# Airy Disk

Excerpt from Field Guide to Geometrical Optics

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.

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

 Radius r Peak E Energy inRing (%) Central maximum 0 1.0 E0 83.9 First zero r1 1.22λf⁄#W 0.0 First ring 1.64λf⁄#W 0.017 E0 7.1 Second zero r2 2.24λf⁄#W 0.0 Second ring 2.66λf⁄#W 0.0041 E0 2.8 Third zero r3 3.24λf⁄#W 0.0 Third ring 3.70λf⁄#W 0.0016 E0 1.5 Fourth zero r4 4.24λf⁄#W 0.0

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).