Impulse-response method to predict echo-responses from targets of complex geometry. Part I: Theory

A theoretical model is proposed for the complete solution of the acoustical problem of the radiation of transient ultrasonic pulses, their scattering by targets of arbitrary shape and acoustic impedance and their reception. The model combines Kirchhoff’s retarded potential formula with the impulse-response approach to the field radiated into fluids by wideband pistonlike sources. Kirchhoff’s formula is made explicit with three geometrical assumptions. Further assumptions and stated approximations allow a generalization of the reciprocity principle from its already-known form for point targets. This leads to a formula for the complete acoustical impulse response which is explicit, very compact and easy to compute, requiring integration only over the insonified area of the target. Throughout, particular attention is given to the hypotheses and approximations made in deriving the model with clear definition of its domain of applicability.