  This paper presents a statistical treatment of phasor fields (P-fields) - a
wave-like quantity denoting the slow temporal variations in time-averaged
irradiance (which was recently introduced to model and describe
non-line-of-sight (NLoS) imaging as well as imaging through diffuse or
scattering apertures) - and quantifies the magnitude of a spurious signal which
emerges due to a partial spatial coherence of the underlying optical carrier.
This spurious signal is not described by the Huygens-like P-field imaging
integral which assumes optical incoherence as a necessary condition to describe
P-field imaging completely (as was shown by Reza etal. recently). In this
paper, we estimate the relationship between the expected magnitude of this
spurious signal and the degree of partial roughness within the P-field imaging
system. The treatment allows us to determine the accuracy of the estimate
provided by the P-field integral for varying degrees of partial coherence and
allows to define a P-field signal-to-noise ratio as a figure-of-merit for the
case of a partially coherent optical carrier. The study of partial coherence
also enables to better relate aperture roughness to P-field noise.
