In order to better facilitate the use of aspheres in optical design, metrology systems must become independent from the asphere under test. This requires testing in a non-null sense. Large aspheric departures and steep wavefront slopes must be detected by the metrology instrument. Sub-Nyquist interferometry (SNI) is one such method which has been shown to reconstruct large wavefront departures. Large departures generate high spatial frequency fringes, which must be detected by the interferometer. This requires the use of a sparse array sensor to capture the high spatial frequency fringe data. A custom detector for this purpose has been developed and tested over spatial frequencies up to 400 cycles/mm. Testing in a non-null manner causes the test and reference rays in the interferometer to follow different optical paths through the system. The errors generated by this difference are test part dependent and must be calibrated independently for each test piece. Lens design software can be used to perform reverse optimization of the interferometer and data. This process requires an accurate interferometer model and is sensitive to the relative weighting of the various merit function targets. An iterative reverse optimization process has been developed which eliminates the weighting sensitivity and improves the optimization efficiency. The implementation of reverse optimization in turn generates constraints on the interferometer design. The class of aspheres to be tested also influences the system design. These factors lead to constraints on lens parameters, system apertures, and component verification considerations. A Mach-Zehnder interferometer is designed which satisfies the requirements and is used to build a transmitted wavefront SNI system. Experiments on several test parts were performed to verify the iterative reverse optimization process and to extend the use of SNI to non-rotationally symmetric aspheric wavefronts. Wedge angles were measured to within 1.5 arcseconds, radii of curvature to 0.1% and wavefront departures of up to 200λ were characterized to λ/6 PV and λ/47 rms. The reverse optimization process was shown to successfully remove up to 25 of induced aberration from an aspheric measurement. The results indicate potential for application of the iterative method and its associated design constraints to new interferometers for aspheric testing.
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