  Growing interest in non-line-of-sight (NLoS) imaging, colloquially referred
to as "seeing around corners", has led to the development of phasor-field
($\mathcal{P}$-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
$\mathcal{P}$-field imaging in a transmissive geometry that is a proxy for
three-bounce NLoS imaging [J. Dove and J. H. Shapiro, Opt. Express {\bf 27}(13)
18016--18037 (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 $\mathcal{P}$-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 $\mathcal{P}$ 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.
