Optical dispersions through intracellular inhomogeneities

Transport of intensity equation (TIE) exhibits a non-interferometric correlation between intensity and phase variations of intermediate fields (e.g., light and electron) in biological imaging. Previous TIE formulations have generally assumed a free space propagation of monochromatic coherent field functions crossing phase distributions along a longitudinal direction. Here, we modify the TIE with fractal (or self-similar) organization models based on intracellular refractive index turbulence. We then implement the TIE simulation over a broad range of fractal dimensions and wavelengths. Simulation results show how the intensity propagation through the spatial fluctuation of intracellular refractive index interconnects fractal-dimensionality with intensity dispersion (or transmissivity) within the picometer to micrometer wavelength range. In addition, we provide a spatial-autocorrelation of phase derivatives which allows the direct measurement and reconstruction of intracellular fractal profiles from optical and electron microscopy imaging.