Absolute phase recovery of three fringe patterns with selected spatial frequencies

A new temporal approach is presented for the recovery of the absolute phase maps from their wrapped versions based on the use of fringe patterns of three different spatial frequencies. In contrast to the two-frequency method recently published, the method proposed is characterized by better anti-error capability as measured by phase error tolerance bound. A general rule for the selection of the three frequencies is presented, and its relationship to the phase error tolerance bound is derived. Theoretical analysis and experimental results are also presented to validate the effectiveness of the proposed three frequency technique.     

Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers

This paper presents a method that can recover absolute phase pixel by pixel without embedding markers on three phase-shifted fringe patterns, acquiring additional images, or introducing additional hardware component(s). The proposed three-dimensional (3D) absolute shape measurement technique includes the following major steps: (1) segment the measured object into different regions using rough priori knowledge of surface geometry; (2) artificially create phase maps at different z planes using geometric constraints of structured light system; (3) unwrap the phase pixel by pixel for each region by properly referring to the artificially created phase map; and (4) merge unwrapped phases from all regions into a complete absolute phase map for 3D reconstruction. We demonstrate that conventional three-step phase-shifted fringe patterns can be used to create absolute phase map pixel by pixel even for large depth range objects. We have successfully implemented our proposed computational framework to achieve absolute 3D shape measurement at 40 Hz.     

Statistical searching of deformation phases on wavelet transform maps of fringe patterns

A wavelet transform (WT) analysis is presented to obtain the deformation phases from the fringes with non-uniform carrier frequency, which may appear in the pattern of varied-periodic fringes generated in displacement measurement. Based on the phase maps of the Morlet WT coefficients distributed in a space-scale spectrum, a statistical processing is carried out to search the compacted density of the phase intervals over the scale, and from that the phase modulations related to the object deformation can be determined. Numerical simulation demonstrates the validity of the pattern-processing technique, and the experimental results show the applications to the measurement of the in-plane displacement by the digital speckle pattern interferometry (DSPI) and the measurement of the out-of-plane deflection by the projecting Moiré fringes.     

Evaluation of absolute phase for 3D profile measurement using fringe projection

A new method of absolute phase evaluation for three-dimensional (3D) profile measurement using fringe projection is presented, which combines the gray code and the phase shift technique. Two kinds of fringe patterns are projected onto the object surface respectively, one is sinusoidal intensity distribution used for phase demodulation and the other is gray code fringe pattern for unwrapping. These images are acquired by camera and stored into computer. The absolute phase is obtained by analyzing these images. The validity of this method is verified experimentally. The method is superior to other phase unwrapping methods.     

Patch-wise denoising of phase fringe patterns based on matrix enhancement

We propose a new approach for the denoising of a phase fringe pattern recorded in an optical interferometric setup. The phase fringe pattern which is generally corrupted by high amount of speckle noise is first converted into an exponential phase field. This phase field is divided into a number of overlapping patches. Owing to the small size of each patch, the presence of a simple structure of the interference phase is assumed in it. Accordingly, the singular value decomposition (SVD) of the patch allows us to separate the signal and noise components effectively. The patch is reconstructed only with the signal component. In order to further improve the robustness of the proposed method, an enhanced data matrix is generated using the patch and the SVD of this enhanced matrix is computed. The matrix enhancement results in an increased dimension of the noise subspace which thus accommodates more amount of noise component. Reassignment of the filtered pixels of the preceding patch in the current patch improves the noise filtering accuracy. The fringe denoising capability in function of the noise level and the patch size is studied. Simulation and experimental results are provided to demonstrate the practical applicability of the proposed method.     

散斑干涉相位条纹图的频域滤波处理

为了解决在数字散斑干涉技术测量时,散斑干涉相位条纹图像中大量噪声对相位解包裹结果和精度产生严重影响的问题,介绍了一种条纹正余弦分解和频域低通滤波结合的方法,实现了散斑干涉相位条纹图的高精度滤波。该方法的基本思路是在对相位图像进行滤波处理前,先将相位图通过正余弦函数进行映射转换成两幅图,分别经过频域滤波,然后再合成为相位图。这种分解频域滤波方法可以在滤波的同时,有效保留相位跳变信息。实验结果表明：与传统的图像降噪方法相比,该方法能够在保留图像“尖峰”信息的基础上,较好地滤除图像中的散斑噪声,方法简单有效,有效解决了传统滤波方法应用在相位条纹图中,相图灰度信息丢失10%~40%的问题。     

A new wavelet transform for reliability-guided phase unwrapping of optical fringe patterns

A new daughter wavelet definition for reliability-guided phase unwrapping of the optical fringe pattern is introduced. The new daughter wavelet definition is given by normalized mother wavelet with a new factor including a Gaussian function. The modulus of the wavelet transform coefficients, obtained by using daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter which represents the reliability of the reconstructed phase data. Mathematical demonstration of this parameter is given. Both the computer simulation and experiment reveal the validity of the proposed method.     

Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop

First- and second-order recursive Digital Phase Locked Loops (DPLLs) have been used recently in fringe data processing because it is the fastest way to obtain the unwrapped phase of a carrier frequency fringe pattern due to its minimal computational overhead. Nevertheless these simple DPLLs cannot cope with fringes having high noise and very wide band phase modulation. In this work we present a highly improved DPLL. The system presented is a non-recursive DPLL which is far more robust than previously presented recursive DPLL. The advantage of this newer technique with respect to recursive DPLL is its higher gain in the signal to noise ratio on the detected phase and higher stability. Unfortunately this is obtained at a higher computational cost.     

Camera calibration with planar crossed fringe patterns

We introduced a novel crossed fringe pattern as the model plane for camera calibration. It can provide abundant control points, in extreme case each pixel on the CCD sensor can be taken as control points. Fourier Fringe Analysis is used to extract the phase distributions from the image of this pattern. Each control point consists of the locations of a pixel and the world coordinates, which can be calculated from the phase distributions. It avoids the complex extracting procedure of those classical control points and could produce abundant control points. Both computer simulation and real data have confirmed the proposed technique is easy to use, reliable and high accurate.     

A comparison of phase shifting and fourier methods in the analysis of discontinuous fringe patterns

Phase Shifting Interferometry is a highly accurate data acquisition technique that efficiently utilizes several frames of information for each measurement. In this work, the advantages of phase shifting have been applied to a conventional moiré interferometer, yielding a system capable of recording phase shifted fringe patterns for both in-plane displacement components. Using this method, the phase of a wavefront of interest can be determined at each detector location, so that the resolution of the phase measurements is limited primarily by the detector discrimination and geometry. Unlike traditional Fourier fringe analysis, the noise rejection of phase shift processing algorithms does not degrade image fidelity in the presence of edges and discontinuities. A general discussion of both the phase shifting technique and the Fourier fringe analysis method is included to provide insight into the problems of processing discontinuous fringe patterns.     

A simple method for phase wraps elimination or reduction in spatial fringe patterns

In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation.     

An automated self-marking phase-shifting system for measuring the full field phase distribution of interference fringe patterns

A technique based on the repetition of the interference fringe pattern for the automated marking of the PZT phase shifting interference system is described. A closed-loop control is used to circumvent the inherent hysteresis and nonlinear characteristics of PZT. The whole interference system integrated under LabVIEW graphic programming environment provides users a friendly and ease-of-maintenance interface. An application of the algorithm is used to demonstrate the promotion of the Zygo GPI-LC model interferometer to upgrade its phase resolution ability.     

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.     

低多义性误差的条纹反射技术系统结构研究

条纹反射技术中的多义性误差将直接影响测量结果的精度,现有的多义性误差消除方法会大大增加系统复杂程度,且只能补偿部分的误差。推导了条纹反射系统不含多义性误差的准确相位-梯度解析模型,对该模型仿真分析得出:当系统设置满足进入相机的光线与参考平面和显示屏都成90°夹角条件时,系统多义性误差近乎为0的结论,基于此,提出一种基于同轴光路系统结构,实验证明了所提出的同轴光路系统结构在物体表面高度从0增加至3 mm时多义性误差始终近乎为0,普通系统结构的多义性误差随着物体表面高度从0增加到3 mm时,多义性相位误差从0增加至1.5 rad,实验证明使用提出的同轴系统可以大大抑制条纹反射技术中的多义性误差。     

利用位相信息的条纹微位移测量

详细讨论了在利用位相信息测量条纹亚像素级位移时 ,随机噪声、量化、像元尺寸和像元间隙对位移分辨力的影响 ,并给出了详尽的实验结果。采用一般CCD实现了 1/ 10像素的单次测量精度。     

Sequential demodulation of a single fringe pattern guided by local frequencies

A simple but effective approach for the demodulation of a single fringe pattern is proposed. The phase with an undetermined sign is directly obtained by taking the arccosine value of a preprocessed fringe pattern. The local frequencies, also with an undetermined sign, are then estimated by local matching. The sign ambiguity is then removed simply by forcing the continuity of the local frequencies. The priority of sign determination is guided by the value of total local frequency (fringe density) so that the critical points are processed last. The proposed approach is verified by successful demodulation of a simulated fringe pattern and two experimental fringe patterns.     

载波全息干涉图的自动分析

用正交相干相位检测法实现了载波全息干涉图的自动分析.讨论了分析载波条纹图的边界效应,提出了一种易于在微机上实现的条纹图外插算法.最后给出了一幅实时法载波全息图的分析结果.     

Automatic processing of fringe patterns in integer interferometers

The purpose of this paper is to describe a new method for determination of the total phase difference of light waves without interference fringe counting. One can build up an interferometer for measurement of displacements in which the displacements are determined only by the final values of intensity regardless of the velocity and any prior displacements that caused the present one. The same thing holds true for vibration, relief parameters and other values to be measured. Such an interferometer is devisable thanks to two underlying ideas: first, the application of controllable phase shift, and secondly, the use of properties of integer divisability.