FSD-HSO Optimization Algorithm for Closed Fringes Interferogram Demodulation

Abstract

Due to the physical nature of the interference phenomenon, extracting the phase of an interferogram is a known sinusoidal modulation problem. In order to solve this problem, a new hybrid mathematical optimization model for phase extraction is established. The combination of frequency guide sequential demodulation and harmony search optimization algorithms is used for demodulating closed fringes patterns in order to find the phase of interferogram applications. The proposed algorithm is tested in four sets of different synthetic interferograms, finding a range of average relative error in phase reconstructions of 0.14–0.39 rad. For reference, experimental results are compared with the genetic algorithm optimization technique, obtaining a reduction in the error up to 0.1448 rad. Finally, the proposed algorithm is compared with a very known demodulation algorithm, using a real interferogram, obtaining a relative error of 1.561 rad. Results are shown in patterns with complex fringes distribution.

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

“…It should be mentioned that the fewer the interfering wavefronts, the higher the measurement resolution will tend since the more wavefronts interact, the greater the number of harmonics will be generated in the Fourier spectrum, and at the time of demodulation it will be confusing to interpret which of the interfering wavefronts belongs to each harmonic. Phase demodulation is the more important task in optical interferometry measurements because the physical quantity to be measured is directly related to the phase [1].…”

“…The scientific discipline tasked with measuring and harnessing this interference is known as interferometry. Interferometry plays a pivotal role in various domains, ranging from the precise assessment of aberrations, deformations, and flatness to addressing challenges posed by disturbances and temperature gradients [1].…”

“…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.…”

“…To optimize the FSD algorithm, both evolutionary algorithms, the PSO (proposed optimizer) as well as the HSO (optimizer used in [1]), were applied. The proposed method is summarized in the flowchart shown in Figure 1, where the user can choose among FSD (in black), FSD-HSO or FSD-PSO (both in red).…”

“…In both algorithms, the following parameters will be the same: dimensions of problem 2, lower and upper limits [−1, 1], neighborhood region for energy function 11 and optimal cost value 0.25, as well as the iterations mentioned before were applied, as long as the cost function was less than 2.5. The operation of the FSD-HSO algorithm can be consulted in reference [1].…”