Derivative of Axial Resolution from Rayleigh's Limit

AI Thread Summary
The discussion focuses on the axial resolution of optical microscopes, specifically the equation r(z) = 2pi / (NA)^2, which is influenced by Rayleigh's limit. The user is seeking assistance in deriving this equation using numerical methods, as they are struggling with the process. They reference Born and Wolf's work in section 8.8 of the 7th edition for guidance. A hint provided suggests evaluating the diffraction integral on-axis. Assistance in this derivation would be greatly appreciated.
TS Wong
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I am currently studying optical microscope and discover that the axial resolution is limited as r(z) = 2pi / (NA)^2.
However, while I got hints that it is due to the Rayleigh's limit, I can't derivative the equation using numerical method.
It would be huge thanks if anyone can help me on the solution.
 
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Born and Wolf derive this in section 8.8 (7th edition). My hint is that you are evaluating the diffraction integral on-axis.
 
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