基于S变换的改进窗口傅里叶三维测量法

讨论了一维S变换在处理条纹图中的应用,推导了S变换表达式,提出一种基于S变换脊的自适应窗口傅里叶三维测量法。利用S变换对于频率的敏感性以及S变换脊思想,求得任意点的瞬时频率。推导了在相位跳变剧烈区域相位二阶导φ″(b)对S变换脊的影响,并求得去除此影响后更为准确的瞬时频率。然后将瞬时频率倒数作为经典窗口傅里叶变换(WFT)的窗口大小,解出条纹图的精确相位。最后对去除相位二阶导影响前后基于S脊的WFT进行对比仿真;实验验证其与传统基于小波脊的WFT在抗噪声、解相位精度上的优势。     

Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets

Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method.     

Deformation measurements of dragonfly's wings in free flight by using Windowed Fourier Transform

Grating Projection method was used to measure the height distribution of dragonfly's wings in free flight. Then the fringe patterns on the dragonfly were recorded by a high-speed CCD camera. Since the fringe patterns recorded in such a way have poor contrast and brightness, Windowed Fourier Transform (WFT), which is insensitive to noise and fringe amplitude, was used to process the fringe patterns to extract the phase. Finally, the height distributions of dragonfly's wings in free flight were obtained by using the Weighted Least-Squares Phase Unwrapping method. The choice of integration limits and the size of the window of WFT are briefly discussed here     

Applications of windowed Fourier fringe analysis in optical measurement: A review

The applications of windowed Fourier fringe analysis in the past decade are reviewed. Because fringe patterns from different optical measurement systems are similar, the reviewed applications are classified according to the functions of the windowed Fourier transform being used in fringe pattern analysis: denosing exponential phase fields, demodulating carrier fringe patterns, getting phase derivatives, and utilizing local properties. From these applications, the windowed Fourier transform is shown to be effective and versatile for fringe pattern analysis.     

基准光栅重构傅里叶变换轮廓术

应用傅里叶轮廓变换术进行三维形貌测量中,为了获得待测物体的高度相位信息,通常需要采集两幅图像.因此当光学系统发牛变动时,必须重新采集基准光栅图像,不利于快速测量.提出一种从变形光栅图像中获取基准光栅图像信息的测量方法.首先在变形光栅图像中记录基准光栅信息,然后通过傅里叶分析提取基准光栅频率信息,通过图像分析获得基准光栅相位信息,最后重构出一幅完整的基准光栅图像,实现三维物体形貌测量.实验结果验证了该方法的可行的.     

On window size selection in the windowed Fourier ridges algorithm: Addendum

The windowed Fourier transform is a useful technique for fringe pattern analysis. It has been shown that the proper selection of the window size is a balance between the linear phase approximation error and the influence of noise [Q. Kemao, On widow size selection in windowed Fourier ridges algorithm. Opt Lasers Eng, 2007, accepted for publication]. Since the fringe intensity and noise level usually vary spatially, the window size should also be spatially adaptive in order to reach a good balance for each pixel of the fringe pattern. This addendum first shows that the windowed Fourier transform with a spatially fixed window size (SFWS) is still practically useful and then discusses the window size competition strategies for the windowed Fourier transform with a spatially adaptive window size (SAWS). The windowed Fourier transform with a SAWS is theoretically better than that with a SFWS but it is also more challenging in use. The windowed Fourier ridges algorithm is used for analysis throughout this paper. This analysis is also applicable to the windowed Fourier filtering algorithm.     

基于结构光投影的二维S变换轮廓术

S变换是一种集合了窗口傅里叶变换和小波变换优点的时频分析技术,目前一维S变换已成功应用于结构光投影的条纹相位解调中。由于二维S变换可以对图像在两个方向上进行时频分析,具有更优于一维S变换的分析和处理能力。为了完善S变换的条纹相位解调理论,将二维S变换方法引入到基于结构光投影的三维光学测量中,研究了二维S变换在条纹相位解调中的原理及应用,给出了详尽的理论分析,并同一维S变换结果进行了比较。模拟和实验都表明,在条纹图解相中,二维S变换比一维S变换提取的相位精度更高,即使在存在较严重噪声污染的情况下也表现出良好的可靠性,体现出二维S变换提取相位的优势。     

On window size selection in the windowed Fourier ridges algorithm

The windowed Fourier ridges (WFR) algorithm can be used to extract the frequency and phase information from an exponential or carrier fringe pattern. The selection of the window size for this algorithm is investigated in this paper. For exponential phase fringe patterns, the window size does not need to be adjusted according to the signal frequency. Hence the scaling strategy of the wavelet transform is not necessary. Instead, the window size should be selected according to the balance between the linear phase approximation error and the noise level. For carrier fringe patterns, the influence of the conjugate component should also be considered. However it can be ignored when the lowest frequency of the fringe pattern is higher than 1.5/σ (σ is used to represent the window size).     

基于椭圆形光强分布光栅投影的三维面形测量方法

基于椭圆形光强分布光栅投影测量物体三维面形的方法,将椭圆形光强分布光栅投影到被测物体表面,用摄像机获取变形条纹图,通过系统参量和条纹图携带的相位信息求解出物体的三维面形.推导出通过椭圆形光强分布光栅条纹求解相位的计算公式并对提出方法作了计算机仿真.实验结果表明该方法可以比较准确地测量物体的三维面形,在噪音较大的情况下测量结果仍具有较高准确度.     

基于椭圆形光强分布光栅投影的三维面形测量方法

基于椭圆形光强分布光栅投影测量物体三维面形的方法,将椭圆形光强分布光栅投影到被测物体表面,用摄像机获取变形条纹图,通过系统参量和条纹图携带的相位信息求解出物体的三维面形.推导出通过椭圆形光强分布光栅条纹求解相位的计算公式并对提出方法作了计算机仿真.实验结果表明该方法可以比较准确地测量物体的三维面形,在噪音较大的情况下测量结果仍具有较高准确度.     

Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform

A novel two-dimensional (2D) Gabor continuous wavelet transform (CWT) for phase retrieval and fringe filtering of speckle fringe patterns with spatial carriers is proposed. Theoretical analysis of 2D Gabor CWT is presented and results are compared with advanced fan 2D CWT using both the computer simulated and experimental speckle fringe patterns. It is shown that noise reduction by 2D Gabor CWT demonstrates better results than that of the advanced fan 2D CWT. Two-dimensional Gabor CWT is also compared with 2D Fourier transform and results show that 2D Gabor CWT algorithm has better noise immunity.     

三维测量中一种新的自适应窗口傅里叶相位提取法

针对多尺度窗口傅里叶变换中,窗口尺寸的自适应选取及提取基频时的频谱混叠等问题,提出基于希尔伯特-黄变换(HHT)的自适应窗口傅里叶相位提取法。对变形条纹信号进行HHT后,通过谱分析,自适应确定能够准确描述条纹信号变化情况的瞬时频率及条纹图的背景分量。根据所得的瞬时频率,给出自适应定位条纹信号局部平稳区域的步骤,进而确定窗口尺寸。不需额外计算,可有效去除背景分量以减少基频提取过程中零频频谱的干扰。与现有的用最大脊法确定窗口尺寸的方法相比,本方法不受被测相位必须线性逼近且变化缓慢的前提约束。实验证明本方法有效、可行,且对测量携带陡峭边缘或面形复杂的物体也能进行较为精确有效的测量。     

Three-dimensional Fourier Fringe Analysis

Over the years two-dimensional Fourier Fringe Analysis (2D-FFA) has demonstrated both its capability and its relative robustness in analysing fringe patterns within a short time-frame from static objects. Nowadays, there is an increasing demand to measure dynamic objects. Today 2D-FFA is seen as a fast and flexible method of processing fringe patterns for dynamic objects. But it is still inherently a 2D approach, i.e. it deals with three-dimensional data (video sequences) on an individual 2D frame-by-frame basis. In this paper, a novel three-dimensional Fourier Fringe Analysis (3D-FFA) algorithm is proposed to demodulate fringe pattern sequences taken from dynamic objects. This technique processes the stack of fringe patterns as a single 3D volume, not as a set of individual 2D frames that are each processed in isolation. The proposed algorithm has been evaluated on both computer simulated and real dynamic objects. Results show that the proposed technique is able to demodulate fringe pattern volumes successfully.     

利用强度调制消除零频的傅里叶变换轮廓测量

采用双色正弦条纹投影的傅里叶变换轮廓术中零频分量的扩展对有用基频分量有影响,为此提出一种新型的基于强度调制的零频消除方法提高测量准确度和范围.通过采集一帧变形彩色条纹图并分离颜色通道获得两幅相位差为π的条纹图,对变形条纹做强度调制校正,进而消除零频分量,实现高度解析.理论模拟和实验测试均验证了此方法的有效性.相比传统的相移消除零频分量的方法,此方法具有显著的速度优势,适合于三维物体的实时测量.     

基于图像二维小波多尺度分解傅里叶变换轮廓术

应用傅里叶变换轮廓术测量物体三维面形时,当被测物体形状复杂或是被噪声严重污染时,导致频谱分布展宽,发生频谱混叠现象,基频提取困难,无法准确恢复物体的三维面型.提出了基于小波分解的傅里叶变换轮廓术,采用小波变换的方法对变形条纹图进行二维多尺度分解,重构被测物的背景图像,滤出图像的零频成分,得到相对变形条纹.运用小波变换与傅里叶变换轮廓术相结合的方法,只需拍摄一幅变形条纹图,将被测物体与背景分离,不受背景成分的影响,且易于基频信息的提取,降低了对滤波器的要求.实验证明该方法较好地防止了频谱的混叠问题,提高了测量范围与解相精度.     

傅里叶变换轮廓术中新的相位及高度算法分析

在传统傅里叶变换轮廓术三维面型测量中,为了准确得到被测物体的高度分布,必需保证投影仪出射光瞳和摄像机入射光瞳的连线与参考面平行并且在同一水平面,否则存在较大的误差。着眼于更普通的情况,讨论双瞳连线与参考面成某一夹角时的高度计算,推导出了非平行时的参考面光场及物面变形条纹光场的表达式,并给出了高度映射公式。因而,传统的傅里叶变换轮廓术测量成为角度α=0时的特例。该方法使傅里叶变换轮廓术的测量条件得到了放宽;易于通过移动投影装置或成像装置获取全场条纹;并为在难以实现双瞳与参考面平行的特殊环境下的测量提供了可行的方法。计算机模拟及实验均证实了该方法的有效性。     

Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

In order to measure the displacements of facets on a growing spherical Cu_2−δSe crystal with sub-nanometre resolution, we investigated the reliability and accuracy of standard method of Fourier analysis of digital laser interferograms. Guided by realistic experimental conditions (two-dimensional (2D) interferograms), starting from 2D model interferograms and using original custom designed Gaussian filtering window and multistage unwrapping procedure of the retrieved phase, we demonstrate for a considerable parameter range the non-negligible inherent phase retrieval error due to non-integer number of fringes within the digital image. Our results indicate an intermediate parameter range where the error is acceptably small. We introduce an algorithm modification that significantly reduces the error, especially for low and high fringe densities. In the experimentally most common case of diagonal fringes the reduced error is an order of magnitude smaller than for nearly one-dimensional case within almost entire parameter space.     

Infrared small target enhancement via phase spectrum of Quaternion Fourier Transform

Small target enhancement is one of the crucial stages in infrared small target detection. In this paper, we propose a new method using phase spectrum of Quaternion Fourier Transform to enhance small targets while suppressing backgrounds for infrared images. This is inspired by the property that regularly Gaussian-like shape small targets could be considered as attractively salient signal in infrared images and the location information of such signal is implicitly contained in the phase spectrum from frequency domain. Formally, in the proposed method, we adopt the phase spectrum of Quaternion Fourier Transform instead of using traditional Fourier Transform to enhance the targets since the quaternion provides at most four data channels than only one for the latter, which could be helpful to broad types of background clutters by adding more information. For the construction of the quaternion, we present a second-order directional derivative filter via facet model to compute four second order directional derivative maps from four directions respectively as the four data channels. This filter is used to suppress noises and distinguish the targets and backgrounds into separably different textures so that it would boost the robustness of small target enhancement. In experiments, some typical infrared images with various scenes are tested to validate the effectiveness of the proposed method. The results demonstrate that our method actually has good performance and outperforms several state-of-the-art methods, which can be further used for infrared small target detection and tracking.     

紫外傅里叶变换光谱仪干涉图数据处理

阐述了干涉图数据处理方法 ,采用紫外傅里叶变换光谱仪实验测量了汞灯光谱干涉图。使用四阶Blackman Harris窗函数作为切趾函数 ,采用最小二乘法拟和多项式对光源傅里叶变换光谱进行相位校正 ,获得了高精度的Hg紫外发射光谱     

Spatial Position Detection of Three-Dimensional Objects by Effective Three-Dimensional Correlation Based on Fourier Transform Profilometry

Spatial position detection of a three-dimensional (3D) object by a correlator based on Fourier transform profilometry is discussed. The presence of the 3D object and its precise spatial position can be recognized by the correlator using the position and phase of the correlation peak. The spatial position is obtained by the relative displacement from the position where the reference object is originally placed. The characteristic of the correlator with respect to the moving direction of a 3D object is experimentally verified. Effects of the baseline factor on 3D object recognition are also investigated.