Fast three-step phase-shifting algorithm

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532 x 500 pixels, all with an ordinary personal computer.     

Parallel three-step phase-shifting digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

A new phase retrieval algorithm with pure generalized three-step phase-shifting under matrix norm processing

Phase-shifting interferometry (PSI) is one of the most effective techniques in imaging a phase specimen, in which the phase retrieval is a basic and significant process. A new phase retrieval method based on the matrix norm algorithm in PSI is proposed in this paper. In this algorithm, the value of phase shift can be determined by three different matrix norms of the intensity difference between two phase-shifted interferograms, and then the phase can be retrieved. Neither the iterative calculation nor the extra measurements of other parameters are necessary on account of this algorithm which only requires three phase-shifted interferograms. The feasibility and accuracy of this algorithm are demonstrated by the simulated results. Experimentally, the generalized phase shift can be realized by a simple device which adjusting the angle of glass accurately. It is found that this algorithm has a good application prospect in the field of dynamic imaging.     

Enhanced two-frequency phase-shifting method based on generalized phase-shifting algorithm

In this paper, we develop a novel dual-frequency pattern which not only releases the restriction of conventional two-frequency phase-shifting algorithm that at least six fringe patterns are needed, but reduces the noise impact by decreasing the frequency ratio between the high- and low-components. To decrease the number of necessary patterns to five, a novel composite dual-frequency pattern scheme combining together a high- with a low-frequency pattern is employed. To make the algorithm less sensitivity to noise, the low-frequency component is with more than one period fringes, which is relatively prone to recover the continuous result by simple spatial phase unwrapping approach. Besides, the restriction of special phase shifts between two-frequency components in conventional methods is released by the generalized phase-shifting algorithm. Simulations and experiments are conducted to demonstrate that in addition to maintaining the minimum number of patterns, the proposed method reveals higher accuracy of phase retrieval.     

Phase-shift calibration algorithm for phase-shifting interferometry

We propose a novel phase-shift calibration algorithm. With this technique we determine the unknown phase shift between two interferograms by examining the sums and differences of the intensities on each interferogram at the same spatial location, i.e., I1(x, y) +/- I2(x, y). These intensities are normalized so that they become sinusoidal in form. A uniformly illuminated region of the interferograms that contains at least a 2pi variation in phase is examined. The extrema of these sums and differences are found in this region and are used to find the unknown phase shift. An error analysis of the algorithm is provided. In addition, an error-correction algorithm is implemented. The method is tested by numerical simulation and implemented experimentally. The numerical tests, including digitization error, indicate that the phase step has a root-mean-square (RMS) phase error of less than 10(-6) deg. Even in the presence of added intensity noise (5% amplitude) the RMS error does not exceed 1 deg. The accuracy of the technique is not sensitive to nonlinearity in the interferogram.     

Adaptive phase-shifting algorithm for temporal phase evaluation

Most standard temporal-phase-shifting (TPS) algorithms evaluate the phase by computing a windowed Fourier transform (WFT) of the intensity signal at the carrier frequency of the system. However, displacement of the specimen during image acquisition may cause the peak of the transform to shift away from the carrier frequency, leading to phase errors and even unwrapping failure. We present a novel TPS method that searches for the peak of the WFT and evaluates the phase at that frequency instead of at the carrier frequency. The performance of this method is compared with that of standard algorithms by using numerical simulations. Experimental results from high-speed speckle interferometry studies of carbon fiber panels are also presented.     

Regularized multiframe phase-shifting algorithm for three-dimensional profilometry

In many industrial inspection systems, it is required to have a high-precision three-dimensional measurement of an object under test. A popular technique is phase-measuring profilometry. In this paper, we develop some phase-shifting algorithms (PSAs). We propose a novel smoothness constraint in a regularization framework; we call this the R-PSA method and show how to obtain the desired phase measure with an iterative procedure. Both the simulation and experimental results verify the efficacy of our algorithm compared with current multiframe PSAs for interferometric measurements.     

基于波长移相的改进加权多步算法

在斐索干涉仪中测量光学平板受到多面反射光束的影响,而波长移相干涉技术是通过光源波长的改变来实现干涉信号的移相,原理上可以实现各个干涉信号的分离,在算法上要求能对多次谐波进行较好的抑制,加权多步移相算法可以实现这样的目的.笔者提出了加权多步移相算法的改进算法,可以提高算法对误差的抑制能力,最后用实验验证了改进算法的有效性.     

Spatial carrier phase-shifting algorithm based on least-squares iteration

An advanced spatial carrier phase-shifting (SCPS) algorithm based on least-squares iteration is proposed to extract the phase distribution from a single spatial carrier interferogram. The proposed algorithm divides the spatial carrier interferogram into four phase-shifted interferograms. By compensating for the effects of the variations of phase shifts between pixels and the variations of background and contrast, the proposed algorithm determines the local phase shifts and phase distribution simultaneously and accurately. Numerical simulations show that the accuracy of the proposed algorithm is obviously improved by compensating for the effects of background and contrast variations. The peak to valley of the residual phase error remains less than 0.002 rad when the magnitude of spatial carrier is in the range from pi/5 to pi/2 and the direction of the spatial carrier is in the range from 25 degrees to 65 degrees. Numerical simulations and experiments demonstrate that the proposed algorithm exhibits higher precision than the existing SCPS algorithms. The proposed algorithm is sensitive to random noise, but the error can be reduced by N times if N measurements are taken and averaged.     

An algorithm for profilometry by white-light phase-shifting interferometry

Abstract

In the case of white-light interferometry, the usual phase shifting methods cannot be used because the modulation in the interference intensity is due to both the phase variation and to the coherence envelope. We propose a practical approach in which the coherence envelope is considered as locally linear. The classical four-point calculation algorithm is adapted to a set of seven intensities which are weighted with adapted coefficients in order to compensate for the effect of the coherence envelope. The capabilities of this method are described theoretically.     

Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift

A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry. For a fringe pattern with slow-varying background intensity, the background removal is achieved in the frequency domain. For a speckle pattern, a background removal technique is integrated with the three-frame algorithm. In this process, manual intervention is minimal, and high computational speed is achieved. In addition, high-frequency phase signals would not be removed in the noise-reduction process as is the case in the bandpass-filtering technique. Accuracy of the method is discussed.     

Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography

We propose an algorithm for compensating the phase-shift error of polarization-based parallel two-step phase-shifting digital holography, which is a technique for recording a spatial two-step phase-shifted hologram. Although a polarization-based system of the technique has been experimentally demonstrated, there had been the problem that the phase difference of two phase-shifted holograms had been changed by the extinction ratio of the micropolarizer array attached to the image sensor used in the system. To improve the performance of the system, we established and formulated an algorithm for compensating the phase-shift error. Accurate spatial phase-shifting interferometry in the system can be conducted by the algorithm regardless of phase-shift error due to the extinction ratio. By the numerical simulation, the proposed algorithm was capable of reducing the root mean square errors of the reconstructed image by 1/4 and 1/5 in amplitude and phase, respectively. Also, the algorithm was experimentally demonstrated, and the experimental results showed that the system employing the proposed algorithm suppressed the conjugate image, which slightly appeared in the image reconstructed by the system not employing the algorithm, even when the extinction ratio was 10:1. Thus, the effectiveness of the proposed algorithm was numerically and experimentally verified.     

Algorithm immune to tilt phase-shifting error for phase-shifting interferometers

As a phase shifter usually suffers from both translational and tilt-shift errors during shifting, so every pixel in the same interferogram will have a different phase-shift value. Thus nonlinear phase-measurement errors cannot be avoided, but even translational-shift error has been corrected effectively. However, based on the fact that the shifted phases of all the pixels in the same interferogram remain on the phase-shift plane, by defining this plane one can eliminate a significant number of phase errors. A new algorithm that is immune to both translational- and tilt-shift errors in a phase shifter for phase-stepping interferometers is presented. A first-order Taylor series expansion replaces the nonlinear equations for defining the phase-shift plane, and iteration of the algorithm guarantees its accuracy. Results of a computer simulation show that phase-measurement errors caused by both translation- and tilt-shift error can be compensated for completely, even when the tilt-shift error is not more than ?1%.     

Vibration-resistant phase-shifting interferometry

A method to reduce the sensitivity of phase-shifting interferometry to external vibrations is described. The returning interferogram is amplitude split to form two series of interferograms, taken simultaneously and with complementary properties, one with high temporal and low spatial resolution and the other with low temporal and high spatial resolution. The high-temporal-resolution data set is used to calculate the true phase increment between interferograms in the high-spatial-resolution data set, and a generalized phase-extraction algorithm then includes these phase increments when the topographical phases in the high-spatial-resolution data set are calculated. The measured topography thereby benefits from the best qualities of both data sets, providing increased vibration immunity without sacrificing high spatial resolution.     

Dynamic phase-shifting photoelasticity

The application of phase-shifting photoelasticity to a real-time dynamic event involves simultaneous recording of the four phase-shifted images. Here an instrument, believed to be novel, is developed and described for this purpose. Use of a Multispec Imager is introduced into digital photoelasticity for the first time to our knowledge. This device enables splitting the optical energy of an object into four identical paths, thus permitting recording of the required four phase-shifted images. Experimental demonstration is provided for validation.     

基于LMS算法的移相干涉仪环境振动控制器

环境振动严重影响移相干涉测量的过程。在运用光学外差法测得移相干涉仪环境振动信号的前提下,设计了采用高速DSP芯片的振动控制器,它对电压形式的振动信号进行采样,用自适应LMS算法分析振动信号,同时输出反馈控制信号。反馈控制信号驱动PZT光学移相器对振动引起的光程差(或波前相位)变化进行实时补偿。通过这种闭环控制,系统能够对幅频积小于100waves*Hz的环境振动进行有效补偿,实验中获得了稳定的移相干涉条纹,保证了光学测试的正确性。     

Fourier-transform phase-shifting interferometry

Phase-shifting interferometry is a preferred technique for high-precision surface form measurements, but the difficulty in handling the intensity distortions from multiple-surface interference has limited the general use of the technique to interferometer cavities producing strict two-beam interference. I show how the capabilities of phase-shifting interferometry can be extended to address this problem using wavelength tuning techniques. The basic theory behind the technique is reviewed and applied specifically to the measurement of parallel plates, where surfaces, optical and physical thickness, and homogeneity are simultaneously obtained. Basic system requirements are derived, common error sources are discussed, and the results of the measurements are compared with theory and alternative measurement methods.     

Statistical phase-shifting step estimation algorithm based on the continuous wavelet transform for high-resolution interferometry metrology

We propose a statistical phase-shifting estimation algorithm for temporal phase-shifting interferometry (PSI) based on the continuous wavelet transform (CWT). The proposed algorithm explores spatial information redundancy in the intraframe interferogram dataset using the phase recovery property on the power ridge of the CWT. Despite the errors introduced by the noise of the interferogram, the statistical part of the algorithm is utilized to give a sound estimation of the phase-shifting step. It also introduces the usage of directional statistics as the statistical model, which was validated, so as to offer a better estimation compared with other statistical models. The algorithm is implemented in computer codes, and the validations of the algorithm were performed on numerical simulated signals and actual phase-shifted moiré interferograms. The major advantage of the proposed algorithm is that it imposes weaker conditions on the presumptions in the temporal PSI, which, under most circumstances, requires uniform and precalibrated phase-shifting steps. Compared with other existing deterministic estimation algorithms, the proposed algorithm estimates the phase-shifting step statistically. The proposed algorithm allows the temporal PSI to operate under dynamic loading conditions and arbitrary phase steps and also without precalibration of the phase shifter. The proposed method can serve as a benchmark method for comparing the accuracy of the different phase-step estimation methods.