Analysis of the phase unwrapping algorithm

TLDR

Digital techniques for high‑resolution imaging through turbulent atmosphere rely on calculating and averaging phase angles, but the inherent 2π ambiguities require continuous phase curves before averaging. The algorithm eliminates 2π phase ambiguities via phase tracking (unwrapping) and then averages Fourier‑transform phase angles to suppress atmospheric effects.

Abstract

Several workers have recently proposed digital techniques for high-resolution imaging through the turbulent atmosphere. The basic concept of these algorithms is to calculate and average phase angles of a series of image Fourier transforms to suppress the unwanted atmospheric effects on image resolution. Since computed phase angles contain the ambiguities of integral multiples of 2 pirad, it is necessary to obtain continuous phase curves without the ambiguities before averaging. This process of eliminating the ambiguities is called phase tracking or unwrapping. A similar problem has been discussed by Oppenheim and Schafer and Tribolet in the context of realization of a certain homomorphic signal processing system.