中国物理B ›› 2021, Vol. 30 ›› Issue (8): 84209-084209.doi: 10.1088/1674-1056/abff2f

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

Fang Xue(薛芳)1,2, Ya-Xuan Duan(段亚轩)1,†, Xiao-Yi Chen(陈晓义)1,2, Ming Li(李铭)1,2, Suo-Chao Yuan(袁索超)1,2, and Zheng-Shang Da(达争尚)1   

  1. 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
  • 收稿日期:2021-03-24 修回日期:2021-05-05 接受日期:2021-05-08 出版日期:2021-07-16 发布日期:2021-07-20
  • 通讯作者: Ya-Xuan Duan E-mail:duanyaxuan@opt.ac.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 61705254) and the Key Research and Development Program of Shaanxi Province of China (Grant No. 2020GY-114).

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

Fang Xue(薛芳)1,2, Ya-Xuan Duan(段亚轩)1,†, Xiao-Yi Chen(陈晓义)1,2, Ming Li(李铭)1,2, Suo-Chao Yuan(袁索超)1,2, and Zheng-Shang Da(达争尚)1   

  1. 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
  • Received:2021-03-24 Revised:2021-05-05 Accepted:2021-05-08 Online:2021-07-16 Published:2021-07-20
  • Contact: Ya-Xuan Duan E-mail:duanyaxuan@opt.ac.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 61705254) and the Key Research and Development Program of Shaanxi Province of China (Grant No. 2020GY-114).

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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 0.037λ for 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 0.040λ to 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 0.035λ through 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

Abstract: 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 0.037λ for 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 0.040λ to 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 0.035λ through 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.

Key words: radial shearing interference, chirp Z transform (CZT), phase retrieval

中图分类号:  (Interference)

  • 42.25.Hz
42.30.Kq (Fourier optics) 42.30.Rx (Phase retrieval)