Estimates of wave front distortion from measurements of scattering by model random media and calf liver

An expression based on a perturbation method is employed to estimate the correlation of path length difference in a plane normal to the direction of wave propagation from measurements of ultrasonic scattering by model random media and calf liver. The expression gives the correlation function of path length difference in terms of an integral of the correlation function of the medium variations or an equivalent integral of the power spectrum of medium variations, both for a scattering angle of zero degrees. Power spectra derived from measurements of average differential scattering cross section over a spatial-frequency window are used to fit analytic functions that extend over all spatial frequencies. The results for the windowed and unwindowed data yield correlation functions and corresponding power spectra that are used to estimate the correlation function of path length difference. The results suggest that the correlation length in calf liver is less than 100 microns and that a root-mean-square path length variation of about 20 microns results from propagation through a 100-mm calf liver path.