Interferometric testing with computer-generated holograms: aberration balancing method and error analysis

Abstract

When testing aspheric surfaces with a computer-generated hologram, some problems should be considered. In this paper, first, we compare two types of hologram: Lohmann and interference. The phase error in the Lohmann type hologram is estimated, and a method of compensating the error is described. Second, we discuss the relation between the shape of the required wavefront and the number of resolution cells of the hologram. Since testing smaller f number optical elements increases the required number of resolution cells of the hologram, we propose the aberration balancing method to reduce the number of resolution cells. The optimum values of the defocus aberration are calculated. Especially, it is shown that the number of resolution cells in the hologram is capable of being reduced to 25%. Third, we discuss the error due to incorrect hologram size and due to misalignment of the optical system when the aberration balancing method is applied. Finally, an experimental example for testing an aspheric mirror 150 mm in diameter and 300 mm in focal length is given.