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Chin. Phys. B, 2021, Vol. 30(8): 084209    DOI: 10.1088/1674-1056/abff2f

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 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
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.
Keywords:  radial shearing interference      chirp Z transform (CZT)      phase retrieval  
Received:  24 March 2021      Revised:  05 May 2021      Accepted manuscript online:  08 May 2021
PACS:  42.25.Hz (Interference)  
  42.30.Kq (Fourier optics)  
  42.30.Rx (Phase retrieval)  
Fund: 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).
Corresponding Authors:  Ya-Xuan Duan     E-mail:

Cite this article: 

Fang Xue(薛芳), Ya-Xuan Duan(段亚轩), Xiao-Yi Chen(陈晓义), Ming Li(李铭), Suo-Chao Yuan(袁索超), and Zheng-Shang Da(达争尚) Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique 2021 Chin. Phys. B 30 084209

[1] Gu N, Huang L, Yang Z, Luo Q and Rao C 2011 Opt. Lett. 36 3693
[2] Dong L, Yang Y, Wang L and Zhuo Y 2007 Appl. Opt. 46 8305
[3] Yang Y, Lu Y, Chen Y, Zhuo Y, Zhang X, Chen B and Qing X 2005 SPIE Proc. 5638 200
[4] Zhang Q and Wu Z 2013 Opt. Lasers Eng. 51 253
[5] Murty M and Shukla R 1973 Appl. Opt. 12 2765
[6] Liu D, Yang Y, Weng J, Zhang X, Chen B and Qin X 2007 Opt. Commun. 275 173
[7] Chen Y, Zeng S and Xu M 2018 SPIE Proc. 10815 108151A
[8] Kohno T, Matsumoto D, Yazawa T and Uda Y 1997 SPIE Proc. 3173 280
[9] Edwards C B, Lee P and Tatarakis M 1995 SPIE Proc. 2375 254
[10] Pu H, Li D, Luo P and Zhang C 2020 Opto-Electronic Engineering 47 190390 (in Chinese)
[11] Mochida S, Shinomura M, Hirakawa T, Fukuda T, Awatsuji Y Nishio K and Matoba O 2018 SPIE Proc. 10711 1071114
[12] Debnath S K and Park Y K 2011 Opt. Lett. 36 4677
[13] Toto-Arellano N I, Rodriguez-Zurita G, Meneses-Fabian C and Vázquez-Castillo J F 2009 J. Opt. A: Pure Appl. Opt. 11 045704
[14] Rao K R, Kim D N and Hwang J J 2013 Fast Fourier Transform: Algorithms & Applications pp. 28-95
[15] Hariharan P and Sen D 1961 IOP Science 38 428
[16] Wang Y, Da Z 2016 Infrared and Laser Engineering 45 0317001
[17] Guo Y, Chen X, Zhang T 2014 Opt. Lasers Eng. 63 25
[18] Juarez-Salazar R, Guerrero-Sanchez F and Robledo-Sanchez C 2015 Appl. Opt. 54 5364
[19] Li Y, Guo J, Liu L, Wang T and Shao J 2014 J. Mod. Optic. 61 1519
[20] Pan A, Zhou M, Zhang Y, Min J, Lei M and Yao B 2018 Opt. Commun. 430 73
[21] Nascov V and Logofătu P C 2009 Appl. Opt. 48 4310
[22] Ghiglia D C and Pritt M D 1998 Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software p. 500
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