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.
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[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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