Arbitrary Unknown Phase Research Articles

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

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.

Two-step phase retrieval method with unknown phase shift on non-absorbtion grating X-ray differential phase contrast imaging system

Conventional phase retrieval methods for X-ray differential phase-contrast imaging are carried out with at least three interferograms. In this contribution, we present a novel two-step phase-shifting algorithm with an arbitrary unknown phase shift between 0 and π. Based on the detecting model of a grating interferometer, the unknown phase shifts are extracted by a noniterative algorithm. Then the phase distribution of the detected sample can be further obtained from the retrieval phase shift. This method is experimentally validated based on non-absorbtion grating imaging system and the result verified its effectiveness.

Two-shot point-diffraction interferometer with an unknown phase shift

On the basis of a modified Mach–Zehnder interferometer, this paperproposes a two-shot point-diffraction interferometer (PDI), by which twoπ-shifted interferograms are created according to the principle of half-wave loss and aresimultaneously captured by a single CCD camera. After an arbitrary unknown phase shiftis induced, a second and final shot captures these last two patterns. Then a novel algorithmbased on statistical principles is developed to extract the actual phase shift and thewavefront phase from four interferograms. The combination of two required shots and arobust algorithm allows the proposed PDI to be implemented efficiently and accurately.Related simulation and experiments are conducted to prove the correctness of the proposedmethod.

Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry

A direct phase shift extraction and wavefront reconstruction method in two-step generalized phase-shifting interferometry (GPSI) with arbitrary unknown phase shift is proposed. In this method the unknown phase shift α can be extracted by a determinate formula directly without iteration or additional judgment of its correct value from two or more phase shift solutions as necessary before. By an appropriate formula of GPSI the complex object field in the recording plane can be calculated and then the object wavefront in the original object plane obtained. This method is applicable for GPSI of any frame number K≥2 and for both the amplitude and phase objects. Computer simulations have shown that the phase shift extraction errors are below 0.01 rad in a wide range of 0.4 rad<α<2.6 rad and the computation time is greatly reduced by a factor of about 20 compared with the previous method. The effectiveness and accuracy of this method are also verified by optical experiments.

Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments

An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number >or=2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.

Generalized phase-shifting interferometry with arbitrary unknown phase shifts: Direct wave-front reconstruction by blind phase shift extraction and its experimental verification

A simple wave-front reconstruction method by generalized phase-shifting interferometry (PSI) with arbitrary unknown phase shift between 0 and π for two adjacent frames is proposed. In this method the unknown phase shifts are extracted by a noniterative algorithm with the use of the interferograms and the intensities of object and reference waves, and then the original object field can be further obtained. This method is applicable for generalized PSI of any frame number N (N⩾2) and for both the amplitude and phase objects. Its effectiveness and accuracy are verified by both the computer simulations and optical experiments.

Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift

An iterative algorithm to extract the arbitrary unknown phase shift in two-frame phase-shifting interferometry and then reconstruct the complex object wave is proposed. In combination with the least square principle and some calculation formulae we developed, this algorithm allows us to find the value of unknown phase shift by using only two interferograms without additional knowledge or measurement. Computer simulations have shown that this algorithm works well for both the smooth and diffusing objects to a very high accuracy over a wide range of the phase shift from 0.4 to 2.5 rad.

Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry

A novel fast convergent algorithm to extract arbitrary unknown phase shifts in generalized phase-shifting interferometry (PSI) is proposed and verified by a series of computer simulations. In this algorithm an error function is introduced and then the unknown phase shifts are found by an iterative tangent approach. In combination with the statistical method, this algorithm can give the most exact results in the fewest iteration steps. It can be used for generalized PSI of arbitrary frames for both smooth and diffusing objects and can usually reach the exact phase shifts with only four or five iterations for three- or four-frame PSI.

Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects.

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps.

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.