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Airy Disk explanation from Field Guide to Geometrical Optics


Excerpt from Field Guide to Geometrical Optics

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Because of diffraction from the system stop, an aberration-free optical system does not image a point to a point. An Airy disk is produced having a bright central core surrounded by diffraction rings.

equation_1




where r is the radial coordinate, J1 is a Bessel function, and f /#W is the imagespace working f /#.


 Radius rPeak EEnergy in
Ring (%)
Central maximum01.0 E083.9
First zero r11.22λf⁄#W0.0 
First ring1.64λf⁄#W0.017 E07.1
Second zero r22.24λf⁄#W0.0 
Second ring2.66λf⁄#W0.0041 E02.8
Third zero r33.24λf⁄#W0.0 
Third ring3.70λf⁄#W0.0016 E01.5
Fourth zero r44.24λf⁄#W0.0 

The diameter of the Airy disk (diameter to the first zero) is

D = 2.44λf ⁄#W

In visible light λ ≈ 0.5 μm and D≈f⁄#W in μm

The Rayleigh resolution criterion states that two point objects can be resolved if the peak of one falls on the first zero of the other:

Resolution = 1.22λf ⁄#W

The angular resolution is found by dividing by the focal length (or image distance):

Angular resolution=α=1.22λ ⁄ DEP

Citation:

J. E. Greivenkamp, Field Guide to Geometrical Optics, SPIE Press, Bellingham, WA (2004).



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