference surface to the plate back surface and 3) plate front surface to back surface.
A few techniques are available to overcome this confusion.
Laser Fizeau compared to SCI Fizeau – 1 cm substate with 250 um step in the middle.
ÄPRE has introduced a practical SCI source, a new source modality to Fizeau interferometry. SCI controls the coherence, fringe position (over 100’s of millimeters) and phase modulation of the fringes electronically. SCI aligns in high coherence mode, like a laser, isolates like a white light source, positions the fringes within the cavity, and phase modulates regardless the cavity size, even down to 50um. By isolating
the surface of interest, accuracy is improved and new applications are enabled. This is a new technology and its impact will emerge in the coming years.
Wavelength-Modulation + Fourier Analysis
Modulating laser wavelength will change the observed phase of the interference fringes. The rate of fringe modulation as the wavelength is changed is a function of the interferometer cavity length, long cavities modulate more rapidly than short cavities. Thus when a wavelength scan is performed and the results Fourier analyzed for modulation frequency the various cavities can be separated. By performing phase shifting interferometry analysis on the now separated surfaces thin parts can be measured, surface by surface. The drawbacks of this approach tend to be price and careful set up. To assure proper extraction, the surfaces must be positioned so the modulations are separable and not overlapped which is not always possible. Some versions also provide absolute position in space enabling millimeter length steps to be measured.
Short Coherence Balanced Arms
An incoherent source, like a diode, can produce fringes at a location in front of a Fizeau reference flat IF a secondary interferometer system is coupled to it. By adjusting the coupling cavities length the interference fringes are placed in space in front of the Fizeau reference surface. This method produces high quality, single surface fringes where the front and back surfaces of a thin part can be measured. Another short coherence approach is to use a Twyman-Green equal path interferometer and a diode. The main drawbacks of these systems are price and set up. The fringes exist at a specific point in space and the test part must be moved to within micrometers in tip and tilt and Z to simply see fringes. This can be challenging if separate alignment aids are not provided.
Grazing Incidence
By producing a steeply grazing illumination beam and varying the spatial coherence of the illumination, the back surface of a thin part can be eliminated from measurement. This techniques has been used successfully to measure semiconductor masks and sapphire wafers, though it is not used often in optical testing. The steep grazing incidence angle enable even rough surfaces to reflect specularly, with desensitized fringes (5um equivalent wavelength) and therefore the accuracy is not sufficient for most optical work.
In this blog the measurement of steep spheres and aspheres with a Fizeau interferometer is discussed.
Steep Convex Spheres – Stitching
A limitation of Fizeau interferometry is the inability to measure steep convex spheres with f#’s beyond the reference surface f#. This is a severe limitation for spot polishing machines that require data across the entire surface to apply the necessary corrections. The solution is a stitching system that acquires sub-apertures across the partially covered surface and mathematically combines them into a complete surface. Stitching includes matching overlapping areas for tips and tilts, and sometimes distortions and rotations and is not a simple image stitch. Several manufacturers now offer these systems.
Stitching can introduce errors. Stitching errors are found in the lowest spatial frequencies, particularly power. A simple test for errors in power is the measurement of radius of curvature. Measure a part’s radius of curvature across the vertex sub-aperture and compare this value to the radius of curvature measured across the entire stitched surface. The difference of these two includes the stitching errors, plus the reproducibility of the two radius of curvature measurements. Measuring radius of curvature is challenging and careful metrology practice must be followed to confirm this test. To assess surface irregularity accuracy compare a surface measured with a f/0.75 Transmission Sphere (Fizeau reference) and the same surface area stitched with a
n f/3.3 Transmission Sphere. Best is subtracting the two measurements from each other to highlight the stitching errors, though this is not always easy to implemented due to differing data set sizes. Stitching systems by leading manufacturers appear to have solved these problems, yet understanding potential limitations is important.
A “lattice” of subapertures covers the full aperture of high-numerical-aperture and large-clear-aperture parts1
The major limitations now seem to be cost and speed of measurement.
Asphere Metrology
Aspheres are difficult to measure with Fizeau interferometers. A Fizeau operates best when the surface is a nulled sphere to minimize ray-trace errors, and aspheres can greatly deviate from a sphere. Further the high slopes of aspheres can exceed the slope limit of the imaging system causing the measurement to fail. Multiple approaches to overcome these limitations are used.
Asphere Stitching
Just like spheres an asphere stitching system builds up the surface by measuring sub-apertures. This is more difficult than measuring a sphere as the ray-trace errors will exist in each sub-aperture which must be minimized, or calculated and removed. With steep aspheres even the sub-apertures exhibit slopes exceeding the imaging limit of the interferometer. Complicated compensation techniques (such as rotating wedges) are used to minimize measured slopes, requiring mathematically correction for ray-trace errors, and induced distortions of the variable compensating wedges. Measurement time (>30 minutes) and cost tend to be the major concerns for these systems.
Measurable aspheres are limited to near axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Asphere Scanning Fizeau
Scanning Fizeau zones2
Scanning Fizeau is similar to stitching systems, but scan only in Z, along the parts optical axis. Rings of data paired with the caustic zone Z is compared to the expected Z position and surface surface shape. Since data is acquired at the null of each ring, ray tracing errors are minimized, for low measurement uncertainty. These systems have been used with picometer measurement uncertainty for semiconductor lithography optics asphere manufacture. Limitations due to the reference sphere f# and surface curvatures exist limiting its application to specific lens types. Since a full ring of data is measured these systems tend to measure an entire surface in <5 minutes.
Scanning Fizeau systems promise high accuracy with fast data acquisition. Yet measurable aspheres are limited to near axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Asphere Sub-Nyquist Fizeau
Sub-Nyquist has existed since the 1980’s but only recently introduced commercially. This system pinhole masks the detector allowing fringes beyond the nyquist limit to be detected and thus acquired.
Sub-nyquist fringes by nature are highly tilted, introducing errors that vary from measured part to measured part. These ray-trace errors are calculated and removed mathematically considering both the interferometer optical design AND the part under test. Mathematical ray-trace error removal demands full knowledge of the interferometer optical design, as manufactured, and its sensitivity to varying environmental influences. For this reason sub-nyquist accuracy can be considered limited to commercial grade parts. Sub-nyquist promises fast measurement (<3 minutes) on a limited set of surfaces with limited accuracy.
Sub-nyquist Fizeau promises fast data acquisition with the ability to measure non-axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Tilted Wave Interferometer for Asphere Measurement
A new entrant into asphere metrology is the tilted wave interferometer. In development for the last 10 years the tilted wave promises high speed metrology of asphere surfaces. By moving the source position multiple areas of an aspheric surface can be acquired and then analyzed. The tilted wave can be thought of as a stitching interferometer (without the motion) and yet requires a sub-nyquist type of calibration for every point in the measurement VOLUME.
Tilted wave setup & zone distribution for asphere test piece4
Each point in the measurement volume must be calibrated for each transmission element. These calibrations can be temperature dependent and a function of the manufacturing tolerances. Calibration of the actual system is required and most likely on a repeated basis. This type of system seems close to commercialization and it will be interesting to learn of its measurement uncertainty, correlation to other technologies, speed of measurement (one of it proposed benefits) and cost.
Fizeau Interferometer Limited to Near Axially Symmetric and Monotonically Curved Aspheres
In all cases applying Fizeau interferometers to aspheric surfaces extends its capabilities to perform outside its “sweet spot”. Mathematical combinatorial techniques along with extensive “calibrations” achieve acceptable measurement uncertainty.
Even with these impressive innovations non-monotonically varying slopes and non-axially symmetric surfaces are a major limitation for Fizeau interferometers, especially if the surface reverses curvature relative to the base sphere. In these cases the reflected light does not enter the interferometer and the surface is not measurable. This is especially true for gull-wing and sombrero lenses and free form surfaces which cannot be measured with Fizeau interferometers. This is not to say that modified Fizeau interferometers don’t have their place regarding aspheres. The main benefit, when they are applicable is higher spatial resolution in an acceptable time period compared to stylus profilers. For general purpose measurement of the wide range of potential surface shapes is needed and when a high resolution or 3D image of the surface is not required, contact stylus and optical stylus systems are favored for asphere metrology.
Final Word
Though not generally considered an interferometer, the Luphos optical probe is a single point, multi-wavelength Fizeau interferometer.
Single point multi-wavelength Fizeau interferometer5
It has the same limitations as all Fizeau interferometer with two benefits: Absolute position sensing and single point. The absolute positioning allows the probe to sense a position in space to nanometers within a few millimeters. Thus if the probe “falls off” a part it can regain position, depending on the stability of the metrology frame. Being single point, if the metrology frame and positioning system support the motions the probe can follow non-rotationally symmetric surfaces and potentially reversing curvature (gull-wing) parts. Thus it is more general purpose, and like any other stitching system can measure steep surfaces. Just like any Fizeau, deviations from measuring off the surface normal produce two errors: The signal can be lost if no light returns and ray-tracing errors occur in the probe degrading performance. These errors are accommodated by adding a B axis to an XYZ positioning system. The more complex motion of a B axis requires careful calibration to achieve 50 nm level performance.
Next post: Thin plates measurement
1 A. Kulawiec, “Extended Aspheric Measurement Capability with Subaperture Stitching Interferometry”, http://www.photonics.com/Article.aspx?AID=34816
2 M Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces”, Proc. of SPIE Vol. 7389 738916-1
3J. Greivenkamp ; A. Lowman and R. Palum”Sub‐Nyquist interferometry: implementation and measurement capability”, Opt. Eng. 35(10), 2962-2969 (Oct 01, 1996)
4 E. Garbusi, C. Pruss, J. Liesener, W. Osten, “New technique for flexible and rapid measurement of precision aspheres”, Proc. of SPIE Vol. 6616, 661629, (2007)
5 G.Berger, J. Petter “Non-contact metrology of aspheric surfaces based on MWLI technology”, Proc. SPIE 8884, Optifab 2013, 88840V (September 6, 2013)
The First Phase Measuring Interferometer at Bell Labs
At Photonics West we introduced a new product, upgrading Zygo® GPI™ and Mark IV™ interferometers. This also includes the VeriFire™ line of interferometers. All these system are basically the same with minor variations and which we can accommodate.
We are pleased by the growing excitement about our ÄPRE REVEAL™ software. Its backward compatibility with MetroPro® file types and unique traceable metrology make it the production software of choice.
Also several other exhibitors displayed products run by REVEAL. Davidson Optronics again displayed their 12″ Fizeau interferometer, designed in concert with Äpre Instruments, along with the PSM micro-profiler both using REVEAL. M3 displayed their new 3.39um IR interferometer using REVEAL software.
See you in Frankfurt at Optatec 2016.®™
In this blog measurement of optics in a harsh environment with a Fizeau interferometer is discussed.
For large systems, typically telescopes, vibration and air turbulence hinder or prevent the measurement phase by temporal phase shifting. Also interferometers placed on machine tools to measure in situ experience a vibrating environment. When vibration and turbulence hinder measurement then only a simultaneous phase measuring system (SPMI) will be able to acquire data. These systems acquire phase data fast enough to freeze fringe motion due to vibration and turbulence.
SPMI Data Acquisition: Multi-Camera and Carrier Fringe
There are two primary SPMI data acquisition architectures: Multi-camera1and carrier fringe2. Multi-camera uses polarization to split the intensity data into multiple images with shifted phases which are analyzed for wavefront phase. Carrier fringe uses tilt in the wavefront coupled with several different analytical approaches to extract phase. Both approaches are successfully employed commercially, and are functionally and performance equivalent.
Tower for testing large mirrors at the University of Arizona
Averaging is Required
The SPMI system enables phase to be acquired, but the phase is changing rapidly and by large amounts and any single measurement is meaningless. To achieve stable data, averaging must be employed. The amount of averaging required is a function of the frequency and amplitude of the vibration and turbulence. A useful method to determine how much averaging is required is to acquire 100 data sets in a series as would be performed in an average. Calculate the RMS or P-V of this data set, divide the RMS or P-V by the measurement repeatability desired to obtain a ratio. Square this ratio and set the average to this squared value. For example, if the single measurement repeatability is 6,000 nm P-V and desired is 60 nm P-V then 1002 averages must be taken, at a minimum, to achieve 60 nm P-V repeatability, assuming a gaussian distribution. It is often practical to stir the air with a fan to improve convergence, which can take many hours for large cavities with slowly moving fringes. SPMI systems can often acquire and calculate phase in seconds so averaging can be rapid.
Repeatability is Not Accuracy
Finally, note that repeatability is not low measurement uncertainty, or accuracy. Measurement uncertainty is primarily driven by the optical design of the interferometer, temperature variations in all the optics, mechanical stresses in mountings and optical misalignments and null lenses errors – a la Hubble. Controlling these is much harder than averaging and is a topic unto itself.
SPMI Interferometers are Non-Common Path – Hence Lower Accuracy
Also note SPMI systems are non-common path systems – the polarization paths are different or tilt exists between the test and reference wavefronts. These differing paths degrade the optical performance compared to PMI which can be common path, i.e. the test and reference beams perfectly overlap when a sphere or flat is measured in a nulled condition. So from an accuracy point of view PMI- nulled can outperform SPMI, but when data cannot be acquired due to turbulence or vibration then SPMI is required and an accuracy compromise is acceptable.
Summary
Acquiring data in harsh, vibrating and turbulent environments requires an SPMI data acquisition interferometer. Achieving high accuracy results requires careful attention to the all measurement parameters and is typically of lower accuracy than a nulled laser Fizeau phase shifting interferometer in a quiet environment.
2 Takeda, M. “Spatial-carrier fringe-patter analysis and its applications to precision interferometry and profilometry: an overview, Ind Metrol 1990;1(2):79-99
In this blog the measurement of spherical and flat optics with a Fizeau interferometer that have been spot polished is discussed.
Spot polishers require improved performance over interferometers with standard 6X continuous zoom imaging
Spot polishing machines for rapid manufacture of standard and high accuracy spheres place new requirements on interferometer systems. The spot polishing method can create small ripple in the surface while shaping the overall form. Accurate positioning of the polishing spot is required to correct the surface errors to bring the surface into specification. To guide the spot polishers image distortion, resolution, and pixel scaling (calibration) are important These requirements primarily drive the imaging system of the interferometer. Continuous zoom system do not meet these requirements.
Modern Imaging Systems
Modern interferometers have discrete or fixed magnification imaging to improve resolution, and minimize distortion and ray tracing errors. All the interferometer optics are exposed to coherent laser light which highlights surface defects. Therefore the optics must be high quality to supress bulls eye artifacts (stray fringes) from scratches, pits, dust and reflections. These hight quality optics increase the system cost.
Interferometer Image Resolution
Increased resolution is required to measure mid-spatial frequency surface features. These features can be defined as the residuals present after the removal of 36 Zernike polynomial terms (see REVEAL analysis screen below, the image on the right are the residual mid-spatial frequencies). Mid-spatial frequencies in an optical surface scatters light degrading the image or lowers directed energy concentration. Therefore they must be measured and corrected.
Mid-spatial frequencies are measured with a high resolution imaging system. Typically greater than a megapixel camera is required. The resolution is limited by either the optical design or the camera resolution. If the camera limits then the smallest feature measurable is approximated by 80% of Nyquist frequency
(1-line/mm:2 Pixels), or ~400 lines/aperture for a megapixel camera. At 50 mm field of view, approximately 125 µm feature can be imaged. Continuous zoom interferometers are limited to <100 lines/aperture.
Interferometer Image Distortion
Image distortion maps a surface feature in the wrong position, and the polisher will move to the wrong position. In the best systems the camera limits resolution. As noted 400 lines/aperture is the practical limit of resolution in a megapixel camera, so distortion of 1/400 or 0.25% is required. The polishers polishing function might decrease this requirement, but with 0.25% the interferometer will not be the limiter. For higher resolution cameras the 80% Nyquist again drives distortion… more pixels better distortion requirements, yet practically the polishing function (the shape of the polishing spot) is the limiter. Continuous zoom systems can exhibit up to 2% distortion – 10X higher than modern interferometers.
Interferometer Ray Tracing Errors
When the test part deviates from a sphere many fringes are seen. These fringes indicate high slopes between the reference and test wavefronts. When high slopes occur the test and reference wavefronts traverse different paths through the imaging optics. These divergent paths create wavefront errors in an uncorrected interferometer system. This error can be measured by acquiring data with a null interference cavity, saving the data and then acquiring data with the maximum number of tilt fringes that can be measured and subtracting the two results. The residual error will primarily be due to ray tracing errors and is seen as coma and astigmatism, and sometime spherical aberration. In the old continuous zoom systems thes
e errors can be as large as a wave of error. Even for the small amount of slopes they can measure.
To speed the convergence of the polishing correction process minimizing these ray tracing errors are required. Only the highest quality systems are corrected for ray-trace errors.
Summary
For spot polishing of spherical and flat components a low distortion, high resolution interferometer with low ray trace errors is desired.
Next Post: Next we discuss special applications, starting with Harsh environments
In this blog the alignment of optical systems with a Fizeau interferometer is discussed.
The goal of a system wavefront test is alignment and confirmation of system performance. The measurement of optical system wavefront often requires a custom interferometer. When a fully reflective system is measured a standard HeNe laser Fizeau is sufficient as the wavelength does not matter. For refractive systems the wavelength often must match the optical system design, and optical system wavelengths vary from 10.6 um to 193 nm. Thus these systems are often “custom” except for a few wavelengths that are more common. For this discussion the wavelength is assumed to be matched to the system.
Zernike polynomials are often used to define system wavefront errors during alignment
Null Test
If a null, adjust until near-zero error is the goal then a standard continuous zoom system can be sufficient. At null ray trace errors are minimized and wavefront imaging distortion error minimal. Further mid-spatial frequency errors are not critical when measuring system alignment. Some of these measurements are made with a null corrector lens that matches the system under test wavefront with the interferometer expected wavefront, either spherical or plano.
Non-Null Testing
Subsystem testing can produce non-null wavefronts in the final alignment. For non-null system an interferometer with low ray-trace errors is important. With high fringe density, or high slopes, ray trace errors grow. Ray-trace errors are developed when the test and reference wavefront traverse diverging paths to the camera and are seen primarily as coma and astigmatism, with sometimes spherical errors. If the final “aligned” condition is at 10 waves of spherical aberration then unless the interferometer is well corrected for ray-tracing errors the data will exhibit errors in final alignment.
Precision alignment is important for optimal optical system performance, especially with more complex optical paths.
Small systems
A bench top system test is similar to measuring an optical component and standard phase shifting data acquisition is sufficient.
Real Time Adjustment
Recently the introduction of widely available simultaneous data acquisition interferometers have enabled near real time phase. So alignments can be adjusted continuously for more rapid convergence on alignment.
Large Systems
For large systems, typically telescopes, vibration and turbulence become an issue. If an issue then only a simultaneous phase measuring system will be able to acquire data.
Summary
In most cases a standard interferometer with near matching wavelength is sufficient to test optical system wavefront. Where large or non-nulled cavities are involved a high performance interferometer with low ray-trace errors and/or simultaneous phase measurement need to be used.
