Causal and unique reconstruction of nonminimum reflection phase for a class of submerged structures

Abstract

An approach is presented for uniquely determining the phase of an acoustic reflection from an object whose impedance magnitude approximates the acoustic impedance of the surrounding medium. This approximation defines a semiannular region in the complex impedance plane that lies between the rigid and pressure-release limits. When this region is mapped onto the complex reflection coefficient plane, the approximation allows for a wide range of reflection coefficients. A Taylor series expansion for the square of the reflection coefficient magnitude is used to estimate the phase of the reflecting impedance. The causality condition is invoked to recover the magnitude of the impedance from its phase. Once the magnitude and phase of the impedance is known, the complex-valued reflection coefficient algebraically follows regardless of whether or not the reflection coefficient is minimum phase. The approach is useful in experimental situations that only allow the accurate measurement of reflection magnitude and not phase. As an example, the approach is demonstrated on one-dimensional numerical simulations that simulate uncertainty in target location and ambient noise. [Work supported by ONR.]