Quantitative analysis of hidden particles diffusing behind a scattering layer using speckle correlation

Speckle-correlation imaging is a family of methods that makes use of the "memory effect" to image objects hidden behind visually opaque layers. Here, we show that a correlation analysis can be applied to quantitative imaging of an ensemble of dynamic fluorescent beads diffusing on a 2D surface. We use an epi-fluorescence microscope where both the illumination and detection light patterns are speckled, due to light scattering by a thin disordered layer. The spatio-temporal cross-correlation of the detection speckle pattern is calculated as a function of lag time and spatial shift and is used to determine the diffusion constant and number of fluorescent particles in the sample without requiring any phase retrieval procedure. It is worth to note that the "memory effect" range is not required to extend beyond a distance of few speckle grains, thus making our method potentially useful for nearly arbitrary values of the thickness of the scattering layer.