Improving resolution in imaging through obscuring media with early-time diffusion signals

A short pulse propagating through a medium consisting of randomly distributed scatterers, large compared to the wavelength, is expected to develop an "early-time diffusion" (ETD) behavior: a sharply rising structure in the time-resolved intensity, immediately following the coherent (ballistic) component. Since the ETD signal is attenuated at a rate substantially lower than the coherent wave, it offers a possibility of application in imaging through diverse scattering media, such as atmospheric obscurants (clouds, fog, mist), dust, aerosols, fuel sprays, or biological tissues. We describe here a two-way (reflection) imaging scenario utilizing the ETD phenomenon, and propose a specific image formation technique. We evaluate, by using the radiative transport theory, the resulting point-spread function (PSF) characterizing the image resolution. We show that the directly formed image has an angular resolution comparable to the width of the forward peak in the ensemble-averaged scattering cross section of the medium constituents. Subsequently, we show that, through the application of a regularized deconvolution technique enhancing higher Fourier components of the PSF, the resolution can be further significantly improved-at least by a factor of ${\sim}4$ for a medium layer of optical thickness of the order of 20. Such an improvement can be reached even if the noise level is a few orders of magnitude higher than the coherent (ballistic) image component.