Abstract
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.
Highlights
Many disordered materials, such as rubbers, plastics, foams, suspensions, and biological tissue strongly scatter light, which makes a direct observation of structure and dynamics, for example with light microscopy, very difficult
Since each photon takes a different path through the sample, Laser speckle imaging (LSI) measurements performed on inhomogeneous samples represent averages, resulting from a convolution of dynamic processes in the sample and the spatial probability distribution of photons in the sample[26,27]
We have obtained theoretical expressions for the path length distribution and spatial density distribution of photons in a strongly scattering, semi-infinite medium under plane wave illumination. These expressions allowed us to calculate the dynamic correlation function that would be measured in a backscatter LSI experiment for dynamically heterogeneous materials
Summary
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. To fully appreciate how spatial averaging affects the measured LSI signal at different time scales, a more detailed calculation, taking all possible photon paths into account, is needed Such an analysis has been performed for a multilayer medium, in which the sample is heterogeneous only in the z-direction (perpendicular to the surface)[10,31,32]. We calculate the photon density distribution in the material and we derive an analytical expression that relates the autocorrelation function measured in a particular location to the distribution of mean-square displacements in the material We use this result to evaluate the lateral resolution of LSI, and we show how this depends on the correlation time.
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