Error compensation in computer generated hologram-based form testing of aspheres.

Abstract

Computer-generated holograms (CGHs) are used relatively often to test aspheric surfaces in the case of medium and high lot sizes. Until now differently modified measurement setups for optical form testing interferometry have been presented, like subaperture stitching interferometry and scanning interferometry. In contrast, for testing low to medium lot sizes in research and development, a variety of other tactile and nontactile measurement methods have been developed. In the case of CGH-based interferometric form testing, measurement deviations in the region of several tens of nanometers typically occur. Deviations arise especially due to a nonperfect alignment of the asphere relative to the testing wavefront. Therefore, the null test is user- and adjustment-dependent, which results in insufficient repeatability and reproducibility of the form errors. When adjusting a CGH, an operator usually performs a minimization of the spatial frequency of the fringe pattern. An adjustment to the ideal position, however, often cannot be performed with sufficient precision by the operator as the position of minimum spatial fringe density is often not unique, which also depends on the asphere. Thus, the scientific and technical objectives of this paper comprise the development of a simulation-based approach to explain and quantify typical experimental errors due to misalignment of the specimen toward a CGH in an optical form testing measurement system. A further step is the programming of an iterative method to realize a virtual optimized realignment of the system on the basis of Zernike polynomial decomposition, which should allow for the calculation of the measured form for an ideal alignment and thus a careful subtraction of a typical alignment-based form error. To validate the simulation-based findings, a series of systematic experiments is performed with a recently developed hexapod positioning system in order to allow an exact and reproducible positioning of the optical CGH-based setup. Additionally a CGH phase function using an exact geometric model is compared to the other approaches. The phase function is utilized to enhance the overall reliability of the sensitivity functions with regard to alignment errors in interferometric testing.