基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

单幅载频条纹图的相位恢复新算法

针对单幅载频变形条纹图的相位重构问题,提出了一种快速、高精度和免解包裹的相位恢复新算法。该算法利用两次希尔伯特(Hilbert)变换法从单幅条纹图中分离出正弦分量和余弦分量,然后由这两个分量计算出相位的斜率,对水平和垂直两个方向上的相位斜率进行积分,最后得到全场相位分布。计算机模拟和实验结果表明,该算法仅需一幅变形条纹图即可很好的恢复全场相位分布。与传统的傅里叶方法相比,该算法不需要解包裹处理,简化了计算量,避免了相位解包裹过程带来的误差,并且对阴影和相位不连续点不敏感。     

希尔伯特变换条纹分析法及其在非球面镜测量上的应用

提出了利用离散的希尔伯特变换法解调干涉条纹相位的方法,叙述了希尔伯特变换法解调相位的原理,并从单一的干涉图样中提取出条纹信号的正弦和余弦部分,正弦与余弦比值的反正切即为干涉相位;然后利用泽尼克多项式拟合,实现波前重建;最后讨论了条纹相位的算法,误差修正和测量面形的应用,从而实现对非球面镜的检测。实验表明,该方法可获得均方根(RMS)的精度为λ／10。     

非单调条纹图的相位恢复新方法

在连续小波变换和展开相位拐点识别的基础上,提出一种非单调条纹图的相位恢复新方法.包裹相位通过连续小波变换的方法提取,提出小波变换尺度步长的选择准则及对粗糙尺度作迭代均值滤波的技术.基于展开相位拐点与符号歧义点的单应性,可通过检测并修正展开相化拐点的方法恢复非单调条纹图的真实相位.给出了详细的理论推导、数值模拟及实验验证过程.数值模拟包括一维及二维的含噪声信号,实验为基于显微干涉法的微桥的静动态形貌和变形测试.模拟及实验结果表明,该法只需一幅条纹图即可准确解调非单调条纹的相位,最大误差小于4%,且具有极强的抗噪能力.这为显微干涉测量提供了有效的相位恢复新手段.     

基于二维连续小波变换的ESPI条纹图相位提取方法

提出了一种基于二维连续小波变换的电子散斑干涉(ESPI)条纹图相位提取方法。通过检测二维小波脊确定条纹相位,并引入条纹频率作为向导,有效地避免了相位解调过程中的符号奇异性问题,从而使该算法既能处理开条纹图也能处理闭条纹图,且对散斑噪声具有较强的抑制能力。数值模拟和实验结果表明,该方法在抑制散斑噪声的同时能够有效地提取出条纹相位,对开条纹图和闭条纹图都能处理。     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

一种新的单幅条纹图的相位解调方法

基于非载波条纹图的条纹灰度分布的极值准确定位,提出了一种新的由单幅条纹图解调相位方法.该方法首先准确定位每个条纹灰度的极值包括最大和最小,再基于极值图将条纹的强度值分布线性地变换到-1和1之间,最后利用arcos反余弦取代传统的atan2反正切算法求出相位,结合极值图就能快速准确地解调出含有封闭条纹的条纹图相位.本方法仅用一幅条纹图,不需要传统的条纹定级和对分数级条纹插值与拟合,自动判别条纹相位变化的波谷,准确获得条纹相位分布.这一方法使光测法研究动态和瞬态问题成为可能,而不需引入载波法调制条纹.文中通过实例说明了本方法的处理过程.     

基于条纹中心线的载波散斑条纹解调方法

针对传统傅里叶变换法在处理含有多突起的载波散斑条纹图时,由于存在频谱展宽会出现严重的解调相位失真,提出了一种基于条纹中心线的载波散斑条纹解调方法.根据载波调制时所采用平行调制方式和倾斜调制方式,分别从理论上对相关的中心线解调法进行数学推导,并进一步采用最小二乘三次曲面拟合法获得被测物面全场的离面位移信息.实验结果表明:利用上述中心线解调法和曲面拟合法能解调出复杂的载波条纹图,并获得具有亚像素定位准确度、连续光滑的全场离面位移信息.     

二帧变换光源阴影莫尔技术研究

为了快速测量物体表面三维轮廓,提出一种变换光源位置的相移阴影莫尔技术.该方法通过控制两个光源的亮灭,将相移引入测量视场.使用二维经验模式分解法对条纹图进行正则化,结合螺旋相位变换方法和二帧相移算法对测量高度进行估计,利用发展的迭代自调算法提取精确测量相位.计算机仿真和光学实验结果表明,该方法的解调准确度优于现有的二帧相移解调算法,同时,由于消除了测量过程中必要的机械运动,只需要二帧条纹图进行相位解调,节约了测量时间.     

A numerical spatial carrier for single fringe pattern analysis algorithm

Hilbert transform and continuous wavelet transform are combined to form an algorithm for the analysis of a single fringe pattern with open or closed fringes. Only one recorded fringe pattern is needed to extract the phase information. A second π/2 phase shifted fringe pattern should first be generated from the other using Hilbert transform to superpose numerically the spatial carrier. Several phase extraction techniques are conceived to demodulate fringe patterns. In this paper, the wavelet technique is used to obtain the required phase distribution. The algorithm offers an advantage that it is appropriate when the spatial carrier is impossible to be added experimentally. Finally, a simulation was carried out to validate the algorithm, giving good results.     

空间载频条纹相位分析法中的相位不确定性

分析了单频、双频空间载频光学条纹相位分析技术中的相位不确定性问题,提出采用两频率之比为无理数的双频载频条纹,相位可完全确定,并提出了基于两频率之比为无理数的空间载频条纹相位确定算法,给出了实验结果。     

Hilbert assisted wavelet transform method of optical fringe pattern phase reconstruction for optical profilometry and interferometry

A Hilbert assisted wavelet transform (HWT) method is presented for phase reconstruction of 3D profilometry and interferometry. A rigorous mathematical demonstration about this HWT method is given in this paper. An important conclusion that the phase of the optical fringe pattern is equal to the phase of its HWT coefficients on the ridge is theoretically clarified. The strict relation between the scale parameter and the phase gradient (also called the angular frequency) of the fringe pattern is also given. Computer simulations and experiments reveal the validity of the method and the correctness of the mathematical demonstration. Since the filtering process is avoided in this method, it can deal with the frequency overlapping problem to a certain extent. Applications of this method in both optical profilometry and interferometry are shown and discussed in the experiment section.     

Multi-parameter measuring method of image intensifier based on Fourier transform phase measurement

A new quality parameter measuring method of image intensifier based on Fourier transform phase measurement is proposed. A standard sinusoidal fringe pattern is projected into the measuring system by spatial light modulator and the corresponding reference pattern and deformed pattern are captured by CCD. The Fourier transform and inverse Fourier transform are applied in order to extract the phase distribution of deformed pattern. The magnification, pillow-shaped distortion, barrel-shaped distortion, snake-shaped distortion and shear distortion of image intensifier are obtained at the same time. Experiment has proved its feasibility with real-time performance and without manual intervention.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

Interferometric Phase-Measurement Using a One-Dimensional Discrete Hilbert Transform

A phase demodulation scheme using a discrete Hilbert transform that can change the interferometric phase by /2 has been investigated. In-quadrature components of a fringe pattern are obtained from one captured interferogram using a one-dimensional (1-D) discrete Hilbert transform and a 1-D discrete high-pass filtering that are based on a digital signal processing technique. The phase distribution in the range of 15 (rad) can be demodulated with the proposed method. The 1-D discrete Hilbert transform can be extended to two-dimensional calculation with a raster scanning procedure. © 2005 The Optical Society of Japan     

Phase retrieval of optical fringe patterns from the ridge of a wavelet transform

A new method for phase retrieval of optical fringe patterns is presented. This method is based on a wavelet transform and is capable of extracting the full 2D phase distribution from a single fringe pattern. An important conclusion that the phase of the optical fringe pattern is equal to the phase of its wavelet transform on the ridge of the wavelet transform is theoretically clarified. The method is compared with the Fourier transform and the integration methods. A numerical simulation and an experimental example of phase retrieval are shown.     

Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.