Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique  

作　　者：Fang Xue Ya-Xuan Duan Xiao-Yi Chen Ming Li Suo-Chao Yuan Zheng-Shang Da 薛芳;段亚轩;陈晓义;李铭;袁索超;达争尚(The Advanced Optical Instrument Research Department,Xi'an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi'an 710119,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]The Advanced Optical Instrument Research Department,Xi'an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi'an 710119,China [2]University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Chinese Physics B》2021年第8期398-406,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.61705254);the Key Research and Development Program of Shaanxi Province of China(Grant No.2020GY-114).

摘　　要：The transient radial shearing interferometry technique based on fast Fourier transform(FFT)provides a means for the measurement of the wavefront phase of transient light field.However,which factors affect the spatial bandwidth of the wavefront phase measurement of this technology and how to achieve high-precision measurement of the broad-band transient wavefront phase are problems that need to be studied further.To this end,a theoretical model of phase-retrieved bandwidth of radial shearing interferometry is established in this paper.The influence of the spatial carrier frequency and the calculation window on phase-retrieved bandwidth is analyzed,and the optimal carrier frequency and calculation window are obtained.On this basis,a broad-band transient radial shearing interference phase-retrieval method based on chirp Z transform(CZT)is proposed,and the corresponding algorithm is given.Through theoretical simulation,a known phase is used to generate the interferogram and it is retrieved by the traditional method and the proposed method respectively.The residual wavefront RMS of the traditional method is 0.146λ,and it is 0.037λfor the proposed method,which manifests an improvement of accuracy by an order of magnitude.At the same time,different levels of signal-to-noise ratios(SNRs)from 50 dB to 10 dB of the interferogram are simulated,and the RMS of the residual wavefront is from 0.040λto 0.066λ.In terms of experiments,an experimental verification device based on a phase-only spatial light modulator is built,and the known phase on the modulator is retrieved from the actual interferogram.The RMS of the residual wavefront retrieved through FFT is 0.112λ,and it decreases to 0.035λthrough CZT.The experimental results verify the effectiveness of the method proposed in this paper.Furthermore,the method can be used in other types of spatial carrier frequency interference,such as lateral shearing interference,rotational shearing interference,flipping shearing interference,and four-wave shearing interference.

关 键 词：radial shearing interference chirp Z transform(CZT) phase retrieval 

分 类 号：TN761[电子电信—电路与系统]