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. 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.
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.
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.
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.
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 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.
A ray tracing method of simulating interferometers from source to detector using standard optical design software is presented. The advantages, disadvantages and limitations of the method are discussed. The method is applied to the analysis of a phase measuring interferometer designed to test the form of cylindrical mechanical parts and the predicted performance is compared with experimental results.