Physics · 6 min read
How to Estimate the Diffraction Limit of a Camera or Lens
Entrance pupil D = f / N, then the same θ = 1.22 λ / D
A camera lens is still a circular aperture. The entrance pupil is D = f / N, the focal length divided by the f-number. Plug that D into θ = 1.22 λ / D. This tutorial works a 50 mm f/1.8 at 550 nm to about 4.98″ and the Angular Resolution Calculator.
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D = f / N is the geometric entrance pupil for a thin-lens teaching model. Real stops, vignetting, and pixel pitch can dominate. Stopping down (larger N) shrinks D and coarsens diffraction.
1.The pupil is f divided by the f-number
Photographers write N for the f-number printed on the ring (f/1.8, f/8). The entrance pupil diameter is D = f / N when f is the focal length. A 50 mm lens at f/1.8 has D = 50 / 1.8 ≈ 27.8 mm. At f/8 the same lens has D = 50 / 8 = 6.25 mm. Smaller pupil, larger diffraction angle. This is the same circular D that telescopes use in How to Calculate Angular Resolution with the Rayleigh Criterion.
\[ D=f/N \]
2.Then Rayleigh as usual
Convert D to meters and pick a wavelength. Green 550 nm is a fair visual stand-in; a Bayer sensor also has red and blue. θ = 1.22 λ / D in radians, then ×206265 for arcseconds — How to Convert Angular Resolution from Radians to Arcseconds. Type D in millimetres on the Angular Resolution Calculator once you have f / N. The calculator does not ask for f-number; it asks for diameter.
\[ \theta=1.22\,\lambda/D,\quad D=f/N \]
3.Worked 50 mm f/1.8 at 550 nm
D = 0.050 / 1.8 = 0.02778 m. Then θ = 1.22 × 5.50×10⁻⁷ / 0.02778 = 2.42×10⁻⁵ rad. In arcseconds: 2.42×10⁻⁵ × 206265 ≈ 4.98″. Wide open, this fast normal lens is not a telescope: the pupil is only a few centimetres.
Stop to f/8: D = 0.00625 m, θ = 1.22 × 5.50×10⁻⁷ / 0.00625 = 1.07×10⁻⁴ rad ≈ 22.1″. Stopping down for depth of field makes the Airy disk larger on the sky and, at a given focal length, on the sensor. Pixel size then decides whether you sample that disk or a coarser blur.
\[ 50\,\mathrm{mm}\ f/1.8:\ D=27.8\,\mathrm{mm},\ \theta\approx 4.98^{\prime\prime} \]
4.Pixels, Airy, and what the number is not
An Airy disk diameter on the sensor is roughly 2.44 λ N in the focal plane (the 1.22 λ / D angle times focal length, with D = f / N). Compare that length to pixel pitch. The Aperture Area Calculator gives π(D/2)² for how much light the pupil collects; it does not replace θ. This is still not the Angular Velocity Calculator. Wavelength still matters: How Wavelength Affects Telescope Angular Resolution — IR photography is a coarser diffraction floor at the same N.
5.More angular resolution guides
The Rayleigh pillar: How to Calculate Angular Resolution with the Rayleigh Criterion. Aperture at fixed λ: How Aperture Diameter Sets Diffraction-Limited Resolution. Dawes versus Rayleigh: How to Compare Rayleigh and Dawes Limits for Double Stars. Seeing: How Atmospheric Seeing Limits Real-World Angular Resolution.
Try it yourself
Open the related calculator and put these formulas to work.