Exploiting the early diffusive part of the pulse in object detection in random media

Propagation of short infrared/optical pulses, described by mutual coherence function, in a dilute random medium consisting of large (compared to the wavelength) non-absorbing scatterers is analyzed in the framework of radiative-transfer equation (RTE). A novel and rigorous approach based on analytic complex-contour integration of numerically determined cut and pole singularities of the RTE solution in the Fourier space is presented. It is found that the intensity of a propagating pulse, in addition to a “ballistic” (coherent) contribution and to a long late-time diffusive tail, exhibits also a characteristic sharply rising early-time signal. This early-time diffusive component can be attributed to a distinctive small-angle (diffractive) part of the scattering cross-section on medium particles. Correspondingly, its attenuation in the medium is weaker than that of the coherent component, as it is proportional to the large-angle (non-diffractive) cross-section rather than the total cross-section. Our results may have important implications in high-resolution range imaging as well as communication through obscuring (atmospheric clouds, fog, dust, or aerosols) media.