Phasor field waves: A statistical treatment for the case of a partially coherent optical carrier

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.