Phase-stepping algorithms for synchronous demodulation of nonlinear phase-shifted fringes

TL;DR

This paper develops new phase-stepping algorithms to accurately demodulate nonlinear phase-shifted fringes in interferometry, addressing issues caused by wideband signals and spurious piston artifacts.

Contribution

It introduces a general theory and tailored algorithms for nonlinear phase-stepping in open-loop interferometric fringes, overcoming limitations of linear-phase references.

Findings

Mathematically identified the origin of spurious piston.

Designed nonlinear phase-stepping algorithms for wideband fringes.

Validated the effectiveness of the new algorithms.

Abstract

Standard phase-stepping algorithms (PSAs) estimate the measuring phase of linear carrier temporal-fringes with respect to a linear-reference. Linear-carrier fringes are normally obtained using feedback, closed-loop, optical phase-shifting devices. On the other hand, open-loop, phase-shifting devices, usually give fringe patterns with nonlinear phase-shifts. The Fourier spectrum of linear-carrier fringes is composed by Dirac deltas only. In contrast, nonlinear phase-shifted fringes are wideband, spread-spectrum signals. It is well known that using linear-phase reference PSA to demodulate nonlinear phase-shifted fringes, one obtains an spurious-piston. The problem with this spurious-piston, is that it may wrongly be taken as a real optical thickness. Here we mathematically find the origin of this spurious-piston and design nonlinear phase-stepping PSAs to cope with open-loop, nonlinear phase-shifted interferometric fringes. We give a general theory to tailor nonlinear phase-stepping PSAs to demodulate nonlinear phase-shifted wideband fringes.