Interferometry

Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis

[+] Author Affiliations
Kemao Qian

Nanyang Technological University, School of Computer Engineering, Singapore 639798

Seah Hock Soon

Nanyang Technological University, School of Computer Engineering, Singapore 639798

Opt. Eng. 44(7), 075601 (July 13, 2005). doi:10.1117/1.1948107
History: Received May 24, 2004; Revised September 27, 2004; Accepted January 14, 2005; Published July 13, 2005
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The two-dimensional continuous windowed Fourier transform has been shown to be effective for fringe pattern analysis in our previous work. In this paper, we first estimate the sampling intervals, using frame theory, to discretize the transform. Suitable sampling intervals are estimated as 1σx and 1σy, which is verified by simulations. Noise reduction using windowed Fourier frames is then investigated and compared with that using the orthogonal wavelet transform. Due to the coherence of its kernels and fringe patterns and its redundancy, windowed Fourier frames are able to reduce noise more effectively, which is verified by processing both simulated and experimental fringe patterns. The relative errors are reduced by half, in various simulations, from those with orthogonal wavelet filtering.

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© 2005 Society of Photo-Optical Instrumentation Engineers

Citation

Kemao Qian and Seah Hock Soon
"Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis", Opt. Eng. 44(7), 075601 (July 13, 2005). ; http://dx.doi.org/10.1117/1.1948107


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