What is an Airy disk?

When a point source of light passes through a circular aperture, diffraction spreads the image into a bright central spot surrounded by faint rings. This central bright spot is the Airy disk. Its size sets the fundamental resolution limit of any diffraction-limited optical system.

What formula is used?

The Airy disk radius (first dark ring) follows r = 1.22 · λ · f / D, where λ is wavelength, f is focal length, and D is aperture diameter. The angular resolution limit (Rayleigh criterion) is θ = 1.22 · λ / D in radians.

What is the Rayleigh criterion?

Two point sources are just resolvable when the center of one Airy disk falls on the first dark ring of the other. This gives θ = 1.22 · λ / D. For a 100 mm aperture at 550 nm, this is about 1.37 arcseconds.

The 1.22 factor comes from the first zero of the Bessel function J₁(x), which describes the diffraction pattern of a circular aperture. It equals the first root of J₁ divided by π: 3.8317 / π ≈ 1.2197.

What is the Dawes limit compared to the Rayleigh criterion?

The Dawes limit uses a slightly different constant: θ (arcsec) = 116 / D(mm). It was derived empirically for visual observation of double stars and gives a slightly optimistic resolution compared to the theoretical Rayleigh criterion.

Does this apply to radio telescopes too?

Yes — the formula θ = 1.22 · λ / D applies to any wave optics system. For a radio dish, just use the radio wavelength (meters) and dish diameter (meters). This is why radio telescopes must be very large to achieve useful angular resolution.

Airy Disk Calculator

Name: Airy Disk Calculator
Availability: InStock
Author: Nham Vu

Enter aperture diameter, wavelength, and focal length to get the Airy disk diameter and angular/spatial resolution limit.

Aperture & Wavelength

Aperture Diameter (D) mm

Examples: camera lens 25–200 mm, telescope 70–500 mm

Wavelength (λ) nm

Visible: 380–700 nm. Green peak ~550 nm.

Focal Length (f) mm (optional)

Required to compute Airy disk size on the image plane.

Quick Presets

Enter aperture and wavelength above, then click Calculate.

Summary

Enter aperture diameter, wavelength, and focal length to get the Airy disk diameter and angular/spatial resolution limit.

How it works

Enter the aperture diameter (D) in millimeters — the clear opening of your lens or mirror.
Enter the wavelength of light (λ) in nanometers (visible: 380–700 nm).
Optionally enter the focal length (f) in millimeters to get the Airy disk size on the image plane.
Click Calculate to get the angular resolution limit (Rayleigh criterion), Airy disk radius, and full disk diameter.
Use the results to compare against camera pixel pitch or detector element size.

Use cases

Determine the diffraction limit of a telescope or microscope objective.
Check whether a camera sensor's pixel size is matched to the lens's diffraction limit.
Compare resolution limits across different aperture and wavelength combinations.
Calculate the minimum resolvable angular separation of two point sources.
Estimate the Airy disk size for astrophotography planning.
Evaluate optical system design constraints for scientific instruments.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu