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This paper presents a statistical treatment of phasor fields (P-fields) - awave-like quantity denoting the slow temporal variations in time-averagedirradiance (which was recently introduced to model and describenon-line-of-sight (NLoS) imaging as well as imaging through diffuse orscattering apertures) - and quantifies the magnitude of a spurious signal whichemerges due to a partial spatial coherence of the underlying optical carrier.This spurious signal is not described by the Huygens-like P-field imagingintegral which assumes optical incoherence as a necessary condition to describeP-field imaging completely (as was shown by Reza etal. recently). In thispaper, we estimate the relationship between the expected magnitude of thisspurious signal and the degree of partial roughness within the P-field imagingsystem. The treatment allows us to determine the accuracy of the estimateprovided by the P-field integral for varying degrees of partial coherence andallows to define a P-field signal-to-noise ratio as a figure-of-merit for thecase of a partially coherent optical carrier. The study of partial coherencealso enables to better relate aperture roughness to P-field noise.

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