Phase retrieval from single interferogram without carrier using Lissajous ellipse fitting technology

Abstract

Phase extraction from single interferogram is of high significance and increasingly interest in optical metrology. In this contribute we propose an advanced Pixel-level Lissajous Ellipse Fitting (APLEF) method to extract the phase from single interferogram without carrier. At each pixel, a Lissajous figure is created by plotting N against D, where N and D are subtractions and additions of intensities of adjacent pixels in a small window. The so created Lissajous figure is already in phase quadrature because of the subtraction and addition process, and the Lissajous Figure is forced to be closed by taking the opposite values of N and D, i.e. –N and -D into account. The closed and in phase quadrature Lissajous Figure is the key point for APLEF to demodulate the single inteferogram without carrier in theoretically. The simulation shows its higher accuracy than existed SPT and Garbusi’s method and the experiments finally corroborate its effectiveness.

Fast and high precision phase recovery technology of single-shot ineterferogram based on depth convolution neural network

“…This end-to-end image phase recovery model can avoid the phase sign inversion problem in the single-frame closed fringe demodulation process. This is a problem that we have already addressed in two other papers using APLEF [19] and Vision Transformerbased semantic segmentation models [20].…”

Enhanced Frequency-Guided Method with Particle Swarm Optimization for the Phase Recovery of a Single Interferogram

“…Sci. 2023, 13, 11969 2 of 12 use different computational strategies, such as the combination of genetic algorithms and parametric methods [3][4][5]; soft computing techniques applied to Zernike polynomials [6]; a combination of genetic algorithms and frequency-guided sequential demodulation [7]; combined harmony search optimization and frequency-guided sequential demodulation [1]; demodulate directly with Particle Swarm Optimization [8]; unwrapping of phase maps with sign changes [9]; demodulation with symmetric wavefront and tilt [10]; two-dimensional regularized phase-tracking technique [11]; different techniques of deep learning [12,13]; convolutional neural network [14]; and Lissajous ellipse fitting [15], among others.…”