Smoothing filters in phase-shifting interferometry

The images used in phase-shifting interferometry are usually noisy and smoothing filters are frequently used. Filtering can be done on the fringe patterns before phase retrieving or on the phase map after phase retrieving. Filtering fringe patterns—a form of preprocessing, requires the same processing to be done on at least three patterns. Filtering phase map, on the other hand, needs processing of only one pattern. Preprocessing prevents noise from being carried through while post-processing might clip parts of the signal. Thus there is a need to evaluate which one is better. A theoretical analysis was carried out for this basic problem, followed by computer simulations and a real experiment for verification. The comparison was also extended to phase difference measurement which uses similar but slightly different phase retrieval algorithms.     

移相干涉测量中的抗振技术

移相干涉测量技术是一种众所周知的非接触式的高精密测量方法,具有广泛的应用范围。环境振动是移相干涉仪测量误差的主要来源之一,国际上一些从事干涉测量的工作人员提出了许多抗振的方法,大体上分为主动技术和被动技术。主动抗振技术主要是系统自身探测振动并通过反馈回路对振动进行补偿,被动抗振技术则是通过各种技术措施尽量减小干涉仪对环境振动和气流影响的敏感度。从这两方面对干涉仪的抗振技术研究的进展做简单介绍,并介绍了作者所在课题组在这两个方面所进行的研究工作。     

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.     

一种新的移相干涉技术

本文提出了一种对连续采得的大量移相干涉图通过干涉条纹光强定标或傅里叶变换方法求出被测波前相位分布的新的移相干涉技术。此技术充分利用了近代计算机和ＣＣＤ数字图像处理技术的新成果，不仅可使干涉仪的硬件系统简化，成本降低，还可明显提高仪器的抗干扰能力，促进移相干涉技术的普及和推广应用。     

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.     

双散斑场相移数字干涉计量

本文介绍了一种检测散射表面变形的自动测量系统。将相移和数字图像处理技术应用于数字散斑干涉计量中,毋须中间记录过程,在计算机控制下采集数据和计算相位,产生相位条纹而非相关条纹。用图像处理技术消除散斑随机性引起的噪声。文中给出了面内、离面变形的测量结果。     

相移干涉术及广义相移数字全息干涉术

在基础光学框架内说明了传统的相移干涉术及近年来发展的广义相移数字全息干涉术的基本原理;前者要求特殊值等步长相移,而后者则可以采用任意未知相移值.着重介绍了广义相移干涉术中的物波恢复算法,以及基于衍射场统计特性的未知相移提取算法.从一个侧面沟通了基础光学与近代光学之间的关系.     

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.     

Efficient iterative algorithm for phase-shifting interferometry

This paper presents an efficient iterative least-squares algorithm for phase-shifting interferometry. If the phase shifts contain errors, the residuals (i.e. the differences between the recorded intensities and their recalculated values) of least-squares algorithm are dependent on these errors. Based on this fact, an approach that allows estimating the phase shift errors from these residuals is derived. Using the results, the values of phase shifts are corrected. By iterating the two steps: phase evaluation and phase shift correction, the phase distribution can be accurately reconstructed. Its validity and performances have been investigated by both the numerical simulation and experiment results. The convergence condition with this algorithm is also discussed.     

Fast image-processing technique in phase-shifting holographic interferometry

A fast image-processing method in phase shifting holographic interferometry is proposed, in which the complicated phase calculation is completed with a logic circuit and look-up table. An electronic circuit was designed for the purpose. With these techniques, the processing time can be greatly reduced.     

Full-phase image encryption by two-step phase-shifting interferometry

We have proposed a full-phase image encryption method based on double random-phase encoding in Fresnel domain and pixel random permutation (PRP) technique with the use of two-step phase-shifting interferometry (PSI) we reported recently, and verified the effectiveness of this method and its robustness against occlusion and noise attacks by a series of numerical simulations. Comparing with other similar methods, this approach can decrease the number of the interferograms to be delivered from at least three needed in ordinary PSI to only two, give much better performance of image reconstruction than amplitude-based encryption, and provide much higher security level. This method is usable for both the gray-level images and binary images, and usually the latter will lead to better results.     

Improved accuracy phase retrieval in spatial phase-shifting interferometry

Algorithms for phase retrieval in spatial phase-shifting interferometry are examined. It is noticed that the classical Carré technique based on four neighbor pixels may introduce shaped phase residuals that affect the accuracy of the reconstruction. A variant of the technique is proposed, taking into consideration five pixels and steering the phase retrieval algorithm to the appropriate subset so that residuals are free of underlying errors. Computational results are presented illustrating the approach and demonstrating the accuracy improvement in a case study.     

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.     

Closed-loop phase-shifting interferometry with a laser diode

A closed-loop phase-shifting Fizeau-type interferometer at lambda=633 nm was constructed with the direct frequency modulation of laser diodes. The interferometer is servo controlled fully in the phase domain where optical phases are detected by a two-frequency optical heterodyne method. Stepwise phase shifting was accomplished with good stabilization against external disturbances (vibration, air flow, etc.) and laser frequency fluctuations.     

Analysis of the principal component algorithm in phase-shifting interferometry

We recently presented a new asynchronous demodulation method for phase-sampling interferometry. The method is based in the principal component analysis (PCA) technique. In the former work, the PCA method was derived heuristically. In this work, we present an in-depth analysis of the PCA demodulation method.     

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.     

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.     

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     

Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time.     

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.