Windowed Fourier transform for fringe pattern analysis

TLDR

Fringe patterns in optical metrology require demodulation to extract parameters, and time‑frequency analysis using a windowed Fourier transform is employed to determine phase and its derivative. The study aims to extract phase and phase derivatives from phase‑shifted or single‑carrier fringe patterns. Two methods are developed: a filtering approach and a best‑match approach using computer‑generated windowed exponential elements. The methods are shown to be effective through principles and illustrative examples.

Abstract

Fringe patterns in optical metrology systems need to be demodulated to yield the desired parameters. Time-frequency analysis is a useful concept for fringe demodulation, and a windowed Fourier transform is chosen for the determination of phase and phase derivative. Two approaches are developed: the first is based on the concept of filtering the fringe patterns, and the second is based on the best match between the fringe pattern and computer-generated windowed exponential elements. I focus on the extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single carrier fringe pattern. Principles as well as examples are given to show the effectiveness of the proposed methods.