Find the minimum resolvable angle for circular-aperture diffraction, θ = 1.22λ/D. For evaluating the resolution limit of telescopes, microscopes and camera lenses.
圆孔衍射的最小可分辨角。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Rayleigh resolution limit | θ = 1.22 λ / D (radians), D = aperture diameter | Lord Rayleigh (1879) |
| Airy disk | First dark-ring angular radius 1.22λ/D from circular-aperture Fraunhofer diffraction | Airy (1835) / Hecht, Optics, §10.2 |
Constants used on this page and their authoritative sources, for verification and citation
| Constant | Value | Unit | Source |
|---|---|---|---|
| Rayleigh criterion coefficient (circular aperture) | 1.2196699… (≈ 1.22) | — | = first non-zero zero of J₁ divided by π (mathematical constant, exact) |
| First zero of J₁, j₁,₁ | 3.8317059702075125 | — | Mathematical constant (exact) |
| One arcminute (1′) | 2.908882e-4 | rad | = π/(180×60), derived from the radian definition |
Note: the Rayleigh criterion θ = 1.22λ/D applies to Fraunhofer diffraction by a circular aperture (Airy disc); a slit or square aperture has a different first-zero factor (λ/D for a slit).