Page 64 - Summer 2021

ECHO CLASSIFICATION
Figure 3. The echo fluctuations depend on the type of scatterer. Left: for a simple small (“point”) scatterer, the echoes are constant from ping to ping, as indicated by the single value in the echo histogram. Right: for elongated irregular scatterers whose orientation changes from ping to ping, the fluctuations are significant, as indicated by the broad range of values in the echo histogram. Adapted from Stanton et al., 2018, license by Creative Commons.
Figure 4. The echo fluctuations also vary with numerical density of the scatterers. Left: for low densities, the echo histogram deviates strongly from the Rayleigh distribution (smooth curve) and depends on density. Right: for high densities, the echo histogram tends to the Rayleigh distribution and there is little deviation from the Rayleigh curve. Copyright © 2021 Timothy K. Stanton, all rights reserved.
fitting the physics-based PDF model to the data histogram, the parameters of the best fit PDF can be used to infer meaningful characteristics of the scatterers, such as their type [related to fb(si)] and numerical density (related to N). The accuracy of the inferences depends on the accu- racy of the model, presence of noise, and goodness of fit between the model and data. Also, to be clear, the echo statistics described here concerns the variability of the echo from transmission to transmission. The characteris- tics of this variability are exploited to classify the echo in terms of the meaningful properties of the scatterers. The echo statistics here are not to be confused with goodness- of-fit statistics, such as a chi-square test.
Causes of Echo Fluctuations
As discussed, there are many causes of echo fluctua- tions, including those associated with the (1) type of scatterer (Figure 3); (2) numerical density (Figure 4); (3) patchiness (such as variability in numerical density); (4) sensor parameters (beamwidth, signal type); and (5) environment (presence of boundaries, variation in medium type).
For the simplest case of a single point scatterer fixed in the sensor beam, the echo remains constant through repeated transmissions (Figure 3). This scatterer could be, for example, an underwater spherical bubble (sonar) or a scatterer of any shape (sonar, medical ultrasound, or radar) whose dimensions are much smaller than a wavelength. For a scatterer with a realistic shape, such as elongated with an irregular boundary, the echo will vary as the scatterer changes orientation (Figure 3). This scat- terer could be, for example, a fish or submarine (sonar) or aircraft (radar) whose dimensions are much greater than a wavelength. Because of the elongated shape, the echo is generally the loudest for broadside incidence, weakest for end-on incidence, and at intermediate levels for oblique angles. Irregularities will further complicate the variabil- ity in echoes because destructive interference from the various portions of the object’s boundary will reduce the echoes, even at broadside incidence.
When there are multiple scatterers present, interference between the echoes from the individuals will cause fluc- tuations through repeated transmissions. For example,
64 Acoustics Today • Summer 2021