AiryDiffraction

Airy diffraction refers to the diffraction pattern produced when light passes through a circular aperture or around a circular obstacle. Named after George Biddell Airy, who analyzed the pattern in the 1830s, it is the characteristic diffraction effect for circular pupils in optical systems. The intensity distribution on a screen is described by I(θ) ∝ [2 J1(β)/β]^2, where J1 is the first-order Bessel function and β = (π D sin θ)/λ, with D the aperture diameter and λ the wavelength. The central bright region is called the Airy disk, surrounded by concentric diffraction rings. The first minimum occurs when sin θ = 1.22 λ / D; equivalently, in a focused image plane, the first minimum lies at a radius r ≈ 1.22 λ f / D, where f is the system’s focal length.

In imaging, Airy diffraction sets the diffraction-limited resolution of circular apertures. The Rayleigh criterion states that two point sources are just resolvable when the maximum of one Airy disk aligns with the first minimum of the other, yielding a practical angular resolution ≈ 1.22 λ / D. This pattern is fundamental to telescopes, microscopes, and cameras, and it scales with wavelength and aperture size. Real systems may modify the pattern through obstructions, noncircular apertures, or apodization, which reshapes the point spread function and alters the distribution of energy among the rings. Airy diffraction thus links wave optics to practical limits of imaging performance and underpins discussions of optical resolving power.