On-line textile quality control using optical Fourier transforms

Fourier transformation and spatial filtering offer the possibility of detecting structural defects in a fabric. In this paper a method based on an optical Fourier transform technique during the weaving process is described. Significant variations in the Fourier pattern occurring in the presence of defective fabric are recognised with a CCD sensor joined to an electronic hardware system performing a simple algorithm.     

Spectrum measurement in the fractional Fourier domain

Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of real-time measurement of the spectrum of a signal in the FRFT domain. In this paper, we propose two approaches for real-time measurement of the FRFT of a signal based on modulation and bandpass filtering systems. The relation is established between the linear frequency modulation (LFM or chirp) spectrum and the FRFT of its envelope. In addition, two applications for spectrum measurement are presented in the FRFT domain. The LFM signal can be bandlimited in the Fourier transform (FT) domain through spectrum measurement associated with bandpass filtering method. The results can also be useful in the problems related to swept-frequency filter for measurement in the FRFT domain.     

Generalized three-dimensional windowed Fourier transform for fringe analysis

A 3D windowed Fourier transform is proposed for fringe sequence analysis, which processes the joint spatial and temporal information of the fringe sequence simultaneously. The 2D windowed Fourier transform in the spatial domain and the 1D windowed Fourier transform in the temporal domain are two special cases of the proposed method. The principles of windowed Fourier filtering and windowed Fourier ridges are developed. Experimental verification shows encouraging results despite a longer processing time.     

傅立叶变换与流体数值计算的耦合并行算法

针对傅立叶变换和流体数值计算耦合并行存在的问题,采用两种方式解决:多物理耦合通信方法和二维并行FFTW方法;并对这两种方法进行性能比较,结果表明:当处理器数目少时,采用多物理耦合通信方法计算效率高,当处理器上千时,采用二维并行FFTW方法可扩展性更好;最后,在上万处理机上采用上亿网格测试,并行效率达到50%,并给出数值模拟结果,验证了激光成丝现象.     

分数傅里叶变换啁啾滤波

针对常规傅里叶变换所不能解决的啁啾噪声滤除问题,利用Wigner分布函数分析分数傅里叶变换的空域和频域特性,提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中,对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真,获得了满意的效果,结果表明该方法在图像处理中的有效性。     

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.     

Fourier transform profilometry based on defocusing

Sinusoidal fringe patterns are popularly used in conventional Fourier transform profilometry. There are numerous harmonics in the Fourier spectrum, so as to avoid spectrum overlapping; the maximum range of measurement is limited. The present paper studies FTP based on properly defocusing a binary square wave. There are only odd harmonics in the Fourier spectrum of a binary square wave, and the maximum range of measurement is expanded 1.5 times. Defocusing has a low-pass filtering effect and higher-order odd harmonics are suppressed. Therefore, the fundamental spectrum is easy to extract. The proposed method overcomes the filtering problem of conventional FTP. Measurement experiments show that the proposed method has a good measurement result and the measurement accuracy is improved.     

Characterizing Young's fringes’ orientation and spacing by Fourier transform and Radon transform

Orientation and spacing are important features of fringe patterns, especially in speckle photography when the displacement information of the object is determined by pointwisely filtering the double-exposure specklegram. The Fourier transform and Radon transform are both simple and effective tools for solving this problem, which extract the information in spectral domain and spatial domain, respectively. A hybrid method combining Radon transform and Fourier transform is also possible. The results can be further improved by enhanced Fourier transform and enhanced Radon transform. The theories, as well as real applications, are given in this paper.     

基于级联分数傅里叶变换系统的数字水印技术

提出一种基于分数傅里叶变换和随机相位编码的光学加密数字水印技术,可成为一种信息隐藏及保护的有效方案.该数字水印技术对于噪音叠加和常见的图像处理操作具有较强的稳健性.该技术根据光学级联分数傅里叶变换系统,利用两个随机相位分布函数对水印信息编码并经过迭代分数傅里叶变换嵌入到变换域的载体图像中.在水印检测和提取过程中,两个相位分布函数作为密钥.随机相位编码技术的引入,进一步提高了数字水印系统的密钥空间.增强了系统的安全性.该数字水印技术基于光学分数傅里叶变换原理,可以利用光学变换系统方便地实现.     

Image recovery from double amplitudes in fractional Fourier domain

The classical Gerchberg--Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg--Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].     

Acoustic features based on auditory model and adaptive fractional Fourier transform for speech recognition

It is well known that auditory system of human beings has excellent performance which automatic speech recognition(ASR) systems can’t match,and fractional Fourier transform (FrFT) has unique advantages in non-stationary signal processing.In this paper,the Gammatone filterbank is applied to speech signals for front-end temporal filtering,and then acoustic features of the output subband signals are extracted based on fractional Fourier transform. Considering the critical effect of transform order for FrFT,an order adaptation method based on the instantaneous frequency is proposed,and its performance is compared with the method based on ambiguity function.ASR experiments are conducted on clean and noisy Putonghua digits,and the results show that the proposed features achieve significantly higher recognition rate than the MFCC baseline,and the order adaptation method based on instantaneous frequency has much lower complexity than that based on ambiguity function.Further more,the FrFT-based features achieve the highest recognition rate using the proposed order adaptation method.     

A simple phase unwrapping approach based on filtering by windowed Fourier transform: A note on the threshold selection

A simple phase unwrapping approach based on windowed Fourier filtering was proposed recently [K. Qian et al. A simple phase unwrapping approach based on filtering by windowed Fourier transform. Opt Laser Technol 2005;37:458–62]. The windowed Fourier filtering algorithm is an essential ingredient that suppresses the noise effectively and makes the phase unwrapping trivial. This paper adds a note on the threshold selection in the windowed Fourier filtering algorithm. A large interval can be selected as the threshold to obtain almost optimal filtering results. Once the selected threshold is suitable, it is almost optimal. This makes the threshold selection in the windowed Fourier filtering algorithm extremely easy.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations

Fringe patterns from optical metrology systems need to be demodulated to get the desired parameters. Two-dimensional windowed Fourier transform is chosen for the determination of phase and phase derivatives. Two algorithms, one based on filtering and the other based on similarity measure, are developed. Some applications based on these two algorithms are explored, including strain determination, phase unwrapping, phase-shifter calibration, fault detection, edge detection and fringe segmentation. Various examples are given to demonstrate the ideas. Finally implementations of these algorithms are addressed. Most of the work has appeared in various papers and its originality is not claimed. Instead, this paper gives an overview and more insights of our work on windowed Fourier transform.     

Convolution and Filtering in Fractional Fourier Domains

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.     

Velocity and Acceleration Measurement from the Spatio-Temporal Fourier Transform of Low Light Level Images

The spatio-temporal Fourier transform is usually applied to determine the velocity of an object from a series of standard light intensity frames. In this paper the technique has been extended to determine the object acceleration. The techniques for velocity and acceleration determination based on the spatio-temporal Fourier transform have been applied to experimental low light level images. Under these conditions, the processing time is reduced so that, in those cases in which it is necessary to quickly obtain the object velocity or acceleration, low light level conditions would be advantageous, using intensity filters if necessary.     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

一种提高静态傅里叶干涉仪光谱分辨率的方法

为了在不改变静态傅里叶变换干涉具尺寸的前提下提高光谱分辨率,设计了正交斜楔型静态傅里叶变换干涉具,采用两个正交的等效斜楔形成连续的光程差变化.通过推导传统干涉具与正交斜楔型干涉具的光程差函数,设计了采用正交斜楔型干涉具增加有效探测长度,从而提高光谱分辨率的方法.经仿真计算,正交斜楔型干涉具的最大光程差为0.323 4 mm,比传统干涉具的0.080 8 mm大4倍左右,即光谱分辨率提高了4倍.实验证明,由于正交斜楔的探测原理使干涉具边缘的干涉条纹产生畸变,故要对干涉条纹进行边缘切除及滤波,给出了切除大小的计算公式.采用WQF520型光谱仪进行对比实验,检测800 nm的激光,该干涉具误差小于1 nm.该方法可有效地提高静态傅里叶变换干涉具的光谱分辨率.     

空间调制型干涉光谱成像仪数据处理方法

干涉型光谱成像技术是一种新型的光谱成像技术,近些年来发展迅速。干涉成像光谱仪获得的是间接数据干涉图,不能被用户直接使用,需要进行干涉数据反演处理,包括数据预处理(干涉图修正)、切趾、相位修正、傅里叶变换、光谱辐射定标等一系列复杂的处理,目前国内外尚未有文献对干涉数据处理技术进行全面的分析,文章基于作者单位对此技术多年的研究,针对空间调制型干涉光谱成像仪的数据处理方法,结合环境与灾害卫星超光谱成像仪的数据,提出了一套有效的数据反演方法和流程,获得了很好的数据反演结果。