Phase-shifting digital holography in image reconstruction

A phase-shifting digital holography scheme developed to investigate internal defects in artworks is described. Phase-shifting is utilized to obtain a clear reconstructed object wave from a rough surface texture. A reverse-transform algorithm is employed to reconstruct the object wave on its original position of unknown distance or the imaging position from the object wave information on the holographic plane. To get the clearest reconstruction the exact registration of the unknown distance is determined by applying the intensity sum as the auto-focusing function, The spatial resolution of the reconstruction image is also investigated for a variety of affecting factors. Laboratory results of reconstruction images under deformation are presented.

Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.

An encryption scheme based on phase-shifting digital holography and amplitude-phase disturbance

In this paper, we propose an encryption scheme based on phase-shifting digital interferometry. According to the original system framework, we add a random amplitude mask and replace the Fourier transform by the Fresnel transform. We develop a mathematical model and give a discrete formula based on the scheme, which makes it easy to implement the scheme in computer programming. The experimental results show that the improved system has a better performance in security than the original encryption method. Moreover, it demonstrates a good capability of anti-noise and anti-shear robustness.

Multiple-image encryption by two-step phase-shifting interferometry and spatial multiplexing of smooth compressed signal

A multiple-image encryption method based on two-step phase-shifting interferometry （PSI） and spatial multiplexing of a smooth compressed signal is proposed. In the encoding and encryption process, with the help of four index matrices to store original pixel positions, all the pixels of four secret images are firstly reordered in an ascending order; then, the four reordered images are transformed by five-order Haar wavelet transform and performed sparseness operation. After Arnold transform and pixels sampling operation, one combined image can be grouped with the aid of compressive sensing （CS） and spatial multiplexing techniques. Finally, putting the combined image at the input plane of the PSI encryption scheme, only two interferograms ciphertexts can be obtained. During the decoding and decryption, utilizing all the secret key groups and index matrices keys, all the original secret images can be successfully decrypted by a wave-front retrieval algorithm of two-step PSI, spatial de-multiplexing, inverse Arnold transform, inverse discrete wavelet transform, and pixels reordering operation.

Three-step self-calibrating generalized phase-shifting interferometry

An accurate and fast three-step self-calibrating generalized phase-shifting interferomertry(SGPSI) is proposed. In this approach, two new phase-shifting signals are constructed by the difference interferograms normalization and noise suppressing, then the unknown phase shift between the two difference phase-shifting signals is estimated quickly through searching the minimum coefficient of variation of the modulation amplitude, a limited number of pixels are selected to participate in the search process to further save time, and finally the phase is reconstructed through the searched phase shift. Through the reconstruction of phase map by the simulation and experiment, and the comparison with several mature algorithms, the good performance of the proposed algorithm is proved, and it eliminates the limitation of requiring more than three phase-shifting interferograms for high-precision SGPSI. We expect this method to be widely used in the future.

Two-step phase-shifting Fresnel incoherent correlation holography based on discrete wavelet transform

Fresnel incoherent correlation holography(FINCH)has the ability to generate three-dimensional images with a superresolution by using incoherent sources.However,there are unwanted direct current term and twin image in interferograms,so it is of great significance to find a method to eliminate them.Phase-shifting technology is a most widely used technique for this task,but its three-step phase-shifting is not suitable for the instantaneous measurement of dynamic objects,and the quality of reconstructed image with the traditional two-step phase-shifting is lower.In this paper,we present a method of enhancing the resolution through using a two-step phase-shifting technology based on the discrete wavelet transform.After two-step phase-shifting,the resulting hologram is a superposition of multiple forms.The frequency of the resulting hologram is decomposed into different levels through using discrete wavelet transform,then the image is reconstructed after retrieving the low frequency band.Various experiments have verified the effectiveness of this method.

Research on the Intelligent Control Strategy of the Fuel Cell Phase-Shifting Full-Bridge Power Electronics DC-DC Converter

focus of all countries.As an effective new energy,the fuel cell has attracted the attention of scholars.However,due to the particularity of proton exchange membrane fuel cell(PEMFC),the performance of traditional PI controlled phase-shifted full-bridge power electronics DC-DC converter cannot meet the needs of practical application.In order to further improve the dynamic performance of the converter,this paper first introduces several main topologies of the current mainstream front-end DC-DC converter,and analyzes their performance in the fuel cell system.Then,the operation process of the phase-shifted fullbridge power electronics DC-DC converter is introduced,and the shortcomings of the traditional PI control are analyzed.Finally,a double closed-loop adaptive fuzzy PI controller is proposed,which is characterized by dynamically adjusting PI parameters according to different working states to complete the intelligent control of phase-shifted full-bridge DC-DC converter.The simulation results in MATLAB/Simulink show that the proposed algorithm has good a control effect.Compared with the traditional algorithm,the overshoot and stabilization time of the system are shorter.The algorithm can effectively suppress the fluctuation of the output current of the fuel cell converter,and is a very practical control method.

Arbitrary n-step phase-shifting Fourier single-pixel imaging

In this Letter,we innovatively present general analytical expressions for arbitrary n-step phase-shifting Fourier single-pixel imaging(FSI).We also design experiments capable of implementing arbitrary n-step phase-shifting FSI and compare the experimental results,including the image quality,for 3-to 6-step phase-shifting cases without loss of generality.These results suggest that,compared to the 4-step method,these FSI approaches with a larger number of steps exhibit enhanced robustness against noise while ensuring no increase in data-acquisition time.These approaches provide us with more strategies to perform FSI for different steps,which could offer guidance in balancing the tradeoff between the image quality and the number of steps encountered in the application of FSI.

The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement

Phase-shifting measurement and its error estimation method were studied according to the holographic principle.A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period(N-step phase-shifting function for short)was proposed.In N-step phase-shifting measurement,the interferograms are seen as a series of in-line holo-grams and the reference beam is an ideal parallel-plane wave.So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave.In ideal conditions,the proposed method is a kind of synchro-nous superposition algorithm in which the complex ampli-tude is separated,measured and superposed.When error exists in measurement,the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method.In the above method,the N+1-step phase-shifting function can be obtained from the N-step phase-shifting function.It shows that the N-step phase-shifting function can be separated into two parts:the ideal N-step phase-shifting function and its errors.The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function.The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error esti-mation method.Meanwhile,the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.

A novel random phase-shifting digital holographic microscopy method

This paper proposes a new method that reconstructs the information of specimen by using random phase shift step in digital holographic microscopy (DHM). The principles of the method are described and discussed in detail. In practical experiment, because the phase shifter is neither perfectly linear nor calibrated, digital holograms with inaccurate phase shift step are recorded by the charge-coupled device (CCD). The phase could be accurately reconstructed from the recorded digital holograms by using the random phase-shifting algorithm, which makes up for reconstructed phase error caused by ordinary phase-shifting algorithm. The phase aberration compensation is also discussed. In order to verify the flexibility of the proposed method, numerical simulation of random phase-shifting DHM was carried out. The simulation results illustrated that the presented method is effective when the phase shift step is unknown or random in DHM.

A new route for length measurement by phase-shifting interferometry

By the mathematic models of flexible hinge,the accurate relationship between the phase-shifting and pressure acting on the hinge is deduced and verified by experimental results.Through the optimization of the geometric parameter of flexible hinge,a phase-shifting generator is developed to determine the length of an object precisely by interferometry.The experiments show that the triple phase-shifting produced using this generator is up to 1 m.With this generator,an example for the application in length measurement is introduced.The result shows the length uncertainty is 0.5 nm when the temperature uncertainty is limited in 2 mK.This paper provides a novel technique to measure the dimension of an object,especially to the diameter of a silicon sphere for Avogadro constant project.

Study on an improved five-interferogram phase-shifting algorithm

Using traditional five-interferogram algorithm to unwrap phase for length measurement, the phase steps must be equal to π/2 exactly, but it is almost impossible to achieve in nanometer positioning technique. Aiming to overcome this defect of traditional five-interferogram algorithm, an improved five-interferogram algorithm is presented. This improved algorithm not only keeps the high accuracy of traditional fiveinterferogram algorithm, but also does not need absolute equal step to unwrap phase. Instead, this algorithm only needs measuring phase-shifting. With the numerical simulation, the improved five-interferogram algorithm shows high accuracy, high reliability, and feasibility in practice. It is very valuable for accurate length measurement with Fizeau interferometer and Fabry-Perot interferometer.

The Effect of Phase-Shifting between Pumping and Signal Lights on Transmission Performance of Optical Fiber Communication Systems with in-Line PSA

In this paper, the effect of phase-shifting between pumping lightand input signal light in a optical Phase-Sensitive Amplifier(PSA)ondispersion compensation for optical fiber communication systems usingPSA as In-line amplifiers is theoretically analyzed by computersimulation. From ur simulation we've got the result that Theeye-pattern degradation of the high-speed signal increase rapidlywith the accretion of fiber dispersion and also Increase with theincreasing of phase shift. But if the phase shift is controlled in acertain range, it won't affect the System performance. Otherwise, thesystem performance will be seriously degraded. At all events, theshifting Range of PSA's phase, which shifts at both sides of zero,will be half of that which shifts at only one side.

A general method of designing phase-shifting algorithms for grating lateral shearing interferometry

We propose a general method of designing phase-shifting algorithms for grating lateral shearing interferometry. The algorithms compensate for the zeroth-order effect error and phase-shifting error in varying degrees. We derive a general expression of the phase-shifting algorithm in grating lateral shearing interferometer and introduce the corresponding design method. Based on the expression and method, four phase-shifting algorithms are designed with different phase-shifting errors to obtain high measurement accuracy. A new 13-frame phase-shifting algorithm is designed and simulated with a large zeroth-order effect. Simulation results verify the general expression and the corresponding design method.

Holography and speckle in phase-shifting digital holography(Invited Paper)

The correlation properties of the optical field diffusely reflected from a rough surface under coherent illumination are analyzed numerically. The cross-correlations of the complex amplitudes and the intensities before and after translation and/or tilt of the surface are calculated at an arbitrary observation plane in three-dimensional （3D） space. The results provide us with the 3D distributions of phase changes and speckle displacement that lead to the distributions measured by holographic interferometry and speckle relationships and physical interpretation of them are and signal-to-noise ratio of the displacement to be correlation technique. Comparisons with analytical also discussed.

Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry

This study describes a novel fringe-shaping technique developed to alleviate the fringe truncation problem engendered by the acquired saturated and/or weak fringe images from high-/low-reflectance surfaces of three-dimensional（3D） objects in phase-shifting profilometry. The particle swarm optimization algorithm is employed to perform the recovery of the truncated fringes with optimal fitting for compensation after single-trial acquisition. The results show that the proposed method improves phase recovery accuracy to accomplish 3 D surface reconstruction with only one set of phase-shifting fringes under different truncation sceneries.

Spatial phase-shifting interferometry with compensation of geometric errors based on genetic algorithm(Invited Paper)

We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properties that change rapidly in time than the temporal phase-shifting interferometry. However, it is more susceptible to the geometric errors since the positions at which interferograms are collected are different. In this letter, we propose a spatial phase-shifting interferometry with separate paths for object and reference waves. Also, the object wave estimate is parameterized in terms of geometric errors, and the error is compensated by using a genetic algorithm.

Improved phase-shifting diffraction interferometer for microsphere topography measurements

In this study, an improved phase-shi^ng diffraction interferometer for measuring the surface topography of a microsphere is developed. A common diode-pumped solid state laser is used as the light source to facilitate ap- paratus realization, and a new polarized optical arrangement is designed to filter the bias light for phase-shifting control. A pinhole diffraction self-calibration method is proposed to eliminate systematic errors introduced by optical elements. The system has an adjustable signal contrast and is suitable for testing the surface with low reflectivity. Finally, a spherical ruby probe of a coordinate measuring machine is used as an example tested by the new phase-shifting diffraction interferometer system and the WYKO scanning white light interferometer for experimental comparison. The measured region presents consistent overall topography features, and the resulting peak-to-valley value of 84.43 nm and RMS value of 18.41 nm are achieved. The average roughness coincides with the manufacturer＇s specification value.

Phase-shifting technique applied to circular harmonic-based joint transform correlator

The phase-shifting technique is applied to the circular harmonic expansion-based jointtransform correlator. Computer simulation has shown that the light efficiency and the discrimination capability are greatly enhanced, and the full rotation invariance is preserved after the phase-shifting technique has been used. A rotation-invariant optical pattern recognition with high discrimination capability and high light efficiency is obtained. The influence of the additive noise on the performance of the correlator is also investigated. However, the anti-noise capability of this kind of correlator still needs improving.

Four-quadrant demodulation fiber sensor for wavelength monitoring of a wavelength phase-shifting interferometer

Real-time monitoring of wavelength is important for high-speed wavelength phase-shifting interferometry.In this paper,a wavelength sensor based on a polarization-maintaining fiber interferometer with four-quadrant demodulation was proposed.We built the wavelength sensing system with resolution better than 0.005 pm and 0.1 ms sampling interval and measured the response time of the tuned wavelength at 35 ms in the phase-shifting process of a commercial wavelength phase-shifting free-space interferometer,as well as the wavelength drift velocity of 0.01 pm per second in the hysteresis process.The optical fiber wavelength sensor with four-quadrant demodulation provides a real-time wavelength sensing scheme for high-speed wavelength phase-shifting interferometers.