# Robust Wrapping-free Phase Retrieval Method Based on Weighted Least-square Method

## TL;DR

This paper introduces a robust wrapping-free phase retrieval method that combines Perciante's approach with weighted least-squares to effectively handle phase singularities, noise, and discontinuities in profilometry.

## Contribution

It extends Perciante's wrapping-free phase retrieval by incorporating weighted least-squares and derivative variance correlation mapping to manage complex singularities.

## Key findings

- Successfully handles objects with phase singularities and discontinuities
- Outperforms Perciante's method in noisy and complex scenarios
- Validated through simulations and real experiments

## Abstract

For many profilometry techniques, phase unwrapping is one of the most challenging process. In order to sidestep the phase unwrapping process, Perciante et. al [Appl Opt 2015; 54(10):3018-23] proposed a wrapping-free method based on the direct integration of the spatial derivatives of the patterns to retrieve the phase. But it is only applicable for the case of the phase continuity for the tested object, which means it may fail to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. In view of this problems, a robust wrapping-free phase retrieval method is proposed in this paper, which is based on combined Perciante's method and weighted least-squares method. Two partial derivatives of the desired phase is obtained from the fringe patterns, meanwhile the carrier is eliminated using direct phase difference method. The phase singularities are determined using derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. Results are analyzed and compared with those of Perciante's method, demonstrating that the proposed method can be available for measuring objects with some kinds of singularities sources.

---
Source: https://tomesphere.com/paper/1703.01435