Accuracy verification methodology for computer-generated hologram used for testing a 3.5-meter mirror based on an equivalent element

Abstract

Interferometry with computer-generated holograms (CGHs) is a unique solution for the highly accurate testing of large-aperture aspheric mirrors. However, no direct testing method for quantifying the measurement accuracy of CGHs has been developed. In this study, we developed a methodology for verifying CGH accuracy based on an element that is functionally equivalent to a large-aperture mirror in terms of accuracy verification. The equivalent element decreased the aperture by one or higher orders of magnitude, implying that the mirror could be replaced by a non-CGH technology in a comparison test. In this study, a 281 mm diamond-turned mirror was fabricated as the equivalent element of a 3.5 m aspheric mirror and measured using CGH and LUPHOScan profilometers. Surface error composition and root-mean-square (RMS) density analyses were performed. The methodology verification accuracy of the CGH was 4 nm (RMS) in the low- to mid-frequency bands, with a measured surface accuracy of approximately 10 nm (RMS). This methodology provides a feasible solution for CGH accuracy verification, ensuring high-accuracy and reliable testing of large-aperture aspheric mirrors.

Keywords

• accuracy verification methodology
• computer-generated hologram
• large-aperture mirror testing
• equivalent element