Airy Disk — Diffraction Limit & Rayleigh Criterion

Far-field (Fraunhofer) diffraction through a circular aperture of diameter D. I(r) ∝ [2J₁(x)/x]² where x = πDr/(λf). Rayleigh criterion: resolvable when separation = 1.22λf/D.

Aperture D 40 Wavelength λ 550 nm Source sep. 1.22×

Left: 2D intensity pattern for two point sources. Right: radial profile. The Rayleigh limit is where the central max of one coincides with the first zero of the other (≈1.22 λ/D in angular units).