Multi-step phase-shifting algorithms insensitive to linear phase shift errors

We describe and analyse a group of multi-step phase calculation algorithms for evaluation of interferometric measurements using the phase-shifting technique. Phase-shifting algorithms are proposed, with a constant but arbitrary phase shift between captured frames of the irradiance of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process is not dependent on linear phase shift errors. An advantage of the described algorithms is their ability to determine the phase shift value at every point of the detector plane. Moreover, a complex error analysis of proposed algorithms is performed and the algorithms are compared to several common error compensating phase stepping algorithms.     

PHASE SHIFT INTERFEROMETRY FOR ACCURATE TEMPERATURE MEASUREMENT AROUND A VAPOR BUBBLE

An interferometric measurement technique for determining accurately the temperature field around an axial symmetric vapor bubble that might be used for boiling investigations was developed. The specific setup of optical components and the fluid test cell for the generation of a single vapor bubble are described. The procedure and main steps to derive an accurate temperature field from the recorded interferograms are explained in detail. These are: wrapped phase calculation based on a four frames algorithm, phase unwrapping using Itoh algorithm, and Abe inversion for the calculation of the local temperatures. The results from interferometry are verified by point wise measurements using micro-thermocouples. Compared to formerly applied measurement techniques the presented phase shift interferometry leads to higher accuracy and higher spatial resolution.     

Computer aided evaluation of fringe patterns

The crucial step in computer aided evaluation of interferometric fringe patterns is the determination of the interference phase distribution from the recorded and stored intensity pattern. Methods for determination of the interference phase distributions from fringe patterns are presented and the most important methods, which are skeletonising, temporary heterodyning, phase shifting and Fourier transform evaluation are compared with regard to experimental requirements, achievable resolution and precision, as well as inherent noise suppression and image enhancement. The comparison shows that whenever phase shifting is possible, it is the best choice. If only one interference pattern is offered, Fourier transform evaluation is recommendable. For demodulation of the wrapped phase a path-independent algorithm is presented. Practical examples are given from holographic interferometric measurements.     

Phase shifting technique using generalization of Carre algorithm with many images

The present work offers new algorithms for phase evaluation in optics measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. The algorithms are derived similarly to the so called Carre algorithm. The idea is to develop a generalization of Carre that is not restricted to four images. Errors and random noise in the images cannot be eliminated, but the uncertainty due to its effects can be reduced by increasing the number of observations. The advantages of the proposed algorithm are its precision in the measures taken and immunity to noise in images.     

Blind phase error suppression for color-encoded digital fringe projection profilometry

Color-encoded digital fringe projection profilometry (CDFPP) has the advantage of fast speed, non-contact and full-field testing. It is one of the most important dynamic three-dimensional (3D) profile measurement techniques. However, due to factors such as color cross-talk and gamma distortion of electro-optical devices, phase errors arise when conventional phase-shifting algorithms with fixed phase shift values are utilized to retrieve phases. In this paper, a simple and effective blind phase error suppression approach based on isotropic n-dimensional fringe pattern normalization (INFPN) and carrier squeezing interferometry (CSI) is proposed. It does not require pre-calibration for the gamma and color-coupling coefficients or the phase shift values. Simulation and experimental works show that our proposed approach is able to effectively suppress phase errors and achieve accurate measurement results in CDFPP.     

光纤干涉成像阵列全息相位校正研究

针对光纤传输和干涉成像阵列中的相位误差, 提出了一种基于特殊光子晶体的全息相位校正方法。首先分析了光纤干涉阵列成像的基本原理和相位信息的传输过程, 以一维线性阵列建立成像系统相位误差模型, 通过对参考光束和探测器前的快门交替打开和闭合, 来分别实现在晶体上写入由光纤阵列的出射光束与参考光束干涉形成的含有相位误差的光栅函数, 和光纤中出射光束被该光栅衍射和相位偏移以消除相位误差, 从理论上分析了上述基于光子晶体的全息法相位校正原理。最后采用所建立的含有相位误差的干涉阵列进行成像仿真, 对未加校正、采用本文方法和采用冗余基线校正的结果进行了对比分析。     

Linear Phase Shift Response with High Dynamic Range for Holographic Recording in As2S3

Amorphous As₂S₃ films are real-time photographic materials for phase holograms. This work focuses on the phase shift in As₂S₃ films as a function of the exposure. A method for measuring the phase shift response and the exposure simultaneously is presented. A relative displacement determination of interferometric patterns allows precise measurements insensitive to changes of experimental conditions. The phase shift dependence on the intensity of the writing beam is evaluated for two different films. As a result, a linear phase shift response is obtained with a dynamic range of nearly n. It is independent of the intensity over four orders of magnitude. The results are proofed by diffraction efficiency measurements.     

基于白光干涉测量色散补偿薄膜的群延迟色散

为精确测量超快激光色散补偿薄膜的群延迟色散,提出了一种基于窗口傅里叶变换和样条插值去噪算法的新型白光干涉测量方案。计算机模拟表明此方法测试精度可达0.58fs2。分析了高斯噪声和光强平均效应对测试精度的影响,并使用此方法对实验制备的Gires-Tournois干涉反射镜和啁啾镜进行了测试,在宽光谱范围内测试误差小于10fs2。该方法相比其他算法可以更快速、更精确地实现薄膜相位信息的提取,具有更高的测试精度和实用性。     

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。     

相移阴影莫尔条纹正交化解调技术

提出一种基于克莱姆正则化分析法的三帧自标定相移阴影莫尔三维轮廓技术.该技术首先采用移动光栅的方法获得相移条纹图,然后通过不同帧相移条纹图相减去除条纹图背景,进而结合克莱姆正交化法和最小二乘法,发展了一种相位解调方法,提取了测量相位.以五步Harlharan算法为参考,用不同算法对同一物体表面进行测量.结果表明,相对于典型的三步相移法和主量分析方法,提出的方法测量得到的相位误差最小(0.5rad),且简化了测量过程.     

INTERFEROMETRIC DETECTION OF OPTICAL PHASE SHIFT USING TWIN BEAMS

An interferometric detection scheme to measure optical phase shift with sensi tivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N^-1/2 and approach the Heisenberg limit N^-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.     

激光高阶横模的相对相位判定与锁定

本文通过理论计算与数值模拟,提出了不同阶数的高阶模式间相对相位的判定与锁定方法。在像平面对两束光的干涉光斑进行空间取样,计算其干涉光强随相对相位的变化,并在此基础上提出了判定与锁定两束不同阶厄米高斯光束HGmn以及不同阶拉盖尔高斯光束LGpl相对位相的方案,并对厄米高斯光束相位判定与锁定进行了实验验证。     

双点干涉法位相缺陷检测中的解相算法比较

双点光源移相干涉测量是大口径光学元件位相缺陷检测的一种重要方法。为了分析双点干涉中误差对解相算法的影响,首先给出相位缺陷检测的系统结构和理论模型,在此基础上,针对测量过程中主要存在的一次移相误差、二次移相误差、光强误差和随机振动误差,研究了Hariharan 5帧移相算法、13帧移相算法和迭代随机移相算法的解相误差,并进行了仿真分析。结果表明,针对这几种误差源,13帧算法解相精度整体优于5帧法,迭代随机移相算法解相效果优于13帧法和5帧法,当这几种误差按实际指标同时作用时,迭代随机移相算法解相误差RMS小于5帧法和13帧法,PV值稳定在0.5 nm以内。由于随机振动占主要作用,说明迭代随机移相算法受误差影响很小。     

Instantaneous quadrature components or Jones vector retrieval using the Pancharatnam-Berry phase in frequency domain low-coherence interferometry

We use the Pancharatnam-Berry phase as a multifunctional tool for low-coherence interferometry. This geometric phase shift enables instantaneous retrieval of the quadrature components of the complex interferometric signal. The phase shift is independent of wavelength and allows for a complex conjugate suppression of 40?dB for an optical bandwidth of 115?nm. Furthermore, this paper investigates the versatility of the geometric phase to perform polarization sensitive measurements. The Jones vector of the sample was obtained numerically, allowing sample birefringence and optical axis calculation.     

Phase-stepping interferometry: Five-frame algorithm with an arbitrary step

The present paper offers a new formula for calculating the phase in interferometric measurements by the phase-stepping method. The proposed five-frame algorithm utilizes equal phase steps with an arbitrary value. Results are presented on computer simulation of the errors occurring at a phase-step different from 90 ° and due to vibrations in the system ‘interferometer-object’.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements

A new two-frame interferometric method with a blind phase shift of a reference wave is proposed for the reconstruction of smooth surface relief areas. In this method, a correlation approach based on the determination of correlation coefficient between intensity distributions of two interferograms is applied for the phase shift extraction. An algorithm for this method realization is developed and its performance is verified on test surfaces. An experimental setup containing a Twiman-Green interferometer was used in the reconstruction of smooth surfaces of metal specimens using the developed algorithm. Surface displacement phase fields were generated in case of a CT-notched specimen made of an aluminum alloy by the interactive procedure of element stitching of two surface reliefs and subtracting the surface relief after cyclic loading from the initial one. The received surface displacement fields allow us to determine the studied specimen fatigue process zone (FPZ) and FPZ size.     

Comparative analysis of interferogram noise filtration using wavelet transform and spin filtering algorithms

The aim of this paper is to analyze 2D fringe pattern denoising performed by two chosen methods based on quasi-1D two-arm spin filter and 2D discrete wavelet transform (DWT) signal decomposition and thresholding. The ultimate aim of this comparison is to estimate which algorithm is better suited for high-accuracy measurements by phase shifting interferometry (PSI) with the phase step evaluation using the lattice site approach. The spin filtering method proposed by Yu et al. (1994) was designed to minimize possible fringe blur and distortion. The 2D DWT also presents such features due to a lossless nature of the signal wavelet decomposition. To compare both methods, a special 2D histogram introduced by Gutman and Weber (1998) is used to evaluate intensity errors introduced by each of the presented algorithms.     

基于相位展开及拼接算法的一种高精度大量程宽光谱干涉显微术

宽光谱干涉显微术广泛应用于高精密检测领域,它测量样品形貌通常采用垂直扫描干涉术对亚微米至毫米级特征进行测量,以及相移干涉术对纳米级特征进行测量。其中,相移干涉术精度可达纳米级,但量程有限,高度变化对应的相位需限制在区间内。采用包裹相位展开算法可以扩展相移干涉术的量程,也仅适用于平滑表面,当高度起伏超出焦深或者光源相干长度的限定范围时,干涉条纹模糊或对比度丧失,所解算的结果将产生较大误差甚至错误。提出一种基于相位展开及拼接算法的高精度、大量程宽光谱干涉显微测量方法,以干涉条纹调制度量化条纹质量,条纹对比度高、成像清晰的区域对应调制度较高,定义当前焦面条纹调制度高于阈值的区域为理想区域,定义焦面条纹调制度低于阈值的区域为问题区域。以相位展开算法获得理想区域中的样品相位分布,问题区域的包裹相位不进行展开。使用微位移结构纵向移动物镜焦平面,选择合理的步长,使相邻焦面位置理想区域展开后的真实相位保持部分区域重合,根据重合区域的相位值均差可以实现不同焦面位置的高精度相位拼接,最终获得扩展量程的高精度真实相位结果,进而可以恢复样品完整的表面形貌分布。该算法通过对理想区域的筛选,避免了相位在问题区域展...     

Uncertainty analysis of temporal phase-stepping algorithms for interferometry

We have addressed the problem of the uncertainty evaluation of phase values rendered by two popular algorithms: the N-bucket and the (N + 1)-bucket, both used to exploit temporal phase-stepping techniques. These algorithms, are mainly affected by errors in the calibration of the piezoelectric transducers used to achieve the phase shift, external vibration and optical noise. We have characterized and compared the influences of these errors on the phase uncertainty. We applied a Monte Carlo-based technique of uncertainty propagation that allowed us to consider in the uncertainty evaluation the simultaneous contributions of different error sources. The uncertainty evaluation was performed for phase values in the range (0, 2π), with different values of N and assuming that the phase was calculated from fringe patterns generated by using either Moiré interferometry or electronic speckle-pattern interferometry. We found that the uncertainties associated with the phases rendered by both algorithms are similar and they can be significantly affected by the optical noise and the value of N.