Abstract

Non-line-of-sight (NLOS) imaging is an inverse problem that consists of reconstructing a hidden scene out of the direct line-of-sight given the time-resolved light scattered back by the hidden scene on a relay wall. Phasor fields transforms NLOS imaging into virtual LOS imaging by treating the relay wall as a secondary camera, which allows reconstruction of the hidden scene using a forward diffraction operator based on the Rayleigh-Sommerfeld diffraction (RSD) integral. In this work, we leverage the unitary property of the forward diffraction operator and the dual space it introduces, concepts already studied in inverse diffraction, to explain how Phasor Fields can be understood as an inverse diffraction method for solving the hidden object reconstruction, even though initially it might appear it is using a forward diffraction operator. We present two analogies, alternative to the classical virtual camera metaphor in Phasor Fields, to NLOS imaging, relating the relay wall either as a phase conjugator and a hologram recorder. Based on this, we express NLOS imaging as an inverse diffraction problem, which is ill-posed under general conditions, in a formulation named Inverse Phasor Fields, that we solve numerically. This enables us to analyze which conditions make the NLOS problem formulated as inverse diffraction well-posed, and propose a new quality metric based on the matrix rank of the forward diffraction operator, which we relate to the Rayleigh criterion for lateral resolution of an imaging system already used in Phasor Fields.

Results

We compare the hidden object reconstructions using Phasor Fields and our method, Inverse Phasor Fields, on the (up) letter4 and (bottom) NLOSletter scenes from Liu et al. dataset.

Teaser

Scenes have been illuminated with a single virtual wavelength λ = 0.06m. We show the amplitude of the reconstructed wavefield. The geometry part of the reconstruction are similar for both methods, but the surrounding artifacts vary between Phasor Fields and Inverse Phasor Fields. This is due to the stability of the inverse diffraction operator gz. For more results, including the analysis of our new quality metric, please see the paper.

Paper

Bibtex

@article{Garcia-Pueyo:25, author = {Jorge Garcia-Pueyo and Adolfo Mu\~{n}oz}, journal = {Opt. Express}, keywords = {Diffraction theory; Extended depth of field; Fourier transforms; Image resolution; Imaging systems; Superresolution}, number = {5}, pages = {11420--11441}, publisher = {Optica Publishing Group}, title = {Forward and inverse diffraction in phasor fields}, volume = {33}, month = {Mar}, year = {2025}, url = {https://opg.optica.org/oe/abstract.cfm?URI=oe-33-5-11420}, doi = {10.1364/OE.553755} }

Acknowledgments

The authors thank Pablo Luesia-Lahoz for proofreading the manuscript. This work has received funding from the European Commission’s HORIZON EUROPE Research and Innovation Actions project Sestosenso under GA number 101070310. Jorge Garcia-Pueyo was supported by the FPU23/03132 predoctoral grant.