Coherence coefficient measuring system and its application to some acoustic measurements

The coherence coefficient defined by the so-called zero-delayed correlations for two sine functions can be given as a function of the phase difference only. Consequently, some acoustic responses resulting from the phase synthesis are capable of being analysed making use of this characteristic of the coherence coefficient.The measuring system based on the definition of coherence coefficient and some examples applying the system to acoustic measurement are discussed in this paper. In addition, the paper shows that the measured values agree well with the theoretical ones.     

Temporal coherence of acoustic rays and modes using the path integral approach

Acoustic propagation can be described by rays and normal modes. Applying the path integral to refractive rays in three dimensional space, Dashen et al. [J. Acoust. Soc. Am. 77, 1716-1722 (1985)] derived the mutual coherence function of the acoustic field. For shallow water where sound interacts with boundaries, the acoustic field can be described by vertical modes and horizontal rays. Applying the path integral to the horizontal rays, one obtains the mutual coherence function of the normal modes. This paper applies this formulation to the derivation of the temporal coherence function of individual modes and also that of the acoustic field in the presence of linear internal waves. The effects of mode coupling due to internal waves on temporal coherence loss are illustrated with numerical calculations.     

Acoustic propagation through anisotropic internal wave fields: transmission loss, cross-range coherence, and horizontal refraction

Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.     

Limits of coherence-based aeroacoustic analysis in the presence of distributed sources

Coherence-based analysis techniques utilizing a small number of microphones are often applied in aeroacoustic measurements. These techniques can remove statistically incoherent noise, electronic or hydrodynamic, from acoustic signals measured by microphones, at significantly lower cost than array methods. However, the assumptions involved in the usage of the ordinary coherence function technically limit analysis to a single-source field. In the presence of multiple sources the coherence function breaks down and ordinary analysis techniques under-predict true acoustic levels. This phenomenon is demonstrated mathematically and illustrated using experimental trailing edge noise data.     

Spatial structure of the coherence parameter of the sound field in an irregular arctic waveguide

Results of numerical simulation of the total and coherent sound fields and the coherence parameter for a multimode acoustic signal excited by a monochromatic sound source and propagating in an irregular arctic waveguide are presented. Expressions used as the basis for the algorithm of the sound field calculation by the method of coupled normal modes are given. Both regular and stochastic sound scattering by horizontal inhomogeneities of the bottom, water medium, and ice cover are taken into account. It is found that, in the course of sound propagation in an arctic waveguide, an anomalous variation of the energy coherence parameter of the sound field as a function of distance is observed. This variation manifests itself in the form of local peaks of the field coherence parameter. This fact should be taken into account in both the measurements of the ice cover characteristics by acoustic methods and the evaluation of the efficiency of the operation of receiving arrays.     

Temporal coherence of acoustic signals in a fluctuating ocean

Temporal coherence of acoustic signals propagating in a fluctuating ocean is important for many practical applications and has been studied intensively experimentally. However, only a few theoretical formulations of temporal coherence exist. In the present paper, a three-dimensional (3D) modal theory of sound propagation in a fluctuating ocean is used to derive closed-form equations for the spatial-temporal coherence function of a broadband signal. The theory is applied to the analysis of the temporal coherence of a monochromatic signal propagating in an ocean perturbed by linear internal waves obeying the Garrett-Munk (G-M) spectral model. In particular, the temporal coherence function is calculated for propagation ranges up to 10(4) km and for five sound frequencies: 12, 25, 50, 75, and 100 Hz. Then, the dependence of the coherence time (i.e., the value of the time lag at which the temporal coherence decreases by a factor of e) on range and frequency is studied. The results obtained are compared with experimental data and predictions of the path-integral theory.     

Features determining compensation of counter energy flows in acoustic fields of the ocean

The phenomenon of compensation of counteracoustic energy flows in the ocean was studied using the example of superposition of acoustic fields of a moving vessel and of the surface noise of a tropical shower using combined receivers at depths of 150 and 500 m. We demonstrate that comparison of the z-component of the spectrum of function of simple one-point coherence or the z-component of the cross-spectrum with the spectrum of phase difference between the acoustic pressure and the z-component of the vibrational speed is sufficient for unambiguous determination of the process of compensation. The criteria are the “dips” of the coherence function in a frequency range, common to these fields, which correspond to the jumps of the phase difference by ± (π/2).     

Optimisation using measured Green's function for improving spatial coherence in acoustic measurements

Aberrating materials can degrade acoustic measurements by distorting the acoustic wavefront and causing acoustic speckle (as opposed to speckle noise which is a manifestation of coherent backscatter). The amplitude and phase fluctuations associated with acoustic speckle can introduce considerable measurement uncertainty which is difficult to deal with. This paper demonstrates a new technique which optimises the spatial distribution of the generation of the ultrasound to compensate for the aberration. This technique uses experimentally measured Green's functions to allow the calculation of the field resulting from the generation wavefront during optimisation. The technique is used to improve the accuracy of velocity measurements in a steel sample using 82 MHz SAW waves. This is achieved by optimising for improved spatial coherence in the measurement region which suppresses the speckle noise. Experimental evidence of acoustic aberration arising from grain structure is shown for steel and aluminium and the measured Green's function optimisation technique is shown to overcome the resulting acoustic speckle. The technique was performed using the Adaptive Optical Scanning Acoustic Microscope (AOSAM) at Nottingham University, UK.     

浅水时变多途信道特性分析与模型实验研究

时变多途水声信道是影响水声通信性能的一个重要因素,深入了解水声信道挣性并对水声信道进行建模具有重要的研究意义。本文在分析传统时变信道模型基础上,从时域角度出发,提出采用AR(ρ)模型对已有的浅水时变多途信道模型中的小尺度衰落分量进行修正。然后基于莲花湖实测信道数据,分析了时变信道各个路径的幅度、时延、时间相干系数、系统传递函数等特性,并对修正模型进行了验证正。从仿真结果来看,修正模型与试验结果拟合的很好。本文从多个方面对水声信道特性进行了分析,有助于对水声信道的深入了解,同时为水声通信系统性能评估提供了一种仿真信道模型。     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Properties of underwater acoustic communication channels in shallow water

Underwater acoustic channels are band-limited and reverberant, posing many obstacles to reliable, phase-coherent acoustic communications. While many high frequency communication experiments have been conducted in shallow water, few have carried out systematic studies on the channel properties at a time scale relevant for communications. To aid communication system design, this paper analyzes at-sea data collected in shallow water under various conditions to illustrate how the ocean environments (sea surface waves and random ocean medium) can affect the signal properties. Channel properties studied include amplitude and phase variations, and temporal coherence of individual paths as well as the temporal and spatial coherence of multipaths at different time scales. Reasons for the coherence loss are hypothesized.     

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Aberrations in materials with random inhomogeneities

Materials that consist of a random microstructure can affect ultrasonic measurements--reducing signal strength, increasing noise, and reducing measurement accuracy--through scattering and aberration of the acoustic field. To account for these adverse effects a phase screen model, alongside the stochastic wave equation, has been developed. This approach allows the field and study aberrations to be modeled from a statistical point of view. Experimental evidence of aberration and statistical properties of the measured acoustic field are shown. A measured correlation function of the acoustic field is interlinked to mean crystallite size by using a theoretical coherence function that can be mainly described by the correlation length and wave velocity variation of microstructure. The estimation of the mean crystallite size using this technique would provide some insight into material characterization.     

Acoustically modified optical Fresnel diffraction by a slit and a periodic object in relation to periodic partial coherence

Optical Fresnel diffraction by a slit and a periodic rectangular wave object, illuminated with accoustically phase-modulated laser light, is investigated in association with partial coherence. The periodic partial coherence, produced by acousto-optic interaction, much deformes the Fresnel diffraction patterns of the respective objects. A nearly flat-top diffraction pattern by the slit is obtained if the acoustic and slit parameters are adjusted. The self-image by the periodic rectangular wave object is reversed in contrast if the acoustic power exceeds a critical value.     

Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.     

Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Green's function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.     

Quantitative elastography provided by surface acoustic waves measured by phase-sensitive optical coherence tomography

We report on a quantitative elastography technique achieved by combining phase-sensitive optical coherence tomography (PhS-OCT) with the surface acoustic wave (SAW) method. Different from traditional optical coherence elastography, the elastography is achieved by impulse-stimulated SAW, rather than by shear waves. PhS-OCT serves not only as a detector to measure SAW signals but also as a means to provide a cross-sectional image of the sample. The experimental results indicate that the combination of PhS-OCT with SAW is feasible to provide quantitative elastography of heterogeneous tissue samples.     

Cross-correlation in band-limited ocean ambient noise fields

Observations of ambient noise in the ocean are generally band limited, because of the natural spectral shape of the noise or the restricted bandwidth of the detection system. Either way, the noise may be regarded as white noise to which a band-limiting filter has been applied. An analysis of the two-point cross-correlation function of such filtered noise is presented for two cases, isotropic and surface-generated noise. The most pronounced effects occur with high-pass and bandpass filters when the low-frequency cut-off falls well above the first few zeros in the coherence function. In this situation, the sensor separation is very many times the longest acoustic wavelength (associated with the lowest frequency) in the passband. The filtering then produces sharp pulses at correlation delays equal to the numerical value of the acoustic travel time between the sensors. Although these pulses are narrow, they have a finite width, within which a fine structure appears in the form of multiple rapid oscillations, due to the differentiating action of the filter. The number of such oscillations increases as the low-frequency roll-off of the filter becomes steeper. This fine structure is evident in several recently published experimental determinations of the cross-correlation function of band-limited ocean ambient noise.     

Ultrafast breathinglike oscillation in the exciton density of ZnSe quantum wells

The spatial density profile of a low-density exciton ensemble in ZnSe quantum wells shows a breathinglike oscillation on a 30-ps time scale. This breathing results from the emission of the first acoustic phonon at the end of the quasiballistic transport phase of the excitons which reverses their direction of propagation. Since the scattering destroys the phase of the excitonic wave function, one can deduce simultaneously the coherence length and the coherence time of excitonic transport by evaluation of the oscillation measured from a single experiment. The breathing, which can be modeled by Monte Carlo simulations, is quenched for rising lattice temperature, i.e., increasing phonon absorption, and in samples with significant disorder. These results were obtained by time-resolved nanophotoluminescence with 5 ps and 250 nm temporal and spatial resolution, respectively.