Using speckle correlations for single-shot 3D imaging

Recovery of a 3D object behind a scattering medium is an important problem in many fields, including biomedical and defense applications. Speckle correlation imaging can recover objects in a single shot but contains no depth information. To date, its extension to 3D recovery has relied on multiple measurements, multi-spectral light, or pre-calibration of the speckle with a reference object. Here, we show that the presence of a point source behind the scatterer enables single-shot reconstruction of multiple objects at multiple depths. The method relies on speckle scaling from the axial memory effect, in addition to the transverse one, and recovers objects directly, without the need for phase retrieval. We provide simulation and experimental results to show object reconstructions at different depths with a single-shot measurement. We also provide theoretical principles describing the region where speckle scales with axial distance and its effects on the depth of field. Our technique will be useful where a natural point source exists, such as fluorescence imaging or car headlights in fog.