Resolving power

A fundamental law of optics is that you can't magnify detail that isn't there. No matter how perfect its optics, no telescope can show an infinite amount of fine detail. Resolution is limited by two things: diffraction and the turbulence of the air.

Diffraction is the spreading of light waves as they pass through an opening. You may have seen it demonstrated with tiny pinholes or narrow slits. In a high-powered telescope, even the telescope aperture - several inches in diameter -produces a visible amount of diffraction.

Diffraction makes stars look like disks surrounded by rings rather than perfect points. Figure 5.4 shows a pair of stars, close together, as seen in 4-inch (10-cm) and 8-inch (20-cm) telescopes. The larger telescope forms smaller star images. Diffraction also blurs fine detail on planets; larger telescopes show more detail.

Figure 5.4. A close double star viewed with a 4-inch (10-cm) telescope (left) and an 8-inch (20-cm) telescope (right). Simulated image generated with Aberrator.

Table 5.2 Resolution limits

Aperture Dawes limit Rayleigh limit (550 nm)

Dawes limit (for double stars that are barely split) and Rayleigh limit (for a somewhat cleaner split) are functions of telescope aperture.

The effect of diffraction on resolving power is expressed as the Dawes limit and Rayleigh limit:

Dawes limit

Rayleigh limit (for 550 nm) =

aperture (inches) aperture (cm)

aperture (inches) aperture (cm)

The Rayleigh limit is theoretical; the Dawes limit was determined by actual observation of double stars with components of equal brightness. Table 5.2 summarizes these limits for common telescope sizes. For example, a double star with components separated 1 arc-second (1") is close to the limit of a 5-inch (12.5-cm) telescope but is easily split by an 8-inch (20-cm) in steady air.

If diffraction were the only limiting factor, the largest telescope would always show the best image. But we always observe through the Earth's turbulent atmosphere, which makes the image seethe and boil in a constantly moving blur.

The air is much steadier at some times than others, but even under the best conditions, telescopes larger than about 20 to 30 inches (50 to 75 cm) are unlikely to show additional detail. That's why the Palomar 5-meter (200-inch) telescope is seldom used for planetary work. Under average conditions, the practical aperture limit is more like 8 to 16 inches (20 to 40 cm), and when the air is really rough, even smaller telescopes work best.

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