Two-step fringe pattern analysis with a Gabor filter bank

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

“…As described by [16,[31][32][33][34][35], a Gabor Filter (GF) is a complex band-pass filter created from the modulation of a complex sinusoidal function with a Gaussian filter (G). The complex response from this filter is modeled as:…”

“…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.…”

“…Consequently, it is improved the accuracy on the es-timation of the relevant parameters by reducing the overfitting of the ellipse to residual noise. Our method consists of three stages: First, we preprocess the fringe patterns using a Gabor Filter Bank (GFB) in order to remove the background variation, normalize the amplitude modulation and filter-out noise [16]. Second, we calculate the phase step through the two term expression of the ellipse equation by using the Least Square (LS) method; alternatively, by minimizing a cost function based on the Leclerc's potential to define a Robust Estimator (RE) of the coefficients.…”

Two-step phase shifting algorithms: Where are we?

“…For the evaluation of the TS-PSAs presented in section 3, we implemented 3 different normalization methods which are shown in Figure 16. Figures 16b and 16f present the normalized patterns using the Gabor Filters Bank (GFB) proposed in [14,42]. We implemented the filters considering 8 orientations (θ k = kπ/8 for k = 0, 1, 2, .…”

“…Given that the GFBs are capable of delivering the phases (ψ 1 and ψ 2 ) and the magnitudes of the interferograms but with the sign ambiguity [14] , we use these phases as arguments in (5), obtaining: Then, if we simplify the expression by using the trigonometric properties sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y) and…”