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 first-dark-ring diameter · λ wavelength · N f-number f/D
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.
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