Limitations Imposed by Aperture

I live in the country, surrounded by farmland, 40 miles east of Pittsburgh, Pennsylvania, and 15 miles from any other major source of light pollution.

On the clearest moonless nights I can reliably detect stars as faint as 11.3 magnitudes with an 80-mm f/11 refractor. This is in accord with the relationship m = 1.8 + 5 log D

where D is the diameter of the objective in millimeters.

Although magnitude limits as faint as 12.1 have been quoted for 80-mm refractors, this is much too faint for the average observer. The value given above is more realistic.

Because of the obstruction of light by the secondary mirror, the effective aperture for a 90-mm Maksutov is 84 mm. Since there is additional light lost by two reflecting surfaces, the limiting magnitude for these telescopes is the same or slightly less than that of the 80-mm refractor.

The diffraction of light by a circular aperture imposes limitations on telescope resolving power and magnification. Diffraction produces an image of a star that consists of a bright central maximum surrounded by faint concentric rings. Faint stars at low magnification appear as points of light. For bright stars at high magnification the central maximum becomes perceptible as what is termed the "Airy disk." The diameter of the Airy disk decreases with increasing telescope aperture. If two components of a binary star are separated by a distance that is less than the diameter of the disk for a particular aperture, they cannot be resolved as individual stars. This criterion defines the resolving power of a telescope. It is given approximately in arc seconds by

for D in millimeters. For an 80-mm refractor it is 1.4 arc seconds.

Telescopes are usually classified by the term "f/ratio." This is equal to the effective focal length of the objective lens divided by its aperture. An 80-mm refracting telescope having a focal length of 900 mm is designated as an 80-mm f/11.3 refractor.

While magnification of a telescope is equal to the effective focal length of the objective lens divided by the focal length of the eyepiece, for a Maksutov the effective focal length is the focal length of the combined mirror system.

Magnification can be changed by the use of eyepieces of differing focal lengths. But there is a limit to the magnification that can be achieved. At very high magnification the diffraction of light causes the image of a planet to loose contrast and sharpness. Consequently, the maximum magnification for a telescope depends on its aperture. In general 2x per millimeter of aperture is a good rule to apply for maximum useful magnification. On exceptional nights, when the air is extremely stable, this limit can be extended to 2.5x per millimeter.

The presence of the secondary mirror in Newtonian and Maksutov telescopes removes light from the Airy disk and distributes it to the secondary rings of the diffraction pattern. As a result the maximum useful magnification and image contrast are usually considered to be less than for a refractor. The effect is most noticeable for short focus Newtonians with relatively large secondary mirrors. It is negligible if the diameter of the secondary mirror, the diagonal minor axis for Newtonians, is 25% or less than 25% of the diameter of the primary mirror This occurs at about f/8 for Newtonians.

Design restrictions for Maksutov telescopes constrain the secondary mirror to a diameter of about 34% of the primary. However, their freedom from chromatic and other aberrations tends to offset the effect of diffraction by the secondary mirror. As a result, a 90-mm Maksutov can produce images comparable to those obtained with an 80-mm refractor.

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