Solving optimal carrier frequencies of a CGH null compensator through a double-constrained searching method based on iterative ray-tracings

Abstract

Interferometry based on a computer-generated hologram (CGH) null compensator is a general method for high-precision metrology of aspherics. Because the most commonly used CGHs are the Ronchi type with only two quantization steps, tilt and defocus carrier frequencies must always be introduced to separate the disturbing diffraction orders (DDOs). Determining the amount of carrier frequencies is a pivotal but difficult issue in the CGH design process. Previous studies have only drawn qualitative conclusions or obtained some approximate results under specific conditions. This paper proposes a double-constrained searching method based on iterative ray-tracings, which can directly and accurately give the optimal combination of tilt and defocus carrier frequencies, as long as the aspheric under test is a concave one and has an analytical expression. The optimal carrier frequencies solved by the proposed method will minimize the line density of the CGH on the premise of separating all DDOs, which will reduce the cost and difficulty of fabrication as much as possible. The proposed method is almost error-free and holds a clear advantage over the previous methods in terms of versatility. Several typical design examples are presented to verify the feasibility and versatility of the proposed method. Its accuracy is also verified through making comparisons of the ray-tracing results between another method and Zemax models based on these examples.