Optimal design of tilt carrier frequency computer-generated holograms to measure aspherics

Computer-generated holograms (CGHs) provide an approach to high-precision metrology of aspherics. A CGH is designed under the trade-off among size, mapping distortion, and line spacing. This paper describes an optimal design method based on the parametric model for tilt carrier frequency CGHs placed outside the interferometer focus points. Under the condition of retaining an admissible size and a tolerable mapping distortion, the optimal design method has two advantages: (1) separating the parasitic diffraction orders to improve the contrast of the interferograms and (2) achieving the largest line spacing to minimize sensitivity to fabrication errors. This optimal design method is applicable to common concave aspherical surfaces and illustrated with CGH design examples.