Index of content:
Volume 63, Issue 1, January 1978

Variance of the wave amplitude in a random medium with a nonuniform background
View Description Hide DescriptionVariance of the wave amplitude in a random medium with a nonuniform background is obtained by the method of geometrical optics. A minor discrepancy of earlier results is clarified.

Acoustics of finite beams
View Description Hide DescriptionWe derive the expression for the most general possible finite acoustic beam, i.e., for a beam finite in two dimensions, which emerges from an arbitrarily shaped collimating aperture at an arbitrary angle and with an arbitrary amplitude profile. We investigate the spreading of such a beam for two amplitude profiles; a Gaussian profile and a flat‐topped square profile. In both cases the spreading is determined as a function of the ratios between the collimating aperture sizes (σ or R _{ o }) and three parameters; wavelength, axial distance from the aperture plane, and radial distance from the beam axis. The general applications of this analysis are numerous, particularly when one considers that almost all physically realizable acoustic sources project finite sound beams as opposed to waves of infinite extent. As a specific application of this general theory, we evaluate the scattering of a finite beam from a rigid sphere in an e x a c t fashion for the two amplitude profiles of the finite beam mentioned above, and we finally compare plots for the bistatic cross sections to the results obtained in previous work of ours using the approximate Kirchhoff method.

Plane wave diffraction by a wedge with finite impedance
View Description Hide DescriptionA theory is presented for the diffraction of acoustic waves by barriers with finite acoustical impedance, the shape of the barriers being such that, insofar as diffraction into the shadow zone is concerned, they may be idealized as semi‐infinite wedges. The analytical development is based on the known exact solution for plane wavediffraction by a finite impedance wedge, versions of which have been previously given in the literature by Williams [Proc. R. Soc. London Ser. A: 252, 376–393 (1959)], by Senior [Commun. Pure Appl. Math. 12, 337–372 (1959); Proc. R. Soc. London Ser. A: 213, 436–458 (1952)], and by Maliuzhinets [Sov. Phys. Acoust. 1, 152–174; 240–248 (1955)]. This solution is described in detail and the asymptotic limit is derived in a form which demonstrates the satisfaction of the reciprocity principle. Practical implementation is discussed, both through numerical examples and through the presentation of graphs of quantities which will be helpful in barrier design.

Generalized Fourier transform diffraction theory for parabolically anisotropic media
View Description Hide DescriptionA convenient diffraction formalism is presented for a planar ultrasonic source of arbitrary shape radiating into a medium which is parabolically anisotropic (or isotropic). Under the Fresnel approximation, the field amplitude is shown to be a Fourier transform of the aperture source function for both the nearfield and farfield. For the two‐dimensional (surface‐wave) case, closed‐form field expressions were obtained for the following source shapes: rectangular, Gaussian, truncated cosine, and truncated Gaussian. Diffraction loss and phase advance curves for equal and unequal apertures show that the nearly ideal characteristics of a Gaussian source can be approximated well by truncated source shapes.

Reflectivity of the ocean bottom at low frequency
View Description Hide DescriptionThe theoretical reflectivity of the ocean bottom estimated from a model composed of fluid sediment layers is misleading because the effects of shear propagation are ignored. Reflectivity computations which include the effects of shear may be made using Thomson–Haskell matrix theory. The delta‐matrix extension of this theory provides a method for computation of plane‐wave reflectivity of a viscoelastic layered ocean bottom at the frequencies of interest in acoustics. The results from a hypothetical turbidite section show that when elastic parameters vary continuously with depth, conversion of compressional to shear energy is unimportant at frequencies above 20 Hz. However, at discontinuities, conversion to shear does occur. This strongly affects the reflectivity at all frequencies, except at small grazing angles and near‐normal incidence.

Low‐frequency sound absorption in the ocean
View Description Hide DescriptionRecent work on low‐frequency sound absorption in the ocean and laboratory has been examined with regard to temperature dependence, pH dependence, boron concentration, and pressure effects in an effort to arrive at a practical expression consistent with existing knowledge for use in sonar prediction and design applications. It is found that, over the range of pH observed in the ocean, the maximum absorption per wavelength depends exponentially on the pH at the sound‐channel axis depth. The relaxation‐frequency dependence on temperature is examined in terms of the temperature dependence of seawaterviscosity and the activation energy of the relaxation process. The relaxation‐frequency dependence on the square root of the salinity is consistent with available data and theory.

Quantitative schlieren visualization of unipolar acoustic transients
View Description Hide DescriptionImage intensity distributions have been calculated for the schlieren observation of Gaussian, unipolar acoustic pulses. The optical intensity distributions in both the Fourier transform plane (stop plane) and the image plane are discussed. Experimental observations are presented for Gaussian‐like pressure transients generated by narrow voltage pulse excitation of thick piezoelectric plates. These observations are compared to the results of the calculations. It is suggested that this technique is ideally suited for the determination of transducer transfer functions.

Acousto‐optic effect in nematic liquid crystals
View Description Hide DescriptionAcoustically induced birefringence has been studied in homeotropic cells of nematic liquid crystals. Annular rings associated with the edge of the ultrasonic beam have been observed in agreement with the model based on acoustic streaming. Other observed features of the spatial distribution of the optical signal are not described by this theory. The increased sensitivity near the nematic‐isotropic transition is shown to be due primarily to the increased sound absorption.

Measurement of acoustic fields using schlieren and holographic techniques
View Description Hide DescriptionTwo methods, schlieren imaging and acoustical holography, are shown to be useful for quantitatively measuring detailed nearfield and farfield acoustic radiation patterns from a submerged cylindrical target. The two imaging methods are discussed so as to illustrate the fundamental mechanisms of imaging involved. The advantages and limitations of each are made clear, and examples of typical laboratory acoustic field measurements are shown for a cylindrical aluminum target. The farfield of the target is computed from an emerging theory for nonrigid cylinders, and the experimental farfield data obtained holographically is shown to agree with that theory. The nearfield of the same target is plotted directly from the photo intensity of the schlieren image.

Scattering of longitudinal waves incident on a spherical cavity in a solid
View Description Hide DescriptionExperimental data are compared with theoretical calculations for the scattering of ultrasonic pulses from a single spherical cavity embedded in a metallic solid. Except at high frequencies, the data are in reasonable agreement with theory, bearing out the notable features predicted for the angular dependence and the mode conversion between longitudinal and transverse waves. At high frequencies the disagreement can be accounted for by the lack of monochromicity in the ultrasonic pulse, and the technique for analyzing the data taking into account the broadband spectrum must be applid. The experimental parameters were chosen to span the regime where the wavelength is of the order of the size of the spherical cavity (0.8 mm) on samples of diffusion bounded Ti–6% Al–4% V.

Locally optimum detection of discrete‐time stochastic signals in non‐Gaussian noise
View Description Hide DescriptionTwo basic models are considered for the problem of detecting small, zero‐mean stochastic signals in non‐Gaussian noise processes. Appying the theory of local tests, a general detector structure is derived for each of these models. A third (suboptimal) scheme based on null‐zone detection is also proposed and a technique for optimizing its parameters is discussed. Using the criterion of asymptotic relative efficiency, the performance of these three detectors and of a power detector are compared under each of the proposed models.

Optimum detection of signals in non‐Gaussian noise
View Description Hide DescriptionThe purpose of this paper is to derive optimum processing structures for use in the detection of signals in additive non‐Gaussian noise. The cases chosen for analysis are of particular interest in sonar detection problems since it has been reported that ambient oceannoise may, under sone conditions, deviate from the Gaussian model. The processing structures are considered to be models of the likelihood ratio which is an optimum test no matter what the signal and noise statistics, and optimum single channel and array processors are derived for the small signal‐to‐noise ratio cases where (1) the signal is completely known, and (2) the signal is a noiselike, not necessarily Gaussian, zero‐mean process. Expressions are derived which compare the performance of processors optimized for non‐Gaussian noise with those optimized for Gaussian noise for each of the two cases, with transfer functions for the required optimum nonlinear filters and the expected improvements in performance determined using some ’’typical’’ non‐Gaussian probability density functions. Justification of these particular density functions is beyond the scope of this paper except to note that very good agreement is obtained with some published experimental data. New results include the derivation of optimum array processors for the detection of plane wave signals when the array is steered at the signal arrival angle, in a non‐Gaussian noise field and the development of expressions to predict their performance for the case where the signal is a zero‐mean, noiselike process.

Passive bearing estimation: The removal of bias and 2π ambiguities
View Description Hide DescriptionAveraging across frequency presents one means of combating noise in split‐beam bearing estimation. Unfortunately, simple phase averaging is a biased estimator, and, in the case of split‐beam analysis, suffers as well from spatial aliasing. Both of these difficulties arise from the 2πn uncertainty inherent in any phase angle observation. This paper provides several algorithms utilizing an iterative averaging technique which circumvents these problems. Convergence theorems are provided for the algorithms and an evaluation on synthetic data shows them to be highly successful. The techniques developed are quite general and should find use in many situatios in which angle averaging or averaging of functions of angles is pertinent.

Remote detection of turbulence from observations of reverberation spectra
View Description Hide DescriptionThe narrowness of normally occurring, oceanic high‐frequency reverberation spectra is attributed to scatterers at rest relative to the water. Turbulentscatterer motion induced by any mechanism is revealed in a broadening of these spectra, and its localization is afforded by comparisons of spectra obtained from contiguous portions of the insonified volume. Fundamental constraints are imposed on turbulence detection and localization processes by the instrumentation geometry and signal waveform, and their delineation is a primary goal of the present investigations. Methods for overcoming these constraints through modifications of the signal waveform, refinement of the receiver and application of postdetection processing schemes are considered. Limitations arising from platform motion and their circumvention are also examined.

Rejection of sonar interference of finite bandwidth by amplitude shading of transducer arrays
View Description Hide DescriptionFollowing the work reported in an earlier paper, the possibility of rejecting coherent interference of finite bandwidth and distributed direction of incidence by purely amplitude shading of a transducer array is investigated. Using the same linear transducer array immersed in the same distributed interference and ambient noise fields, it is demonstrated that, if the array shading is optimized by assuming all the interference power to be concentrated at its band center, interference of bandwidths up to 10% of its center frequency and intensity 70 dB above ambient noise field can be effectively rejected. This confirms that the theroy reported earlier is adequate for applications in narrow‐band receiving systems. If a broadband interference power quadratic is used in the process of shading optimization, the above interference‐rejecting capability can be extended to a bandwidth equal to 40% of its center frequency. These results further suggest that an optimum/adaptive broadband beamformer for passive sonar typically needs to be amplitude shaded in only eight bands.

On cochlear encoding: Potentialities and limitations of the reverse‐correlation technique
View Description Hide DescriptionThis paper presents a description of the interrelation between two major properties of the responses recordable from auditory nerve fibers:f r e q u e n c y s e l e c t i v i t y and p a r t i a l s y n c h r o n y between stimulus and response. In the course of this work the influence of nonlinearity on the cochlear encoding process can be assessed. The theory of the r e v e r s e‐c o r r e l a t i o n t e c h n i q u e is derived in a most general way. It is based on a model in which a filter—assumed to be linear—is followed by a stochastic pulse generator—the probability of producing an output pulse being an instantaneous but nonlinear function of its input signal. Insofar as such a model represents stimulus transformations in a primary auditory neuron, the technique can be applied to the responses recorded from an auditory nerve fiber. Several illustrative examples of experimental reverse‐correlation functions−abbreviated: r e v c o r f u n c t i o n s—are presented and discussed. These functions have the general character of impulse responses of sharp bandpass filters. They show very little phase modulation. For noise stimuli of up to 70 dB per third octave the revcor functions are almost invariant. Above that level some (but not all) of the revcor functions show a loss of frequency selectivity. If a nerve fiber can be contacted for a sufficiently long time, it is possible to compare the response with that of a model filter, in which the revcor function of that fiber is substituted as its impulse response. The output signal of the model filter is shown to be a very good predictor of the firing probability of the fiber under study. This property is demonstrated for noise as well as for tone stimuli. There is surprisingly little evidence of nonlinear filtering in these results. This so‐called simulation method can also be applied when the stimulus is switched on and off. The results show, apart from effects due to filtering, clear manifestations of fast adaptation. Again, the filtering appears to be independent of the latter effect. It is concluded that for wide‐band noise and single‐tone signals the firing probability is predominantly controlled by a linearly filtered version of the acoustical stimulus; this constitutes the principle of s p e c i f i c c o d i n g. The conspicuous absence of nonlinear effects in the results can partly be explained in terms of the response properties of a class of networks in which sharp filtering occurs after the generation of nonlinear distortion products. It can then be predicted that this property will hold only for wide‐band and tonal stimuli. That our results show so little evidence of cochlear distortion appears to be a property of signal transformations and is not due to linearization tendencies of the experimental method.

Coding of information in single auditory‐nerve fibers of the goldfish
View Description Hide DescriptionPatterns of activity in single fibers of the saccular branch of the auditory nerve of goldfish were analyzed in response to acoustic stimulation. Neurons were categorized on the basis of differences in spontaneous activity patterns, rates of adaptation, and frequency response areas. The sensitivity and responsiveness of neurons are presented both in terms of impulse rate and synchronization (phase locking). Nonspontaneous neurons fall into two clear frequency response area categories based upon impulse rate criteria. Spontaneously active neurons have continuously distributed frequency response characteristics based upon synchronization criteria. Functions relating impulse rate responsiveness to frequency indicate that frequency is coded only crudely as an across‐fiber pattern of impulse rates. Synchronization responsiveness functions show that frequency is coded temporally with the same precision in the goldfish auditory nerve that it is in mammals, at 1000 Hz and below.

Threshold and growth of the acoustic reflex
View Description Hide DescriptionMeasurements of the threshold and growth function of the acoustic reflex in man were made utilizing a signal‐averaging technique. Pure tones (250, 500, 1000, 2000, and 4000 Hz) and broadband noise served as the contralateral stimuli delivered at intensity levels from the reflex threshold to 116 dB SPL. The acoustic conductance and susceptance components of admittance, at 220 and 660 Hz, were used to measure the reflex activity. The results are reported as changes in conductance, susceptance, and admittance in cgs mmho. The acoustic reflex thresholds were similar to those reported in other studies, with the 220‐Hz probe yielding thresholds that averaged 3.5 dB higher than those obtained with the 660‐Hz probe. Broadband noise and 1000‐Hz stimuli produced the largest reflex magnitudes, while the smallest were observed with 250‐ and 4000‐Hz signals. The dynamic ranges of the restricted growth functions were frequency dependent for pure tones and ranged from ≳16 dB with 250 Hz to ≳28 dB with 1000 Hz, while that for noise was ≳50 dB. The first derivative of the best‐fit third‐degree polynomial was used to describe the slope characteristics of the growth functions, in which frequency and intensity effects were found. Relationships between the acoustic reflex and tympanometry were observed and are also discussed.

Angle estimation and binaural processing in animal echolocation
View Description Hide DescriptionPhysical structures separate the ears of many mammals, and the ears themselves have complex transfer functions that depend upon the direction of a sound source. Neither of these observations is usually incorporated into standard array analysis. The conventional array problem generally assumes that individual elements are omnidirectional, and there are no physical structures between elements to provide partial isolation. This investigation of binaural angle estimation specifically incorporates the effects of partial isolation and directivity patterns that vary with angle and frequency. Cramér–Rao bounds for the variance of maximum likelihood angle estimates are derived. These bounds, along with a generalized ambiguity function, are used to evaluate the significance of isolation between the ears, angle‐dependent magnitude, and phase variations in the spatial transfer functions of the ears, the use of wide‐band and narrow‐band signals in animal echolocation, symmetry of aural directivity patterns, the transmitted beam patterns that are employed by certain bats, and the angle‐dependent signal variations that have been observed in cetacean echolocation. Only two broadband hydrophones are sufficient for accurate, unambiguous azimuth measurement if the width of the signal autocorrelation function is small relative to the distance between hydrophones. The analysis indicates that many past measurements of transmitted beam patterns and aural transfer functions in animals are incomplete, since they do not consider direction‐dependent phase variations. It may also be necessary to reinterpret the meaning of time difference and pressure difference cues for localization. These insights can be used not only for better correlation of behavioral and physiological measurements, but also for better design of man‐made systems for communication, radar, sonar, and ultrasonic medical diagnosis.

The Fourier–Mellin transform and mammalian hearing
View Description Hide DescriptionA combined Fourier–Mellin transform yields a representation of a signal that is independent of delay and scale change. Such a representation should be useful for speech analysis, where delay and scale differences degrade the performance of correlation operations or other similarity measures. At least two different versions of a combined Fourier–Mellin transform can be implemented. The simplest version (the ‖F‖^{2}−‖M‖^{2}transform) completely eliminates spectral phase information, while a slightly more complicated version (the ?−? transform) preserves some phase information. Both versions can be synthesized with a Fourier transform and an exponential‐sampling algorithm. Exponential sampling produces a frequency scale distortion that is similar to the effect of the cochlea. The ‖F‖^{2}−‖M‖^{2}transform can also be implemented with a bank of proportional bandwidth filters. If the relative phase between spectral components is preserved, then a Fourier–Mellin transformer can perform compression of linear‐period modulated signals. Such signals are used for echolocation by bats and cetaceans. The same approach that gives scale and delay invariance can be used to obtain other transform conbinations that provide insensitivity to a variety of distortions. The combined transforms can also be used for analyzing these distortions.