Speckle Tomography of the Living-Cell Functions

This work is aimed at creating the theoretical basis for the method allowing one to layer-by-layer reconstruct the parameters which characterize the processes occurring in small regions of living cells. The problem of the speckle dynamics in the object-image plane, which is caused by random variations in the optical paths of the waves in various layers inside the cell, is theoretically solved for a model of the cell in the form of a thin phase object located near the phase screen. On the assumption that the random variations in the difference Δ u of the optical paths of the wave pairs are independent in these layers, expressions for the time-averaged radiation intensity Ĩ at an arbitrary point of the image plane and for the time autocorrelation function η ( t 1 , t 2 ) of this intensity are obtained. The formulas relating the parameters which characterize the occurring processes (the cell functions) to the quantities Ĩ and η are obtained. In the formula for Ĩ , such parameters are the average value and variance of the quantity Δ u , which are obtained by averaging over the time and the region whose sizes are equal to the linear resolution of the lens and the layer thickness. The average values and variances of the quantity Δ u at the time instants t 1 and t 2 , as well as the time autocorrelation function η ( t 1 , t 2 ) of the quantity Δ u , which are additionally averaged over the ensemble of objects, are the functional parameters of the regions in the formula for η ( t 1 , t 2 ). It is theoretically shown that the above-mentioned parameters, which are obtained by averaging over the cell thickness, are sums of the similar parameters in the cell layers. The correspondence of the formula for η ( t 1 , t 2 ) to the physical processes occurring in the cells is shown using living cells, which are located on a glass substrate after defrosting. Assuming that four processes, which independently change the wave phases, are observed in the cells, a very good agreement between the theory and experiment is obtained.