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.Comment: 22 pages, 18 figures, 4 table