Broadband matched filtered coherent and incoherent intensity levels scattered from a group of discrete scatterers following a statistically uniform spatial distribution calculated using (a) the analytic model and verified by (b) Monte-Carlo simulations. The spatial PDF for the scatterer distribution is shown in (c) and its wavenumber spectrum in (d). The wavenumber region evaluated by the analytic model coherent intensity corresponding to the source frequency band and the incoherent intensity using the baseband are indicated.
The standard deviations for the Monte-Carlo simulations for the log transformed matched filtered intensity levels shown in Fig. 1(b).
Broadband matched filtered coherent and incoherent intensity levels scattered from a group of discrete scatterers following a Gaussian spatial PDF with group range extent defined by (a) and (b) . Their respective characteristic functions are illustrated in (c) where the wavenumber region evaluated by the analytic model coherent intensity corresponding to the source frequency band and the incoherent intensity using the baseband are indicated.
Effect of varying signal bandwidth to (a) and (b) , in comparison with Fig. 1(a). The radar/sonar approximation given by Eq. (15) is plotted over the scattered intensities for the uniform distribution of scatterers with PDF shown in Fig. 1(c).
Broadband matched filtered returns from two non-random discrete targets located at and as shown in (a). The effects of multiple scattering can be seen in (b) by comparing the singly scattered to the multiply scattered matched filtered returns. This example was implemented with , , and an imaging system with resolution .
Broadband matched filtered coherent and incoherent intensity levels scattered from a group of fish. (a) Echosounder data in terms of volumetric scattering strength are plotted as a function of depth and range. (b) This is converted to volumetric densities in gray using an estimated mean target strength of for Atlantic herring assuming single-scattering; the mean over the 25 measurements is shown in black. Numerical Monte-Carlo models simulate the matched filtered returns from this group characterized by the pair distribution function, illustrated in (d). The Monte-Carlo simulation results using (e) the single-scatter approximation and (f) including multiple scattering show the individual matched filtered signals in light gray, along with the sample mean square, or coherent intensity, and sample variance, or incoherent intensity. Panel (g) compares the incoherent intensities from the numerical Monte-Carlo simulations in (e) and (f) to the coherent and incoherent intensities found using the analytic model. The characteristic function, , for this distribution used in the analytic model is illustrated in (c).
The angular dependent scatter function for the pressure release sphere used in the numerical and analytic models is illustrated. The magnitude, and real and imaginary parts are plotted in polar coordinates, where 0° indicates the forward scatter direction and 180° indicates backscatter.
The differences in the modeled scattered levels from Fig. 6(g) illustrate the effect of multiple scattering over the imaged depth. The difference between the Monte-Carlo multiple scattering model and Monte-Carlo single scattering model is shown in black, while the difference between the Monte-Carlo multiple scattering model and analytic model is shown in gray.
The coherent intensity for the Monte-Carlo model decreases as more independent samples are added. To obtain the analytic result shown in Fig. 6(g), many more samples would be required.
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