Nonparaxial phasor-field propagation.

Abstract

Growing interest in non-line-of-sight (NLoS) imaging, colloquially referred to as "seeing around corners", has led to the development of phasor-field (P-field) imaging, wherein the field envelope of amplitude-modulated spatially-incoherent light is manipulated like an optical wave to directly probe a space that is otherwise shielded from view by diffuse scattering. Recently, we have established a paraxial theory for P-field imaging in a transmissive geometry that is a proxy for three-bounce NLoS imaging [J. Dove and J. H. Shapiro, Opt. Express27(13) 18016 (2019)]. Our theory, which relies on the Fresnel diffraction integral, introduces the two-frequency spatial Wigner distribution (TFSWD) to efficiently account for specularities and occlusions that may be present in the hidden space and cannot be characterized with P-field formalism alone. However, because the paraxial assumption is likely violated in many, if not most, NLoS scenarios, in the present paper we overcome that limitation by deriving a nonparaxial propagation formula for the P field using the Rayleigh-Sommerfeld diffraction integral. We also propose a Rayleigh-Sommerfeld propagation formula for the TFSWD and provide a derivation that is valid under specific partial-coherence conditions. Finally, we report a pair of differential equations that characterize free-space TFSWD propagation without restriction.