Robust phase demodulation of interferograms with open or closed fringes

Abstract

Analysis of fringe patterns with partial-field and/or closed fringes is still a challenging problem that requires the development of robust methods. This paper presents a method for fringe pattern analysis with those characteristics. The method is initially introduced as a phase refinement process for computed coarse phases, as those obtained from partial-field patterns with a full-field method for open fringes analysis. Based on the phase refinement method, it is proposed a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is evaluated in real data with no homogeneous illumination components and shows a superior performance thanstateoftheartmethods.

Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching

“…When neither the phase shifts nor the carrier frequencies can be easily introduced, a single closed fringe pattern has to be demodulated, where high robustness and high accuracy are demanded. Various algorithms have been proposed to make the demodulation of a single closed fringe pattern possible, such as the adaptive quadrature filter [2,3], the regularized phase tracker (RPT) [4][5][6][7], the general n-dimensional quadrature transform [8,9], the genetic algorithm based parametric method [10], the phase propagation algorithm [11], the frequency curvature tracker [12], the frequency-guided sequential demodulation (FSD) [13,6], and the tile-based fast algorithm [14]. In this paper, RPT is further investigated due to its simple principle, easy implementation, and high effectiveness.…”

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.…”

“…Note, however, that if this filtering method is used in conjunction with a robust demodulation algorithm, such as in Ref. 4, this residual noise will be inconsequential for the final result, since it will be eliminated in the demodulation phase. In practice, one finds that underestimating max w to as low as 80% of its true value still produces good results, which means that it is safer to underestimate it slightly in the interactive procedure.…”

“…To illustrate how this filtering effectively helps in the demodulation process, we also include the output (wrapped phase) of a state-of-theart robust demodulation procedure, namely, the one in Ref. 4, applied to these filtered and normalized patterns. This method, which is, to our knowledge, the most robust demodulation procedure available for closed-fringe interferograms, starts by estimating the phase in a subregion of the image with relatively high-quality open fringes and iteratively extends this region by using a variational approach, along directions where the fringes are better defined (highestquality regions).…”