Foote Kenneth G.

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Foote

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Kenneth G.

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0000-0001-6873-9598

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Maintaining precision calibrations with optimal copper spheres

(Acoustical Society of America, 1983-03) Foote, Kenneth G.

Effects of variations in quantities influencing the backscattering cross sections of solid elastic spheres are studied through a particular case. This is that of the 60‐mm‐diam copper sphere, which is being used worldwide to calibrate the 38‐kHz echo sounders instrumental in fisheries surveying. Derived dependences of the backscattering cross section include those characterizing the sphere, immersion medium, and equipment. Some of the dependences are sufficiently weak to permit their neglect in assigning the calibration value of the backscattering cross section, while others must be considered. In every case the dependences are calculable; given measurement of the calibration conditions, necessary corrections to the backscattering cross section can be determined and applied with maintenance of 0.1‐dB accuracy. The wider use of copper spheres in acoustic calibrations, as in the radiation force method, is advocated. The practical use of optimal copper spheres in calibrating echo sounders and echo integrators is treated in detail in an appendix.
Calibration sphere for low-frequency parametric sonars

(Acoustical Society of America, 2007-03) Foote, Kenneth G. ; Francis, David T. I. ; Atkins, Philip R.

The problem of calibrating parametric sonar systems at low difference frequencies used in backscattering applications is addressed. A particular parametric sonar is considered: the Simrad TOPAS PS18 Parametric Sub-bottom Profiler. This generates difference-frequency signals in the band 0.5–6 kHz. A standard target is specified according to optimization conditions based on maximizing the target strength consistent with the target strength being independent of orientation and the target being physically manageable. The second condition is expressed as the target having an immersion weight less than 200 N. The result is a 280-mm-diam sphere of aluminum. Its target strength varies from −43.4 dB at 0.5 kHz to −20.2 dB at 6 kHz. Maximum excursions in target strength over the frequency band due to uncertainty in material properties of the sphere are of order ±0.1 dB. Maximum excursions in target strength due to variations in mass density and sound speed of the immersion medium are larger, but can be eliminated by attention to the hydrographic conditions. The results are also applicable to the standard-target calibration of conventional sonars operating at low-kilohertz frequencies.
Acoustic detection and quantification of benthic egg beds of the squid Loligo opalescens in Monterey Bay, California

(Acoustical Society of America, 2006-02) Foote, Kenneth G. ; Hanlon, Roger T. ; Iampietro, Pat J. ; Kvitek, Rikk G.

The squid Loligo opalescens is a key species in the nearshore pelagic community of California, supporting the most valuable state marine fishery, yet the stock biomass is unknown. In southern Monterey Bay, extensive beds occur on a flat, sandy bottom, water depths 20–60 m, thus sidescan sonar is a prima-facie candidate for use in rapid, synoptic, and noninvasive surveying. The present study describes development of an acoustic method to detect, identify, and quantify squid egg beds by means of high-frequency sidescan-sonar imagery. Verification of the method has been undertaken with a video camera carried on a remotely operated vehicle. It has been established that sidescan sonar images can be used to predict the presence or absence of squid egg beds. The lower size limit of detectability of an isolated egg bed is about 0.5 m with a 400-kHz sidescan sonar used with a 50-m range when towed at 3 knots. It is possible to estimate the abundance of eggs in a region of interest by computing the cumulative area covered by the egg beds according to the sidescan sonar image. In a selected quadrat one arc second on each side, the estimated number of eggs was 36.5 million.
Measurement of fish target strength with a split‐beam echo sounder

(Acoustical Society of America, 1986-08) Foote, Kenneth G. ; Aglen, Asgeir ; Nakken, Odd

Data derived with a 38‐kHz split‐beam echo sounder have been analyzed to yield target strengths suitable for use with echo integrators. This has required compensation for both thresholding and saturation, since these operations can significantly bias data intended for use with systems, such as echo integrators, whose dynamic ranges are much larger. A nonparametric statistical method is introduced for this purpose. Pure‐species acoustic data are extracted in several two‐species cases by a method for separating superimposed frequency distributions. Mean i n s i t u target strengths are presented for cod, saithe, Norway pout, herring, redfish, and greater silver smelt. For com‐ parison with other data, these are expressed through the standard equation ∼(TS) =20 log l +b, where ∼(TS) is the mean target strength in decibels, and l is the fish length in centimeters. For gadoids of lengths from 10 to over 105 cm, b=−67.5 dB. For herring of lengths from 24 to 34 cm, b=−72.1 dB. The often‐ignored problem of obtaining unambiguous biological data by trawl sampling is discussed.
Comparing Kirchhoff-approximation and boundary-element models for computing gadoid target strengths

(Acoustical Society of America, 2002-04) Foote, Kenneth G. ; Francis, David T. I.

To establish the validity of the boundary-element method (BEM) for modeling scattering by swimbladder-bearing fish, the BEM is exercised in several ways. In a computation of backscattering by a 50-mm-diam spherical void in sea water at the four frequencies 38.1, 49.6, 68.4, and 120.4 kHz, agreement with the analytical solution is excellent. In computations of target strength as a function of tilt angle for each of 15 surface-adapted gadoids for which the swimbladders were earlier mapped, BEM results are in close agreement with Kirchhoff-approximation-model results at each of the same four frequencies. When averaged with respect to various tilt angle distributions and combined by regression analysis, the two models yield similar results. Comparisons with corresponding values derived from measured target strength functions of the same 15 gadoid specimens are fair, especially for the tilt angle distribution with the greatest standard deviation, namely 16°.
Further analysis of target strength measurements of Antarctic krill at 38 and 120 kHz : comparison with deformed cylinder model and inference of orientation distribution

(Acoustical Society of America, 1993-05) Chu, Dezhang ; Foote, Kenneth G. ; Stanton, Timothy K.

Data collected during the krill target strength experiment [J. Acoust. Soc. Am. 87, 16–24 (1990)] are examined in the light of a recent zooplankton scattering model where the elongated animals are modeled as deformed finite cylinders [J. Acoust. Soc. Am. 86, 691–705 (1989)]. Exercise of the model under assumption of an orientation distribution allows absolute predictions of target strength to be made at each frequency. By requiring that the difference between predicted and measured target strengths be a minimum in a least-squares sense, it is possible to infer the orientation distribution. This useful biological quantity was not obtainable in the previous analysis which involved the sphere scattering model.
Averaging of fish target strength functions

(Acoustical Society of America, 1980-02) Foote, Kenneth G.

A general model for averaging the acoustic target strength functions of fish is stated in calculable form. It accounts for the influences of the distribution of generally coupled spatial and orientation states of fish, geometric perspective, and beam patterns on observations of target strength. The model is developed and applied to observation of fish by directional, downward‐looking sonars. A particular example is considered in which the sonar is represented by an ideal circular piston, the spatial distribution of fish is homogeneous, and the orientation distribution is spatially homogeneous and characterized by a uniformily distributed azimuthal variable and an independent, essentially normally distributed tilt angle variable. Averaged and averaged‐squared backscattering cross sections are computed from high quality gadoid target strength functions measured at two ultrasonic frequencies. Results for a sonar half‐beamwidth of 2.5 deg for three different realizations of the tilt angle distribution are expressed in the logarithmic domain and regressed linearly on fish length. The significance of species, frequency, and orientation distribution differences among the regressions is noted. Estimates of the mean ratio of averaged‐squared backscattering cross section and squared‐averaged backscattering cross section are presented.
Importance of the swimbladder in acoustic scattering by fish : a comparison of gadoid and mackerel target strengths

(Acoustical Society of America, 1980-06) Foote, Kenneth G.

Previous determinations of the swimbladder contribution to the fish backscattering cross section have been hindered by ignorance of the acoustic boundary conditions at the swimbladder wall. The present study circumvents this problem by direct comparison of target strengths of three gadoid species and mackerel — anatomically comparable fusiform fish which respectively possess and lack a swimbladder. The relative swimbladder contribution to both maximum and averaged dorsal aspect backscattering cross sections is shown to be approximately 90% to 95%, which is higher than most other estimates. The new results were established for fish of 29‐ to 42‐cm length and acoustic frequencies of 38 and 120 kHz.
Detecting Atlantic herring by parametric sonar

(Acoustical Society of America, 2010-03-17) Godø, Olav Rune ; Foote, Kenneth G. ; Dybedal, Johnny

The difference-frequency band of the Kongsberg TOPAS PS18 parametric sub-bottom profiling sonar, nominally 1–6 kHz, is being used to observe Atlantic herring. Representative TOPAS echograms of herring layers and schools observed in situ in December 2008 and November 2009 are presented. These agree well with echograms of volume backscattering strength derived simultaneously with the narrowband Simrad EK60/18- and 38-kHz scientific echo sounder, also giving insight into herring avoidance behavior in relation to survey vessel passage. Progress in rendering the TOPAS echograms quantitative is described.
Performance of the parametric receiving array : effects of misalignment

(Acoustical Society of America, 1987-11) Foote, Kenneth G. ; Tjøtta, Jacqueline Naze ; Tjøtta, Sigve

The difference frequency sound field from two concentric but misaligned, axisymmetric, planar transducers in a nondissipative and nondispersive medium is developed as a special case of the general theory [Garrett et al., J. Acoust. Soc. Am. 75, 769–779 (1984)]. Effects of misalignment of pump, source, and hydrophone on the performance of the parametric receiving array are quantified in numerical examples. These include the effect of interaction in the nearfields of both pump and source transducers. The results show that the best performance is obtained for good alignment, high pump frequency, and placement of the hydrophone within or not far from the source nearfield.
Linearity of fisheries acoustics, with addition theorems

(Acoustical Society of America, 1983-06) Foote, Kenneth G.

An experiment to verify the basic linearity of fisheries acoustics is described. Herring (Clupea harengus L.) was the subject fish. Acoustic measurements consisted of the echo energy from aggregations of encaged but otherwise free‐swimming fish, and the target strength functions of similar, anesthetized specimens. Periodic photographic observation of the encaged fish allowed characterization of their behavior through associated spatial and orientation distributions. The fish biology and hydrography were also measured. Computations of the echo energy from encaged aggregations, derived by exercising the linear theory with the target strength functions of anesthetized fish and gross behavioral characteristics of encaged fish, agreed well with observation. This success was obtained for each of four independent echo sounders operating at frequencies from 38 to 120 kHz and at power levels from 35 W to nearly 1 kW. In addition to demonstrating the basic linearity of fisheries acoustics, the experiment verified both conventional acoustic measurements on anesthetized fish, at least for averaging purposes, and the echo integration method. Two simple theorems summarizing the meaning of linearity for use with the echo integration method are stated.
Optimizing copper spheres for precision calibration of hydroacoustic equipment

(Acoustical Society of America, 1982-03) Foote, Kenneth G.

An operational definition of backscattering cross section is developed for the wideband reception of finite echoes. This is supported by relative measurements on a set of copper spheres by each of four echo sounders operating at frequencies from 38 to 120 kHz. Experiential and theoretical arguments are advanced for the superiority of commercial, electrical–grade copper in the application. An optimization problem for determining the sphere size is then formulated, and solved for the case of calibration of a 38 kHz echo sounder by a sphere of the described material. The solution: that the copper sphere diameter be 60.00 mm, is tested through a variety of measurements. These demonstrate an accuracy of 0.1 dB. The further exercise of theory indicates the feasibility of precision calibration of diverse hydroacoustic equipment by copper spheres over most of the kilohertz frequency range.
Acousto-optic effect compensation for optical determination of the normal velocity distribution associated with acoustic transducer radiation

(Acoustical Society of America, 2015-09-28) Foote, Kenneth G. ; Theobald, Peter D.

The acousto-optic effect, in which an acoustic wave causes variations in the optical index of refraction, imposes a fundamental limitation on the determination of the normal velocity, or normal displacement, distribution on the surface of an acoustic transducer or optically reflecting pellicle by a scanning heterodyne, or homodyne, laser interferometer. A general method of compensation is developed for a pulsed harmonic pressure field, transmitted by an acoustic transducer, in which the laser beam can transit the transducer nearfield. By representing the pressure field by the Rayleigh integral, the basic equation for the unknown normal velocity on the surface of the transducer or pellicle is transformed into a Fredholm equation of the second kind. A numerical solution is immediate when the scanned points on the surface correspond to those of the surface area discretization. Compensation is also made for oblique angles of incidence by the scanning laser beam. The present compensation method neglects edge waves, or those due to boundary diffraction, as well as effects due to baffles, if present. By allowing measurement in the nearfield of the radiating transducer, the method can enable quantification of edge-wave and baffle effects on transducer radiation. A verification experiment has been designed.
Speed of sound in Euphausia superba

(Acoustical Society of America, 1990-04) Foote, Kenneth G.

The speed of longitudinal sound waves in Antarctic krill has been measured by the time‐of‐flight method. The result of 17 separate measurement series on different assemblages of living krill is that the animal’s sound speed exceeds that of seawater at the same temperature by 2.79±0.24%. The mean lengths vary from 29.4 to 38.9 mm, with overall mean 32.2 and s.d. 2.5 mm. The corresponding density of krill of mean length 31 mm is 1.0647±0.0069 g/cm3 . Measurement temperatures varied from 5.3 to 12.1°C; corresponding salinities varied from 32.5 to 33.87 ppt, which also represent the ambient state. The ambient sea temperature was 2.0±0.3°C.
Correcting acoustic measurements of scatterer density for extinction

(Acoustical Society of America, 1990-09) Foote, Kenneth G.

Extinction is sometimes a major problem in acoustic surveys of fish stocks, as it often occurs when the fish are concentrated and easiest to survey. The same may be true of certain macrozooplankton, such as krill in swarms. This study aims to describe how to correct single‐ping measurements of the vertical distribution of scatterer density for extinction. The general case is considered in which the aggregation density is variable and the mean backscattering and extinction cross sections vary with depth. By dividing the water column into a finite number of layers, with constant properties within each, a closed‐form mean‐field solution is derived. Methods of applying this to single‐ping echo records and the quality of the solution are both examined. Extinction is discussed vis‐à‐vis multiple scattering. Application of the technique in other areas, e.g., in remote probing of the atmosphere by lidar, is mentioned.
Acoustic sampling volume

(Acoustical Society of America, 1991-08) Foote, Kenneth G.

Knowledge of the acoustic sampling volume is necessary in many quantitative applications of acoustics. In general, the sampling volume is not merely a characteristic of the transmitting and receiving transducers, but also depends on the concentration and scattering properties of the target, the kind of signal processing performed on the echo, and the detection threshold. These dependences are stated explicitly in formulas for the sampling volume and a differential measure, the effective equivalent beam angle. Numerical examples are given for dispersed or dense concentrations of both point scatterers and directional fish scatterers. Application of theory to optical and other remote sensing techniques is mentioned.
Range compensation for backscattering measurements in the difference-frequency nearfield of a parametric sonar

(Acoustical Society of America, 2012-05) Foote, Kenneth G.

Measurement of acoustic backscattering properties of targets requires removal of the range dependence of echoes. This process is called range compensation. For conventional sonars making measurements in the transducer farfield, the compensation removes effects of geometrical spreading and absorption. For parametric sonars consisting of a parametric acoustic transmitter and a conventional-sonar receiver, two additional range dependences require compensation when making measurements in the nonlinearly generated difference-frequency nearfield: an apparently increasing source level and a changing beamwidth. General expressions are derived for range compensation functions in the difference-frequency nearfield of parametric sonars. These are evaluated numerically for a parametric sonar whose difference-frequency band, effectively 1–6 kHz, is being used to observe Atlantic herring (Clupea harengus) in situ. Range compensation functions for this sonar are compared with corresponding functions for conventional sonars for the cases of single and multiple scatterers. Dependences of these range compensation functions on the parametric sonar transducer shape, size, acoustic power density, and hydrography are investigated. Parametric range compensation functions, when applied with calibration data, will enable difference-frequency echoes to be expressed in physical units of volume backscattering, and backscattering spectra, including fish-swimbladder-resonances, to be analyzed.
Target strengths of Antarctic krill (Euphausia superba) at 38 and 120 kHz

(Acoustical Society of America, 1990-01) Foote, Kenneth G. ; Everson, Inigo ; Watkins, Jonathan L. ; Bone, Douglas G.

Encaged aggregations of live krill in good to pristine condition have been ensonified at 38 and 120 kHz. Concurrent underwater television observations of behavior resemble those made by underwater divers in naturally occurring swarms, with comparably high densities of the order of 104 animals/m3 . Mean, single‐animal target strengths have been inferred from measurements of echo energy. For aggregations with mean lengths in the range [30,39] mm, the mean single‐krill target strengths are in the range [−88,−83] dB at 38 kHz and [−81,−74] dB at 120 kHz. Collateral measurements on some of the same encaged specimens determined a density contrast of 1.0357±0.0067 and sound‐speed contrast of 1.0279±0.0024, relative to seawater. These numbers have been used with the fluid‐sphere model as stated by Greenlaw [Limnol. Oceanogr. 24, 226–242 (1979)] . Computed backscattering cross sections have been averaged over the length distributions of each measured aggregation, resulting in target strength predictions in the range [−86,−80] dB at 38 kHz and [−79,−76] dB at 120 kHz.
Rather‐high‐frequency sound scattering by swimbladdered fish

(Acoustical Society of America, 1985-08) Foote, Kenneth G.

A new model describes acoustic scattering by swimbladdered fish of lengths from at least 8 to 36 wavelengths. It represents a fish by an ideal pressure‐release surface having the exact size and shape as the swimbladder. The backscattering cross section, or target strength, is computed by means of the Kirchhoff approximation. To test the model, predictions of target strengths based on swimbladder morphometries of 15 gadoids of lengths from 31.5 to 44.5 cm are compared with conventional target strength measurements on the same, surface‐adapted fish, anesthetized before acoustic measurement, and shock‐frozen immediately afterwards. Details are given of the swimbladder morphometry. In essence, this consists of slicing the frozen fish with a microtome, photographing the exposed swimbladder cross sections, digitizing the contours, and triangulating the surface between pairs of contours on adjacent, parallel planes. Theory and experiment are compared through the dorsal and ventral aspect target strength functions, their averages, and simulated probability density functions.
Coincidence echo statistics

(Acoustical Society of America, 1996-01) Foote, Kenneth G.

Two scatterers at similar range give an echo which may appear to be due to a single scatterer. Methods for determining target strength that depend on resolving single scatterers may fail in this instance. Statistics associated with the described special case of coincidence are derived and illustrated by theoretical computation for the SIMRAD EK500 echo sounder system with the ES38B split‐beam transducer resonant at 38 kHz. Connections to angle measurement in radar and swath bathymetry and to bottom‐scattering‐strength measurement are noted.

Foote Kenneth G.

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