Digital transform processing of carrier fringe patterns from speckle-shearing interferometry

Abstract

The Fourier transform (FT) and the wavelet transform (WT) methods are used to process the fringe carrier pattern resulting from speckle-shearing inteferometry, in which the carrier frequency is modulated by deformation of a bending plate. Both the amount and the sign of the first derivative of the out-of-plane displacement can be obtained by these two transform techniques in the whole field. Phase distributions of the deflection slope are compared, which shows the wavelet analysis gives a better solution with noise reduction and without deficiency of filter window choice as for that in the Fourier transform. Meanwhile, the phase values in the path along the maximum WT amplitudes give a direct map of the second derivative patterns of the deflection, which presents the same image as that given by the shearing subtraction of the phase patterns from the inverse Fourier transformation but avoids the processing of unwrapping for the phase reconstruction.     

基于EEMD和低秩稀疏分解的超声缺陷回波检测方法

针对应用超声对金属材料微小缺陷检测时缺陷回波容易被噪声干扰的问题,提出了一种基于集合经验模态分解(EEMD)和低秩稀疏分解相结合的检测方法,以避免传统基于经验模态分解(EMD)的去噪方法难以消除结构噪声的问题.首先对缺陷检测信号进行EEMD得到一系列本征模态函数(IMF),采用基于概率密度函数的相似性测量方法选取相关模...     

Polarization averaged short-time Fourier transform technique for distributed fiber birefringence characterization using Brillouin gain

A polarization averaged short-time Fourier transform (PASTFT) technique is developed for distributed fiber birefringence characterization based on counterpropagating stimulated Brillouin scattering (SBS) gain signal. This technique can be used for the birefringence characterization of the general elliptical birefringent fiber. A theoretical model on polarization matching of counterpropagating SBS process is established. The performance of the short-time Fourier transform (STFT) method and the PASTFT technique is analyzed by using the simulation of the theoretical model. Simulation results show that the process of polarization average could effectively reduce the birefringence characterization error caused by the polarization dependence of the local period of SBS gain. A less than 8% normalized root mean square error is achieved for the characterization of the length of the birefringence vector on elliptical birefringent fibers. The PASTFT technique is experimentally verified by the distributed measurement of beat length and differential group delay of a standard single-mode fiber via the Brillouin optical time domain analysis system.     

Optimal signal processing of nonlinearity in swept-source and spectral-domain optical coherence tomography

We demonstrate the efficiency of the convolution using an optimized Kaiser-Bessel window to resample nonlinear data in wavenumber for Fourier-domain optical coherence tomography (OCT). We extend our previous experimental demonstration that was performed with a specific swept-source nonlinearity. The method is now applied to swept-source OCT data obtained for various simulated swept-source nonlinearities as well as spectral-domain OCT data obtained from both simulations and experiments. Results show that the new optimized method is the most efficient for handling all the different types of nonlinearities in the wavenumber domain that one can encounter in normal practice. The efficiency of the method is evaluated through comparison with common methods using resampling through interpolation prior to performing a fast-Fourier transform and with the accurate but time-consuming discrete Fourier transform for unequally spaced data, which involves Vandermonde matrices.     

基于多分辨分析的时频分析

短时傅里叶变换由于采用固定宽度的时域窗，在缓变与瞬变信号共存的宽频带信号分析中，其时间与频率分辨力矛盾突出。采用Mallat算法的小波变换能够将信号正交分解成多尺度的信号分量，然而所提供的时频信息不很直观，难以识别其时频谱。通过对短时傅里叶变换和小波变换在时频分析中的优缺点分析，发现两者具有互补性。因此本文提出基于多分辨分析的短时傅里叶变换（取名为WAVSTFT），即采用Mallat算法将信号分解成多个尺度信号分量，再对各分量分别做与其尺度相适应的短时傅里叶变换，最后把得到的各时频谱在同一个不相平面上叠加，从而得到信号的总体时频构造。经理论分析与实例验证，该方法有效可行，为工程测试中的时频分析提供了一种有效的手段。     

调频初相位补偿的广义Warblet变换时频分析

信号时频分析的长时间窗时频分析法通常可提高输出信噪比和频率分辨率,但对于调频信号,会降低线谱时频能量聚集度并影响瞬时频率估计。对于调频信号广义Warblet变换(Generalized Warblet Transform,GWT),具有较短时傅里叶变换(Short Time Fourier Transform,STFT)更优的时频分析性能,但在长时间窗分析时,调频初相位估计误差会使算法性能下降甚至失效。针对该问题,提出调频初相位补偿的GWT(Frequency Modulation Initial Phase CompensationGWT,FMIPC-GWT)时频分析方法。在调频参数估计时将一半时间窗长所经过的相位补偿到调频初相位中,提高调频参数估计的准确性以增加瞬时频率估计精度。仿真和实验数据验证了,相比STFT法和GWT法,FMIPC-GWT法对于非线性调频信号时频分析性能更优。FMIPC-GWT法在调频信号线谱检测与瞬时频率估计等方面具有应用前景。     

混响背景下基于分数阶傅里叶变换的自适应LMS滤波算法

针对强混响背景下经典的最小均方误差(Least Mean Square,LMS)滤波算法难以有效地实现信混分离的问题,提出一种基于分数阶傅里叶变换的自适应LMS算法。首先将混响信号和自适应LMS滤波算法中的参考信号进行分数阶傅里叶变换,寻找最优变换域,并在分数阶域进行带通滤波,然后将得到的信号进行分数阶傅里叶反变换,最后将基于正态分布曲线的变步长LMS算法应用于此混响条件下进行滤波。仿真和海试数据验证结果表明,在信混比为0 dB的情况下,算法仍可以有效地滤除混响,使信混比提高6dB。     

超宽带信号的时频分析

超宽带(UWB)信号的特性更多表现为非平稳信号的特性,而对非平稳信号采用时频域的变换更能描述信号频谱的分布情况.首先引入了一种基于布莱克曼窗的短时傅立叶变换,然后给出两种典型的UWB信号,利用这种时频分析方法对两种UWB信号进行了时频分析.分析结果表明,无论是PAM-DS-UWB信号还是OFDM-UWB信号都符合FCC对UWB信号的功率限制.     

Fast numerical algorithm for the linear canonical transform

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.     

Optical implementation of the continuous wavelet transform

A simple optical implementation for the one-dimensional wavelet transform (WT) is proposed. In contrast with previous WT optical implementations, the obtained WT is continuous along both axes (dilation and shift). An optical implementation to the inverse WT is proposed as well. Thus an optical continuous WT processor can be implemented.     

Spectrum-sliced Fourier-domain low-coherence interferometry for measuring the chromatic dispersion of an optical fiber

We present a novel spectrum-slicing method for measuring the chromatic dispersion of an optical fiber in Fourier-domain low-coherence interferometry. Broadband spectral interference data obtained from a low-coherence interferometer is sliced with Gaussian window functions. Each sliced spectral datum is used to calculate a relative group delay with Fourier transformation at the peak wavelength of a narrow window function. We have demonstrated that our proposed method is very powerful and simple for measuring chromatic dispersion and second-order dispersion in optical fibers and optical devices. Comparison of the proposed method with a conventional measurement method agrees within 0.5%.     

Incoherent fractional Fourier transform and its optical implementation

The fractional Fourier transform is redefined for working with incoherent light. As a real transformation, the incoherent fractional Fourier transform overcomes coherent system disadvantages such as the speckle effect and the need for incoherent-coherent conversion. It also might have some applications for digital image and signal processing owing to its decreased computing complexity. An incoherent optical implementation of the new transform based on the shearing interferometer is suggested. Laboratory experimental results are given.     

时频分析法在锅炉承压管线泄漏检测中的应用研究

准确检测锅炉承压管线泄漏是保障锅炉安全运行的关键技术,音频分析法是检测承压管线泄漏故障的主要手段,提出一种基于联合时频分析(Joint Time-Frequency Analysis, JTFA)研究锅炉背景声和承压管线泄漏声的时频特征,判定泄漏故障的方法。设计了由前置放大、程控滤波、增益补偿处理的双通道音频信号采集电路;采用快速傅里叶变换获取信号广义谱特征,采用程控滤波对采集信号加动态频率窗,再采用短时傅里叶变换对采集信号时间加窗,多角度分析信号的时频特征,以判定承压管线运行是否存在泄漏故障。相比于传统的RC滤波加快速傅里叶变换分析方法,这种动态加双窗的时频分析法能够提高泄漏信号采集的灵敏度和泄漏故障判定的准确性。     

基于卡尔曼滤波的STFT域回声抵消算法

提出了一种低复杂度的短时傅里叶变换域卡尔曼滤波算法来解决声学回声抵消问题。首先在短时傅里叶变换域建立了基于频域卷积传递函数的观测方程,并利用一阶马尔科夫模型对频域回声路径进行建模,给出了精确的卡尔曼滤波方程,并讨论了过程噪声和观测噪声的估计问题。为降低算法计算复杂度,提出了低复杂度卡尔曼滤波算法。另外,在更新滤波器时加入远端信号邻近频点的信息来进一步提高回声抵消性能。实验结果表明,所提算法对近端干扰不敏感,不需要额外的双端对讲检测算法,且比传统的频域自适应滤波算法具有更快的收敛速度。     

Optical aperture synthesis imaging with fractional Fourier-domain filtering

The fractional Fourier transform, which is a generalization of the classical Fourier transform, is introduced into an optical aperture synthesis (OAS) system by which imaging of an astronomical object can be achieved. We introduce fractional Fourier optical imaging and fractional Fourier-domain filtering (FFDF), and then present the schematic diagram of an OAS imaging system with FFDF. The modulation transfer function of an OAS system with FFDF is compared with that of an OAS system in the same condition. The result indicates that the OAS system with FFDF has larger practical cutoff frequency when the fill factor is smaller. Furthermore, the quality of imaging and restoration also demonstrates this conclusion.     

基于EMD和STFT柴油机缸盖振动信号时频分析

以柴油机缸盖振动信号为研究对象,提出经验模式分解（EMD）和短时傅里叶变换（STFT）相结合的时频分析法。该方法首先利用EMD对缸盖振动信号进行自适应分解,得到一系列本征模态分量（IMF）。根据各分量的特点有针对性地选择高斯窗和汉明窗分别进行STFT,并以时频聚集性指标为目标函数计算各分量的最佳时频分布,最后叠加得到原始信号的最佳时频分布。经对比分析,该方法解决了窗函数及窗宽的选择问题,有效提高STFT的时频分辨率,准确描述柴油机缸盖振动信号的时频分布。     

Wavelet transform-based strain estimator for elastography

A new signal processing algorithm based on a wavelet transform (WT) is proposed for instantaneous strain estimation in acoustic elastography. The proposed estimator locally weighs ultrasonic echo signals acquired before tissue compression by a Gaussian window function and uses the resulting waveform as a mother wavelet to calculate the WT of the postcompression signal. From the location of the WT peak, strain is estimated in the time-frequency domain. Because of the additive noise in signals and the discrete sampling, errors are commonly made in estimating the strain. Statistics of these errors are analyzed theoretically to evaluate the performance of the proposed estimator. The strain estimates are found to be unbiased, but error variances depend on the signal properties (echo signal-to-noise ratio and bandwidth), signal processing parameter (time-bandwidth product), and the applied strain. The results are compared with those obtained from the conventional strain estimator based on time-delay estimates. The proposed estimator is shown to offer strain estimates with greater precision and potentially higher spatial resolution, dynamic range, and sensitivity at the expense of increased computation time.     

S变换时频谱SVD降噪的冲击特征提取方法

为了从滚动轴承故障振动信号中提取出冲击特征,以进行轴承故障诊断,提出基于S变换时频谱奇异值分解(SVD)的信号降噪方法。S变换是一种信号时频表示方法,适合于处理与分析非平稳的冲击特征信号。在SVD降噪过程中,数据矩阵由信号的S变换谱系数构成;奇异值序列的置零阈值位置坐标可由奇异值差分谱最前面部分峰值群的最后一个峰值点序号来确定。最后对降噪的数据矩阵进行S逆变换,获得信号的时域冲击特征。仿真研究表明,基于S变换时频谱的SVD降噪方法可以成功地从低信噪比信号中提取出周期性的冲击特征。将本方法用于处理与分析滚动轴承故障振动信号,根据所提取出的冲击特征出现频率,能够方便有效地实现轴承相关故障的诊断。     

Frequency domain analysis by the exponential window method and SGBEM for elastodynamics

Dynamic analysis of a system can be carried out either in the time or frequency domain. Time responses/ histories of this system may be directly obtained using time-domain analysis. In case of frequency domain analysis in the Fourier space, the inverse fast Fourier transform (inverse FFT) would naturally be an appropriate choice for converting frequency solutions to the desired time responses. However, the standard FFT can not be applied to undamped systems as the free-vibration terms of these systems never decay which violates the periodic nature of the standard FFT algorithm. In addition, the FFT may be computationally expensive for lightly damped systems. An alternative to overcome the above limitations is the so-called exponential window method (EWM) commonly used in digital signal processing. This paper presents a combination of the EWM and the symmetric-Galerkin boundary element method for 2-D elastodynamic analysis in the frequency domain of undamped and lightly damped systems. Several numerical examples, including fracture problems, are given to illustrate the efficiency and accuracy of the proposed frequency domain analysis.     

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spatial domain, which is totally space variant, to the spectral domain, which is totally space invariant, with the chromatic correction remaining unaltered.