Rapid phase extraction method based on the difference image between interferograms with unknown phase-shifting amount

In phase-shifting interferometry, based on the difference image between interferograms with unknown phase-shifting amount, a rapid phase extraction method is proposed. In this method, first, by means of the simple subtraction operation between interferograms captured in one phase-shifting period, a sequence of difference images are generated easily; second, to decrease the random phase-shifting errors induced during the phase-shifting procedure, the summation operation is performed for these difference images; third, based on one time phase recovery operation and one time phase-unwrapping operation, the measured phase with high precision can be obtained rapidly. Moreover, in the proposed method, by means of a simple phase summation operation for all pixel-phases in one interferogram, the corresponding phase-shifting amount of interferogram can be determined conveniently.     

Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter

Parallel two-step phase-shifting interferometry for microscopy is presented, and the recording condition for generalized two-step phase-shifting interferometry is discussed. A 45° tilted cube beamsplitter enables to replicate the orthogonally linear polarized object and reference waves into two parallel beams, respectively. As a consequence, two interferograms with quadrature phase shift are obtained along the two beams, and phase reconstructed with an improved algorithm. To reconstruct the phase distribution from the two-step phase-shifting interferograms, a certain recording condition should be satisfied. However, the recording condition has not ever been discussed before. In this paper, the recording condition for the two-step phase-shifting interferometry is derived and that is: the intensity of reference wave should be no less than two times object wave intensity.     

Wavefront reconstruction by two-step generalized phase-shifting interferometry

A wavefront reconstruction method by two-step generalized phase-shifting interferometry (GPSI) with blind phase shift extraction algorithm is verified by both the computer simulations and optical experiments. This method can retrieve complex object wave field by using two interferograms, the recorded object and reference wave intensities, and an unknown phase shift without additional processing. The simulations with irregular wavefronts have shown the effectiveness and high accuracy of this method for blind phase-shift extraction and wavefront reconstruction over a wide range of phase-shifts, while the optical experiments for both the direct and indirect objects have yielded satisfactory results with a higher resolution of reconstructed image than those reported recently.     

Phase Retrieval of Phase-Shifting Interferometry with Iterative Least-Squares Fitting Algorithm: Experiments

We report our experimental results of phase-shifting interferometry with an iterative least-squares fitting technique to estimate both the wave front phases and the phase shifts. The method allows phase retrieval from phase-shifting interferograms even though the calibration data of the phase shifter is unknown. The algorithm is used to analyze two sets of experimental interferograms. One records by moving a piezoelectric transducer shifter randomly and therefore has embedded random phase shifter errors, and the other samples the interference movie recorded by a video recorder while driving a stepping motor and therefore has embedded random intensity noises. The results are comparable with that of the conventional M-frame algorithm. Investigation of the effects of the intensity noises and phase shift errors shows the algorithm to perform well in both. Problems such as convergence, unique solution and reliability are also discussed.     

3-D surface profilometry using simultaneous phase-shifting interferometry

Urgent needs for high-speed, non-contact and on-line measurement with high accuracy and repeatability are of great interest for automatic optical inspection (AOI) industries. Therefore, optical phase-shifting interferometry for precision 3-D surface profilometry has become an important metrological method due to its non-contact and high measurement accuracy. Traditional phase-shifting interferometry is very sensitive to vibrations because image acquisition in various phase-shifting sequences could easily introduce measurement errors from environmental influences, such as air disturbance and system structure vibrations. In this paper, we introduce a new simultaneous phase-shifting interferometer for 3-D surface profilometry which employs a single glass plate to generate simultaneous phase-shifted interferograms. Phase reconstruction is performed by using a developed phase-shifting algorithm which uses a three-step phase-shifting method with phase differences of 90°, 180°, and 270° for three interferograms. To verify measurement accuracy and repeatability, the system was employed to measure surface profiles of surface of a flat mirror and set of Mitutoyo gauge blocks. The experiment result shows that the method is proven to be capable of performing one-shot interferometric measurement and minimizing influences from environmental disturbances with measurement repeatability down to 10 nm or less.     

基于倾斜相位的抗振动干涉面形测量

环境振动会在干涉测量过程中产生随机倾斜、移相误差,导致测量精度下降。为了降低环境振动对移相干涉测量的影响,提出了一种基于倾斜相位的抗振动干涉面形测量方法。首先,利用Fourier变换将干涉图变换到频域;然后,利用频域细分操作对峰值坐标进行亚像素精度定位,求解出振动倾斜平面;最后,利用最小二乘法计算出待测面的相位分布。实验结果表明,本方法与同步移相法的复原结果具有高度一致性,波面峰谷值和均方根值的偏差较小;且本方法无需对硬件进行改动,可为振动环境下的移相干涉测量提供一种低成本、高精度的解决方案。     

Accurate phase-shifting digital interferometry

In phase-shifting interferometry experiments, the accuracy of the phase shift is a major issue. Many experimental and data analyses are done to cancel phase-shift errors inherent to the modulation techniques used. We propose to remove most of the phase-shift error by recourse to a frequency-shifting method. This approach can be applied to both holography and interferometry. We validate the idea with a holographic experiment.     

相移相位测量的全息再现算法及测量误差分析

用全息原理和方法研究相移相位测量,得到了N步整周期相移再现物光波复振幅同步叠加函数(N步相移函数),同时提出一种新的相移相位测量误差分析和最大误差估计方法。N步相移干涉图是以理想平行光为参考光的无衍射同轴全息图,将其与对应的相移参考光相乘后求和得到N步相移函数;在理想情况下,这是一种复振幅分离、测量和物光波复振幅函数同步叠加方法,存在误差时计算出的相位是最小二乘方法的最佳期望结果。利用N步相移函数得到的N 1步相移函数,说明非理想N步相移函数是理想N步相移函数与误差函数之和,可以把相位型误差转化为与振幅和强度相对误差同等的误差来对待,降低了相位测量中误差估计的难度,给出了N步相移算法最大误差的估计方法和公式。     

Four-step spatial phase-shifting shearing interferometry from moiré configuration by triple gratings

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.     

Punctuated quadrature phase-shifting interferometry

We describe a method and algorithm for reducing the sensitivity of phase-shifting interferometry to external vibrations. Using an interline-transfer camera, a shutter, and a fast phase shifter, we acquire a series of paired interferograms in quadrature, with the pairs spaced to maximize residual phase-error cancellation. The rapid acquisition of quadrature pairs significantly improves resistance of interferometry to low-frequency vibrations.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

基于联合变换相关和相移干涉的图像加密

提出了一种在联合变换相关器结构中引入三步相移干涉和二元置乱技术的图像加密方法.用纯相位空间光调制器同时调制原始图像和两个随机相位掩模,利用三步相移技术分别将图像信息和主密钥加密为全息图,并用CCD在输出面上接收,再利用二元置乱技术置乱图像信息的全息图.在获得置乱密钥和附加密钥的情况下,可以通过一定的算法快速、清晰的重建原始图像.用计算机仿真验证了它的可行性和有效性.     

Generalized phase-shifting algorithm for dynamic phase measurement in electron-wave interferometry

A generalized phase-shifting algorithm is implemented in the electron-wave interferometry with a transmission electron microscope, based on simultaneous measurement of the initial phases of the interferograms. The initial phase of each interferogram that has inherent linear carrier fringes is calculated using the Fourier co-efiicients of the interferogram itself corresponding to the carrier-frequency. Taking advantage of this phase-shifting method in both spatial resolution and precision, the phase distribution of a biological weak phase object is successfully measured. This promises to be one of the most spectacular application fields for this new technology.     

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.     

Discussions about FFT-based two-step phase-shifting algorithm

An FFT-based two-step phase-shifting (TPS) algorithm is described in detail and implemented by use of experimental interferograms. This algorithm has been proposed to solve the TPS problem with random phase shift except π. By comparison with the visibility-function-based TPS algorithm, it proves that the FFT-based algorithm has obvious advantages in phase extracting. Meanwhile, we present a π-phase-shift supplement to the TPS algorithm, which combines the two interferograms and demodulates the phase map by locating the extrema of the combined fringes after removing the respective backgrounds. So combining this method and FFT-based one, one could really implement the TPS with random phase shift. Whereafter, we systematically compare the TPS with single-interferogram analysis algorithm and conventional three-step phase-shifting one. The results demonstrate that the FFT-based TPS algorithm has a satisfactory accuracy. At last, based on the polarizing interferometry, a schematic setup of two-channel TPS interferometer with random phase shift is suggested to implement the simultaneous collection of interferograms.     

基于主元分析的随机相移算法

将统计理论中的主元分析应用到干涉条纹分析中,提出一种基于主元分析的随机相移算法。该算法先将多帧条纹数据分解成不相关的主元成分,然后从主元成分中提取2维相位信息。数值模拟结果表明:该算法不需要迭代运算就能从4帧完全随机相移干涉图中有效提取相位信息,运算时间少,精度高。实验结果表明主元分析相移算法比现有迭代相移算法更适合于随机相移干涉图分析。     

两步广义相移干涉术的光学实验验证

提出了一种基于两步广义相移干涉术的波前再现技术以及基于衍射场统计特性的未知相移值提取算法,并且进行了光学实验验证.该方法中可仅利用两幅干涉图及一次不需精确预设的未知相移,参照物光光强和参考光光强,即可通过计算提取真实的相移量,进而恢复出物波波前复振幅,而无需借助傅里叶谱分析或数字滤波等操作.在光学实验中,对借助于空间光调制器（SLM）的间接输入和三维漫反射物体直接输入两种情况进行了详细地研究,得到的光学实验结果验证了所提方案的有效性和可行性. 关键词： 信息光学 相移干涉术 波前再现 数字图像处理     

一种提高干涉相位识别精度的方法

针对开环相移驱动下的单色光干涉测量,提出一种满足四步法的高精度相位识别的方法。首先选取干涉场中存在适当相位差的两像素点,建立相移驱动单周期内两像素点灰度序列值之间的干涉方程组。运用椭圆拟合获取相应干涉方程组参数,然后通过反算序列相位确定逐点驱动步长或序列相位信息。结合序列相位信息,运用Lagrange抛物插值算法,设计计算满足四步法的4幅干涉图,并计算各像素点的初相位。最后,运用多波长算法计算表面形貌并进行误差分析。实验表明:计算得到的方波多刻线样板的Ra值为0.439 0 m,测量误差为0.23%,此方法降低了对测量条件的硬件与环境要求,满足表面形貌高精度测量的要求。     

Dual-channel phase-shifting interferometry for microscopy with second wavelength assistance

Dual-channel phase-shifting interferometry for simultaneous phase microscopy is presented. Red and blue light beams are used for microscope illumination. A 45 tilted beamsplitter replicates the object and reference waves in red light together with the object wave in blue light into two parallel beams. The two resulting quadrature phase-shifting interferograms in red light and the object waves in blue light are generated in the two channels. The two interferograms are recorded simultaneously by a color charge-coupled device (CCD) camera, and can be separated via RGB components of the recorded color patterns without crosstalk. As a result, the phase of tested specimen can be retrieved. The feasibility of the proposed method is demonstrated by test performed on a microscopic specimen.     

Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier

In this paper we propose a new method for phase retrieval in an interferogram with a spatial linear carrier. We demonstrate that from the primary interferogram one can extract multiple interferograms (with lower resolution than the original one) with arbitrary phase-shift amounts between them. Then, by applying well-known phase-shifting algorithms, from these phase-shifted interferograms the phase can be retrieved. The method does not require sophisticated data-processing and is computationally efficient. Numerical simulations and validation experiments are presented.