Today’s optics industry demands this level of optimal performance and precision. Read our feature in Laser Focus World to see how you can use SCI to your advantage.
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The laser Fizeau interferometer has experienced several transformations from its original design. Like all evolutionary processes, some vestigial design elements remain in commonly used interferometers, which do not address and can impede measurements required to control and optimize today’s optical manufacturing processes.
Circa 1850: Fizeau Interferometer
Armand Hippolyte Louis Fizeau (1819 – 1896) invented the interferometer configuration, now named after him, for measurements of glass parameters which he presented at the French Academy of Sciences in 1862. Earlier, in 1851 he used a version of this interferometer in his famous experiment devised to test the ether-drag theory. The results seemed to support a partial ether-drag, that were later confirmed by Michelson and Morley. In a twist of fate the ether theory was disproved shortly after by the more famous Michelson-Morley experiment, but the results of BOTH of these experiments lead the way to Einstein’s theory of relativity. “Einstein later pointed out the importance of the [Fizeau] experiment for special relativity, in which it corresponds to the relativistic velocity-addition formula when restricted to small velocities,” Wikipedia
Armand Hippolyte Louis Fizeau1st Fizeau Interferometer
Pre-1960’s
Before the invention of the laser in the 1960’s optical test interferometers were difficult to use and often had to be custom built for each application. Low-coherence illumination favored equal path interferometers like a Twyman-Green or Mach-Zehnder configuration. The Fizeau – though already commercially available – were large, very heavy, difficult to use and limited to measurements of flat surfaces.
The most popular interferometer, though rarely considered one, is the Test Plate using Newton’s Rings. A test plate is strikingly similar to a Fizeau configuration with only several micrometers of working distance. The test plate consists of one reference surface for each surface an a low coherence filtered source
Twyman-Green InterferometerTest Plate
1960’s – The Laser becomes Practical
The laser made interferometry much easier to implement. “Bob Hopkins…was quick to realize how much the laser could be used to improve the testing of optical components” (J.C. Wyant, “Short history of interferometric metrology”). With the laser, fringes were easy to find making interferometry a practical tool supporting optical manufacture. Much progress was made in testing configurations, yet interferometry remained an experts tool, custom made for the application and developed and run by engineers and scientists. Plus to use a HeNe laser, the most widely available required stabilizing it to have only one frequency of output. Low cost unstablized HeNe lasers had short coherence, around 200 mm and were limited to use in a Twyman Green configuration where the test and reference could be balance. These stabilized lasers were very expensive, in 2020 dollars they would cost $35,000!
The 1st HeNe Laser – Bell Labs (J. Hecht, “History of Gas Lasers, Part 1 Continuous Wave Gas Lasers”, Opt. Phot, January 2010)
1970’s – The Modern Fizeau Architecture is Created
What is now considered a Fizeau interferometer was created in the 1970’s by two different events: The invention of the modular Fizeau interferometer with a laser source, plus computerized phase measurements.
The Fizeau Optical/Mechanical Architecture
The HeNe laser promised to make interferometers much easier to use, but its cost blocked interferometers from becoming a commercial success. The key insight at Zygo that enabled the modern Fizeau interferometer design was that a simple polarizer in front of a multi-mode, low cost laser produced meters long coherence. This insight was applied in 1972 by Carl Zanoni and George Hunter at ZYGO constructing the GH (for George Hunter the principle designer) and the follow-on Mark II™ in 1976 when modern interferometry was born.
GH Interferometer: Transmission Sphere/Interferometer Architecture with Polaroid fringe captureMark II™ interferometer: Vidicon Tube Camera introduced for live fringe viewing
It is important to understand the architecture of the Mark II™ to know WHY interferometers are designed as they are today. The ZYGO innovations were a low cost, long coherence laser, a flexible optical architecture, a simple alignment system, with a clean fringe image. The architecture combines an interferometer (“mainframe” in ZYGO terminology in a nod to the 1970’s Tektronix Oscilloscope architecture) with quickly interchangeable reference lenses/reference-surfaces they named transmission spheres (TS) and transmission flats (TF).
With the long working distance due to long laser coherence one TS eliminated the need for large libraries of Test Plates – bringing cost savings and convenience. Plus Test Plates are used in virtual contact, separating the optical test surface from the reference surface eliminated the possibility of scratching and damage.
Ease of use was augmented by the alignment system. The twin spot alignment visually indicated when the cavity alignment was close enough for interference fringes to be found. Now non optical engineers could align and configure an interferometer.
The imaging system of Mark II™ REQUIRED a zoom lens to measure a wide range of part diameters since the only imager available was a vidicon camera. Both the zoom lens and the vidicon produced back reflections and secondary fringe patterns. The solution was a rotating ground glass, “coherence buster”, at an intermediate image that was then imaged incoherently through the zoom lens and onto the vidicon.
Zygo Mark II™ optical design architecture – from the patent drawing
Mark Interferometer Design Limitations
This design was so successful that even today’s interferometers with ground glass and 6X zoom are IDENTICAL to the optical system designed for the Mark II™. This is important to understand since the original optical system was designed for a vidicon camera AND only considered the visual measurement of spherical and flat optics manufactured with pitch polished processes.
If a megapixel camera is used in this design, the magnification by the zoom lens is empty, meaning resolution is not increased and potentially degraded. Further, imaging distortion of one or two pixels at 128X128 was acceptable but is problematic when spot polishing techniques are employed that require interferometer feedback for correction. These limitations lead to the development of fixed or stepped magnification imaging systems in the 2000’s, to be discussed later.
The historical influence of the Mark II™ optical architecture cannot be underestimated. All commercially successful interferometers follow the laser + “mainframe” + Transmission Reference architecture. Plus commercially successful alternative optical imaging design were only developed in the 2000’s, where even today (2018) historical inertia drives buying decisions.
The Data Acquisition System
Bell Labs patented computer data acquisition phase measuring interferometry. John Bruning and Donald Harriott’s group and Tropel (now CORNING) worked together to develop the a phase measuring system.
In the 1970’s Bell Labs was pushing the leading edge of semiconductor manufacturing technology. Lenses to support semiconductor manufacture were difficult to build due to their, at the time, extreme tolerances. Conventional visual or fringe center data analysis was not sufficient. Minicomputers were available and enabled in-the-lab data acquisition, as opposed to central batch processing of a few years earlier. Add to this signal processing was a core technology at Bell Labs. This combination enabled retrieving interferogram phase, pixel by pixel, an innovation that started the explosion of development that has continued until today.
Phase acquisition was achieved by changing the interference cavity length by λ/4, stopping, capturing a 32 X 32 sampled camera frame, moving another λ/4 step, frame grab…until four camera frames were captured. A simple calculation eliminates the background intensity term and isolates the phase for each pixel. This is commonly called Phase Stepping Interferometry. Phase Stepping was used to minimize errors due to phosphor hysteresis.
TROPEL (CORNING) developed the first commercial computerized Phase Stepping systems. These were vertical laser interferometers that operated in the Twyman-Green and Fizeau mode. Data processing included a 32X32 array data acquisition off a vidicon tube camera.
A few years later Jim Wyant at WYKO introduced Phase Shifting, where a phase was continuously swept and not stepped, improving accuracy and measurement speed. This method was enabled by the use of CCD sensors.
1980’s – The Digital Age
Developments in the 1980’s centered upon improving data acquisition. In-fact data acquisition was the locus of improvements over the next 20 years. ZYGO became the dominant provider of interferometers with TROPEL deciding to concentrate on in-house development supporting ultra-high accuracy metrology and application focused systems (to be discussed later).
Digital Cameras
Digital cameras were now commercially available. The ZYGO Mark III™ had a 100 X 100 pixel array CCD and a home built board level computer with a frame grabber, with data acquired using a 4 frame data acquisition algorithm.
Vidicon Tube and CCD Imager
Software and Computers Enhance Performance
The second half of the 1980’s saw the development of the ZYGO Mark IV™ with a “high-density processor” system with a 256×256 array CID camera. The Mark IV HDP system was based on ZYGO’s own computer, computer operating system and internally developed Basic-like software language that was then scripted into a user interface. The software package allowed for custom scripting which required intensive software support. The software was slow and expensive to develop, difficult to use and quickly out of date.
Zygo® MarkVI Software User Interface
In the 1980’s Wyko Corporation emerged to commercialize the phase shifting microscope and then the Fizeau interferometer. WYKO was innovative regarding data acquisition and software. Based on commercially available computers, operating systems and development software, innovative uses of cameras and phase modulators, WYKO data acquisition systems evolved more quickly than ZYGO.
WYKO’s Innovation enabled the industry to quickly see the value of software to present easy to understand data and also employ algorithms to improve the quality and speed of data analysis.
Wyko 6000 Laser Fizeau Interferometer and software
These innovations include color plots, extended analysis in MTF, PSF, and Fourier based analysis that pushed the industry forward.
This competitive pressure drove ZYGO to develop MetroPro™ the program which became the industry standard software for the next 25 years. MetroPro™ was based on Objective-C an early and quickly obsolete programming language. Yet using the object oriented software gave MetroPro™ the flexibility to survive all those years.
The competition between WYKO® and ZYGO® benefited the optics community tremendously as they challenged each other to improve.
MetroPro™ Software
Innovation in the 1980’s
Wavelength Modulated PSI
Phase shifting data acquisition require the phase of the cavity to change. Changing the cavity OPL can be accomplish by slightly changing the wavelength [Gary Sommargren], its commercial application was not fully implemented until 15 years later. (Note: cavity phase can also be modulated via phase modulating the source spectrum, see SCI in the 2000’s)
Vibration Insensitive Interferometry
Two significant inventions that would not become commercially successful until the 2000’s were invented in the 1980’s: Carrier fringe [Takeda, H. Ina and S. Kobayashi] and multi-camera frame simultaneous interferometry [Smythe & Moore]. Both of these enable phase measurement at microsecond rates enabling interferometry in vibrating and turbulent environments.
1990’s – Software and Computers Improve Performance
The Personal Computer revolution of the 1990’s and continuous improvements in semiconductor imaging (CCD’s) were the basis of most improvements in the 1990’s. The Mark II architecture was maintained and repackaged, while faster computers, improving software analysis and higher density cameras were added.
Algorithms
A new concentration on algorithms occurred. It was seen that a robust algorithm could compensate for errors in the data acquisition and environment. New multi-frame algorithms [Creath, Degroot] were created throughout this period.
In tangential fields of speckle interferometry, vibration correction algorithms were being developed that would find their way into Fizeau interferometry after 2000. These so called Vibration Tolerant PSI algorithms make Fizeau Interferometry more accurate in environments where data can be obtained but ripple appears in the data.
High Volume Manufacturing
The growth of high volume manufacture in Asia led to new entrants. The relative expense of WYKO and ZYGO systems positioned them in the market as the R&D and QC standards for wavefront measurement and Fujinon and Olympus emerged as the small aperture interferometers providers for surface and wavefront production measurement.
Molded optics, pioneered at KODAK in the USA in the early 1980’s, led to new consumer cameras and optical data storage devices driving the need for high volume asphere metrology. Interferometers were not able to measure these lenses or molds, leading to rise of stylus profilers from Taylor Hobson and Panasonic. It was not until the early 2000’s that interferometers were developed to measure aspheres.
In the early 1990’s Dr. Michael Küchel, of Carl Zeiss, developed the Direct 100 laser Fizeau, a multi-wavelength optical interferometer with advanced optical architecture and data acquisition based on carrier fringe. Custom electronics acquired data at frame rates. The Direct 100 architecture is still employed today in some non-commercial applications. Phase Shift Technology also introduced a multi-camera interferometer on a custom basis. The expense of these interferometers limited their commercial success.
New Source Modality Discovered
A “White Light Fizeau Interferometer” was created by Professor Schwider in 1997. The light source was a broadband source with spectral content. The unique result was interference fringes a fixed distance from the Fizeau reference surface.
Modern History
It is difficult to determine what are the “landmark” developments without the passage of time. For the last 18 years we will simply review some of the major technology and products introduced to solve a greater range of application via Fizeau interferometry
2000’s – Data Acquisition, Imaging, Illumination, Aspheres and Workstations
Deterministic optical manufacturing drove innovation in the interferometry market. The dominant manufacturing technique up to the 2000’s was pitch polished spheres and flats, which the old Mark II™ could handle. Now, new spot polishing computer controlled machines rendered the capabilities of old style interferometers insufficient. In order to keep pace with the advances in optical manufacturing, optical polishing production had to be capable of the following:
Minimizing image distortion for accurate positioning
Calibrating image size in order to know artifact position
Contain a high resolution optical system in order to detect the mid-spatial frequencies
The ability to produce sharp images all the way to the edge of the image in order to minimize coherent artifacts at the object’s edge
Measure very steep surfaces approaching hemispheres
CNC Polishing Drove the Need for Improved Fizeau Interferometers
Imaging Improvements
In order to accommodate the industry’s new demands, the Mark II type instruments had to be abandoned. Interferometers with fixed magnification and low distortion imaging, calibrated image size and high pixel resolution emerged.
Workstations
Integrated workstations were developed primarily in Germany in order to move interferometers out of the quality control laboratory and next to the polishing equipment. The advantage of a workstation was the efficiency of integrating an interferometer directly into the production process to measure both surface form and radius of curvature easily and occupy as little floor space as possible.
Commercial laser Fizeau workstation
Data Acquisition
Vibration Insensitive Commercially Viable
4D Technology introduced a Simultaneous Phase Measuring Interferometer (SPMI) that was the first commercially successful interferometer of its kind. By combining the TROPEL 4-camera approach onto a single detector, the system became robust and easy to use [Novak et. al.]. The expanded manufacture of large mirrors for space and terrestrial application gave 4D Technology an application to establish their business and become a major player in the interferometry market.
4D Data Acquisition System: 1 Camera with 4 Phases
A different approach to eliminating vibration sensitivity was developed by ESDI [Szwaykowski et.al.], which introduced the concept of a spatially split source using a high coherency laser in a Fizeau interferometer. This allowed for the simultaneous capture of 3 phase-shifted interferograms.
Carrier Fringe data acquisition also became common as simple PC computers became fast enough to acquire and analyze data sets.
Scanning Fizeau Asphere
An asphere measuring interferometer was introduced by ZYGO. This was a scanning Fizeau [Küchel] that built up rings of data as the part scanned along its optical axis to measure each asphere zone. The zones were then combined to map the as much of the surface as could be accessed.
Scanning Fizeau Interferometer for Asphere Measurement
Stitching of Fast Convex Spheres & Aspheres
QED introduced a practical stitching system [Forbes et.al.] to measure steep, approaching hemispherical spheres. Beside more coverage of steep spheres, higher accuracy due to averaging and potentially higher spatial frequencies were being reported.
Light Source
Several modifications to the point source were introduced in the late 1990’s/early 2000’s which attempted to reduce diffraction artifacts caused by dust particles and other imperfections in the optical system of the interferometer. These were based mostly on increasing the size of the source by projecting a pattern using highly coherent light from the laser onto a rotating ground glass. Such sources with a decreased degree of spatial coherency can eliminate coherent patterns produced by diffraction on small particles and can be very effective, especially when such particles are located far away from the imaging plane.
In order to handle measurements of optical components with parallel front and back surfaces, ZYGO introduced a tunable, coherent laser source [Deck] in which the wavelength of light can be swept in a controllable way. This innovation enabled analysis based on a Fourier transformation. Additionally, separate reflections from the front and back surfaces of the sample could be taken in one measurement, which allowed for independent measurements of those surfaces. This method also made it possible to take measurements of the sample optical thickness. This technique is limited to ~1.5 mm optical thickness, limited by the scanning range of lasers. Also the thinner the part the longer the measurement time, up to 60 seconds, making the acquisition vulnerable to environmental vibrations and air turbulence decreasing repeatability of measurements.
Vibration Insensitive/Low Coherence
4D technology introduced a system to solve the long-standing problem of errors caused by vibrations in the machine and testing environment while minimizing coherent artifacts. They used a delay line and a synchronous translation of two components: the reference element and one of the mirrors in the delay line to achieve the vibration-insensitive performance in their model of the Fizeau interferometer. The drawback of such an approach was that it led to complicated architectural design.
Ring Source/Partial Coherence
ZYGO introduced the ring illumination system [ Küchel]. It is similar to a method used by Zeiss [Küchel] in their high performance interferometers. The ring increasingly lowers image artifacts contributions to the measurement the FARTHER the artifact is from image plane. So dust near the launch of the illumination beam is more suppressed than in the reference element. At catseye the ring must be reduced to a spot or no interference is observed due to the wavefront flipping. Similar approaches with a simple enlarged dot illumination are also utilized over shorter optical cavities. The dot could be considered temporally coherent and spatially incoherent.
2010’s – High Resolution Imaging, Low Retrace Errors and Spectral Source
CNC polishing machines require rapid and precise feedback between measurement results and fabrication processes. Ideally, an interferometer should be used in a closed loop as a guiding tool in the polishing operation; these needs drive the requirement for low retrace errors, low image distortion, high spatial resolution and acceptance of large departures from “null” condition.
New Interferometer Designs
The older systems, with Mark II™ legacy 6X zoom optics and intermediate fringe images projected on rotating ground glass disks, are inadequate to support CNC polishing applications. In response, 4D Technology and later ZYGO introduced high pixel count interferometers with better image resolution. These systems have better imaging and higher slope acceptance.
Äpre Instruments took interferometer design a step further with balanced optical designs. The HR interferometers for computer controlled polishing applications and the SR interferometers for General Purpose optical shop testing,
HR-High Resolution
ÄPRE S-Series HR interferometers for computer controlled polishing applications or where the highest image resolution and wavefront slopes are required.
Diffraction limited 2K X 2K spatial resolution (not just pixel count)
<0.1% image distortion
<λ/20 retrace errors at 500 fringes of tilt
Up to 650 fringes of slope across the aperture
SR – Standard Resolution
ÄPRE S-Series SR interferometers are for general purpose optical ship testing. The SR finally replaces the 40-year-old Mark II optical design; outperforming the old design by large measure, without increasing the price to the user.
Diffraction limited 1K x 1K spatial resolution (not just pixel count)
<0.1% image distortion
<λ/20 retrace errors at 250 fringes of tilt
Up to 375 fringes of slope across the aperture
Surface of Interest Isolation
Spectrally Controlled Interferometry (SCI™)
ÄPRE has introduced a practical SCI source [Olszak], 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.
Laser Fizeau compared to SCI Fizeau – 1 cm substate with 250 um step in the middle.
Delay Line Surface Isolation
4D Technologies introduced a light source based on a coupled delay-line to project low coherence fringes. Working in a plano-cavity it can place low coherence fringes a distance from the TF and move them over ~25 mm range. Isolating the surface of interest.
Appendix – Hidden Developments
Throughout the history there have been groups developing interferometers whose performance was never made public due to proprietary or classified project constraints, e.g. Perkin Elmer, ITEK, Zeiss, Nikon, Canon, Tropel, etc. Some of these systems were more advanced than available commercial systems, or even disclosed technology in open publications of the time.
Unfortunately these pioneers are not recognized in the open literature, but they too have significantly advanced the state-of-the-art of interferometry and optical manufacturing.
Fizeau Interferometer to Measure Precision Aspheres
Summary
The Fizeau interferometer has a long history and promising future. Interferometers will continue to evolve as applications and processes drive the need for change and new technologies enable these changes to be implemented.
Contact ÄPRE to discuss your interferometery needs to apply the best source + interferometer to your application.
Note: We welcome your comments or additions to make this history more complete.
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.
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 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 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.
Today’s optics industry demands this level of optimal performance and precision. Read our feature in Laser Focus World to see how you can use SCI to your advantage.
