Paul E. Murphy

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.

Interference imaging for aspheric surface testing

Peak-valley accuracy of lambda/20 over a range of 2lambda is not unusual in an interferometric null test. For the larger dynamic ranges of a nonnull test, however, the fringe-imaging optics degrades the accuracy. We classify the errors introduced and analyze them in the context of both general and third-order aberration theory. We can predict the measurement error from known interferometer parameters, and we illustrate this for a single mirror. The errors are tabulated for the specific case of a fourth-order asphere with 100 mum of sag. We show that the third-order approximation is comparable with exact ray-trace results for this case.

Measurement and calibration of interferometric imaging aberrations

Phase-shifting interferometry is the standard method for testing figure error on optical surfaces. Instruments measuring spheres and flats are readily available, but the accurate measurement of aspheres requires null correction. One problem with the general (nonull) testing of aspheres is the loss of common path. Systematic errors are introduced into the measurement by the fringe imaging optics. The sources and types of error are reviewed, as well as their effect on a wave-front measurement. These nonnull errors are predicted generally, with third-order analytic expressions derived for a tilted or a defocused test surface. An interferometer is built to test the expressions. The imaging system is a single lens, nominally image telecentric. Measurements are performed on a test surface defocused from -5 to 5 mm. The resulting measurement bias is shown to be in good agreement with third-order aberration theory predictions.

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.

Cost-effective subaperture approaches to finishing and testing astronomical optics

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. QEDs 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.

Measurement of high-departure aspheric surfaces using subaperture stitching with variable null optics

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).

Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VON)

Aspheric surfaces are proven to provide significant benefits to a wide variety of optical systems, but the ability to produce high-precision aspheric surfaces has historically been limited by the ability (or lack thereof) to measure them. Traditionally, aspheric measurements have required dedicated null optics, but the cost, lead time, and calibration difficulty of using null optics has made the use of aspheres more challenging and less attractive. In the past three years, QED has developed the Subaperture Stitching Interferometer for Aspheres (SSI-A®) to help address this limitation, providing flexible aspheric measurement capability of up to 200 waves of aspheric departure from best-fit sphere. Some aspheres, however, have thousands of waves of departure. We have recently developed Variable Optical Null (VON) technology that can null much of the aspheric departure in a subaperture. The VON is automatically configurable and is adjusted to nearly null each specific subaperture of an asphere. This ability to nearly null a local subaperture of an asphere provides a significant boost in aspheric measurement capability, enabling aspheres with up to 1000 waves of departure to be measured, without the use of dedicated null optics. We outline the basic principles of subaperture stitching and VON technology, demonstrate the extended capability provided by the VON, and present measurement results from the new Aspheric Stitching Interferometer (ASI®).

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.