Regularized quadrature and phase tracking from a single closed-fringe interferogram

Abstract

A new sequential phase demodulator based on a regularized quadrature and phase tracker system (RQPT) is applied to demodulate two-dimensional fringe patterns. This RQPT system tracks the fringe pattern's quadrature and phase in a sequential way by following the path of the fringes. To make the RQPT system more robust to noise, the modulating phase around a small neighborhood is modeled as a plane and the quadrature of the signal is estimated simultaneously with the fringe's modulating phase. By sequentially calculating the quadrature of the fringe pattern, one obtains a more robust sequential demodulator than was previously possible. This system may be applied to the demodulation of a single interferogram having closed fringes.

Robust phase demodulation of interferograms with open or closed fringes

“…The phase refinement is achieved using the previously presented method [based on (4)]. As it is known, RPT method 9,14,12 may produce a wrong phase due to an unsuccessful normalization of the fringe pattern. In our approach, the grown pixels are chosen such that they minimize the risk of growing a wrong phase.…”

“…This problem has captured the attention of researchers in fringe analysis for the last years, see Refs. [5]- [14]. Although there has been important advances, the performance of the reported methods is seriously reduced if the processed fringe pattern has a wide band, it is not normalized and it is corrupted by noise.…”

“…Since then, this is the underlying idea in closed fringe analysis methods: propagation of frequency signs or entire phase. 6,8,9,12,14 In our method, a quality map leads the propagation path. The needed of a quality map was noted by Villa et al Unfortunately, the performance of the fringe quantization is degraded by noise and spatial variations in background/contrast illumination components.…”

Direct demodulation of closed-fringe interferograms based on active contours

“…Although there have been proposed methods to deal with this problem, such as regularized phase tracking [1], single-interferogram demodulation methods using fringe orientation [2], or a combination of both methods [3], the performance of the reported methods is seriously reduced if the fringe patterns to process have a wideband spatial frequency, they are not normalized, or they are corrupted by noise [4]. Moreover, these methods are of no help when the closed-fringe interferograms have a background and/or contrast term with a spatial frequency similar to the spatial frequency of the equivalent normalized interferogram.…”

Adaptive monogenic filtering and normalization of ESPI fringe patterns

“…The difficulty of this problem stems from the fact that, although the absolute value of the local phase may be estimated from local (linear) operators-e.g., from the normalized intensity gradient-the determination of the phase sign requires tracking the local direction across the image and is therefore a global property. [1][2][3][4] For this reason demodulation algorithms are very sensitive to noise and local contrast variations, since even a small bad region may send the algorithm off track and have disastrous global consequences. This is true even when robust schemes, like the ones in Refs.…”