Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source

The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.     

On the sampling conditions for reconstruction of an acoustic field from a finite sound source

A simple and accurate method for the estimation of ultrasonic transducer fields is developed. In the method, the angular spectrum is employed to evaluate the three-dimensional propagation from a measured plane to an arbitrary parallel plane. The implementation uses a discrete convolution that is described in detail. Relative to conventional spatial-frequency representations, the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts, enabling sample spacing to be greater than one half wavelength, using memory efficiently, and interpolating the measured data. The loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three-dimensional acoustic field from a coarse sound pressure measurement on single plane.     

数字散斑亚像素小角位移测量的曲面拟合法

与传统测量方法相比,数字散斑相关法由于其目标特征单元网格划分的灵活性,能够更好地满足不同场合小角位移的测量需求。针对该方法亚像素小角位移测量的曲面拟合参数选择问题,研究了亚像素测量图像小角旋转前后的九点二次曲面拟合法,并根据计算机生成模拟散斑进行模拟实验分析,得到最佳误差效率优化条件下的曲面拟合法求解亚像素小角位移的最佳散斑尺寸3.5 pixel、计算窗口尺寸41×41 pixel和拟合窗口尺寸3×3 pixel。实验验证了上述测量参数的有效性,为进一步的曲面拟合法数字散斑成像角位移测量提供参考。     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

基于联合变换相关器的像移测量仿真分析

对基于联合变换相关器的像移测量数学原理进行了说明,介绍了面阵CCD的安装位置以及输入图像的获取方法,分析了低信噪比输入图像、相对转动位移对测量精度的影响。应用MATLAB对输入图像进行傅里叶变换得到联合功率谱,对二值化处理的功率谱进行傅里叶变换得到相关输出,用质量中心算法计算出像移量。分析得出,输入图像信噪比大于5dB,测量均方误差小于0.05像素;输入图像相对转动位移在0.1°的范围内,转动位移对测量精度和峰噪比的影响可以忽略不计。综合分析表明像移测量均方误差小于0.05像素。     

The calculation research of classical diffraction formulas in convolution form

Based on the angular spectrum diffraction theory and the sampling theorem, the sampling conditions for calculation the Kirchhoff formula, the Rayleigh-Sommerfeld formula, the angular spectrum diffraction formula and the Fresnel diffraction formula in convolution form were studied. The results indicate that the diffraction calculation result is correct if the angular spectrum corresponding to the main energy of diffraction field can be fully transmitted by means of transfer functions when the samplings of initial wave fields satisfy the sampling condition. Compared with previous work, the sampling condition in this paper is less restricted. The diffraction calculation results are in agreement with experimental results.     

High performance BLAS formulation of the multipole-to-local operator in the fast multipole method

The multipole-to-local (M2L) operator is the most time-consuming part of the far field computation in the fast multipole method for Laplace equation. Its natural expression, though commonly used, does not respect a sharp error bound: we here first prove the correctness of a second expression. We then propose a matrix formulation implemented with basic linear algebra subprograms (BLAS) routines in order to speed up its computation for these two expressions. We also introduce special data storages in memory to gain greater computational efficiency. This BLAS scheme is finally compared, for uniform distributions, to other M2L improvements such as block FFT, FFT with polynomial scaling, rotations and plane wave expansions. When considering runtime, extra memory storage, numerical stability and common precisions for Laplace equation, the BLAS version appears as the best one.     

轴锥镜光强分布的角谱衍射数值分析法

针对理论上推导轴锥镜的衍射光场分布解析式较为困难,且用菲涅耳衍射理论分析时存在近轴近似及不能适用于近场衍射光场分析的问题,采用了严格遵从标量衍射亥姆霍兹方程的角谱衍射波前重建方法,对轴锥镜在单色和准单色高斯光波照射下的横向和轴向衍射光强分布特性,以及在单色均匀平面光波照射下的轴向衍射光强分布进行了数值计算和分析。结果表明,轴锥镜后单色光衍射光强分布在几何光束重叠的菱形区域内为近似无衍射贝塞尔光强分布,轴上光强沿光轴方向呈振荡变化,轴上光强分布规律与入射光波的垂轴横向光强分布有关;入射光的准单色性使得贝塞尔衍射条纹对比度略下降、轴上光强沿光轴方向振荡程度减小,但分布规律与单色光一致。     

基于液晶空间光调制器的全息显示

在传统的纯相位全息显示系统中, 一般基于快速傅里叶变换(FFT)算法来计算相位全息图, 在FFT的计算中需要遵循Nyquist采样定理, 因此, 重建图像的尺寸往往受限于空间光调制器的固定采样率. 这个限制可以通过卷积算法或者两步菲涅耳衍射算法来解决, 但是需要使用多个FFT的计算, 导致计算量增大. 鉴于此, 提出了一种基于透镜的纯相位全息图计算方法. 在全息图的计算中, 通过透镜的成像原理建立一个采样率可变的虚拟全息面, 通过调节相应的距离参数使得在全息图的计算中可以任意调节原始图像的采样率, 摆脱了传统方法中液晶空间光调制器带宽积对重建图像尺寸的限制, 并且这种算法只需使用一次FFT就能达到变采样率的衍射计算, 大幅提高了全息图的计算速度. 数值模拟及光学实验结果证明了此方法可以在全息显示光学系统中清晰地重建不同尺寸的图像. 同时该系统可以有效地消除由空间光调制器的像素化结构带来的零级衍射.     

基于光学相关的空间相机像移测量方法研究

为了测量由卫星姿态不稳定或振动等原因引起的空间相机的亚像元像移,使用了光学联合变换相关的方法对安装在相机焦面上的辅助面阵CCD采集到的相邻两帧图像进行相关运算.给出了使用该方法测量像移的原理,提出对联合变换相关器的输入面采用拉普拉斯卷积核进行边缘锐化,对功率谱相减并以0值进行二值化的处理方法提高像移测量准确度,并使用该方法对不同信噪比下的不同景物进行了像移测量仿真.结果表明:对于信噪比SNR=1的输入图像,当像移范围在 0~55个像元内时,该方法的像移测量误差小于0.2个像元.     

Study of the deformation characteristics of window security film by digital image correlation techniques

This paper presents a speckle-displacement measurement technique based on the digital image correlation to study the notch sensitivity and crack bridging of window security film. It is used to protect existing glazing against hurricanes, blast and terrorist explosions. The window security film is laminated to the interior side of the glass window by means of a special adhesive. When the glass is breaking, the window film keeps all glass fragments together.The proposed sub-pixel registration of the displacement field is achieved using a calculation technique based on the centre of mass localization of the complex spectrum. This approach increases the computational efficiency for displacements smaller than one pixel and performs with high precision when optimal values of the input correlation parameters are used. In order to achieve a high accuracy of the algorithm, optimization of these input image correlation parameters is offered. For larger displacements an iterative procedure which preserves the precision is successfully implemented.The speckle pattern is created by small white dots sprayed on the previously black painted film surface. As a result, white light illumination can be used which significantly simplifies the experiments.     

超短脉冲激光与乙醇微滴相互作用中超热电子的双叶状角分布

测量了聚焦光强为1016W/cm2的超短脉冲激光与乙醇微滴相互作用中产生的能量大于50?keV的超热电子的角分布和电子能谱.观察到的超热电子角分布明显依赖于激光的偏振特性，在与激光偏振平面平行的平面上超热电子相对于激光入射方向呈对称的双叶状分布.超热电子的能谱显示超热电子的最大能量大于750?keV.以上超热电子的角分布可用一个基于共振吸收机制的模型加以解释. 关键词： 超短脉冲激光 超热电子 微滴 共振吸收     

Nonuniform sampled angular spectrum method by using trigonometric interpolation

The angular spectrum method(ASM) is a popular numerical approach for scalar diffraction calculations. However,traditional ASM has an inherent problem in that nonuniform sampling is precluded. In an attempt to address this limitation,an improved trigonometric interpolation ASM(TIASM) is proposed, in which the fast Fourier transform(FFT) is replaced by a trigonometric interpolation. The results show that TIASM is more suitable to situations in which the source field has a simple and strong frequency contrast, irrespective of whether the original phase distribution is a plane wave or a Fresnel zone plate phase distribution.     

Off-axial elliptical cosine-Gaussian beams and their propagation properties

In this paper, a new kind of light beam called off-axial elliptical cosine-Gaussian beam (ECosGBs) is defined by using the tensor method. An analytical propagation expression for the ECosGBs passing through axially nonsymmetrical optical systems is derived by using vector integration. The intensity distributions of ECosGBs on the input plane, on the output plane with the equivalent Fresnel number being equal to 0.1 and on the focal plane are respectively illustrated for the propagation properties. The results indicate that an ECosGB is eventually transformed into an elliptical cosh-Gaussian beam. In other words, ECosGBs and cosh-Gaussian beams act in a reciprocal manner after propagation.     

An improvement of image registration based on phase correlation

This paper is dedicated to studying the extended phase correlation method that applies to the sub-pixel evaluation of translational displacement between images. On the basis of experiments, this paper proposes an improved version of classical Hanning window, with involving parameters optimization in the process. We add a window function to the input images in the space domain and a weighting function to the spectrum in the frequency domain. The statistics and distribution of errors prove the applicability of the proposal. The experimental results of the proposed extended phase correlation algorithm show the registration accuracy of 1/100 pixel.     

像面数字全息的重建相位误差分析和改善

像面数字全息是数字全息技术中常用的测量和成像方式,它通常采用离散傅里叶变换和频率滤波的方法进行物光波的重建.本文讨论了这些算法对重建相位的影响.首先分析了频谱泄露对于相位误差的影响,结果表明当采样周期为整数时,重建相位误差很小,因此具有极高的相位重建精度;而当不满足整周期采样时,相位重建误差有了明显的增加.为了改善频谱泄露所引起的相位误差,采用Hanning函数对数字全息图进行了预处理,结果表明Hanning窗的加入能够有效地提高重建相位的准确程度.     

High-pass filtering and frequency spectrum correlation for larger size image recognition

A new method for larger size images recognition is proposed based on high-pass filtering and frequency spectrum correlation. The input images are first filtered by a high-pass filter. Then the filtered input images, which are overlapped rather than displaced from each other in the input plane, serve as the input images for frequency spectrum correlator. As a result, only one sharp correlation peak yields in the center of output plane when the target image matches with the reference image. More importantly, the method is especially suitable for larger size image recognition because of the input and correlation ways, which ensures better utilization of the space-bandwidth product and efficient utilization of the spatial light modulator and detector. Computer simulation results are presented to demonstrate the feasibility and effectiveness of this method.     

面阵像元细分用于法布里珀罗标准具间隔测量

法布里珀罗(F-P)标准具间隔d的高准确度测量对干涉测量结果具有非常重要的影响。论文基于F-P干涉成像图片信息，结合峰位坐标局域细分原理和圆方程回归，尤其应用了一种新型的虚拟面阵像元细分和信号平滑化技术，准确地求出干涉图像各同心圆环直径D_i，实现干涉级次整数部分k₀和小数部分ε的准确计算，完成F-P间隔d的三波长小数重合法测定。实验对比分析了细分和非细分方式对测量结果的影响，测得细分方式下的d=(2 009.961 91±0.000 06) μm，d的不确定度粗估值(U_ε/k₀)=9.8×10-7。实验验证了像元细分方法的有效性，为提高间隔d的测量准确度提供了有效的途径和方法。     

The validity of high-pass angular spectrum filter in solid immersion lens system

应用矢量方法计算了具有高通角谱滤波器的固体浸没透镜（SIL）系统的焦场分布。数值结果显示，对于径向（角向）偏振输入光，高通角谱滤波器可以减小SIL系统的光斑（暗斑）大小。然而，对于线性偏振输入光，简单的高通角谱滤波器不能够优化SIL系统的光场分布，也不能够改进系统的光存储密度。     

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures.