Physics

Pure mathematics

Diffuser (optics)

Light source

Mathematics

Aperture (computer memory)

Speckle pattern

Optics

Modulation (music)

Optical field

Power (physics)

Acoustics

Phasor

Phase (matter)

Quantum mechanics

Electric power system

Field (mathematics)

Electric field

Optics Express

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.

Phasor field waves: a mathematical treatment