Appendix B: Telescope Resolving Power

The resolving power of a telescope is its ability to image fine detail. Due to the wave nature of light telescopic images can never be perfectly sharp. A diffraction pattern occurs around each point in the image. The size of the pattern decreases as the size of the telescope aperature (mirror or lens) increases. The pattern size also depends on the wavelength of light. These effects are shown in the following simulated images which are shown very highly magnified (roughly 3000-4000X when viewed from about 20 inches. Varies with screen size. A typical useful high power is about 60x per inch of aperature under very good conditions).

The next three images show a single star as imaged by a 6 inch telescope.

Wavelength = 4500 Angstroms	Wavelength = 5500 Angstroms	Wavelength = 6500 Angstroms

The tick marks along the edge of the images are spaced 1 arc second apart. The images are overexposed to show the first few diffraction rings. The rings continue outward with decreasing brightness. The central disk is called the Airy disk and contains about 85% of the total light of the star. As can be seen, the pattern size increases as the wavelength of light increases. That means the actual diffraction pattern will show colored fringes as shown in the simulated color image.
This is not chromatic aberration, it is due to diffraction from the wave nature of light. These images have been highly magnified and show a perfect optical system (no aberrations or other defects). This is also not the image of the star itself which is normally far too small to be resolved other than a few exceptional cases for large telescopes.

Larger telescopes show smaller diffraction patterns. Below are patterns for a 12 inch telescope.

Wavelength = 5500 Angstroms	Color view

Normally the diffraction rings are quite small and faint and atmospheric turbulence causes the pattern to jump around so much it may not be seen at all as shown below in an image made using 100 random positions. Remember, the actual view through a telescope would be rapidly changing, looking almost like it was boiling. Such a state is called bad seeing.

This makes it harder to split close double stars:

0.7 arc second double	Same with some turbulence

The following shows 4 telescopes of increasing size viewing a 0.7 arc second double star with no turbulence. Note that the images in the larger telescopes would be far more brilliant because more light is collected and it is focused into smaller areas.

6 inch telescope	12 inch telescope	26 inch telescope	60 inch telescope

Dawes Limit is a measure of the maximum resolution of a telescope. A double star at Dawes limit has the center of one Airy disk on the edge of the other. The value in arc seconds is given by: ang = 4.56/D where D is the aperature diameter in inches. A more useful working value is twice Dawes limit. For the double star shown above, the 6 inch telescope is at about Dawes limit. The 12 inch is at double that, the more useful working value.

Appendix C Notes on how these images were computed.