The role of Wigner Distribution Function in Non-Line-of-Sight Imaging

Non-Line-of-Sight imaging has been linked to wave diffraction by the recent phasor field method. In wave optics, the Wigner Distribution Function description for an optical imaging system is a powerful analytical tool for modeling the imaging process with geometrical transformations. In this paper, we focus on illustrating the relation between captured signals and hidden objects in the Wigner Distribution domain. The Wigner Distribution Function is usually used together with approximated diffraction propagators, which is fine for most imaging problems. However, these approximated diffraction propagators are not valid for Non-Line-of-Sight imaging scenarios. We show that the exact phasor field propagator (Rayleigh-Sommerfeld Diffraction) does not have a standard geometrical transformation, as compared to approximated diffraction propagators (Fresnel, Fraunhofer diffraction) that can be represented as shearing or rotation in the Wigner Distribution Function domain. Then, we explore differences between the exact and approximated solutions by characterizing errors made in different spatial positions and acquisition methods (confocal, non-confocal scanning). We derive a lateral resolution based on the exact phasor field propagator, which can be used as a reference for theoretical evaluations and comparisons. For targets that lie laterally outside a relay wall, the loss of resolution is geometrically illustrated in the context of the Wigner Distribution Function.