Near-to-far-field transition distance of backscattering from prolate spheroids and fish

Using an equation for the scattering amplitude of prolate spheroids, near-to-far-field transition distances for backscattered waves from spheroids and fish are derived. In addition, transition distances are obtained from target strength analysis of Atlantic salmon (Salmo salar) by Pérez-Arjona, Godinho, and Espinosa [Acta Acustica, 104, 25–38 (2018)], which employed the method of fundamental solutions, and the results are consistent with those of the spheroidal model. For practical use, the transition distances derived by the spheroidal model according to several definitions are synthesized as an approximate function of the body-length (L) to wavelength-in water (λ) ratio, i.e., 0.025L/λ1.4. The formula for the transition distance of ultrasonic transducers should not be used to estimate that of the fish.