Optical dispersions through intracellular inhomogeneities

The transport of intensity equation (TIE) exhibits a noninterferometric correlation between the intensity and phase variations of intermediate fields (e.g., light and electrons) in biological imaging. Previous TIE formulations have generally assumed free-space propagation of monochromatic, coherent field functions crossing phase distributions along a longitudinal direction. In this study, we modify the TIE with fractal (or self-similar) organization models based on intracellular refractive index turbulence. We then implement TIE simulations 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. Additionally, we provide a spatial autocorrelation of phase derivatives, which allows for the direct measurement and reconstruction of intracellular fractal profiles from optical and electron microscopy imaging.