Spherical angular spectrum and the fractional order Fourier transform

The notion of a spherical angular spectrum leads to the decomposition of the field amplitude on a spherical emitter into a sum of spherical waves that converge onto the Fourier sphere of the emitter. Unlike the usual angular spectrum, the spherical angular spectrum is propagated as the field amplitude, in a way that can be expressed by a fractional order Fourier transform.     

Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.     

Calibration of hydrophones in a field with continuous radiation in a reverberating pool

We examine a method for estimating the transient impedance of an emitter and a receiver in a free field based on sliding complex averaging of the frequency dependence of the transient impedance of the emitter and the receiver obtained under continuous emission in an undamped pool. The method makes it possible to weaken the influence of reflected signals and to obtain frequency characteristics almost coinciding with measured ones in free-field conditions. We present results from experimental studies of the method and its application for calibration of hydrophones by field with the reciprocity method in a reverberating field.     

驻波法测量声速实验的讨论

根据声波在2个换能器之间多次反射和声波在空气中的衰减,研究了驻波法测量声速实验中接收器输出信号随接收器到发送器间距离的变化.理论推导结果表明:声波在一般情况下不是严格的驻波,但是当反射比接近-1时则是双曲函数形式的驻波,这与实验测量结果一致.只有接收器到发送器的距离比较远,反射比接近-1时,才能得到几乎理想的驻波.     

声速测量实验原理讨论

对空气中声速测量实验原理进行了讨论,考虑了空气对声波的吸收,分别用平面波和球面波表示发射探头和接收探头之间的声波,导出了接收声压的表达式,分析了声压随探头间距的变化规律.结果表明,尽管声场不是理想驻波,但声压极值随探头间距按半波长周期性的变化规律与驻波共振原理得到的结论相一致,然而3种原理在解释接收声压幅值衰减规律时存在差异,其中球面波原理与实验现象最吻合.     

On the effect of absorption on multiple wave-scattering in a magnetized turbulent plasma

Multiple scattering of electromagnetic waves by a plane layer of a turbulent magnetized collision plasma is considered. The influence of the distance between both the emitter and the receiver and the layer boundaries is analysed. It is found that the width of the angular spectrum of the received radiation for sufficiently strong absorption in the plasma is greater than in the collisionless plasma; the spectral maximum is substantially displaced with respect to the direction of the source. It is shown that these effects are weakened when the emitter approaches the layer. The relationship between the spectral width and also the displacement of its maximum and the distance from the receiver to the layer boundary may be substantially non-monotonic.     

Wave field synthesis of moving virtual sound sources with complex radiation properties

An approach to the synthesis of moving virtual sound sources with complex radiation properties in wave field synthesis is presented. The approach exploits the fact that any stationary sound source of finite spatial extent radiates spherical waves at sufficient distance. The angular dependency of the radiation properties of the source under consideration is reflected by the amplitude and phase distribution on the spherical wave fronts. The sound field emitted by a uniformly moving monopole source is derived and the far-field radiation properties of the complex virtual source under consideration are incorporated in order to derive a closed-form expression for the loudspeaker driving signal. The results are illustrated via numerical simulations of the synthesis of the sound field of a sample moving complex virtual source.     

On the effect of absorption on multiple wave-scattering in a magnetized turbulent plasma

Abstract

Multiple scattering of electromagnetic waves by a plane layer of a turbulent magnetized collision plasma is considered. The influence of the distance between both the emitter and the receiver and the layer boundaries is analysed. It is found that the width of the angular spectrum of the received radiation for sufficiently strong absorption in the plasma is greater than in the collisionless plasma; the spectral maximum is substantially displaced with respect to the direction of the source. It is shown that these effects are weakened when the emitter approaches the layer. The relationship between the spectral width and also the displacement of its maximum and the distance from the receiver to the layer boundary may be substantially non-monotonic.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

Increasing the frequency resolution in the processing of acoustic signals by sliding complex weighted averaging

We investigated the possibilities of estimating the transient impedance of an emitter and receiver in a free field, and we present our results, which are based on sliding complex weighted averaging of the frequency dependence of emitter and receiver’s transient impedance in a nonanechoic bath. We show that the procedure makes it possible to reduce reflection effects and to form free-field conditions in baths with various reflections that differ sharply in shape and many times in size. We suggest a procedure of repeat use of sliding complex weighted averaging together with spectrometry of reflection functions, which makes it possible to increase the frequency resolution of the method.     

声速测量实验中界面反射问题的探讨

探讨在声速测量实验中,声波在发射器和接收器两个端面之间反向形成极大值的位置和条件,以及声波强度随距离变化的规律。这有利于学生正确实验和理解声波特性。     

利用分数傅里叶变换设计衍射光学元件

讨论了分数傅里叶变换与菲涅尔衍射的关系,提出球面衍射过程就是一种具有尺度因子的分数傅里叶变换,并应用分数傅里叶变换进行衍射光学元件的设计。     

Near-field ultrasound tomography

In this paper, a near-field tomographic solution is introduced to solve the imaging problem of fluid objects assumed to be weakly heterogeneous (Born approximation) and excited by spherical waves. The solution to the forward problem is based on the Huygens-Fresnel principle which describes the scattered field as the result of the interference scheme of all the secondary spherical waves. From the derivation of the scattered field, a new Fourier transform that has been called the elliptical Fourier transform is defined: It differs from the standard Fourier transform in that instead of a plane wave decomposition, a harmonic ellipsoidal wave decomposition is obtained. Based on this spectral analysis, a near-field Radon transform is designed that complements the "far-field tools" published in diffraction tomography literature. Then, assuming that the measuring distance is greater than one wavelength, the feasibility of reconstructing either the impedance or the velocity maps of an acoustical (perfect fluid) model is demonstrated. Numerical simulations were performed which confirmed the validity of the theory presented here; a theory which has many potential applications in future wave theory research.     

Subwavelength localization of near fields in coupled metallic spheres for single-emitter polarization analysis

We numerically demonstrate selective near-field localization determined by the polarization state of a single emitter coupled to a plasmonic nanocluster. Seven gold nanospheres are carefully arranged such that up to 10 polarization states of the single emitter, including linear, circular, and elliptical polarizations, can be distinguished via the distinct field localization in four gaps. The ability to transform polarization states into field spatial localizations may find application in single emitter polarization analysis.     

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.     

端窗透射微型X光管的结构优化

为了得到场约束方式下,金属陶瓷封装端窗透射微型X光管发射电流的最大化和焦斑尺寸的最小化,对热阴极发射体的几何结构进行仿真计算,为设计实物模型提供技术方案。首先,从理论上推导了直热式阴极发射体、发射电流密度与几何结构的关系,其次讨论了有限积分算法在求解电场分布数值解过程中的离散化思路,最后利用CST粒子工作室软件,建立了几何模型,对阴极发射体的几何结构进行了优化。在灯丝距离控制极0.4 mm、控制极开孔直径为0.6 mm的位置,能够得到较小的焦斑和较高的电荷密度分布。试制的阴极发射体最大发射电流可达85 A。     

Statistical characteristics of radiation of a point source scattered by a layer of turbulent collisional magnetized plasma

We consider multiple scattering of electromagnetic waves by a layer of turbulent magnetized collisional plasma. The influence of the distances from the layer's boundaries to the emitter and receiver is analyzed. We find out that, provided absorption in the plasma is strong enough, the width of the angular spectrum of the received radiation can be larger than in the collisionless plasma, and the maximum of the spectrum is substantially shifted with respect to the direction to the source. It is shown that these effects weaken as the emitter approaches the layer. The dependence of the width of the spectrum and the shift of its maximum on distance from the receiver to the layer's boundary can be substantially nonmonotonic. Lobachevsky State University, Nizhny Novgorod, Russia; Georgian Technical University, Tbilisi, Georgia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No. 4, pp. 340–354, April 1999.     

Sound source localization in an ocean waveguide

A robust algorithm for sound source localization in shallow sea based on a 2D Fourier transform of source motion interference patterns is developed. A spectrogram in time-frequency coordinates obtained after a Fourier transform contains localized areas of spectral density intensity of constructively interfering modes and a distributed area of noise spectral density. Signal spectral density is localized in an area whose linear sizes are determined by the lowest frequency and spatial scales of field variability. The peak input signal-to-noise ratio is estimated for a single receiver when robust detection is ensured and estimates of speed and initial distance to the receiver are close to the actual values. The high robustness of the algorithm is based on the coherent summation of mode amplitudes occurring at different times. Experimental results demonstrating the effectiveness of the algorithm are presented. For higher than peak signal-to-noise ratios, random estimates of the parameters are close to their statistically average values.     

Fast transient capacitance measurements for implanted deep levels in silicon

The present diffraction problem is solved by means of a perturbation calculus in the transition conditions and by repeated application of the method of steepest descent to two-dimensional Fourier integrals. We obtain a reflection coefficient for the rough surface resulting in a geometrical-optics approximation for the space wave field strength. In the case of a periodic roughness profile the application of the method of steepest descent in the transform space can be avoided and we get the electromagnetic field through differentiation of the Bromwich potentials. The numerical results of the two methods are discussed in the case of a one-dimensional cosine profile. We show that the influence of the earth's roughness increases with increasing receiver heights and fixed receiver distance. On the other hand, we point out that the geometric optical approach is a rather good approximation for the space wave field strength.     

Mid-range adiabatic wireless energy transfer via a mediator coil

A technique for efficient mid-range wireless energy transfer between two coils via a mediator coil is proposed. By varying the coil frequencies, three resonances are created: emitter–mediator (EM), mediator–receiver (MR) and emitter–receiver (ER). If the frequency sweeps are adiabatic and such that the EM resonance precedes the MR resonance, the energy flows sequentially along the chain emitter–mediator–receiver. If the MR resonance precedes the EM resonance, then the energy flows directly from the emitter to the receiver via the ER resonance; then the losses from the mediator are suppressed. This technique is robust against noise, resonant constraints and external interferences.