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

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 esti- mated as 1/x and 1/y, which is verified by simulations. Noise reduc- tion 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 or- thogonal wavelet filtering. © 2005 Society of Photo-Optical Instrumentation