Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

Kulkarni, Rishikesh; Rastogi, Pramod K.

doi:10.1016/j.optlaseng.2018.05.012

Cited by 17 publications

(10 citation statements)

References 24 publications

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“…On the other hand, Figures 10g and 10h illustrate the normalized patterns using GFB. For these results applied a Winner-Take-All (WTA) strategy for the GFB corresponding to the periods equal to [20,35,45,55] and eight orientations. Since the main problem of the GFB is the detection of low frequencies, we usê…”

Section: Resultsmentioning

confidence: 99%

“…Note that in this ideal case, (20) is fulfilled for all the pixels. In case that the pre-filtering process does not guarantee an effective normalization of the patterns, the scatter set of points (Î add ,Î sub ) lay in an uncentered ellipse.…”

Section: Least Squares Based Slefmentioning

confidence: 99%

“…As mentioned before, due to the tendency of reducing the number of steps to estimate the phase distribution, the two-step algorithms have attracted considerably the attention in the past few years; for these reason, several algorithms have been proposed such as Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22]. Particularly, various algorithms based on the LEF method have been designed to improve the estimation of the phase step and the phase distribution in two-step intertferometry, such as: iterative processes based on the least square technique [23], the use of the Gram-Schmidt orthonormalization to transforms the ellipse into a circle [24], the application of a Hilbert-Huang Transform (HHT) pre-filtering with the LEF algorithm [25] or the computation of the Euclidean distance from the points to the ellipse [26]; just to mention some of the novel techniques.…”

Section: Introductionmentioning

confidence: 99%

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Robust two-step phase estimation using the Simplified Lissajous Ellipse Fitting method with Gabor Filters Bank preprocessing

Flores

Rivera

2020

Optics Communications

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We present the Simplified Lissajous Ellipse Fitting (SLEF) method for the calculation of the random phase step and the phase distribution from two phase-shifted interferograms. We consider interferograms with spatial and temporal dependency of background intensities, amplitude modulations and noise. Given these problems, the use of the Gabor Filters Bank (GFB) allows us to filter-out the noise, normalize the amplitude and eliminate the background. The normalized patterns permit to implement the SLEF algorithm, which is based on reducing the number of estimated coefficients of the ellipse equation, from five terms to only two. Our method consists of three stages. First, we preprocess the interferograms with GFB methodology in order to normalize the fringe patterns. Second, we calculate the phase step by using the proposed SLEF technique and third, we estimate the phase distribution using a two-steps formula. For the calculation of the phase step, we present two alternatives: the use of the Least Squares (LS) method to approximate the values of the coefficients and, in order to improve the LS estimation, a robust estimation based on the Leclerc's potential. The SLEF method's performance is evaluated through synthetic and experimental data to demonstrate its feasibility.

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Section: Resultsmentioning

confidence: 99%

Section: Least Squares Based Slefmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust two-step phase estimation using the Simplified Lissajous Ellipse Fitting method with Gabor Filters Bank preprocessing

Flores

Rivera

2020

Optics Communications

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“…The quadratic phase parameter estimation algorithm for phase demodulation was recently proposed by Kulkarni and Rastogi [15]. This method is formulated to obtain the parameters of a state space formulation by using the extended Kalman filter.…”

Section: Qpp Variabilitymentioning

confidence: 99%

“…The use of this components in the experimental setup can lead to an erroneous step tuning since if the implementation of the arrangement does not include characterized components. This detuning of the phase displacement causes the presence of harmonics in the recovered phase [6], for this reason, the Two-Steps Phase Shifting Algorithms (TS-PSAs) consider that the phase step is unknown and include, implicitly or explicitly, its calculation [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Two-step phase shifting algorithms: Where are we?

Flores

Reyes-Figueroa

Carrillo-Delgado³

et al. 2020

Optics & Laser Technology

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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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Optical Metrology and Optoacoustics Techniques for Nondestructive Evaluation of Materials

Nazarchuk

Muravsky

Kuryliak

2023

Springer Series in Optical Sciences

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Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

Cited by 17 publications

References 24 publications

Robust two-step phase estimation using the Simplified Lissajous Ellipse Fitting method with Gabor Filters Bank preprocessing

Robust two-step phase estimation using the Simplified Lissajous Ellipse Fitting method with Gabor Filters Bank preprocessing

Two-step phase shifting algorithms: Where are we?

Optical Metrology and Optoacoustics Techniques for Nondestructive Evaluation of Materials

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