消除移相干涉测量中线性移相误差的五帧算法

在移相干涉测量中存在着移相器的移相误差,这对测量结果的精度有很大的影响。提出了消除移相器线性误差的五帧算法,使用该算法对五帧干涉图像进行处理。使用MATLAB软件针对移相干涉测量过程进行了模拟仿真。仿真结果表明,该算法在相位提取过程中可以消除移相器的线性误差因子,并对于常见的高斯噪声影响不敏感,从而提高了表面形貌测量精度。     

General Phase-stepping Algorithm Using Lissajous Figures Technique

A new phase-stepping algorithm is proposed, the algorithm can be implemented without knowing or calculating the phase steps. New phase extraction expressions based on using Lissajous figures and ellipse fitting are derived by introducing a simple difference transform for the intensity of the interferograms. The simulating results indicate that the new algorithm is insensitive to phase-stepping errors and the accuracy of the new algorithm is only limited by the computation truncation errors.     

Phase-shift extraction from twice-normalized light intensity changes recorded with random phase shifts

A simple phase-shift extraction algorithm is proposed for interferograms recorded with random phase shifts that vary over at least 2π. The phase-shift-dependent changes in the intensity at two pixels having different phases, selected from one frame, are taken out and normalized. The sum and difference of the two normalized changes are calculated, and both the changes are normalized again along the phase shifts. The normalized sum and difference become the cosine and sine of a term including the random phase shift, respectively. Thereby, the phase shifts are extracted from both twice-normalized intensity changes. An experiment using an interference microscope equipped with a piezoelectric-transducer positioner of an objective lens is conducted to estimate the validity of the algorithm. The algorithm is verified to have satisfactory results when the multiple interferograms used have a sample size of more than 15 frames recorded with random phase shifts.     

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。     

An Effective Phase Unwrapping Algorithmfor Phase-stepping Interferometry

1.IntroductionInrecentyears,manyinterestshavebeenconcentratedontheproblemofphaseunwrappingforthefringepatternanalysis.Thewrappedphaseisintheformofthetangentfunctioninthecomputer.Thecalculatedphasevaluesarewrappedinto--rsto rs,whilethepracticalphasevaluesarereconstructedafterphaseunwrapping.Ifthecasesof'noise,steepwavefront,lowmodulation,andspeckleexistinthefringepatterns,thephaseunWrappingprocesswillfailthroughtheconventionalphaseunwrappingalgo-rithm[1'2].Asaresult,manystripswillbegeneratedin…     

基于DCT算法的种子点相位解包算法

移相干涉术由于其高精度被广泛应用在光学元件的面形测量上,而由移相算法得到的相位数据被包裹在[-π,π]之间。基于区域生长理论的相位解包算法(种子点法)可以高精度地实现连贯区域的相位解包,基于离散余弦变换的最小二乘解包(DCT)算法可以实现矩形区域的相位解包,而实际测量中,经常会碰到被测件的有效区域为非矩形的分离区域。因此,在分析前两种算法优缺点的基础上,提出了基于DCT算法的种子点相位解包算法。首先运用DCT算法对整个包裹相位进行解包,然后运用种子点法分别解包各分离区域,再通过DCT算法求得的种子点干涉级次实现各分离区域解包相位的统一。实验结果表明,该方法克服了种子点法和DCT算法的缺点,可以准确、快速地实现分离区域干涉图包裹相位的解包,且比这两种算法具有更好的稳定性和更高的精度。     

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.     

基于相位跳变区划分的相位展开方法

提出了一种相位跳变区域的确定方法，在此基础上提出一种基于相位跳变区划分的相位展开方法。计算机模拟和实验结果均证明：此方法对噪声有很强的抗干扰能力，能有效地实现带噪声的主值相位图的相位展开。     

基于自适应加权窗口的相位质量图提取

加权相位解缠算法的解缠精度取决于所提取的质量图的可靠性。目前提取相位质量图的方法大多采用以各个像素为中心的固定窗口法,但当某些像素被噪声严重干扰时,采用固定窗口法提取质量图往往得不到正确的解缠结果。因此,提出了几种自适应加权窗口方法来提取相位质量图,并给出了具体的实现方法和步骤,同时采用加权小波变换相位解缠算法进行相位解缠。实验结果表明,采用自适应加权窗口方法提取相位质量图来确定初始权重系数能获得比较好的解缠效果。     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

An effective method in calibrating nonlinear errors for phase-shifting interferometry

In phase measurement or digital holography for phase-shifting interferometry, the key role is the variation of reference light wave and recover algorithm based on interferograms and reference phase, so the calculation result is directly affected by phase-shift accuracy. However, because of the errors of nonlinear and other random factors, it is difficult to control the actual phase-shifting amount accurately. In this paper, we aim to propose an efficient method for phase-shifting interferometry which does not require accurate initial estimation of phase-shift amounts, only a few pixels with several randomly shifted interferograms are sufficient for accurate extraction of phase information. This method has reduced the dependence of reference phase, and can obtain phase-shifting amount directly without using complex revised algorithm for correcting phase-shifting nonlinear errors.     

在随机和倾斜移相下光强归一化的迭代移相算法

由于存在振动和导向误差,干涉仪移相器在移相过程中产生随机的平移误差和倾斜误差,会给测量结果带来影响。因此高精度测量中对环境的稳定性和移相器的性能要求很苛刻。为了降低此种要求,针对随机和倾斜移相下干涉图背景光强和调制度的不均匀会影响移相平面计算的问题,对采集得到的干涉图做归一化处理,并利用迭代最小二乘法对归一化的干涉图做相位求解。迭代过程中,将干涉图分块来求解移相值,并对各移相值做平面拟合得到移相平面。仿真结果表明,该方法消除了背景光强和调制度的不均匀对倾斜系数计算的耦合作用,能够有效补偿倾斜移相误差对面形相位的影响,与其他方法相比,具有收敛速度快、求解精度高的特点。实验结果进一步验证了该方法的有效性。     

基于可靠性的相位去包裹算法

提出了一种新的基于可靠性的相位去包裹算法。采用了队列算法及去包裹可靠性的判别标准。与传统方法相比,能够自动避开噪声区域,解决了相位去包裹中的阴影遮挡以及空洞等问题,克服了传统去包裹方法中的误差传播效应,能准确快速地对全场进行相位去包裹。设计了一套基于此算法的三维形面测量系统。     

An Improvement of Spatial Carrier Phase-shifting Method

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An Improvement of Spatial Carrier Phase-shifting Method

Spatial-carrier phase-shifting method (SCPM) retrieves the phase distribution from carrier interferograms by assuming that the phases of the processed pixel and its adjacent pixels are uniform,which introduces considerable theoretical error. A new method is presented in this paper to improve the SCPM accuracy: (1) A quadric curve is used to describe the phase distribution of the adjacent pixels; (2) The linear and quadric terms of the phase are considered as phase shifter errors; (3)Suitable phase shifting algorithms insensitive to these errors are selected. Two "5-step" algorithms are used and their properties are analyzed. An example ofphase retrieving by SCPM is given and the result shows that SCPM has high theoretical accuracy. With the potential high accuracy, ability of measuring dynamic phase andcomputational simplicity, SCPM will become a much more useful phase measurement method.     

基于界面信号的扫频光学相干层析成像系统相位矫正方法

由于扫频光源的采集触发信号和采样时钟信号存在时间上的随机延时,导致扫频光学相干层析成像(SS-OCT)系统干涉信号光谱的整体错移,进而引发OCT空间域信号的相位跳变,阻碍了基于相位信息的功能成像.为了获得稳定的相位,便于开展功能OCT的研究,提出了一种基于界面信号的数字相位矫正方法.对界面附近相邻A-line间同一深度的相位信号进行差分运算,计算得到相位跳变的A-line位置与光谱错移量(以像素为单位),然后在原始干涉信号上对齐光谱,重新傅里叶逆变换,得到矫正后的复信号.该数字矫正算法不会引入额外的相位噪声,可以实现OCT信噪比受限的相位探测.通过对反射镜、荧光板和小鼠脑皮层血流的多普勒成像验证了该方法的可行性.     

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.     

General Phase-stepping Algorithm Using Lissajous Figures Technique

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Phase-stepping : New Algorithm Immune to Linear Reference Phase Error

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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.