Representation Method of Optical Freeform Surface Based on Gaussian Radial Basis Function

Abstract

A characterization method for optical free-form surfaces based on Gaussian radial basis functions is disclosed, by clarifying the expression of Gaussian radial basis functions, obtaining the data point set to be fitted to the optical free-form surface to be fitted, and normalizing the data to be fitted , Calculate the gradient vector according to the normalized data to be fitted, analyze and process the gradient vector, divide the sub-aperture, set the number of Gaussian radial basis function bases, obtain the number of Gaussian radial basis functions in each sub-aperture, and obtain the Gaussian radial basis function The total number of basis functions, the center point of the Gaussian radial basis function uniformly distributed in the sub-aperture, the optimal value range of the coefficient A, the final fitting effect, and the final total number of basis functions are specified, so that complex optical free-form surfaces can be processed High-precision characterization can meet the needs of modern optical system design, processing and testing. This method is simple to calculate, easy to implement, and has strong surface shape adaptability. It is suitable for any caliber and can realize high-precision characterization of optical free-form surfaces.

Description

technical field [0001] The present invention relates to the technical field of optical surface shape fitting, in particular to a characterization method for optical free-form surfaces based on Gaussian radial basis functions, which aims to use Gaussian radial basis functions to characterize free-form surfaces to form a new free-form surface Characterization method. Background technique [0002] Optical free-form surfaces are aspheric surfaces, which refer to optical surfaces that do not have rotational symmetry. The main types of common optical free-form surfaces include continuous polynomial surfaces, off-axis aspheric surfaces, discontinuous surfaces, and fine periodic structures, among which continuous polynomial surfaces and off-axis aspheric surfaces are widely used. Due to the multi-degree-of-freedom characteristics of the optical freeform surface, which can improve the performance of the optical system, simplify the structure of the optical system and reduce the weig...

AI Technical Summary

Problems solved by technology

However, when using it to characterize optical free-form surfaces, the number of Gaussian radial basis functions, the distribution of the center points of Gaussian radial basis functions, and the value of the shape factor corresponding to each Gaussian radial basis function have a greater impact on the representation effect. influences

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