Echo statistics associated with discrete scatterers: A tutorial on physics-based methods

Abstract

When a beam emitted from an active monostatic sensor system sweeps across a volume, the echoes from scatterers present will fluctuate from ping to ping due to various interference phenomena and statistical processes. Observations of these fluctuations can be used, in combination with models, to infer properties of the scatterers such as numerical density. Modeling the fluctuations can also help predict system performance and associated uncertainties in expected echoes. This tutorial focuses on “physics-based statistics,” which is a predictive form of modeling the fluctuations. The modeling is based principally on the physics of the scattering by individual scatterers, addition of echoes from randomized multiple scatterers, system effects involving the beampattern and signal type, and signal theory including matched filter processing. Some consideration is also given to environment-specific effects such as the presence of boundaries and heterogeneities in the medium. Although the modeling was inspired by applications of sonar in the field of underwater acoustics, the material is presented in a general form, and involving only scalar fields. Therefore, it is broadly applicable to other areas such as medical ultrasound, non-destructive acoustic testing, in-air acoustics, as well as radar and lasers.

Speckle statistics of biological tissues in optical coherence tomography

“…[11][12][13][14][15][16] Studies of speckle amplitude statistics in acoustics and optics have led to the usage of various probability density functions (PDFs) such as the Rayleigh distribution, the K distribution, the Rice distribution, gamma distributions, and many others. [17][18][19][20][21] Although OCT is an interferometric technique and ultrasound utilizes time-of-flight measurements, the mathematics describing wave propagation and wave phenomena such as speckle can be applicable to both acoustical and optical imaging modalities. Recently, a new model hypothesized that in normal soft tissue, the dominant scattering elements are cylinders from fractal branching vasculature.…”

Nonlinear time-warping made simple: A step-by-step tutorial on underwater acoustic modal separation with a single hydrophone

“…These days, acoustic signal processing also provides a major avenue for conducting oceanographic research. For example, active acoustics allows estimation of fish populations (Makris et al, 2006;Stanton et al, 2018) while passive acoustic monitoring (PAM) permits study of marine mammal seasonality and regional presence (Mellinger et al, 2007). One factor common to all of these applications, civilian and military, is the need for robust algorithms that incorporate the complexity of the ocean environment, whose properties are only partially known and variable in time and space.…”

Statistical modeling of corneal OCT speckle. A distributional model-free approach

“…Since the speckle field amplitude follows the Rayleigh distribution, it is of interest to estimate the parameter of this distribution for the pixel values. In practice, it is usually considered to normalize the amplitude by dividing it by its root mean square (RMS) value [9,22], i.e., A/ A 2 . Such normalization, in many cases, leads to simplified parameter estimation procedures, in which one of the parameters (i.e., that of scale) achieves a particular constant value.…”