The objective of RIM is to compute the variance (the spread or difference) in the intensity of the images.
Intensity at camera plane depends on ρ sample fluorescence density, h the Point spread function(PSF) of the optical system and S the illumination intensity and distance of the focal plane.
As the light passes through the modulator, it gets scattered in random directions, creating interference, which produces a random, grainy pattern of bright and dark spots known as the speckle pattern.
Each speckle illumination creates a different intensity pattern on the sample. Electrically tunable lens made of a shape-changing polymer, is used here.
Bessel speckle is created by a bessel beam to maintain focus over extended distances which helps to capture fine details across different depths.
Image reconstruction is done by Wiener filter which enhance high frequencies and remove noise
where h bar is the Fourier transform of the extended depth PSF.
Here, to achieve super-resolved reconstruction, Tikhonov regularization method is used. The equation for Fluorescence density is
μ is the Tikhonov regularization parameter.
For simulation, lateral distribution follows the equation ρ(r,θ) = 1 + cos(40θ), which generates a pattern of higher spatial frequencies towards the center of the patter.
Application: EDF- RIM is used in microscope to image larger, thicker biological samples with super-resolution.
https://www.nature.com/articles/s41377-024-01612-0
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