伸缩窗口傅里叶变换在三维形貌测量中的应用

为了克服窗口傅里叶变换在分析非平稳信号所存在的缺陷,基于窗口傅里叶变换技术提出了伸缩傅里叶变换法并应用于三维形貌测量中。通过对窗函数在空间尺度上引入伸缩变换,得到一个可调宽度的空间一频率窗,实现空间频率分辨率随光栅图像条纹频率变化自动可调的实时快速测量。该方法克服了窗口傅里叶变换分析中所有频率窗口的大小形状固定不变的缺点,适合复杂物体形貌的测量。给出了理论分析、计算机模拟以及实验研究结果。     

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。     

S变换引导的窗口傅里叶变换相位提取

提出了一种基于S变换引导的自适应窗口傅里叶变换相位提取方法.通过连续S变换,得到局部条纹的最佳变换窗口,可以保证窗口尺寸随变形条纹的频率变化而自动调整,适合复杂物体的面形测量.计算机模拟和实验验证表明,该方法克服了传统窗口傅里叶变换窗口大小固定的缺点,相位提取的误差由-2～8rad降低为-1～1rad,而且还可以得到被...     

无阈值窗口傅里叶变换滤波法

为减少噪音对散斑相位图的影响,提出了一种无阈值的窗口傅里叶变换滤波方法.通过对窗口内条纹频率幅值扫描,寻找条纹频率幅值的最大值作为滤波标准,得到最佳滤波图像,缩短了计算时间,解决了窗口傅里叶变换滤波中需要设定阈值的问题.在无阈值窗口傅里叶变换滤波算法基础上,对散斑条纹图像进行了滤波,证明了该算法的可行性和良好的滤波效果,可用于各类条纹图像的低通滤波.     

小波变换在载频条纹相位分析法中的应用研究

为了克服在非平稳信号分析中傅里叶变换的全局性缺陷,以及窗口傅里叶分析的单一分辨率和伸缩窗口傅里叶分析的尺度不确定性问题,采用伽博解析小波变换技术对空间载频光栅条纹进行相位分析,有效地提取出相对于载频条纹基频的完整相位信息,从本质上解决了上述问题。以三维轮廓术为例,与傅里叶分析进行了对比研究,给出了小波分析应用在空间载频条纹相位分析中详细而完整的理论推导证明、计算机模拟以及实验验证结果。     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

光学测试 光学元件测试与设备

TB922006010673自适应窗口傅里叶变换三维面形检测技术=3D measure-ment techniques using adaptive window Fourier transform[刊,中]/郑素珍(四川大学光电科学技术系.四川,成都(610064)),陈文静…∥光电工程.—2005,32(9).—51-54通过小波脊变换,得到局部条纹的最佳变换窗口,在傅里叶变换三维测量时,可以保证窗口尺寸随变形条纹频率变化而自动调整。实验研究表明,此方法克服了窗口傅里叶变换空间-频率分辨率无法调整的问题,可以最大限度地抑制变形条纹的频谱混叠,准确地提取基频信息,大大地提高了测量精度,误差范围由-2~8mm降低为-1~1mm…     

复杂脉冲单发频域干涉测量

以傅里叶变换极限脉冲作参考脉冲,利用单次测量分析法对复杂的皮秒脉冲进行测量,用窗口傅里叶变换代替傅里叶变换对干涉条纹进行时间-频率分析,直接提取出复杂脉冲的啁啾特性或光谱成分,将光谱图中的功率密度S(ω,t)沿ω轴求和重建脉冲的时域包络.分别用该方法和传统频域干涉测量法测量一个线性啁啾脉冲和一个复杂脉冲.结果表明,该方法可实现复杂整形脉冲的实时测量,且时间分辨率为70 fs.     

从变形光栅条纹提取基准光栅信息

基于傅里叶变换轮廓术,提出一种直接从变形光栅条纹中提取基准光栅条纹信息并重建基准光栅的测量方法.分析了基准光栅条纹和参考平面的功能,揭示变形光栅条纹和基准光栅条纹的关系;应用窗口傅里叶变换对变形光栅条纹中的各个微小区域进行频谱分析,从中识别并提取基准光栅的频率和相位信息;重构出一幅完整的基准光栅条纹,实现三维物体形貌测量.实验结果表明该方法是可行的,为三维形貌测量提供一种新手段.     

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.     

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.     

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.     

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).     

Fringe pattern analysis by S-transform

S-transform proposed in 1996 by Stockwell R.G is a simple and popular technique for the time–frequency analysis. It has been introduced in optical three-dimensional shape measurement, recently. In this paper, a study about applications of S-transform in the demodulation of deformed fringe patterns is performed. We focus on discussing not only the S-transform spectrum filtering technique, the S-transform ridge technique and the phase gradient calculation method based on S-transform used in fringe pattern demodulation, but also the phase unwrapping technique. In addition, a generalized S-transform was introduced to analyze fringe patterns, which is helpful to improve the measurement accuracy and flexibility of the method based on S-transform. The reconstruction results based on S-transform were compared with that on wavelet transform and windowed Fourier transform in fringe analysis.     

Signal processing of double-beam and double-scattering laser Doppler velocimeter

The common method of laser Doppler velocimeter (LDV) signal processing is fast Fourier transform (FFT). Because of the restraint of spectral interference, fence effect and spectrum leakage, the precision of FFT is not high. In order to improve the accuracy of double-beam and double-scattering laser Doppler velocimeter signal processing, an algorithm based on spectral refinement and interpolation is put forward. First, high-pass filter is adopted to remove the baseplate of LDV signal. Second, FFT is adopted to get the estimate of Doppler frequency and then Zoom-FFT is used to refine the local range of Doppler frequency. Third, four-term fifth derivative Nuttall windowed interpolation is used to correct the refined spectrum. Then the accurate estimate of Doppler frequency can be obtained. Simulations and experiments based on the LDV system built in laboratory show that Zoom-FFT can improve the resolution of spectrum and four-term fifth derivative Nuttall windowed interpolation can further increase the precision of signal processing.     

Orthogonal projection technique for resolution enhancement of the Fourier transform fringe analysis method

The spatial resolution of the phase map in the Fourier transform fringe analysis method is determined by the size of the filter’s window in frequency domain. This article reports a straightforward technique to improve the method’s resolution by a factor of nearly two. The technique requires capturing a second image with a fringe pattern orthogonal to the first one, therefore using the information from both patterns to eliminate the central component in frequency space. The resulting spectrum supports double sized filter windows for removal of the carrier frequency without leaking into adjacent orders. The overall spatial resolution of the method is thus increased. In the following, the Fourier fringe analysis method is briefly reviewed, the new technique is described and analyzed and the experimental results are shown and discussed.