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.

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.

Optimization of the seismic processing phase-shift plus finite-difference migration operator based on a hybrid genetic and simulated annealing algorithm

Although the phase-shift seismic processing method has characteristics of high accuracy, good stability, high efficiency, and high-dip imaging, it is not able to adapt to strong lateral velocity variation. To overcome this defect, a finite-difference method in the frequency-space domain is introduced in the migration process, because it can adapt to strong lateral velocity variation and the coefficient is optimized by a hybrid genetic and simulated annealing algorithm. The two measures improve the precision of the approximation dispersion equation. Thus, the imaging effect is improved for areas of high-dip structure and strong lateral velocity variation. The migration imaging of a 2-D SEG/EAGE salt dome model proves that a better imaging effect in these areas is achieved by optimized phase-shift migration operator plus a finite-difference method based on a hybrid genetic and simulated annealing algorithm. The method proposed in this paper is better than conventional methods in imaging of areas of high-dip angle and strong lateral velocity variation.

Cavitation Diagnostics Based on Self-Tuning VMD for Fluid Machinery with Low-SNR Conditions

Variational mode decomposition(VMD)is a suitable tool for processing cavitation-induced vibration signals and is greatly affected by two parameters:the decomposed number K and penalty factorαunder strong noise interference.To solve this issue,this study proposed self-tuning VMD(SVMD)for cavitation diagnostics in fluid machinery,with a special focus on low signal-to-noise ratio conditions.A two-stage progressive refinement of the coarsely located target penalty factor for SVMD was conducted to narrow down the search space for accelerated decomposition.A hybrid optimized sparrow search algorithm(HOSSA)was developed for optimalαfine-tuning in a refined space based on fault-type-guided objective functions.Based on the submodes obtained using exclusive penalty factors in each iteration,the cavitation-related characteristic frequencies(CCFs)were extracted for diagnostics.The power spectrum correlation coefficient between the SVMD reconstruction and original signals was employed as a stop criterion to determine whether to stop further decomposition.The proposed SVMD overcomes the blindness of setting the mode number K in advance and the drawback of sharing penalty factors for all submodes in fixed-parameter and parameter-optimized VMDs.Comparisons with other existing methods in simulation signal decomposition and in-lab experimental data demonstrated the advantages of the proposed method in accurately extracting CCFs with lower computational cost.SVMD especially enhances the denoising capability of the VMD-based method.

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.

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.

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.

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.

Self-tuning virtual synchronous generator control for improving frequency stability in autonomous photovoltaic-diesel microgrids

This paper investigates the use of a virtual synchronous generator(VSG) to improve frequency stability in an autonomous photovoltaic-diesel microgrid with energy storage. VSG control is designed to emulate inertial response and damping power via power injection from/to the energy storage system. The effect of a VSG with constant parameters(CP-VSG) on the system frequency is analyzed. Based on the case study, self-tuning algorithms are used to search for optimal parameters during the operation of the VSG in order to minimize the amplitude and rate of change of the frequency variations. The performances of the proposed self-tuning(ST)-VSG, the frequency droop method, and the CP-VSG are evaluated by comparing their effects on attenuating frequency variationsunder load variations. For both simulated and experimental cases, the ST-VSG was found to be more efficient than the other two methods in improving frequency stability.

Convergence of Self-Tuning Regulators Under Conditional Heteroscedastic Noises with Unknown High-Frequency Gain

In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH(autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal.Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

Modeling the Spike Response for Adaptive Fuzzy Spiking Neurons with Application to a Fuzzy XOR

A spike response model(SRM)based on the spikes generator circuit(SGC)of adaptive fuzzy spiking neurons(AFSNs)is developed.The SRM is simulated in MatlabTM environment.The proposed model is applied to a configuration of a fuzzy exclusive or(fuzzy XOR)operator,as an illustrative example.A description of the comparison of AFSNs with other similar methods is given.The novel method of the AFSNs is used to determine the value of the weights or parameters of the fuzzy XOR,first with dynamic weights or self-tuning parameters that adapt continuously,then with fixed weights obtained after training,finally with fixed weights and a dynamic gain or self-tuning gain for a fine adjustment of amplitude.

Development of surface reconstruction algorithms for optical interferometric measurement

Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing.A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications,but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy,speed,robustness,and dynamic range,especially in on-line or on-machine conditions.This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements.Principles,configurations,and applications of typical optical interferometers with different capabilities and limitations are presented.Theoretical background and recent advances of fringe analysis algorithms,including coherence peak sensing and phase-shifting algorithm,are summarized.The new developments in measurement accuracy and repeatability,noise resistance,self-calibration ability,and computational efficiency are discussed.This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement.To address these challenges,advanced techniques in image stitching,on-machine measurement,intelligent sampling,parallel computing,and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.