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

A Gaussian radial basis and function technology, applied in optics, optical components, instruments, etc., can solve problems such as the influence of Gaussian radial basis function characterization effect, and achieve the effect of strong surface adaptability, high-precision characterization, and simple calculation.

Active Publication Date: 2021-10-26
BEIJING INSTITUTE OF TECHNOLOGYGY
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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

Method used

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

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Embodiment Construction

[0033] Such as figure 1 As shown, this optical free-form surface characterization method based on Gaussian radial basis function includes the following steps:

[0034] (1) It is clear that the expression of Gaussian radial basis function is formula (1):

[0035]

[0036] Among them, Z(X i ,Y i ) is the sagittal height of the optical free-form surface to be fitted, w j is the coefficient, (X i ,Y i ) is the Cartesian coordinate system coordinates, where ε j is the shape factor of the jth Gaussian radial basis function, (x 0j ,y 0j ) is the center point of the jth Gaussian radial basis function, m is the number of data points to be fitted, and n is the total number of Gaussian radial basis functions;

[0037] When fitting an optical free-form surface, if Z(X i ,Y i ), ε j and (x 0j ,y 0j ) is known, according to formula (1) to get w j , the fitting result is formula (2):

[0038]

[0039] The fitting deviation is formula (3)

[0040] Z error (X i ,Y i )=...

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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...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G02B27/00
CPCG02B27/0012
Inventor 郝群胡摇常旭程雪岷
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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