Diffraction-limited 3D cell volume derivation for scattering data analysis

Ultrasound speckle carries information about the interrogated scattering microstructure. The complex signal is represented as a superposition of signals due to all scatterers within a resolution cell volume, VE. A crossbeam geometry with separate transmit and receive transducers is well suited for such studies. The crossbeam volume, VE is defined in terms of the overlapping diffraction beam patterns. Given the focused piston transducer's radius and focal distance, a Lommel diffraction formulation suitable for monochromatic excitation is used to calculate VE as a function of frequency and angle. This formulation amounts to a Fresnel approximation to the diffraction problem and is not limited to the focal zone or the far field. Such diffraction corrections as VE are needed to remove the system effects when trying to characterize material using moment analysis. Theoretically, VE is numerically integrated within the overlapping region of the product of the transmit-receive transfer functions. Experimentally, VE was calculated from the field pattern of a medium-focused transducer excited by a monochromatic signal detected by a 0.5mm diameter PVDF membrane hydrophone. We present theoretical and experimental evaluations of VE for the crossbeam geometry at frequencies within the transducers' bandwidth, and its application to tissue microstructure characterization.

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