Question by Hayden: How does increased diffraction as a result of increased numerical aperture cause finer airy disks?
How does increased diffraction as a result of increased numerical aperture cause finer airy disks?
I.e., when I change the NA, (increasing cone of light going into the aperture), why does more diffraction occur, and how does that diffraction end up as a more resolved image?
Answer by kirchwey
It’s based on the Rayleigh criterion for resolution, and is closely related to spectrographic slit diffraction. The Airy disk is the circular equivalent of the central peak of single-slit diffraction, and it applies to any aperture, whether filled by a lens or not. Airy disk size is inversely proportional to aperture. See the refs.
For your particular question, increasing the aperture is equivalent to widening the slit in a spectroscope. For a slit, the limit of the central peak is the point where the light-path length difference to the edges of the slit is one wavelength, which results in cancellation. Clearly the wider the slit, the smaller the width of the central peak (see 3rd ref.).
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