Greg Forbes

An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces

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.

Stitching Interferometry: A Flexible Solution for Surface Metrology

The fabrication of large high-quality optics continues to be a challenge, in part because of the difficulty of measuring extensive surface areas. One alternative is to measure many subapertures of the surface and “stitch” the results together to synthesize a full aperture map.

An Adaptive Simulated Annealing Algorithm for Global Optimization over Continuous Variables

A method is presented for attempting global minimization for a function of continuous variables subject to constraints. The method, calledAdaptive Simulated Annealing (ASA), is distinguished by the fact that the fixed temperature schedules and step generation routines that characterize other implementations are here replaced by heuristic-based methods that effectively eliminate the dependence of the algorithms overall performance on user-specified control parameters. A parallelprocessing version of ASA that gives increased efficiency is presented and applied to two standard problems for illustration and comparison.

High precision metrology of domes and aspheric optics

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. QEDs 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 approaches for asphere polishing and metrology

This paper summarizes some of QED Technologies’ latest developments in the field of high-precision polishing and metrology. Magneto-Rheological Finishing (MRF) is a deterministic sub-aperture polishing process that overcomes many of the fundamental limitations of traditional finishing. MRF has demonstrated the ability to produce optical surfaces with accuracies better than 30 nm peak-to-valley (PV) and surface micro-roughness less than 0.5 nm rms on a wide variety of optical glasses, single crystals, and glass-ceramics. The MR fluid forms a polishing tool that is perfectly conformal and therefore can polish a variety of shapes, including flats, spheres, aspheres, prisms, and cylinders, with either round or rectangular apertures. QED’s Sub-aperture Stitching Interferometer (SSI) complements MRF by extending the effective aperture, accuracy, resolution, 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 map of figure error. 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. By addressing these matters up front, we avoid limitations encountered in earlier stitching work and significantly boost reproducibility beyond that of the integrated interferometer on its own.

Recent advances in sub-aperture approaches to finishing and metrology

This paper summarizes some of latest developments by QED Technologies (QED) in the field of high-precision polishing and metrology. Magneto-Rheological Finishing (MRF) is a deterministic sub-aperture polishing process that overcomes many of the fundamental limitations of traditional finishing. The MR fluid forms a polishing tool that is perfectly conformal and therefore can polish a variety of shapes, including flats, spheres, aspheres, prisms, and cylinders, with round or non-round apertures. Over the past several years, QEDs Q22 family of polishing platforms, based on the MRF process, have demonstrated the ability to produce optical surfaces with accuracies better than 30 nm peak-to-valley (PV) and surface micro-roughness less than 0.5 nm rms on an ever-widening variety of optical glass, single crystal, and glass-ceramic materials. The MRF process facilitates the correction of the transmitted wavefront of single elements and/or entire systems, as well as enabling the inducement of specific desired wavefront characteristics (i.e., other than making surfaces perfectly flat or spherical), which is beneficial for applications such as phase correction or other freeform applications. QEDs Sub-aperture Stitching Interferometer (SSI) complements MRF by extending the effective aperture, accuracy, resolution, 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 map of figure error. Aside from the correction of sub-aperture placement errors (such as tilts, optical power, and registration effects), the SSI software also accounts for reference-wave error, distortion, and other aberrations in the interferometers imaging optics. By addressing these matters upfront, we avoid limitations encountered in earlier stitching work and significantly boost reproducibility beyond that of the integrated interferometer on its own.

Recent Advances in Subaperture Stitching Interferometry

It is well known that stitching can boost the aperture capability. Stitching can also improve the accuracy, lateral resolution, and testable aspheric departure. We demonstrate these improvements on our subaperture stitching interferometer (SSI®).

Design of systems involving easily measurable aspheres

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.

New methods for calibrating systematic errors in interferometric measurements

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.

Calibrating interferometric imaging distortion using subaperture stitching interferometry

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. QEDs 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.