Depth-resolved speckle correlation imaging using the axial memory effect

Speckle correlation imaging (SCI) recovers the angular size of a 2D object hidden behind a scatterer, but it fails to recover its depth. Here, we extend SCI to obtain object depth by capturing speckled images at two detector distances and exploiting the scaling properties of the axial memory effect. This noninvasive method does not require access to the object side of the scatterer, e.g. for pre-calibration or addition of a guide star, and will be useful in any scenario where SCI is applicable, such as biological imaging or seeing through fog.