Phase extraction from interferograms with unknown tilt phase shifts based on a regularized optical flow method

In this study, a simultaneous dual-wavelength phase-shifting interferometry system using two reference arms was built, and a simple phase retrieval method for the system with blind phase shifts was proposed using five phase-shifted interferograms. First, the unknown phase shifts were controlled independently to separate the information of single wavelength, which can be calculated directly by using the Euclidean matrix norm algorithm. Second, a wrapped phase of a single wavelength was obtained using a three-step phase-shifting algorithm. Finally, a continuous phase of a synthetic wavelength was obtained. The simulation and experimental results indicated the feasibility and greater accuracy of the proposed method. Moreover, the strict requirement of the phase shifter was eliminated because of the use of arbitrary and unknown phase shifts, thereby making experimental operation easier.

Phase-shifting shadow moire is an efficient technique for three-dimensional (3-D) shape measurement, but the technique is always suffered from the error of phase shifter. A three-frame random phase-shifting algorithm is proposed to relax the requirements of repeatability and accuracy of the phase shifter in a shadow moire system. The proposed method can act as a bridge between the three phase-shifting analysis methods and two-shot phase-shifting methods. The value of introduced arbitrary and unknown phase shift can be calculated by a determinate formula. The algorithm has the advantages of being free from the disturbance of background elimination and less computation. In addition, the proposed method is immune to nonsinusoidal fringe patterns and can be implemented easily in many applications. Both simulation and optical experimental results verify the feasibility of this method.

Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry

Three-frame generalized phase-shifting interferometry by a Euclidean matrix norm algorithm

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.

An algorithm is proposed for extraction of the unknown phase shift steps and correction of the phase shift error in partially coherent illuminated phase-shifting digital holography. The mean contrast of noise (MCN) of the reconstructed amplitude image is developed to evaluate the noise level resulting from phase shift error. Actual phase shift steps are first extracted by minimizing the MCN. Then the extracted actual phase shift steps are used to retrieve the original object wave without phase shift error. The validity of the proposed method is verified by simulations, and then implemented in partially coherent illuminated phase-shifting digital holography where a spatial light modulator with unknown phase modulation characteristic is used as the phase shifter. The results demonstrated that the actual phase shift steps can be extracted and the phase shift error is corrected effectively.

A quantitative phase measuring technique is presented that estimates the object phase from a series of phase shifted interferograms that are obtained in a common-path configuration with unknown phase shifts. The derived random phase shifting algorithm for common-path interferometers is based on the Generalized Phase Contrast theory [pl. Opt.40(2), 268 (2001)10.1063/1.1404846], which accounts for the particular image formation and includes effects that are not present in two-beam interferometry. It is shown experimentally that this technique can be used within common-path configurations employing nonlinear liquid crystal materials as self-induced phase filters for quantitative phase imaging without the need of phase shift calibrations. The advantages of such liquid crystal elements compared to spatial light modulator based solutions are given by the cost-effectiveness, self-alignment, and the generation of diminutive dimensions of the phase filter size, giving unique performance advantages.

Two-step phase extraction and random phase shift estimation in phase-shifting profilometry based on least-squared optical flow method

This paper combines virtual simulation technology to improve the traditional foreign language teaching mode. Aiming at the problems of traditional phase-shift shadow Moiré profiler, a three-step quadrature-phase demodulation technique using unknown phase shift was developed. Then, the paper compares the proposed method with the GS method using MATLAB simulation. It can be seen from the simulation and demodulation results that the two methods obtain similar results, thus proving the equivalence of the two methods.

We consider how the conventional spectroscopic and interferometric schemes can be rearranged to serve for reconstructing quantum states of physical systems possessing SU(2) symmetry. The discussed systems include a collection of two-level atoms, a two-mode quantized radiation field with a fixed total number of photons, and a single laser-cooled ion in a two-dimensional harmonic trap with a fixed total number of vibrational quanta. In the proposed rearrangement, the standard spectroscopic and interferometric experiments are inverted. Usually one measures an unknown frequency or phase shift using a system prepared in a known quantum state. Our aim is just the inverse one, i.e., to use a well-calibrated apparatus with known transformation parameters to measure unknown quantum states.

The application of structured illumination for enhanced resolution requires accurate knowledge of phase shifts in the sinusoidal illumination. This work proposes a method to estimate random, unknown phase shifts and subsequent image reconstruction.

Pulses of a fluorinated analog of leucine, 5',5',5'-trifluoroleucine, reset the phase of the circadian rhythm of K(+) uptake in Lemna gibba G3 under continuous light conditions. The trifluoroleucine pulse caused the largest delay phase-shifts during the early subjective phase but it caused only small phase advances. The action of trifluoroleucine was investigated and the following results were obtained. (a) The uptake of trifluoroleucine was essentially the same at all circadian phases, even though phase shifting was dramatically different at different phases. At effective phases, the magnitude of phase shifting was well correlated with the amount of trifluoroleucine taken up by the duckweed. (b) The trifluoroleucine pulse lowered the endogenous content of valine and leucine but these decreases did not correlate with phase shifting. (c) Protein synthesis was not affected by trifluoroleucine pulses which caused large phase shifts. (d) Pulses of 4-azaleucine, a different structural analog of leucine, also caused phase shifting. However, neither the direction nor the effective times of phase shifting were similar to those of trifluoroleucine. Taken together, these results negate the proposition that trifluoroleucine and azaleucine caused phase shift by disturbing amino acid metabolism and/or inhibiting protein synthesis, but they suggest instead that these analogs are incorporated into some protein(s) which are necessary for normal clock operation.

We develop a laser-diode phase-shifting interferometer that can capture frame-rate phase-shifted interferograms on a video tape with a high capacity for their storage. The number of the video frame is simultaneously recorded on an audio track of the video tape. In a four- step manner, the injection-current variation of the laser diode is synchro- nized with the field pulse of a CCD camera to producep/2-step phase shifts at a frame rate of 1/30 s. An intensity distribution of the interfero- gram on any frame can be determined through a video tape with a frame memory using the recorded frame number. The four successive phase- shifted interferograms are used to calculate a distribution of frozen phase by a phase-extraction algorithm. The phase error due to the frame-by- frame intensity repeatability is theoretically analyzed. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)01812-7)

We propose an all-optical phase-shifting method using Yb-doped optical fibers and demonstrate its potential in on-axis digital holography microscopy (DHM) system. The Yb-doped optical fiber induces a phase change under optical pumping conditions. The induced phase shift shows a good linear response to applied pumping currents, and N-step phase-shifting up to 2p can be properly performed. Four-, six-, and eight-step phase-shifting methods are performed, and the phase retrievals from their phase-shifted interferograms are achieved using an interframe correlation matrix method. An 8-step phase shifting-based reconstruction, which is effective for background noise reduction, is used for 3D imaging of an indium tin oxide (ITO) thin film and an organic light-emitting diode (OLED) thin film. The reconstructed surface profile was in agreement with the step structure of the samples. The proposed all-optical phase-shifting method is expected to be applied to various optical imaging systems using fiber-based phase-shifting interferometers.

Tracking of single fluorescent probes along the axial (depth) dimension is an important task in the biological and physical sciences. In this paper, we propose and analyze the use of fluorescence phase-shifting interferometry (FPSI) for axial single particle tracking (SPT) along 1 μm-depth (z) trajectories. FPSI is a photon-efficient, self-interference method that collects and coherently combines the 4π steradian emission wavefronts of a single fluorescent particle while introducing multiple phase shifts between the wavefronts to axially localize the particle with high precision over an extended depth-of-field. We employ vectorial imaging analysis and Monte-Carlo simulations of diffusive and directed motions to present a detailed comparative study of spatial and temporal FPSI for axial SPT based on simultaneous and time sequential collection of four phase-shifted interferograms using a single camera, respectively. The results of the numerical simulations show that for ≤0.105 μm2/s diffusion, spatial FPSI attains a maximal twofold improvement in the trajectory reconstruction precision at the expense of a fourfold reduced field-of-view compared to temporal FPSI. Furthermore, the analysis predicts that for sufficiently slow random linear motions, temporal FPSI is superior to spatial FPSI and achieves a smaller trajectory reconstruction error.