Research On Optical Homogeneity Interferometry Of Parallel Plates Based On Nonuniform Fast Fourier Transform

Optical homogeneity is an important parameter of optical transmission materials.The inhomogeneity of optical material will cause the deviation of transmission wavefront,increase the aberration of optical system,and then affect the performance of optical system.Therefore,measuring the optical homogeneity of optical materials precisely is with great importance.Among many methods of measuring optical homogeneity,the interference method is the most accurate one.However,the interference between the front and back surfaces of parallel plates brings great difficulties to the homogeneity measurement.When using the wavelength-tuning interferometer to measure,the interference fringes formed by multiple surfaces can be separated by the Fourier transform algorithm.This method needs to capture a large number of interferograms.However,upon increasing the number of captured interferograms,the wavelength-tuning nonlinearity becomes more pronounced,resulting in the nonlinear change of the phase shifts.When the interferometric intensities are transformed into the frequency domain,the spectrum will spread,and the spectra corresponding to different frequencies are aliased.If the FFT method is used directly in the calculations,this will result in errors in the final wavefront.In this paper,two methods of measuring the optical homogeneity of parallel plates based on nonuniform Fourier transform are proposed for the nonlinear error in the process of wavelength-tuning.In this paper,two methods of measuring the optical homogeneity of parallel plates based on nonuniform Fourier transform are proposed for the nonlinear error in the process of wavelength-tuning.The principle of wavelength-tuning interferometry is firstly researched.Combined with the time-domain Fourier transform algorithm,the multi-surface interferometry technology is analyzed theoretically.Then,to solve the problem of unequal interval sampling in the measurement of optical homogeneity by wavelength tuning,the nonuniform Fourier transform algorithm is used to suppress the phase-shifting error.The principle of fast Gauss gridding method and nonuniform Fourier transform algorithm based on low rank matrix approximation are introduced.At the same time,the process of optical homogeneity measurement is simulated.The simulation results show that the nonuniform Fourier transform algorithm can avoid the phenomenon of spectrum broadening and aliasing of multi-surface interference signals,and get better restoration results.Finally,according to the design of the system,an experimental device is built to measure a square brick.The measurement results are basically consistent with the measurement results of Zygo GPI phase-shifting interferometer,which verifies that the principle of the measurement algorithm proposed in this paper is valid and feasible.