How the Airy disk is calculated
Light that passes a round aperture does not form a point but a bright disk surrounded by faint rings, the Airy disk. The first dark ring lies at the angle 1.22 × wavelength ÷ aperture diameter. On the sensor this gives a disk with the diameter
d = 2.44 × λ × N
with the wavelength λ and the f-number N, for focus at infinity. At f/8 and 550 nm (green) the Airy disk is 10.7 µm wide. It does not depend on the focal length, only on the f-number.
When diffraction becomes visible
There is no standard value. This calculator compares the diameter of the Airy disk with the pixel pitch and by default calls diffraction visible when the disk is two pixels wide or wider. The criterion can be set to 1, 2 or 3 pixels: a smaller value marks the limit earlier, a larger one later.
The result is a guide and no rule against small apertures. A small aperture can still be the right choice for depth of field or long exposures, and diffraction is only one of several factors that limit the detail of a real lens.
Typical sensors
The f-number at which the Airy disk (550 nm) reaches 1 and 2 pixels.
| Sensor | Pixel pitch | 1 px at | 2 px at |
|---|---|---|---|
| 1-inch, 20 MP | 2.4 µm | f/1.8 | f/3.6 |
| Four Thirds / MFT, 20 MP | 3.4 µm | f/2.5 | f/5 |
| APS-C, 26 MP | 3.8 µm | f/2.8 | f/5.6 |
| APS-C, 40 MP | 3.0 µm | f/2.3 | f/4.5 |
| Full frame, 24 MP | 6.0 µm | f/4.5 | f/8.9 |
| Full frame, 45 MP | 4.4 µm | f/3.3 | f/6.5 |
| Full frame, 61 MP | 3.8 µm | f/2.8 | f/5.6 |
| Medium format 44 × 33, 100 MP | 3.8 µm | f/2.8 | f/5.7 |
Limits of the calculation
The calculation covers only diffraction at a round aperture with focus at infinity. Lens aberrations, the colour filter of the sensor, noise and later processing are not included. The Airy disk is also no hard limit: its brightness falls off towards the edge, and the visible effect depends on the viewing size.
The NPF rule for star photography assumes a larger diffraction disk than the first-minimum diameter used here: it takes the diameter between the first and the second ring, 4.47 × λ × N.
More tools
Frequently asked questions
What is the Airy disk?
The bright central spot that forms when light from a point passes a round aperture. Its diameter is 2.44 × wavelength × f-number and sets the smallest spot a lens can form at that aperture.
From which f-number is a camera diffraction limited?
It depends on the pixel pitch. With the criterion of 2 pixels and green light, a 24 megapixel full frame sensor (6.0 µm) reaches the limit at about f/9, with the criterion of 1 pixel at about f/4.5.
Does the focal length matter?
No. The Airy disk depends on the f-number and the wavelength only, because the f-number is the ratio of focal length to aperture diameter.
Why does a sensor with more megapixels reach the limit earlier?
Its pixels are smaller, so the same Airy disk covers more of them. A 61 megapixel full frame sensor (3.8 µm) reaches 2 pixels at about f/5.6.
Should small apertures be avoided because of diffraction?
Not in general. Diffraction is one effect among others. Depth of field, shutter speed or starbursts can be reasons for a small aperture. The table shows how large the Airy disk is, so that the trade-off can be judged.
Sources
- R. Nave, HyperPhysics, Georgia State University: Circular Aperture Diffraction (first minimum at 1.22 λ/d). http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html
- OpenStax College Physics (Rice University): Limits of Resolution: The Rayleigh Criterion (θ = 1.22 λ/D). https://courses.lumenlearning.com/suny-physics/chapter/27-6-limits-of-resolution-the-rayleigh-criterion/
- Société Astronomique du Havre (F. Michaud): Les coulisses de la règle NPF (diffraction disk of the NPF rule). https://sahavre.fr/wp/les-coulisses-de-la-regle-npf/