Tools / Diffraction & resolution
Diffraction & Resolution Calculator
Use the working f-number. At close focus it grows to N·(1 + m), where m is the magnification, so macro and short-distance setups are more diffraction-limited than the lens marking suggests.
Airy disk on the pixel grid, to scale
DiffractionPixel apertureCombined
Across the f-number range
Diffraction for this wavelength and pixel pitch at standard f-stops. Contrast at Nyquist is the diffraction MTF alone; real lenses add aberrations at wide apertures, so the sharpest real f-number is usually one or two stops below where softening starts.
| f-number | Airy diameter | In pixels | Cutoff | MTF at Nyquist |
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Formulas
For an ideal circular aperture with wavelength λ and f-number N: Airy disk diameter to the first dark ring 2.44·λ·N, Rayleigh resolution 1.22·λ·N, and incoherent cutoff frequency fc = 1 / (λ·N). Pixel Nyquist frequency is fN = 1 / (2p).
Diffraction MTF: MTF(s) = (2/π)·(acos s − s·√(1 − s²)) with s = f / fc. A 100% fill-factor pixel adds |sinc(f·p)|, about 0.64 at Nyquist. Softening starts where diffraction MTF at Nyquist drops to 50% (N ≈ 0.81·p / λ); Nyquist detail is gone where fc = fN (N = 2·p / λ). Bayer color sensors resolve less than their pixel Nyquist, so they reach these limits about a stop sooner.
Background reading: Choosing a circle of confusion for small sensors