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Rayleigh criterion

Estimate the angular separation of two distant points imaged through a circular pupil.

Two diffraction patterns

A circular, unobscured pupil forms an Airy pattern around each point. For two equally bright, mutually incoherent points, Rayleigh’s criterion places the central maximum of one pattern at the first dark ring of the other.

A 25 mm pupil in green light

At small angles the separation in radians is θ ≈ 1.22 λ/D. With λ = 550 nm and D = 25 mm, θ ≈ 26.84 µrad. A 100 mm focal length converts this angle into 2.684 µm between the image centers.

Where the sensor enters

A sensor with 5 µm pixels samples this example less than once across that separation. The diffraction calculation and the pixel spacing describe different stages. Compare the lens MTF and sensor sampling when predicting camera contrast.

Further reading