Interferogram analysis by a modified sinusoid fitting technique

Single‐Image Interferogram Demodulation

“…In this section, we show another class of spatial phase shifting algorithms that do not require to know the carrier frequency. These algorithms are known in the literature as asynchronous or nonlinear phase shifting algorithms [11,[19][20][21].…”

“…After this, Ransom and Kokal [19] and independently Servin and Cuevas [20] presented a three-step nonlinear algorithm to demodulate interferograms with an unknown amount of spatial carrier. The formula presented by Servin and Cuevas [20] is as follows: where the function sign½I 0 ðx; yÞ returns À1 if I 0 ðx; yÞ < 0, otherwise it returns 1.…”

“…19 Demodulation results obtained using the vortex transform. (a) Fizeau interferogram, (b) demodulated phase, (c) photoelastic fringe pattern, (d) and demodulated phase (see text for details).…”

Complex-wave retrieval from a single off-axis hologram

“…21,22 The latter require several interferograms to be recorded, each corresponding to a particular shift of the reference's phase; the phase estimation is done at each pixel by using the pixels at the same location in the other interferograms. In contrast, spatial phase-shifting algorithms 17,[23][24][25][26][27][28] use the neighboring pix- els (on the same line) of a single interferogram to carry out the estimations. The phase to retrieve is assumed to vary slowly and the carrier frequency to be constant.…”

Phase gradients from intensity gradients: a method of spatial carrier fringe pattern analysis

“…Applying non-LTI systems to the fringe pattern is helpful for solving this problem. For example, assuming the local phase variation to be linear within a small region allows deducing SCPS formulas insensitive to linear phase errors [29,30]; Employing a least-squares algorithm enables us estimating the local spatial frequencies of a pixel from its neighborhood and further calculating its phase by use of a two-dimensional (2D) SCPS algorithm [31]; Using an iterative strategy can improve the measurement accuracy of phase map by updating the phase shifts [32]; and in [33], the principal component analysis (PCA) as an effective tool for revealing the internal structure of data is applied for calculating the phase of a point from its neighborhood. In addition, some algorithms combine the spatial operation and spacefrequency analysis.…”