Methods to determine best-fit sphere for off-axis aspheric surface

Li-xin Zheng; Zheng Zhu

doi:10.1117/12.783644

29 November 2007 Methods to determine best-fit sphere for off-axis aspheric surface

Li-xin Zheng, Zheng Zhu

Proceedings Volume 6722, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Advanced Optical Manufacturing Technologies; 672245 (2007) https://doi.org/10.1117/12.783644
Event: 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Large Mirrors and Telescopes, 2007, Chengdu, China

Abstract

In this paper we present an approach which can calculate the radius R of best-fit sphere in optical replication of off-axis aspheric surface. For regular shape, we choose the marginal points as constraint condition to get the radius R of best-fit sphere, which satisfies the root mean square of asphericity minimal. The aspheric rms under different constraints can be compared on the condition that the optical parameters, such as the paraxial radius R₀ and conic constant k, are same for the parent aspheric surface of the circle, sector and regular hexagon-shaped off-axis aspheric surfaces. Moreover, we used the Golden Section Method and Cyclic Coordinate Method for optimization to solve the rms, and analyze the constraint conditions for the best-fit spheres.

Citation Download Citation

Li-xin Zheng and Zheng Zhu "Methods to determine best-fit sphere for off-axis aspheric surface", Proc. SPIE 6722, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Advanced Optical Manufacturing Technologies, 672245 (29 November 2007); https://doi.org/10.1117/12.783644

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