Phase correction method for least-squares wavefront calculation in statistical generalized phase-shifting digital holography

The conventional phase-shifting techniques commonly suffer from frequency aliasing because of their number of phase shifts below the critical sampling rate. As a result, fringe harmonics induce ripple-like artifacts in their reconstructed phase maps. For solving this issue, this paper presents an anti-aliasing phase-measuring technique. Theoretical analysis shows that, with phase-shifting, the harmonics aliased with the fundamental frequency component of a fringe signal depend on the greatest common divisor (GCD) of the used phase shifts. This fact implies a possibility of removing such aliasing effects by selecting non-uniform phase shifts that together with 2π have no common divisors. However, even if we do so, it remains challenging to separate harmonics from the fundamental fringe signals, because the systems of equations available from the captured fringe patterns are generally under-determined, especially when the number of phase shifts is very few. To overcome this difficulty, we practically presume that all the points over the fringe patterns have an identical characteristic of harmonics. Under this constraint, using an alternate iterative least-squares fitting procedure allows us to estimate the fringe phases and the harmonic coefficients accurately. Simulation and experimental results demonstrate that this proposed method enables separating high order harmonics from as few as 4 fringe patterns having non-uniform phase shifts, thus significantly suppressing the ripple-like phase errors caused by the frequency aliasing.

In this work, we deduce explicit conditions to design phase shifting algorithms (PSAs) in order to suppress errors in phase measurement, the double-frequency ripple distortion and the spurious piston. These errors arise when non-uniform phase-shifting interferograms are processed with conventional PSAs which assume uniform phase shifts. By modeling the non-uniform phase shifts as a polynomial of the unperturbed phase shift value !0, we show that the conditions for eliminating those errors are associated to the m-th derivative of the PSA's frequency transfer function (FTF). Thus, we propose an approach to design robust algorithms based on the FTF formalism, and we present a ready-to-apply eight-frame PSA. Finally, our conclusions are supported by computer simulations.

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.

This paper presents a method for obtaining the shape of an object using digital shearography. The technique makes use of two types of phase shifting. One provides a nonuniform phase shift which is related to the shape of the object. The other is independent of the shape of the object and utilizes uniform phase shifting. Theory together with experimental verification are demonstrated.

Recently, it has become necessary to detect cracks in structures such as buildings and bridges. Phase-shifting digital holography is one valuable method that can be used to measure the strain distribution on the surface of an object. However, to simplify the optical measurement setup, more compact equipment is required. An interferometric trigger method with dual piezo actuators for phase shifting is proposed. This method is useful for designing a head discrete-type measurement system that uses phase-shifting digital holography with multiple imaging sensors. The ability to phase shift using the proposed trigger method was confirmed with the reconstruction of an object and an experiment that was performed to measure the displacement distribution.

In this study, we propose a phase correction method for a type of neutron spin echo spectroscopy, known as modulation of intensity with zero effort using a time-of-flight method (TOF-MIEZE). The phase of the MIEZE signal sensitively varies with the neutron flight path lengths. The geometrical lengths from the sample position to the flat detector plane differ depending on the positions on the detector plane. Integrating the phase-shifted signals may decrease the signal contrast solely through the geometrical path-length deviations. To measure the decrement of contrast accurately, which corresponds to the intermediate scattering function, the position-dependent phase shifts must be corrected. The data correction is performed by shifting the MIEZE signal in time depending on path-length deviations, the MIEZE frequency, and neutron wavelengths. In the calculation of path-length deviations, the sample is assumed to be a point scatterer while a detector inclination is taken into account. We also discuss the relation between the frequency shift of TOF-MIEZE signal and path-length deviation, which is helpful to quantify phase shifts larger than 2π. The presented phase correction method is demonstrated with a 32 × 32 cm2 area detector for a 200 kHz TOF-MIEZE signal scattered from an elastic sample.

A comprehensive theoretical study on the head-on collision between two solitary waves in a thin elastic plate floating on an inviscid fluid of finite depth is investigated analytically by means of a singular perturbation method. The effects of plate compression are also taken into account. The Poincare–Lighthill–Kuo method has been used to derive the solution up to the fourth order of the resulting nonlinear differential equation, which in principle gives the asymptotic series solution. It is found that after collision, both the hydroelastic solitary waves preserves their original shape and positions. However a collision does have imprints on colliding waves with non-uniform phase shift up to the third order which creates tilting in the wave profile. Maximum run-up amplitude, wave speed, phase shift and distortion profile have also been calculated and plotted for two colliding solitary waves.

A singularly perturbed Korteweg--de Vries (KdV) equation $ \e^2 \eta_{xxxx} +\eta_{xx}-\eta +\eta^2=0$ for $ -\infty < x < + \infty$ is studied, where $\e > 0$ is a small parameter. It is known that the equation has homoclinic solutions connected to small periodic orbits at infinity. The relationship between amplitude and phase shift of the periodic orbits was established for noncritical cases. To study the critical cases, an asymptotic method is introduced here to formally derive the homoclinic solutions to periodic orbits with arbitrary phase shift. The exact asymptotic formula relating the amplitude of oscillations to the phase shift is obtained. The amplitude of oscillations is determined by the phase shift, and the range of the amplitude can be from $o(\e^n)$ with any $n\ge 1 $ up to $O(\e^{-2} \exp (-\pi /\e ))$ for different phase shift of the oscillations.

Eliminating the strong self-interference signal in chipless radio frequency identification (RFID) readers is key for enabling a reliable and long range reading in chipless RFID readers. The suggested method is to add a compensation signal to cancel the leakage signal vectorially before the first stage of the receiver front-end. An ultra-wideband (UWB) polyphase power divider (PPPD) generates the vector compensation signal of any arbitrary amplitude and phase. Unfortunately, the reported PPPD cannot meet the requirements for the realization of a UWB compensation unit (CU). A microstrip wideband differential phase shifter capable of producing a wide range of phase shifts is presented in this paper. The delay lines, including transmission line (TL) segments loaded with shorted stubs (SSs), generate prescribed phase shift values with respect to the universal reference line. It is shown that an arbitrary phase shift (up to 360°) with an in-band return loss (RL) better than 15 dB within an octave bandwidth is obtainable. Its full-range phase shift capability alongside the universal reference line and simple structure ensure its suitability for polyphase applications. To verify the proposed structure, a set of C-band phase shifters ranging from 60° to 300° is designed and fabricated, and a phase deviation from ±1° to ±9° is obtained. Finally, based on the proposed differential phase shifter, a four-phase power divider is implemented and utilized in the CU of a chipless RFID reader. Excessive isolation of better than 35 dB over 4–8-GHz frequency band is attained.

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.

Calculating the nonstationary flow around a lattice of arbitrary profiles which vibrate with an arbitrary phase shift

We introduce what we believe to be a novel phase-shifting digital holography (PSDH) method leveraging a hybrid event-based vision sensor (EVS). The key idea of our method is the phase shift during a single exposure. The hybrid EVS records a hologram blurred by the phase shift, together with the events corresponding to blur variations. We present analytical and optimization-based methods that theoretically support the reconstruction of full-complex wavefronts from the blurred hologram and events. The experimental results demonstrate that our method achieves a reconstruction quality comparable to that of a conventional PSDH method while enhancing the acquisition efficiency.

The standard stochastic two-step phase shift phase demodulation method analyzes the tangent function of the phase to be measured to extract the phase to be evaluated. It is necessary to eliminate the background light intensity of interference fringes, which has a significant impact on phase reconstruction accuracy. A random three-step phase shift algorithm (RTP) is suggested in this study. The phase shift between two adjacent interference fringes is extracted using the least squares approach in conjunction with a K-order twodimensional polynomial. Additionally, it employs the interference fringe graph’s difference operation to reduce the background light intensity and actualize the restoration of the measurement phase. The experimental and simulations results reveal that phase shift, luminous non-uniformity, and random noise have little effect on the random three-step phase shift method and have strong environmental adaptability.

We consider the production of second-harmonic light in gratings resonant with the generated field, through a Green's function approach. We recover some standard results and obtain new limits for the uniform grating case. With the extension to nonuniform gratings, we find the Green's function for the second harmonic in a grating with an arbitrary phase shift at some point. We then obtain closed form approximate expressions for the generated light for phase shifts close to π/2 and at the center of the grating. Finally, comparing the uniform and phase-shifted gratings with homogeneous materials, we discuss the enhancement in generated light and the bandwidth over which it occurs, and the consequences for second-harmonic generation in optical fiber Bragg gratings.

In surface shape measurement with phase-shifting interferometry, the extraction accuracy of initial phase is significant and it will influence the correct of measurement result. A least-squares algorithm is proposed to solve the parameters of interferograms with random and known phase shifts. It can rapidly extract the initial phase, modulation amplitude and background intensity without any iteration. Numerical simulations and optical experiments are implemented to demonstrate the performance of the proposed method. The simulation and experiment results show that the presented method is effective, rapid and accurate.