Science
Rayleigh Diffraction Limit Angular Resolution & Airy Disk Diameter
Calculate circular-aperture Rayleigh angular resolution theta = 1.22 * lambda / D (in radians and arcseconds) and focal-plane Airy disk spot diameter d_Airy = 2.44 * lambda * N (in micrometers).
Compare telescope aperture resolution and camera sensor diffraction blur!
Even an aberration-free circular lens or primary mirror spreads a point source into a concentric Bessel diffraction pattern whose central bright core—the Airy disk—contains 83.8% of total wave energy! By Lord Rayleigh's criterion, two equal point sources are just resolved when the peak of one Airy disk lands on the first dark ring of the second: theta_rad = 1.22 * lambda / D (multiplying radians by 206,264.806 converts directly into arcseconds)!
On a digital camera or microscope sensor at focal ratio N = f / D (the f-number), multiplying angular radius by focal length f cancels aperture D and yields the physical Airy Disk Spot Diameter: d_Airy = 2.44 * lambda * N! Stopping a green-light lens (lambda = 0.55 um) down to f/8 produces a 10.74 um Airy disk—so pixels smaller than ~5.4 um become diffraction-limited rather than sensor-limited!
| Optical System (Green Light lambda = 550 nm = 5.5e-7 m) | Aperture D (m) | f-Number N = f / D | Rayleigh Limit / Airy Spot |
|---|---|---|---|
| 200 mm Amateur Telescope | 0.20 m | f/8.0 | 0.692 arcsec | 10.74 um spot |
| 6.5 m Space Telescope Mirror | 6.50 m | f/20.2 | 0.0213 arcsec (32.5x sharper!) |
| Stopped-Down Camera Lens | 0.003 m | f/16.0 | 21.47 um Airy blur spot |
Rayleigh Criterion Angular Resolution (Arcseconds)
Converts theta = 1.22 * lambda / D from radians to arcseconds using 1 rad = 206,264.806 arcsec, guarding against non-positive wavelength B2 or aperture diameter B3.
=IF(OR(B2 <= 0, B3 <= 0), "Wavelength & Aperture Must Be > 0", ROUND(((1.22 * B2) / B3) * 206264.806, 3))Focal-Plane Airy Disk First-Null Spot Diameter (Micrometers)
Evaluates d_Airy = 2.44 * lambda_um * f_number from wavelength B2 (meters) and focal ratio N in B4.
=IF(B4 <= 0, "f-Number Must Be > 0", ROUND(2.44 * (B2 * 1000000) * B4, 2))Try the example
Use the original values or change them to test your understanding.