# Robust Two-Step phase estimation using the Simplified Lissajous Ellipse Fitting method with Gabor Filter Banks preprocessing

## TL;DR

This paper introduces a robust two-step phase estimation method that combines Gabor Filter Banks preprocessing with a simplified ellipse fitting algorithm, effectively handling noise and background variations in interferogram analysis.

## Contribution

The paper proposes a novel simplified ellipse fitting approach integrated with Gabor Filter Banks for improved phase estimation in interferometry, reducing computational complexity and enhancing robustness.

## Key findings

- Effective noise filtering and background normalization with Gabor Filter Banks.
- Accurate phase step estimation using least squares and robust Leclerc's potential methods.
- Validated performance on synthetic and experimental interferogram data.

## Abstract

We present the Simplified Lissajous Ellipse Fitting (SLEF) method for the calculation of the random phase step and the phase distribution from two phase-shifted interferograms. We consider interferograms with spatial and temporal dependency of background intensities, amplitude modulations and noise. Given these problems, the use of the Gabor Filters Bank (GFB) allows us to filter--out the noise, normalize the amplitude and eliminate the background. The normalized patterns permit to implement the SLEF algorithm, which is based on reducing the number of estimated coefficients of the ellipse equation, from five terms to only two. Our method consists of three stages. First, we preprocess the interferograms with GFB methodology in order to normalize the fringe patterns. Second, we calculate the phase step by using the proposed SLEF technique and third, we estimate the phase distribution using a two--steps formula. For the calculation of the phase step, we present two alternatives: the use of the Least Squares (LS) method to approximate the values of the coefficients and, in order to improve the LS estimation, a robust estimation based on the Leclerc's potential. The SLEF method's performance is evaluated through synthetic and experimental data to demonstrate its feasibility.