Spatial blurring in laser speckle imaging in inhomogeneous turbid media

Laser speckle imaging (LSI) has developed into a versatile tool to image dynamical processes in turbid media, such as subcutaneous blood perfusion and heterogeneous dynamics in soft materials. Spatially resolved information about local dynamics is obtained by measuring time-dependent correlation functions of multiply scattered light. Due to the diffusive nature of photons in highly scattering media, the measured signal is a convolution of the local dynamics in the material and the spatial distribution of photons. This spatial averaging inevitably leads to a loss of resolution, which must be taken into account for a correct interpretation of LSI measurements. In this paper we derive analytical expressions to quantify the effects of spatial blurring in backscatter LSI for materials with heterogeneous dynamics. Using the diffusion approximation, we calculate the photon density distribution for a semi-infinite material, and we predict the effect of dynamic heterogeneity on the measured correlation function. We verify our theoretical expressions using random walk simulations. Our results show that LSI measurements in dynamically heterogeneous materials should be interpreted with caution, especially when only a single wavelength and correlation time are used to obtain the dynamical map.