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Register a new userComputation of the phase step between two-step fringe patterns based on Gram--Schmidt algorithm
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Added by
Victor Flores
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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We present the evaluation of a closed form formula for the calculation of the original step between two randomly shifted fringe patterns. Our proposal extends the Gram--Schmidt orthonormalization algorithm for fringe pattern. Experimentally, the phase shift is introduced by a electro--mechanical devices (such as piezoelectric or moving mounts).The estimation of the actual phase step allows us to improve the phase shifting device calibration. The evaluation consists of three cases that represent different pre-normalization processes: First, we evaluate the accuracy of the method in the orthonormalization process by estimating the test step using synthetic normalized fringe patterns with no background, constant amplitude and different noise levels. Second, we evaluate the formula with a variable amplitude function on the fringe patterns but with no background. Third, we evaluate non-normalized noisy fringe patterns including the comparison of pre-filtering processes such as the Gabor filter banks and the isotropic normalization process, in order to emphasize how they affect in the calculation of the phase step.
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Two steps phase shifting interferometry has been a hot topic in the recent years. We present a comparison study of 12 representative self--tunning algorithms based on two-steps phase shifting interferometry. We evaluate the performance of such algorithms by estimating the phase step of synthetic and experimental fringe patterns using 3 different normalizing processes: Gabor Filters Bank (GFB), Deep Neural Networks (DNNs) and Hilbert Huang Transform (HHT); in order to retrieve the background, the amplitude modulation and noise. We present the variants of state-of-the-art phase step estimation algorithms by using the GFB and DNNs as normalization preprocesses, as well as the use of a robust estimator such as the median to estimate the phase step. We present experimental results comparing the combinations of the normalization processes and the two steps phase shifting algorithms. Our study demonstrates that the quality of the retrieved phase from of two-step interferograms is more dependent of the normalizing process than the phase step estimation method.
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