Measurement method of optical uniformity of parallel flat plate based on NUFFT (Nonuniform fast Fourier transform)

Abstract

The invention discloses a measurement method of optical uniformity of parallel flat plate based on NUFFT (Nonuniform fast Fourier transform). firstly, performing phase shifting and sampling on placedparallel flat plate to be detected and interference patterns under a cavity in an Fizeau type wavelength phase shift interferometer; secondly, performing nonuniform fast Fourier transform based on FGG(fast Gaussian grid method) on interference light intensity data of each point of the interference patterns, transforming to a frequency domain for spectral analysis; finally, extracting frequency components corresponding to different interference cavity length, performing inverse Fourier transforms to obtain phase information of the interference patterns, After restoring the phase information tothe wavefront information, calculating to obtain optical uniformity of the parallel flat plate to be detected. By adopting the nonuniform fast Fourier transform spectral analysis method, the measurement method provided by the invention has the advantages that measurement errors caused by nonlinear error during wavelength phase shifting are reduced, the operation is simple, the steps are less, andcan be applied to high precision measurement of optical uniformity of large aperture optical materials.

Description

technical field [0001] The invention relates to the field of optical interferometric measurement, in particular to a method for measuring the optical uniformity of a parallel flat plate based on non-uniform Fourier transform. Background technique [0002] As the most commonly used optical components in optical systems, optical transmissive materials have a significant impact on the optical properties of the entire optical system. Optical uniformity is an important index to evaluate the optical performance of optical transmissive materials, which reflects the inconsistency of the internal refractive index of the same optical material. The optical uniformity of the optical transmission material will directly lead to the change of the transmitted wavefront, change the wave aberration of the optical system, and then make the output of the optical system deviate. Therefore, high-precision optical uniformity measurement has important theoretical and practical significance. [00...

AI Technical Summary

Problems solved by technology

In view of the fact that the oversampling process of the NUFFT algorithm requires a large amount of computation and large physical storage, Kunis proposed in "Nonequispaced fast Fourier transforms without oversampling" (Proceedings in Applied Mathematics and Mechanics, 2008) that the multidimensional Taylor expansion method does not require oversampling The fast algorithm saves a lot of storage space that the oversampling method needs to consume, but it is only limited to some points with better performance. The reason is that the Taylor expansion is an expansion in the local field of the independent variable, and only maintains a high value in a small field. Approximate accuracy

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