Abel transform and its inverse

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elham sa 2015-7-28

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评论： Leigh Stanger 2019-7-4

I know that Line Spread Function (LSF) is the integral of the Point Spread Function (PSF). and I know that LSF is Abel transform of PSF. Does MATLAB have Inverse Abel Transform to recover a circularly symmetric PSF from a given LSF?

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Answer 1

elham sa 2015-7-29

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You don't need Abel Transform here, if you have a circularly symmetric PSF.

A slice of a full MTF is 1D Fourier transform of LSF. full 2D MTF is 2D Fourier transform of PSF. Using Central slice theorem, you can stack your LSF, and do an inverse Radon transform (iradon in Matlab), you get your circularly symmetric 2D PSF!

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Leigh Stanger 2019-7-4

Hi

I dont know if this is still of interest but could you point to some literature showing that you do not need to do an inverse abel transform to the LSF to get a radially symmetric PSF.

A report by NIST on thermal camera metrology suggests you do.

https://nvlpubs.nist.gov/nistpubs/ir/2016/NIST.IR.8098.pdf

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