## Abstract

We implement a proposed method for noise-immune phase unwrapping through
the calculation of what may be called wrap regions. The theory of this method
is reformulated and discussed with regard to random wrapping, a phenomenon
that occurs with diffusely reflecting objects if the optical phase change
caused by a deformation is calculated by subtraction of the phases calculated
before and after the deformation. Two methods of eliminating random wrapping
are presented. The algorithm for phase unwrapping is described, and
experimental results are presented.

© 1997 Optical Society of America

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### Equations (9)

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(1)
$$\left|\mathrm{\Delta}\mathrm{Ph}+{\mathrm{\u220a}}_{1}-{\mathrm{\u220a}}_{2}\right|>\mathrm{\pi},$$
(2)
$$\mathrm{\Delta}\mathrm{\Phi}=\mathrm{arctan}\left[\left({d}_{1}{n}_{2}-{n}_{1}{d}_{2}\right)/\left({n}_{1}{n}_{2}+{d}_{1}{d}_{2}\right)\right],$$
(3)
$${\mathrm{\varphi}}_{0}\left(x,y\right)=\mathrm{arctan}\left(n/d\right),$$
(4)
$${\mathrm{\varphi}}_{90}\left(x,y\right)=\mathrm{arctan}\left(d/-n\right),$$
(5)
$${\mathrm{\varphi}}_{180}\left(x,y\right)=\mathrm{arctan}\left(-n/-d\right),$$
(6)
$${\mathrm{\varphi}}_{270}\left(x,y\right)=\mathrm{arctan}\left(-d/n\right),$$
(7)
$${\mathrm{\varphi}}_{90}\left(x,y\right)={\mathrm{wrap}}_{\pm \mathrm{\pi}}\left[{\mathrm{\varphi}}_{0}\left(x,y\right)+\mathrm{\pi}/2\right],$$
(8)
$${\mathrm{\varphi}}_{180}\left(x,y\right)={\mathrm{wrap}}_{\pm \mathrm{\pi}}\left[{\mathrm{\varphi}}_{0}\left(x,y\right)+\mathrm{\pi}\right],$$
(9)
$${\mathrm{\varphi}}_{270}\left(x,y\right)={\mathrm{wrap}}_{\pm \mathrm{\pi}}\left[{\mathrm{\varphi}}_{0}\left(x,y\right)+3\mathrm{\pi}/2\right],$$