Table of Contents
What Is Angular Resolution?
Angular resolution is the smallest angle between two point sources that an optical system can distinguish as separate objects. It is limited by diffraction, which causes light passing through an aperture to spread into an Airy pattern. Larger apertures and shorter wavelengths produce better (smaller) angular resolution.
This concept is critical for telescopes, microscopes, cameras, radar systems, and any imaging instrument. The angular resolution determines how much detail can be seen: a telescope with 1 arcsecond resolution can separate two stars that are only 1 arcsecond apart in the sky.
Rayleigh Criterion
Where theta is the minimum resolvable angle in radians, lambda is the wavelength of light, and D is the aperture diameter. Both must be in the same units. The factor 1.22 comes from the first zero of the Bessel function describing the Airy diffraction pattern.
Telescope Angular Resolutions
| Telescope | Aperture | Resolution (arcsec) |
|---|---|---|
| Human eye | 7 mm | ~60 |
| Small refractor | 80 mm | 1.45 |
| 8-inch SCT | 200 mm | 0.58 |
| Hubble | 2,400 mm | 0.05 |
| JWST | 6,500 mm | 0.07 (IR) |
FAQ
Does atmospheric seeing limit resolution?
Yes. For ground-based telescopes, atmospheric turbulence typically limits resolution to about 1-2 arcseconds, regardless of aperture size. Adaptive optics systems can partially correct this, approaching the diffraction limit. Space telescopes like Hubble avoid this problem entirely.
Why use shorter wavelengths?
Shorter wavelengths diffract less, producing tighter Airy patterns and better resolution. This is why electron microscopes (using extremely short de Broglie wavelengths) achieve far better resolution than optical microscopes, and why UV astronomy can reveal finer detail than visible light.
What is the Dawes limit?
The Dawes limit is an empirical resolution formula (116/D in mm giving arcseconds) that represents the practical limit for separating equal-brightness double stars. It is slightly more optimistic than the Rayleigh criterion because experienced observers can detect the elongation of overlapping Airy patterns.