## Abstract

An algorithm for phase demodulation of a single interferogram that may contain closed fringes is presented. This algorithm uses the regularized phase-tracker system as a robust phase estimator, together with a new scanning technique that estimates the phase that initially follows the bright zones of the interferogram. The combination of these two elements constitutes a powerful new method, the fringe-follower regularized phase tracker, that makes it possible to correctly demodulate complex, single-image interferograms for which traditional methods fail.

© 2001 Optical Society of America

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### Equations (11)

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(1)
$$I(x,y)=a(x,y)+b(x,y)cos[\varphi (x,y)],$$
(2)
$${\varphi}_{1}(x,y)=\left\{\begin{array}{ll}-\varphi (x,y)+2k\pi & (x,y)\in S\\ \varphi (x,y)& (x,y)\notin S\end{array},\right.$$
(3)
$$cos[\varphi (x,y)+\alpha ]\ne cos[{\varphi}_{1}(x,y)+\alpha ].$$
(4)
$${I}^{\prime}(x,y)\approx cos[\varphi (x,y)].$$
(5)
$$U(x,y)=\sum _{(\u220a,\eta )\u220a({N}_{x,y}\cap P)}\{[{I}^{\prime}(\u220a,\eta )-cosp(x,y,\u220a,\eta ){]}^{2}+\beta [{\varphi}_{0}(\u220a,\eta )-p(x,y,\u220a,\eta ){]}^{2}m(\u220a,\eta )\},$$
(6)
$$p(x,y,\u220a,\eta )={\varphi}_{0}(x,y)+{\omega}_{x}(x,y)(x-\u220a)+{\omega}_{y}(x,y)(y-\eta ),$$
(7)
$${\mathbf{r}}^{k+1}(x,y)={\mathbf{r}}^{k}(x,y)-\mu {\nabla}_{r}U(x,y),$$
(8)
$${\nabla}_{\mathbf{r}}U(x,y)=\left[\frac{\partial U(x,y)}{\partial {\varphi}_{0}(x,y)},\frac{\partial U(x,y)}{\partial {\omega}_{x}(x,y)},\frac{\partial U(x,y)}{\partial {\omega}_{y}(x,y)}\right].$$
(9)
$$U(x,y)=\sum _{(\u220a,\eta )\u220a({N}_{x,y}\cap S)}\{[{I}^{\prime}(\u220a,\eta )-cosp(x,y,\u220a,\eta ){]}^{2}+[{I}^{\prime}(\u220a,\eta )-cos{p}_{1}(x,y,\u220a,\eta ){]}^{2}+\beta [{\varphi}_{0}(\u220a,\eta )-p(x,y,\u220a,\eta ){]}^{2}m(\u220a,\eta )\},$$
(10)
$${p}_{1}(x,y,\u220a,\eta )=p(x,y,\u220a,\eta )+\alpha ,$$
(11)
$${I}_{b}(x,y)=\mathrm{Thresh}[{I}^{\prime}(x,y)**\mathrm{LPF}(x,y)],$$