Techniques
of Observational AstronomyAST3722C
Techniques
of Observational AstronomyThe four basic forms of telescope optics are shown in the figure below. Each of these has an objective that collects the light, bringing it to a focus.
Refracting telescope
An objective lens brings starlight to a focus. Subject to chromatic aberration caused by dispersion in the glass of the objective. Chromatic aberration can be compensated with a lens of several elements of differing materials.
Prime focus reflecting telescope
A (typically) parabolic objective or primary mirror reflects light back to a detector (camera or other device) at the prime focus. Telescopes with only reflecting optics are not subject to chromatic aberration
Newtonian reflecting telescope
A (typically) parabolic primary mirror reflects light to a flat secondary mirror and thence to the focus. The obstruction of the light beam caused by the secondary mirror is typically less than 10% of the total incoming light.
Cassegrain reflecting telescope
A parabolic primary reflects light to a hyperbolic secondary mirror and thence to the focus through a hole in the primary mirror. The secondary mirror has a magnification factor m yielding an effective focal length which is m times the focal length of the primary mirror. This allows a much shorter overall telescope tube length than for the other types of telescopes for the same effective focal length.
The simplest (and easiest to make) objective mirror for a telescope is concave and spherical in cross section. For paraxial rays a spherical mirror is quite adequate. For ray further from the axis, however, spherical aberration limits the sharpness of images that can be formed.
A parabolic cross section fully corrects spherical aberration and parabolic mirrors are common in small and moderate aperature telescopes. A parabolic mirror does introduce other aberrations (coma, astigmatism, distortion, and curvature of field) and large modern telescopes generally have more complex surface figures to minimize specific aberrations.
While the Gregorian optical system is seldom used (it requires a longer tube than the Cassegrain), the Nasmyth and Coudé optical system are common, especially on large modern telescopes. Telescopes such as the Gran Telescopio Canarias typically have several Nasmyth and bent (or folded) Cassegrain instrument stations.
Schmidt and Maksutoff optical systems use a spherical primary mirror (and hence no aberrations other than spherical) and correct the spherical aberration with a lens (a complex thin lens in the case of the Schmidt, a thick meniscus lens for the Maksutoff). These optical systems can have very wide fields of view.
Each of the telescopes shown earlier has the same aperture D and hence the
same light gathering power, which is proportional to the area 
of the objective. For
unresolved objects such as stars the speed of a telescope is proportional to
its light gathering power.
The "f-ratio" of a telescope or camera is given by the ratio of
the focal length to the aperture and is therefore defined as 
. For telescopes
of the same aperture D the size of the image (see image scale) depends on the
focal length. Doubling the focal length (and hence the f-ratio) doubles the
linear size of an extended image and therefore the light is spread over four
times the area. Thus the speed of a telescope for imaging extended objects is
inversely proportional to the square of the f-ratio.
If it is the image in the focal plane that is of interest (as is the case
when a CCD camera is the detector) then it is image scale rather than
magnification that must be calculated. The linear size of an image d of an
object of angular size 
is 
where is in radians. Image scale in mm per arc-second is 
if F is in
meters. For a 46 cm f/10.5 telescope this works out to s= 0.023 mm/arc-second
which gives an inverse scale of 43 arc-seconds per mm.
Diffraction by a circular aperture (such as a telescope objective) results
in point source being imaged as a central maximum surrounded by circular rings.
Rayleigh's criterion says that the limit of resolution of a telescope when
looking at a double star is given by 
radians (about 4.56/D
arc-seconds in the visible if D is in inches). At this limit the maximum of the
diffraction pattern of one star will fall on the first minimum of the other
star.
The magnification of a telescope is only useful for extended objects (e.g. the moon, planets, nebulae, galaxies), not unresolved objects such as stars (though magnification does apply to the angular separation of two stars). It is most easily calculated from the ratio of the effective focal length of the telescope to the focal length of the eyepiece (m = Fscope /feyepiece ). Typical eyepieces are 25 mm, 12.5 mm, and 6 mm. With a telescope of 1 meter focal length these eyepieces would give magnifications of about x40, x80, and x170 power. This means that objects such as the moon would appear 40, 80, or 170 larger in diameter (and hence they would appear to be 40, 80, or 170 times closer).
The pupil of a typical human eye has an opening about 5mm in diameter in subdued daylight. The pupil may contract to as little as 2.5 mm in bright light, and it may open to 8 mm when the eye is dark adapted. Magnifications smaller than values equal to the telescope's diameter in cm. will result in a bundle of light larger than the pupil, thus loosing image brightness. Magnifications larger than about 10 times the aperture in cm. will result in a bundle so small that the image quality will suffer. Example: The RHO 46 cm. scope can use magnifications between about 50x and 500x to good effect. Since the focal length is about 480 cm., thus means eyepieces of about 10 mm (480x) and 100 mm (48 x). Note that eyepieces are generally not available with focal lengths longer than about 50 mm (100x with the 46 cmm. telescope).
In addition to magnification the field of view of an eyepiece is important. The field of view is a function of the optics of the eyepiece itself and its magnification which is a function of the telescope focal length. Typical eyepieces have field of view ranging from 40° to 65° or more. The intrinsic eyepiece FOV must then be divided by the magnification to get the effective field of view at the telescope. A 25 mm eyepiece on a 1 meter focal length telescope has a magnification of x40. This will yield a 1° field of view if the eyepiece has a 40° intrinsic field of view
This page was last edited November 4, 2004 9:09 AM