Fig. 1: Schematics of SWH for NLoS imaging around corners and NLoS imaging through scattering media.

a SWH image formation: A continuous wave (CW) tunable laser illuminates the scene at two slightly different wavelength λ₁ and λ₂. Each field E(λ₁), E(λ₂) is subject to multiple scattering processes in or at the scatterer (which could be wall, tissue, fog,...) and the rough object surface. The introduced maximal pathlength variation Ψ_max leads to a complete randomization of E(λ₁), E(λ₂) (with respective phasemaps ϕ(λ₁), ϕ(λ₂)) when arriving at the detector. However, computational mixing of the speckled fields E(λ₁) ⋅ E^*(λ₂) = E(Λ), yields a complex-valued hologram of the object at a Synthetic Wavelength (SWL) \({{\Lambda }}=\frac{{\lambda }_{1}\cdot {\lambda }_{2}}{| {\lambda }_{1}-{\lambda }_{2}| }\). The object is reconstructed by backpropagating E(Λ) with the SWL Λ. b and c Schematic setups for NLoS imaging around corners (b) and NLoS imaging through scatterers (c) with the SWH principle: The sample beam illuminates a spot on the wall/scatterer (the Virtual Source VS), which scatters light towards the obscured object. A small fraction of the light incident on the object is scattered back to the wall/scatterer where it hits the Virtual Detector (VD). The VD is imaged by the camera, meaning that the synthetic hologram is captured at the VD surface. Details and internals of the light engine are specified in the Supplementary Fig. 4.