Problems on design of computer-generated holograms for testing aspheric surfaces: principle and calculation

摘要

Interferometric optical testing using computer-generated hologram (CGH) has provided an approach to highly accurate measurement of aspheric surfaces. While designing the CGH null correctors, we should make them with as small aperture and low spatial frequency as possible, and with no zero slope of phase except at center, for the sake of insuring low risk of substrate figure error and feasibility of fabrication. On the basis of classic optics, a set of equations for calculating the phase function of CGH are obtained. These equations lead us to find the dependence of the aperture and spatial frequency on the axial distance from the tested aspheric surface for the CGH. We also simulate the optical path difference error of the CGH relative to the accuracy of controlling laser spot during fabrication. Meanwhile, we discuss the constraints used to avoid zero slope of phase except at center and give a design result of the CGH for the tested aspheric surface. The results ensure the feasibility of designing a useful CGH to test aspheric surface fundamentally.