Algebraic solution for phase unwrapping problems in multiwavelength interferometry

Abstract

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX Recent advances in multi-wavelength interferometry techniques (Falaggis et. al. Appl. Opt. 52, 5758-65 (2013)) give new insights to phase unwrapping problems and allow the fringe order information contained in the measured phase to be extracted with low computational effort. This work introduces an algebraic solution to the phase unwrapping problem that allows the direct calculation of the unknown integer fringe order. The procedure resembles beat-wavelength approaches, but provides greater flexibility in choosing the measurement wavelengths, a larger measurement range, and a higher robustness against noise, due to the ability to correct for errors during the calculation.

Absolute phase recovery in structured light illumination systems: Sinusoidal vs. intensity discrete patterns

“…In this work, we show that the ART technique [33] allows obtaining a higher accuracy than current state of the art LUT and CRT techniques for the case of sinusoidal fringe patterns. We demonstrate a successful ART based phase unwrapping using experimental data and present examples of analytical ART solutions for two exemplary sets of integers, i.e.…”

“…In SLI techniques, one seeks to calculate the absolute phase map at the smallest period, or equivalently, the unknown integer fringe order. The development of noise robust phase unwrapping techniques are an on-going field of research, where representative techniques may be based on ART [33], CRT [21], and LUT [26] …”

“…Certainly, irrational valued spatial periods may be used in order to avoid the congruence. Nevertheless, a recently reported phase unwrapping method, the so-called algebraic reconstruction technique (ART) [33] showed that the choice of irrational periods may give an infinite long UMR. However, in presence of noise, only a rational approximation of the ratio of periods determines the performance of the system.…”

“…This determines the maximal order of the rational approximations. Notably, Reference [33] reported an analytical method for mapping a set of phase values to the integer fringe order of the smallest period. This is achieved without using LUTs, and hence, allowing directly calculating the absolute phase map.…”

Phase discontinuity predictions using a machine-learning trained kernel

“…Despite numerous and diverse approaches by workers in the field [10][11][12][13], through the application of a wide variety of techniques [14][15][16][17] to this problem, reliable phase unwrapping remains a key challenging task [18][19][20] within the overall image processing stages required for interferogram analysis [21].…”