Fourier analysis of RGB fringe-projection profilometry and robust phase-demodulation methods against crosstalk distortion

TL;DR

This paper analyzes RGB fringe-projection profilometry using Fourier methods, compares phase-demodulation techniques under different crosstalk levels, and finds squeezing interferometry most robust against severe distortions, supported by simulations and experiments.

Contribution

It introduces a unified approach combining crosstalk compensation and phase-demodulation, and identifies squeezing interferometry as the most robust method for severe crosstalk conditions.

Findings

Squeezing interferometry outperforms other methods under severe crosstalk.

Proposed combined crosstalk compensation and phase-demodulation approach improves efficiency.

Numerical and experimental results validate the robustness of squeezing interferometry.

Abstract

In this paper we apply the frequency transfer function (FTF) formalism to analyze the red, green and blue (RGB) phase-shifting fringe-projection profilometry technique. The phase-shifted fringe patterns in RGB fringe projection are typically corrupted by crosstalk because the sensitivity curves of most projection-recording systems overlap. Crosstalk distortion needs to be compensated in order to obtain high quality measurements. We study phase-demodulation methods for null/mild, moderate, and severe levels of RGB crosstalk. For null/mild crosstalk, we can estimate the searched phase-map using Bruning's 3-step phase-shifting algorithm (PSA). For moderate crosstalk, the RGB recorded data is usually preprocessed before feeding it into Bruning's PSA; alternatively, in this paper we propose a computationally more efficient approach, which combines crosstalk compensation and phase-demodulation into a single process. For severe RGB crosstalk, we expect non-sinusoidal fringes' profiles (distorting harmonics) and significant uncertainties on the crosstalk calibration (which produces pseudo-detuning error). Analyzing these distorting phenomena, we conclude that squeezing interferometry is the most robust demodulation method for RGB fringe-projection techniques. We support our conclusions with numerical simulations and experimental results.