An extrapolation-based method for improving the accuracy of phase retrieval with the transport of intensity equation

Zixin Zhao; Chen Fan; Jinlei Zhao; Yiying Zhuang; Hangying Zhang; Hong Zhao

doi:10.1117/12.2525786

21 June 2019 An extrapolation-based method for improving the accuracy of phase retrieval with the transport of intensity equation

Zixin Zhao, Chen Fan, Jinlei Zhao, Yiying Zhuang, Hangying Zhang, Hong Zhao

Author Affiliations +

Proceedings Volume 11062, Digital Optical Technologies 2019; 1106220 (2019) https://doi.org/10.1117/12.2525786
Event: SPIE Digital Optical Technologies, 2019, Munich, Germany

Abstract

Transport of Intensity Equation (TIE) is a simple and efficient method for phase retrieval by solving the equation between the intensity axial derivative and phase. In this method, the estimation of the axial derivative of intensity is very crucial. Simply, we use two defocused intensity images to estimate the axial derivative by finite difference method. However, the result is still unsatisfactory even though the optimal defocused distance is adopted. The reason lies in that the intensity’s axial change is not linear in the propagation of light. Simply using the finite difference between the two defocused images will ignore higher order axial derivatives. In other words, the estimation of the axial derivative of intensity will contain nonlinear errors. To solve this problem, we propose an extrapolation-based method to estimate the axial derivative of intensity using multiple intensity images. With Taylor expansion and a series of combination and eliminations on these images, high order terms of axial derivative errors are removed. As a result, the nonlinear errors in estimation of the axial derivative will be reduced. The performance of our proposed method for different types of phases under different illumination conditions is investigated. Compared with normal TIE, our method can obtain a much more accurate phase profile.

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Zixin Zhao, Chen Fan, Jinlei Zhao, Yiying Zhuang, Hangying Zhang, and Hong Zhao "An extrapolation-based method for improving the accuracy of phase retrieval with the transport of intensity equation", Proc. SPIE 11062, Digital Optical Technologies 2019, 1106220 (21 June 2019); https://doi.org/10.1117/12.2525786

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KEYWORDS

Phase retrieval

Error analysis

Finite difference methods

Image analysis

Phase measurement

Photovoltaics

Fluctuations and noise

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