Accurate blind extraction of arbitrary unknown phase shifts by an improved quantum-behaved particle swarm optimization in generalized phase-shifting interferometry

Abstract

An optimized method of accurately extracting the arbitrary unknown and unequal phase steps in phase-shifting interferometry is proposed. The approximate phase steps are first calculated based on the statistical nature of the diffraction field, and the mutated adaptive quantum-behaved particle swarm optimization is used to further extract the arbitrary unknown and unequal phase steps. We improve the mutated adaptive quantum-behaved particle swarm optimization by adding mutation operator with Gaussian probability distribution, thereby increasing the population diversity. The developed method here is fast, highly accurate, and can effectively overcomes the “sawtooth-solution phenomenon” often encountered in traditional direct search approach. We demonstrate the speed and quality of the solution by measuring the transmissive object with the four-step phase-shifting interference method, as is verified by both the computer simulations and optical experiments.