Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density

Enhancing single-shot fringe pattern phase demodulation using advanced variational image decomposition

“…Fringes encoding optical phase are regarded as texture. It was shown that VID enables background and noise removal from fringes [22][23][24][25]. We will present a novel contribution corroborating the ability of VID to remove periodic error from the unwrapped phase distribution.…”

“…In the 2D HHT, the 2D empirical mode decomposition (EMD) based techniques (Huang's part of the transform) were successfully employed for fringe pattern pre-filtering [12][13][14][15][16][17]. VID can serve this purpose as well [22][23][24][25]. Residual preprocessing imperfections affect the demodulated phase distribution calculated using the 2D Hilbert spiral transform (HST) [17][18][19][20], however.…”

“…Variational image decomposition is a relatively new method for background and noise removal from fringe patterns [22][23][24][25]. In this method the image is split into three components: the part containing background (structure), the one associated with fringes (texture), and noise.…”

“…Furthermore, the result calculated in each consecutive step should be closer to the correct expected term rather than the one evaluated in the previous step, as long as convergence of the considered algorithm is preserved. In the first version of the variational image decomposition algorithm adapted to the fringe pattern filtration, the number of required steps of the projection operator was one of many parameters chosen by the user [22][23][24][25]. The task was not easy, and the suitable value of the mentioned parameter varies when analyzing different types of fringe patterns.…”

“…In this contribution, without a loss of generality, we focus on phase error reduction in the single-frame phase demodulation techniques exemplified by the HHT [15][16][17]. The novel approach presented deploys variational image decomposition (VID) [22][23][24][25] previously used for fringe pre-filtering. The similarity and difference between fringe and phase filtration will be discussed in section 2.…”