Phase analysis error reduction in the Fourier transform method using a virtual interferogram

• Published in: Optical engineering Vol. 58; no. 8; p. 084103
• Main Authors: Toba, Hidemitsu, Liu, Zhiqiang, Udagawa, Saori, Fujiwara, Naoki, Nakayama, Shigeru, Gemma, Takashi, Takeda, Mitsuo
• Format: Journal Article
• Language: English
• Published: Society of Photo-Optical Instrumentation Engineers 01.08.2019
• Subjects: interferometer; instantaneous measurement; fringe analysis
• ISSN: 0091-3286; 1560-2303
• DOI: 10.1117/1.OE.58.8.084103

We propose a method for reducing artifactual phase errors inherent to the Fourier transform method (FTM) for fringe analysis. The phase obtained by the FTM is subject to ripple errors at the boundary edges of the fringe pattern where fringes become discontinuous. We note that these artifactual phase errors are found to have certain systematic relations to the form of the phase, amplitude, and background intensity distributions, which can be modeled by low-order polynomials, such as Zernike polynomials, in many cases of practical interest. Based on this observation, we estimate the systematic ripple errors by analyzing a virtual interferogram that is numerically created for a fringe model with known phase, amplitude, and background intensity distributions. Starting from a rough initial guess, the virtual interferogram is sequentially improved by an iterative algorithm, and the estimated errors are finally subtracted from the experimental data. We present the results of simulations and experiments that demonstrate the validity of the proposed method.