A new wavelet transform for reliability-guided phase unwrapping of optical fringe patterns

A new daughter wavelet definition for reliability-guided phase unwrapping of the optical fringe pattern is introduced. The new daughter wavelet definition is given by normalized mother wavelet with a new factor including a Gaussian function. The modulus of the wavelet transform coefficients, obtained by using daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter which represents the reliability of the reconstructed phase data. Mathematical demonstration of this parameter is given. Both the computer simulation and experiment reveal the validity of the proposed method.     

超宽带聚合物调制器的优化设计

设计了一种以聚合物作为材料的低损耗、宽带宽的Mach—Zehnder光波导调制器。分析了调制器的脊波导的模式特性,设计了脊波导的结构,并使用BPM软件模拟了脊形波导的光场分布;通过对光场分布的分析,优化了脊形波导的宽度Wg,脊高6,芯层高度H。同时对聚合物调制器的电极进行了优化,包括电极宽度W和电极间距D,使得调制器有较小的导体损耗以及较好的阻抗匹配。并结合了脊波导的结构参数和电极的优化参数,给出了优化结果,它能够使微波的有效折射率与光波的有效折射率达到匹配,从而使带宽达到177GHz,导体损耗为0．2569dB／cm·GHz1／2。     

镉污染水稻高光谱诊断分析与建模

为了快速、准确地探测自然环境下水稻镉污染胁迫状况,提出了一种基于可见光-近红外光谱小波分析技术的快速识别和估算水稻镉污染的方法。根据野外实测水稻高光谱数据、水稻叶片主要生化参数及重金属含量等数据,利用Daubechies小波系的db5小波函数对350～1300nm水稻高光谱反射率进行9层分解,并提取小波能量系数进行镉含量回归建模。结果显示:第5层小波分解(d5)的奇异范围为550～810nm,奇异幅度为0.04,模极大值的中心位于700nm处,对识别水稻镉污染效果最佳;以第3层小波能量系数作为自变量的回归模型对水稻镉含量估算精度最高,其决定系数R2高达0.958,均方根误差RMSE为0.122。小波奇异性分析可以较准确的诊断水稻镉污染胁迫状况,基于小波能量系数的建模能有效估算水稻镉污染胁迫水平。     

基于小波变换和高斯拟合的在线谱图综合处理方法

微小型移动式现场在线检测技术是分析仪器发展的新领域。针对复杂工作环境中谱图存在强噪声干扰、谱峰重叠、不规则峰形等严重影响仪器的定性和定量准确度的瓶颈技术,提出了一种基于小波变换和高斯拟合相结合的谱图在线综合处理方法,用自研的仪器对甲苯和全氟三丁胺两种典型化合物的谱图进行了处理,并与实验室分析仪器普遍应用的算法进行了对比分析。结果表明,综合方法能够有效解决强噪声干扰、谱峰重叠、不规则峰形问题,提高仪器的定性和定量准确性,同时能够实现数据压缩,满足仪器的在线实时检测要求。综合方法处理甲苯特征峰的平均信噪比(SNR)较移动平滑方法提高了1.3倍,峰位误差ΔM降低了3.6倍,处理全氟三丁胺谱图的数据压缩比为197∶1。     

3D particle positioning by using the Fraunhofer criterion

In particle tracking velocimetry, the necessary information is the 3D location of a given particle in space. This information can be obtained by examining the real image or by analyzing the interference fringe recorded on a digital camera. In this work, we measure the three-dimensional position of spherical particles by calculating the Central Spot Size of the interference pattern of a particle diffraction image. The Central Spot Size is obtained by combining the Continuous Wavelet transform and circle Hough transform. The Continuous Wavelet transform allow us in only one step enhanced quality of particle images and sets a threshold to select properly places where a Central Spot Size appear in order to determine its size via the Hough transform. The size and centroid of the Central Spot Size render z and x-y position of a particle image, respectively. The Central Spot Size is related to a criterion of a simplified theory given by the Fraunhofer theory in order to obtain z particle position. Our approach has been applied to simulated and experimental particle images. Simulated particle images show good agreement between actual and calculated Central Spot Size. An average relative error of 0.5% and 1.12% for x-y and z directions, respectively, was found in the analysis. Our experimental particle images were obtained from particle motion inside a channel. The quality of the particle images determines the accuracy of the calculation of the Central Spot Size of a particle image.     

Fine structure of the isoscalar giant quadrupole resonance in Ca due to Landau damping?

The fragmentation of the Isoscalar Giant Quadrupole Resonance (ISGQR) in ⁴⁰Ca has been investigated in high energy-resolution experiments using proton inelastic scattering at Ep=200 MeV$E_{\mathrm{p}}=200\text{MeV}$. Fine structure is observed in the region of the ISGQR and its characteristic energy scales are extracted from the experimental data by means of a wavelet analysis. The experimental scales are well described by Random Phase Approximation (RPA) and second-RPA calculations with an effective interaction derived from a realistic nucleon–nucleon interaction by the Unitary Correlation Operator Method (UCOM). In these results characteristic scales are already present at the mean-field level pointing to their origination in Landau damping, in contrast to the findings in heavier nuclei and also to SRPA calculations for ⁴⁰Ca based on phenomenological effective interactions, where fine structure is explained by the coupling to two-particle–two-hole (2p–2h) states.     

An ultra-fast smoothing algorithm for time–frequency transforms based on Gabor functions

Gabor functions, Gaussian wave packets, are optimally localized in time and frequency, and thus in principle ideal as (frame) basis functions for a wavelet, windowed Fourier or wavelet-packet transform for the detection of events in noisy signals or for data compression. A major obstacle for their use is that a tailored efficient operator acting on the transform coefficients for altering the width of the wave packets does not exist. However, by virtue of a curious property of the Gabor functions it is possible to change the width of the wave packets using just one-dimensional convolutions with very short kernels. The cost of a wavelet-type transform based on the scheme presented below is similar to that of a low order wavelet transform for a compact kernel and significantly less than the algorithme à trous. The scheme can hence easily be employed for the processing of signals in real time.     

基于小波的一维线性波动方程的数值解法

小波的紧支性，正交性和二阶以上的Daubechies尺度函数及小波函数的可微性，很适合作为Galerkin方法的基函数。加上快速小波变换，这已成为数值求解偏微分方程的有力工具，本文利用微分算子的小波表示。对一维线性波动方程的小波数值解法进行了讨论。最后用实例说明了波波方法的有效性和快速性。     

小波级数的Bouligand维数(英)

本文讨论小波级数的上、下Buoligangd维数，在小波级数满足一定的条件下，给出了与Weierstrass函数相应的结果．     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

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