Recent advances in polishing and metrology have addressed many of the challenges in the fabrication and metrology of freeform surfaces, and the manufacture of these surfaces is possible today. However, achieving the form and mid-spatial frequency (MSF) specifications that are typical of visible imaging systems remains a challenge. Interferometric metrology for freeform surfaces is thus highly desirable for such applications, but the capability is currently quite limited for freeforms. In this paper, we provide preliminary results that demonstrate accurate, high-resolution measurements of freeform surfaces using prototype software on QED’s ASI™ (Aspheric Stitching Interferometer).
Aspheric surfaces can provide substantial improvements to optical designs, but they can also be difficult to manufacture cost-effectively. Asphere metrology contributes significantly to this difficulty, especially for high-precision aspheric surfaces. With the advent of computer-controlled fabrication machinery, optical surface quality is chiefly limited by the ability to measure it. Consequently, understanding the uncertainty of surface measurements is of great importance for determining what optical surface quality can be achieved.
We measured sample aspheres using multiple techniques: profilometry, null interferometry, and subaperture stitching. We also obtained repeatability and reproducibility (R&R) measurement data by retesting the same aspheres under various conditions. We highlight some of the details associated with the different measurement techniques, especially efforts to reduce bias in the null tests via calibration. We compare and contrast the measurement results, and obtain an empirical view of the measurement uncertainty of the different techniques. We found fair agreement in overall surface form among the methods, but meaningful differences in reproducibility and mid-spatial frequency performance.
As applications for freeform optics continue to grow, the need for high-precision metrology is becoming more of a necessity. Currently, coordinate measuring machines (CMM) that implement touch probes or optical probes can measure the widest ranges of shapes of freeform optics, but these measurement solutions often lack sufficient lateral resolution and accuracy. Subaperture stitching interferometry (SSI™) extends traditional Fizeau interferometry to provide accurate, high-resolution measurements of flats, spheres, and aspheres, and development is currently on-going to enable measurements of freeform surfaces. We will present recent freeform metrology results, including repeatability and cross-test data. We will also present MRF® polishing results where the stitched data was used as the input “hitmap” to the deterministic polishing process.
To obtain higher spatial resolution interferometric measurements, users of optical shop interferometers generally want to obtain the highest possible number of pixels in the field of view. When the optical surface being tested does not fill the interferometer’s field of view, zoom optics in the viewing system can provide a convenient means to fill the detector. Some users employ zoom to measure subapertures of a larger optical surface to observe mid-spatial frequency (MSF) features that may not be seen in a full aperture test. While the zoom obviously enables the detector to be filled, its capability to increase the MSF measurement performance of the instrument is more difficult to assess.
To investigate how zoom affects the MSF measurement capability, we measured a spherical surface with significant MSF content over a range of lateral magnifications. Two methods were used to obtain equivalent lateral magnifications: zoom and changing the transmission sphere. Differences in the relative MSF content were observed between the two methods. For further comparison, the same surface was measured with the same transmission spheres on a different interferometer with a fixed magnification coherent viewing system. We report on differences observed in measured MSF content between the two interferometers.
Surfaces are commonly specified with peak to valley (PV) and root-mean-square (rms) requirements for surface form and roughness, describing surface quality with a few simple numbers. These specs ignore lateral feature sizes between form and roughness (so-called mid-spatial frequencies, or MSFs), however, making them inadequate for many modern optics fabricated with advanced technologies. Specifications sensitive to the lateral feature size, such as such as slope or power-spectral density (PSD), are increasingly employed to fill this void. Having a detailed view of the surface error as a function of lateral feature size can drive fabrication decisions. For example, a large aperture tool tends to correct small features well but performs less well on large features; while subaperture tools tend to do the opposite.
Therefore after each fabrication step we want to know how the surface features at different lateral sizes evolved, so that we can optimize the choice of the next fabrication step. A spec like PSD often doesn’t inform the fabricator whether it’s failing because of a localized error (such as edge roll), continuous texture, or an artifact of metrology or computation. So while it may indicate the need for additional fabrication steps, it is not ideal for guiding specifically which fabrication step ought to be undertaken next. We have developed analyses to help determine what surface characteristics are failing spec, and thus optimize the next fabrication step. Finally, we demonstrate an example of how we have applied these techniques to fabricate parts with demanding slope and MSF specifications.
Aspheric surfaces provide significant benefits to an optical design. Unfortunately, aspheres are usually more difficult to fabricate than spherical surfaces, making the choice of whether and when to use aspheres in a design less obvious. Much of the difficulty comes from obtaining aspheric measurements with comparable quality and simplicity to spherical measurements. Subaperture stitching can provide a flexible and effective test for many aspheric shapes, enabling more cost-effective manufacture of high-precision aspheres. To take full advantage of this flexible testing capability, however, the designer must know what the limitations of the measurement are, so that the asphere designs can be optimized for both performance and manufacturability. In practice, this can be quite difficult, as instrument capabilities are difficult to quantify absolutely, and standard asphere polynomial coefficients are difficult to interpret. The slope-orthogonal “Q” polynomial representation for an aspheric surface is ideal for constraining the slope departure of aspheres. We present a method of estimating whether an asphere described by Q polynomials is measurable by QED Technologies’ SSI-A system. This estimation function quickly computes the testability from the asphere’s prescription (Q polynomial coefficients, radius of curvature, and aperture size), and is thus suitable for employing in lens design merit functions. We compare the estimates against actual SSI-A lattices. Finally, we explore the speed and utility of the method in a lens design study.
Arithmetic averaging of interferometric phase measurements is a well-established method for reducing the effects of time varying disturbances, such as air turbulence and vibration. Calculating a map of the standard deviation for each pixel in the average map can provide a useful estimate of its variability. However, phase maps of complex and/or high density fringe fields frequently contain defects that severely impair the effectiveness of simple phase averaging and bias the variability estimate. These defects include large or small-area phase unwrapping artifacts, large alignment components, and voids that change in number, location, or size. Inclusion of a single phase map with a large area defect into the average is usually sufficient to spoil the entire result. Small-area phase unwrapping and void defects may not render the average map metrologically useless, but they pessimistically bias the variance estimate for the overwhelming majority of the data. We present an algorithm that obtains phase average and variance estimates that are robust against both large and small-area phase defects. It identifies and rejects phase maps containing large area voids or unwrapping artifacts. It also identifies and prunes the unreliable areas of otherwise useful phase maps, and removes the effect of alignment drift from the variance estimate. The algorithm has several run-time adjustable parameters to adjust the rejection criteria for bad data. However, a single nominal setting has been effective over a wide range of conditions. This enhanced averaging algorithm can be efficiently integrated with the phase map acquisition process to minimize the number of phase samples required to approach the practical noise floor of the metrology environment.
Aspheric surfaces can provide significant benefits to optical systems, but manufacturing high-precision aspheric surfaces
is often limited by the availability of surface metrology. The lack of 3D surface data required to drive aspheric
manufacturing equipment can create risk and unwanted variation in the manufacturing process. One typical approach to
gathering this 3D data is using dedicated null correction optics in addition to the interferometer itself. However, the
cost, lead time, inflexibility, and calibration difficulty of such null optics makes interferometric aspheric testing a far less
attractive solution than the relatively simple spherical test. Subaperture stitching interferometry was originally developed
to allow for the full-aperture 3D measurement of large-aperture spheres and flats using commercially available
interferometers and transmission elements1, 2, 3 The method was then extended to the measurement of mild aspheric
surfaces, by exploiting the local best-fitting and magnification of the high density fringe patterns associated with nonnull
interferometry.4 Subaperture stitching interferometry was then extended by an order of magnitude through the use
of a Variable Optical Null (VON) that allowed the measurement of high-departure aspheres. The automated VON has an
optical system with a range of motion control that generates an optical wavefront that closely matches the surface of the
asphere for each subaperture. The residual wavefront error is measured with a standard interferometer, and the fullaperture
surface profile of the asphere is reconstructed using advanced stitching algorithms. This method allows for the
accurate measurement of aspheres with more than 1000 waves of departure from best-fit sphere, without the use of
dedicated null lenses.
Aspheric surfaces can provide significant benefits to optical systems, but manufacturing high-precision
aspheric surfaces is often limited by the availability of surface metrology. Traditionally, aspheric measurements have
required dedicated null correction optics, but the cost, lead time, inflexibility, and calibration difficulty of null optics
make aspheres less attractive. In the past three years, we have developed the Subaperture Stitching Interferometer for
Aspheres (SSI-A®) to help address this limitation, providing flexible aspheric measurement capability up to 200 waves
of aspheric departure from best-fit sphere.
Some aspheres, however, have hundreds or even thousands of waves of departure. We have recently
developed Variable Optical Null (VONTM) technology that can null much of the aspheric departure in a subaperture. The
VON is automatically reconfigurable and is adjusted to nearly null each specific subaperture of an asphere. The VON
provides a significant boost in aspheric measurement capability, enabling aspheres with up to 1000 waves of departure
to be measured, without the use of null optics that are dedicated to each asphere prescription. We outline the basic
principles of subaperture stitching and the Variable Optical Null, demonstrate the extended capability provided by the
VON, and present measurement results from our new Aspheric Stitching Interferometer (ASITM).
Traditionally, the most accurate measurements of aspheric surfaces have relied on interferometric null tests. These
usually require "null correction" optics, which often take significant time and expense to design and fabricate, and are
specific to a particular asphere prescription. Alignment and calibration of the null correction optics can also be quite
difficult. Thus there is a significant benefit to a flexible, accurate, "operator-friendly" alternative to the null test.
Testing aspheres without null correction (using a spherical wavefront) has been very limited. A typical interferometer
can acquire only a few micrometers of fourth-order aspheric departure before the interference fringes become too dense
to resolve. Other "non-null" issues include accounting for the part's aspheric shape and optical aberrations of the
interferometer. QED's SSI-ATM addresses these limitations, allowing a standard Subaperture Stitching Interferometer
(SSI®) to automatically measure mild aspheric surfaces. The basic principles of how subaperture stitching enhances
asphere capability are reviewed. Furthermore, SSI-A measurements from real aspheres are presented, along with null test measurements where available.
Long measurement times can be a bottleneck in an optics production environment. Ideally the measurement time will be
quicker than polishing times. Large aperture and high precision parts, however, tend toward slower measurement times.
Additionally, such parts usually need dedicated and expensive test setups. In 2004, QED Technologies introduced the
Subaperture Stitching Interferometer (SSI®) to automatically stitch spherical surfaces (including hemispheres) up to 280
mm. The system also reduces measurement uncertainty with in-line calibration of systematic errors.
With stitching, measurement time is a variable that can impact measurement uncertainty. The user can control such
parameters as lattice design, systematic error calibration, and acquisition speed to optimally balance measurement speed
and quality. We empirically demonstrate the trade-offs between measurement uncertainty and cycle time on the SSI.
Interferometric tests of aspheres have traditionally relied on so-called "null correctors". These usually require significant time and expense to design and fabricate, and are specific to a particular asphere prescription. What's more, they are tedious to align and calibrate. Aspheres can also be tested without null correction (using a spherical wavefront), but such capability is extremely limited. A typical interferometer can acquire only a few micrometers of fourth-order aspheric departure due to high-density interference fringes. Furthermore, standard software packages do not compensate for the impact upon a non-null measurement of (i) the part's aspheric shape or (ii) the interferometer's optical aberrations. While fringe density and asphere compensation severely limit the practical utility of a non-null asphere measurement, subaperture stitching can directly address these issues. In 2004, QED Technologies introduced the Subaperture Stitching Interferometer (SSI(R)) to automatically stitch spherical surfaces (including hemispheres). The system also boosts accuracy with in-line calibration of systematic errors. We have recently added aspheric capability, extending non-null aspheric test capability by an order of magnitude or more. As demonstrated in the past on annular zones of nearly nulled data, subaperture stitching can extend the testable aspheric departure. We present a more generally applicable and robust method of stitching non-null aspheric phase measurements. By exploiting novel compensation schemes and in-line system error calibration, our subaperture stitching system can provide significantly better accuracy and increased testable aspheric departure over an unstitched non-null test. Examples of stitched non-null tests are analyzed in this paper, and cross-tested against corresponding null tests.
The fabrication and metrology of astronomical optics are very demanding tasks. In particular, the large sizes needed for
astronomical optics and mirrors present significant manufacturing challenges. One of the long-lead aspects (and primary
cost drivers) of this process has traditionally been the final polishing and metrology steps. Furthermore, traditional
polishing becomes increasingly difficult if the optics are aspheric and/or lightweight.
QED Technologies (QED(r)) has developed two novel technologies that have had a significant impact on the production
of precision optics. Magnetorheological Finishing (MRF(r)) is a deterministic, production proven, sub-aperture polishing
process that can enable significant reductions in cost and lead-time in the production of large optics. MRF routinely
achieves surface figure accuracy of better than 30 nm peak-to-valley (better than 5 nm rms) and microroughness better
than 1 nm rms on a variety of glasses, glass ceramics and ceramic materials. Unique characteristics of MRF such as a
comparatively high, stable removal rate, the conformal nature of the sub-aperture tool and a shear-mode material
removal mechanism give it advantages in finishing large and lightweight optics. QED has, for instance, developed the
Q22-950F MRF platform which is capable of finishing meter-class optics and the fundamental technology is scalable to
even larger apertures. Using MRF for large optics is ideally partnered by a flexible metrology system that provides full
aperture metrology of the surface to be finished. A method that provides significant advantages for mirror manufacturing
is to characterize the full surface by stitching an array of sub-aperture measurements. Such a technique inherently
enables the testing of larger apertures with higher resolution and typically higher accuracy. Furthermore, stitching lends
itself to a greater range of optical surfaces that can be measured in a single setup. QED's Subaperture Stitching
Interferometer (SSI(r)) complements MRF by extending the effective aperture, accuracy, resolution, and dynamic range of
a standard phase-shifting interferometer. This paper will describe these novel approaches to large optics finishing, and
present a variety of examples.
Subaperture polishing technologies have radically changed the landscape of precision optics manufacturing and enabled the production of higher precision optics with increasingly difficult figure requirements. However, metrology is a critical piece of the optics fabrication process, and the dependence on interferometry is especially acute for computer-controlled, deterministic finishing. Without accurate full-aperture metrology, figure correction using subaperture polishing technologies would not be possible. QED Technologies has developed the Subaperture Stitching Interferometer (SSI) that extends the effective aperture and dynamic range of a phase measuring interferometer. The SSI's novel developments in software and hardware improve the capacity and accuracy of traditional interferometers, overcoming many of the limitations previously faced. The SSI performs high-accuracy automated measurements of spheres, flats, and mild aspheres up to 200 mm in diameter by stitching subaperture data. The system combines a six-axis precision workstation, a commercial Fizeau interferometer of 4" or 6" aperture, and dedicated software. QED's software automates the measurement design, data acquisition, and mathematical reconstruction of the full-aperture phase map. The stitching algorithm incorporates a general framework for compensating several types of errors introduced by the interferometer and stage mechanics. These include positioning errors, viewing system distortion, the system reference wave error, etc. The SSI has been proven to deliver the accurate and flexible metrology that is vital to precision optics fabrication. This paper will briefly review the capabilities of the SSI as a production-ready, metrology system that enables costeffective manufacturing of precision optical surfaces.
Interferometers are often used to measure optical surfaces and systems. The accuracy of such measurements is often limited by the ability to calibrate systematic errors such as reference wave and image distortion. Standard techniques for calibrating reference wave include the two-sphere and random-ball test. QED Technologies® (QED) recently introduced a Subaperture Stitching Interferometer (SSI®) that has the integrated ability to perform reference wave calibration. By measuring an optical surface in multiple locations, the stitching algorithm has the ability to compensate for reference wave and imaging distortion. Each of the three reference wave calibration methods has its own limitations that ultimately affect the accuracy of the measurement. The merits of each technique for reference wave calibration are reviewed and analyzed. By using the SSI-computed estimate and the random-ball test in tandem, a composite method for calibrating reference wave error is shown to combine the benefits of both individual techniques. The stitching process also calibrates for distortion, and plots are shown for different transmission optics. Measurements with and without distortion compensation are shown, and the residual difference is compared to theoretical predictions.
Many defense systems have a critical need for high-precision, complex optics. However, fabrication of high quality, advanced optics is often seriously hampered by the lack of accurate and affordable metrology. QED's Subaperture Stitching Interferometer (SSI®) provides a breakthrough technology, enabling the automatic capture of precise metrology data for large and/or strongly curved (concave and convex) parts.
QED’s SSI complements next-generation finishing technologies, such as Magnetorheological Finishing (MRF®), by extending the effective aperture, accuracy and dynamic range of a phase-shifting interferometer. This workstation performs automated sub-aperture stitching measurements of spheres, flats, and mild aspheres. It combines a six-axis precision stage system, a commercial Fizeau interferometer, and specially developed software that automates measurement design, data acquisition, and the reconstruction of the full-aperture figure error map. Aside from the correction of sub-aperture placement errors (such as tilts, optical power, and registration effects), our software also accounts for reference-wave error, distortion and other aberrations in the interferometer’s imaging optics. The SSI can automatically measure the full aperture of high numerical aperture surfaces (such as domes) to interferometric accuracy.
The SSI extends the usability of a phase measuring interferometer and allows users with minimal training to produce full-aperture measurements of otherwise untestable parts. Work continues to extend this technology to measure aspheric shapes without the use of dedicated null optics. This SSI technology will be described, sample measurement results shown, and various manufacturing applications discussed.
Optical surfaces are routinely measured using phase-shifting interferometry. The fringe imaging and other interferometer optics introduce distortion into the measurements. Distortion causes a change in magnification as a function of field position, and is often not quantified and calibrated during measurements of optical surfaces. When calculating the figure of an optical surface, systematic errors such as distortion will ultimately limit the accuracy of the measurement. We present a method for improving the accuracy in interferometric measurements using subaperture stitching interferometry. QED's Subaperture Stitching Interferometer (SSI®) is a six-axis computer-controlled workstation that incorporates a standard Fizeau interferometer with our own stitching algorithms. The SSI is a commercially available product that automatically performs inline calibration of systematic errors such as reference wave and distortion. By measuring an optical surface in multiple orientations both on and off-axis, our stitching algorithms are shown to have the ability to measure the distortion (and other systematic errors) in an interferometer, and compensate for these errors automatically. Using the compensators obtained from stitched measurements, distortion values are calculated and plots are shown for several different transmission optics. Theoretical simulations displaying the effects of distortion on surface metrology are shown. Measurements are taken with and without distortion compensators, and the residual difference is analyzed.
Subaperture stitching is a well-known technique for extending the effective aperture range of phase measuring interferometers. In the past, stitching has successfully been applied to improve the lateral coverage and/or resolution of plano interferometers (including interference microscopes). More recently, QED Technologies has developed a subaperture stitching interferometer (SSI®) for automatic stitching of spherical surfaces, including hemispheres. But stitching can also extend the amount of aspheric departure that can be measured in a non-null test.
Conventional interferometers have some capability to measure mild aspheric surfaces without null correction. The interference fringe resolution of the camera limits the asphericity that can be measured, while the difficulty in inferring the surface form from the measured phase degrades accuracy. Therefore, commercially available interferometers can only measure a few micrometers of fourth-order aspheric departure. Furthermore, standard measurement software does not compensate for the aspheric shape or for the interferometer imaging errors present in a non-null measurement. As a result, non-null aspheric measurements are more difficult, and less accurate, than a spherical null test. Examples are presented in this paper that illustrate these issues. Subaperture stitching can extend the testable aspheric departure of a non-null test. This has been demonstrated in the past on annular zones of near-null data. We present a more generally applicable and robust method of stitching non-null phase data, which can provide better accuracy and increased testable aspheric departure over an unstitched test.
Magneto-rheological finishing (MRF) is a deterministic figuring process capable of quickly achieving extreme surface accuracies. The commercially available Q22 has been instrumental in the manufacture of DUV lithography optics to better than 30 nm P-V figure and 1.0 nm rms microroughness. The requirements for EUV optics, photomask substrates, and silicon-on-insulator (SOI) wafers, however, have taken "extreme accuracy" to new levels. Surface quality is specified over a broad range of spatial frequencies, and allowable error magnitudes shrink ever smaller. These specifications expose some limitations of sub-aperture tool technologies. MRF capabilities, recent developments, and future system improvements that address these concerns are described. We present polishing results on photomasks that pass flatness requirements until year 2010. We further demonstrate extreme precision figure correction capability on SOI wafers, achieving thickness uniformity of better than 2 nm PV and 0.3 nm rms.
Subaperture stitching is a well-known technique for extending the effective aperture and dynamic range of phase measuring interferometers. Several commercially available instruments can automatically stitch flat surfaces, but practical solutions for stitching spherical and aspherical surfaces are inherently more complex. We have developed an interferometer workstation that can perform high-accuracy automated subaperture stitching of spheres, flats, and mild aspheres up to 200 mm in diameter. The workstation combines a six-axis precision stage system, a commercial Fizeau interferometer of 4” or 6” aperture, and a specially developed software package that automates measurement design, subaperture data acquisition, and the mathematical reconstruction of a full-aperture phase map. The stitching algorithm incorporates a general constrained optimization framework for compensating for several types of errors introduced by the interferometer optics and stage mechanics. These include positioning errors, viewing system distortion, and the system reference wave. We present repeatability data, and compare stitched full-aperture measurements made with two different transmission spheres to a calibrated full-aperture measurement. We also demonstrate stitching’s ability to test larger aspheric departures on a 10 mm departure parabola, and compare the preliminary results with a full-aperture null test.
Despite advances in various metrology tools, interferometry remains the method of choice for measurements of optical surfaces. Fizeau interferometers can achieve precisions of X/100 PV (and better) with proper environmental control. The quality of the reference surface, however, usually limits the uncalibrated accuracy to merely X/10 PV or so. Various methods have been developed for "absolute" (unbiased) surface testing, including the N-position, 3- flat, 2-sphere, and random average tests. The basic principle of these tests is that the reference wave error remains invariant when the part is moved. These tests as a rule require multiple parts and/or measurements at different positions. Sub-aperture stitching requires measurements at multiple positions, and thus in principle can measure reference wave error. QED's stitching algorithm exploits this possibility to produce a measurement of the reference surface along with the stitched full-aperture phase. The precision mechanics of QED's stitching workstation make it an excellent platform for performing conventional reference wave calibrations as well. Results obtained from the QED stitching algorithm are compared with other calibration methods performed on the same workstation. The mean results and uncertainties of the various methods are evaluated, and limitations discussed.
The ease of manufacture and testing spherical optical surfaces has made them the default choice for optical systems. Optical designs could greatly benefit form aspheric surfaces; the use of aspherics for projection photolithography in particular puts increasingly greater demands on optical manufacturing. Extreme UV (EUV) lithography requires all reflective elements, some of which will likely be strong aspheres. Modeling software and manufacturing have outpaced aspheric metrology, and we must be able to measure an optical component to have any hope of fabricating it. We seek to extend the dynamic range of optical interferometry to include aspheric surface metrology. We employ two wavelengths to create a vernier effect, allowing the measurement of larger departures without fundamentally sacrificing measurement accuracy. Such large departures impose more rigorous specifications on the interferometer. We explain the new challenges in the acquisition and interpretation of aspheric surface data, and compare to conventional spherical testing. The interferometer optical components are modeled using OSLO SIX design tools. Preliminary experimental results confirm the theory of operation. Some obstacles to practical implementation were also observed, and will be addressed.
30 August 2007 | San Diego, California, United States
SC1039: Evaluating Aspheres for Manufacturability
This course provides an overview of how aspheric surfaces are designed, manufactured, and measured. The primary goal of this course is to teach how to determine whether a particular aspheric surface design will be difficult to make and/or test. This will facilitate cost/performance trade off discussions between designers, fabricators, and metrologists.
We will begin with a discussion of what an asphere is and how they benefit optical designs. Next we will explain various asphere geometry characteristics, especially how to evaluate local curvature plots. We will also review flaws of the standard polynomial representation, and how the Forbes polynomials can simplify asphere analysis. Then we will discuss how various specifications (such as figure error and local slope) can influence the difficulty of manufacturing an asphere. Optical assembly tolerances, however, are beyond the scope of this course - we will focus on individual elements (lenses / mirrors).
The latter half of the course will focus on the more common technologies used to generate, polish, and/or measure aspheric surfaces (e.g. diamond turning, glass molding, pad polishing, interferometry). We'll give an overview of a few generic manufacturing processes (e.g. generate-polish-measure). Then we'll review the main strengths and weaknesses of each technology in the context of cost-effective asphere manufacturing.
This course provides attendees with a broad overview of optical surface metrology, with a focus on how to choose tools and techniques to support modern optical manufacturing processes. First we will review metrology principles and definitions of measurement capability (e.g. accuracy, lateral resolution, etc.). After establishing this basic language, we will discuss the metrology challenges that modern optical applications present (e.g. greater aperture sizes, improved accuracy specifications, and more complex shapes such as aspheres and free-forms).
We will next compare the capabilities and limitations of various tools for the measurement of figure, mid-spatial frequencies, and finish (e.g. Fizeau interferometers, stylus profilometry, interference microscopes, various null tests for aspheres). Examples of "real" data from some measurement tools will be provided. Finally we will review how to identify measurement performance limitations, and techniques for extending capability such as error calibration, averaging, and subaperture stitching.