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Airy Disk explanation from Field Guide to Geometrical Optics
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 in|
|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