Science calculator

Diffraction-limited spot.

Enter wavelength and f-number to find the Airy pattern's first-dark-ring diameter and radius for an ideal circular aperture.

Airy diameter dfirst dark ring
diameter in the focal plane
Airy radius r
d=2.44λN

Assumptions

  • Uniformly illuminated, unobscured circular aperture.
  • Diffraction-limited, aberration-free imaging in the paraxial regime.
  • N is the effective image-space f-number and λ is the wavelength in the image-space medium.
  • The reported spot is the Airy first-dark-ring diameter, not a Gaussian 1/e² width or FWHM.

How it works

A circular aperture produces an Airy diffraction pattern rather than a geometrical point. Its central lobe reaches its first minimum at radius 1.22λN.

The displayed diameter is twice that radius: 2.44λN. Longer wavelengths and larger f-numbers both enlarge the diffraction-limited spot.

Real images can be larger because of aberrations, defocus, sampling or motion. This result is the ideal lower bound under the assumptions above.