Theory of phasor-field imaging

Abstract

Phasor-field (P-field) imaging is a promising recent solution to the task of non-line-of-sight (NLoS) imaging, colloquially referred to as "seeing around corners". It consists of treating the oscillating envelope of amplitude-modulated, spatially-incoherent light as if it were itself an optical wave, akin to the oscillations of the underlying electro- magnetic field. We present a formal analysis of P-field propagation using paraxial wave optics and demonstrate how it can be used to form images of hidden diffuse targets both computationally and with physical lenses. In both cases, we find that hidden target planes can be imaged at the modulation-wavelength diffraction limit, despite the presence of intervening diffusers. To model propagation through more general scenarios, we introduce the two-frequency spatial Wigner distribution and derive primitives that characterize its behavior. These primitives are used to analyze occlusion-aided imaging scenarios as well as to verify intuitive results in the geometric-optics limit. Consistent with prior work, we find that intervening occluders offer the potential to form convolutional images of hidden target planes, even in the absence of time-of-flight information. Additionally, we demonstrate how to extend our frame-work beyond the paraxial regime and include a thorough exploration of the effects of speckle, which we find are likely manageable in realistic scenarios.