Richard L. Weaver
Dept. of Theor. and Appl. Mech., Univ. of Illinois, 104 South Wright St., Urbana, IL 61801
Enhanced backscatter, in which reverberant signal levels at the position of a transient source are greater than mean reverberant signal levels elsewhere, is studied analytically and numerically. Popular weak localization arguments, in which descriptions of responses in terms of incoherent rays are modified to include some effects of coherent interference, indicate that the mean-square response at the source should be twice as large as it is at other points. A modal analysis, however, shows that the actual ratio should be three. A more detailed theory shows that the enhanced return factor is 2 at moderate times, but 3 at late times comparable to the modal density. The theory indicates that the factor of 2 is achieved only if the eigenfrequency statistics have the spectral rigidity predicted by random matrix theory. Thus a connection between spectral rigidity and weak localization is hinted at. Numerical solutions in model undamped two-dimensional reverberation rooms are found to agree with the theory. The effect of damping on these results is also investigated.