Phasor field waves: a mathematical treatment

Non-line-of-sight imaging can use modulated sources to preserve phase information at the modulation wavelength through a scattering interaction with a diffuser or an optically rough wall that scrambles the optical phase. Reza, et al. formulated the preserved information as a phasor field propagation [Opt. Express (in review)] for time-of-flight imaging of hidden scenes using diffusely scattered light. This paper presents a derivation of the underpinning of phasor field propagation to establish its rigor. The result is an expression for the time-modulated irradiance (phasor field) produced by time-modulated coherent illumination of a phase-scrambling aperture. Speckle effects, representing variance in the phasor field, are also quantified.