Fringe-pattern analysis using a 2-D Fourier transform

TLDR

The 2‑D transform permits better separation of desired information components from unwanted components than a 1‑D transform. The paper refines the Fourier transform fringe‑pattern analysis technique by employing a 2‑D Fourier transform. The authors investigate the accuracy of the refined technique on real data from a system with a nonlinear response function. The study yields simple interferogram‑optimization techniques and a reliable error estimate for retrieved fringe shifts, validated on simulated data.

Abstract

A refinement of the Fourier transform fringe-pattern analysis technique which uses a 2-D Fourier transform is described. The 2-D transform permits better separation of the desired information components from unwanted components than a 1-D transform. The accuracy of the technique when applied to real data recorded by a system with a nonlinear response function is investigated. This leads to simple techniques for optimizing an interferogram for analysis by these Fourier transform methods and to an estimate of the error in the retrieved fringe shifts. This estimate is tested on simulated data and found to be reliable.