Sigma telephotoLensfor Canon

Rayleigh’s criterion made me understand the concept of resolution better and was extremely helpful in understanding why longer wavelengths give rise to lower resolution.

sigma telephotolens150-600

I do not pretend to understand the intricacies of the resolution equation but this proves that as wavelength increases the limit of resolution does as well.

sigma telephotolens70-300mm

The general rule is that the limit of resolution is about one half the wavelength of the radiation used to view the specimen.

If the diffraction spectra overlap too much the distance between the central maximas would be less than the distance between the central maxima and the first minima, therefore the object would be unresolved.

The distance between the central maxima and the first minima is d = 0.66λ/N.A. So this is essentially the limit of resolution as an object is just resolved at the point where the central maxima of both diffraction spectra coincides with the first minima of the other:

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Edit: So I googled common microscope apertures and found that they are mostly in the range of 1.0 to 1.35 and so this would very roughly approximate the constant 0.66/N.A to 0.5. So indeed the maths makes it work out. So I guess perhaps an explanation or derivation of Abbe’s equation would suffice. Can’t seem to find a derivation of it on the web!

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But so far I don’t really see or understand why the limit of resolution should be half the wavelength? Am I missing something?

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From my research I came across many interesting concepts like Huygen’s Principle which completely changed my view on diffraction and Abbe’s limit which is: