Jan Posthumas of LaserPeak (on left) and Don Pearson, ÄPRE’s VP Sales (on right)
Don Pearson, our VP Sales and Jan Posthumas, of LaserPeak (ÄPRE Representative) presented ÄPRE’s S100|HR interferometer in Munich this June. Once again we were pleased to meet with, and make new friends while co-exhibiting with the PTB’s HLEM (Hi-Level Experts Meeting) group.
Presented was the S100|HR, part of ÄPRE’s S-Series interferometers with diffraction limited imaging to 50 µm resolution (S50|HR), and all with <0.1% image distortion and <λ/20 retrace errors even at 6.5 fringes/mm.
We were also pleased with the interest in our new SCI based system that electronically remove back reflections from measurements and we look forward to discussing this more in the future.
Rarely are errors due to the interferometer itself considered when measuring optics with a laser Fizeau interferometer. Piotr gives examples of common and significant errors generated in the interferometer. Click to download his presentation with notes here.
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.
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 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.
In this blog the measurement of optics with a Fizeau interferometer that have been lap polished is discussed.
What interferometer is needed to produce good parts? Each manufacturing process requires a specific measurand, the quantity to be measured, to provide the feedback necessary to control the process and produce good parts. In the following posts several applications will be discussed with optional systems highlighted.
Random, Near of Full Sized Tool Polishing
Classic Spindle Polisher/Grinder
The historic method to manufacture optics has been random polishing on a spindle polisher. The procedure of rough forming the surface
shape, grinding to near polish and then lap polishing has been used for hundred of years. The beauty of lap polishing is the random nature, averaging over large areas of the sphere, which self corrects, and lead to high quality surfaces. Further the mid-spatial frequency ripples, the residual surface features remaining after the removal of 36-Zernike polynomials, tends to be suppressed due to averaging. There are limits and caveats as always, yet in general these are reasonable assumptions. Thus the measurand is simply the shape of the surface as defined by 36 Zernike polynomial coefficients.
The Old Zygo® Mark II Optics Sufficient
Since the meaurand is simply low spatial frequency shape, in this application, a continuous zoom imaging interferometer, with the inclusion of phase measurement is sufficient. This is why the Mark II architecture as been useful for over 35 years, it was sufficient for nearly all optics produced until this century. The low spatial resolution of the imaging system (no matter the camera resolution), and inherent image distortion of the zoom lens up to ~2%, and slope induced errors have little effect on measurement uncertainty of flats and spheres when measured at a null fringe condition.
Vibration Tolerant Data Acquisition Important
More important than the optical system for this application is the data acquisition and analysis software. This starts with vibration tolerant phase data acquisition as found in modern systems to report phase data without the influence of the production environment vibration. (We plan to discuss the history and development of vibration tolerant PSI in a future blog.) Further the software must be compatible with standard industry standards including ISO and data formats (.dat formats), and be easy to use.
Upgrading an Old Interferometer Is a Good Option
To stay current and meet the the requirements of lap polished optics there are two choices: Buying new or upgrading. The first option is purchasing a newly constructed system with classic optical components that has a new data acquisition system. The second is simply upgrading a classic system to a modern data acquisition system (with vibration tolerant algorithms). The performance of each will be equivalent, with the upgrade being much less expensive.
Summary
Lap polished Flats, Spheres and Prisms in a normal production environment are sufficiently measured with a continuous zoom system, where the value choice is often a system upgrade.
In the next post we’ll explore what is an appropriate interferometer for transmitted wavefront measurement.
Hippolyte Fizeau, Inventory of the Fizeau Interferometer
In this blog a brief historical outline of the Fizeau interferometer is presented.
Understanding the history of the commercial laser Fizeau interferometer helps to understand the choices available in today’s market. Some systems available today are remnants of historic designs.
Circa 1850: Fizeau Interferometer Invented
Hippolyte Fizeau invented this interferometer configuration for an 1851 experiment that at the time supported the either-drag theory, later disproven by Michelson, leading the way to Einstein’s theory of relativity
1960’s: Lasers
Laser Invented paving way for the laser Fizeau, an unequal path interferometer
1970’s: The architecture is established
The first commercial laser Fizeau interferometer, named for George Hunter the designer
Zygo® invents basic system architecture with sensor (mainframe) and reference (transmission sphere/flat) – the GH Interferometer in 1974.
Zygo® employs twin-spot alignment, with continuous zoom/rotating ground glass imaging design to accommodate low resolution (Vidicon camera) and off the shelf zoom lens (Mark II, in 1978).
Fringe following data acquisition introduced to replace visual fringe evaluation.
Bell Labs invents phase measuring interferometry on a 32X32 array data acquisition using a Vidicon camera, and PDP 8 rack mounted computer.
1980’s: Data acquisition improvements
Digital detectors (up to 256X256 by the late 1980’s), CCD/CID, and workstation computers introduced.
Carrier fringe and four camera simultaneous phase measurement invented (SPMI) for vibration insensitive data acquisition.
1990’s: Software advances
The First Phase Measuring Interferometer at Bell Labs
Enhanced graphics and additional results with faster processing in lower cost personal computers, primarily driven by Wyko and followed by Zygo®
CCD’s with 512×512 pixels introduced – no changes to the ground glass-continuous zoom historic imaging design
2000’s: Data Acquisition and illumination Improved
4D Technologies and ESDI successfully commercialize SPMI
1KX1K custom imaging driven by deterministic, computer controlled spot polishing
Push to better imaging systems in custom designs
Lower spatial coherence illumination (ring) introduced to improve measurement accuracy
2010’s: MegaPixels + Low Ray Trace Errors + Improved imaging
First newly designed interferometer optical systems that break the ground glass-continuous zoom historic design for high-resolution, low distortion imaging plus minimized ray-trace errors for improved accuracy with steeply sloped wavefronts from mild asphere optics
Lasers have dominated since the 1960’, but their limitations are catching up with them. Vertex back reflection fringes limit measurement accuracy, spurious fringe mask mid-spatial frequencies, and lasers are unable to measure domes, plates, prisms due to back surface reflections.
To overcome these limitations low coherent sources have been introduced. Delay line white light sources minimize the back reflections and spurious fringe problem but are nearly impossible to align, like a standard white light source.
ÄPRE’s Spectrally Controlled Interferometry (SCI) retains the ease of use of a laser with a long coherence mode and then switches to short coherence (white light) mode at camera frame rates. SCI can also measure the cavity distance enabling the measurement of radius of curvature, without the external radius rail, at higher accuracy. SCI looks like the source of the future.
Confused fringes with laser source (left), clean fringes with SCI (right)SCI source Spectrum (left) produces Interference fringes (right)
Software
ÄPRE REVEAL software: PVr analysis
The control of the entire measurement process will become possible with every interferometer using the same measurement setup via centralized control without variation user to user. Software will guide the user as to whether a part passes or fails, and databases will track parts through manufacture and data will be reported consistently, all enabling better process control and thus improved parts.
Summary
The Fizeau interferometer has a long history and promising future. Contact ÄPRE to discuss your interferometery needs to apply the best source + interferometer to your application.
In the next post we’ll explore what is an appropriate interferometer for lap polished flats, spheres and prismatic components.
