Astronomical Techniques - Telescopes and Image Formation

For use in the UV through infrared, telescopes are direct imaging systems. We will consider them for now as abstract collections of optical elements, leaving mechanical parts for later. Thus, a telescope has an objective that collects and focuses radiation, and may have one or more auxiliary elements that change the focal length, move the focal position, or reduce aberrations. It is useful to track the locations of focal surfaces and pupil planes.

Eyepieces: For visual use, we employ high-quality magnifiers to inspect the real image formed by all except Galiliean telescopes (in which the eye is an integral part of the optical train). For an objective of focal length F and eyepiece focal length f, the magnification with respect to a naked-eye view is simply F/f. The quality of this view, and its angular (hence apparent) extent are determined by the optical design of the eyepiece, which ranges from simple doublets to elaborate multi-element designs with beautifully corrected, wide fields of view. Note carefully what an eyepiece does - it magnifies the real image in the focal surface (which may be examined just like a physical object), so that rays from any point in the image are parallel and thus seen by the eye as a point source. For a large telescope with no central obscuration or used off the optical axis, the eye can do this directly with no eyepiece. I've heard that the Moon looks really impressive through the Keck telescope with no eyepiece.

The effective focal length of the objective may be extended (and hence magnification increased )by inserting a small negative lens (a Barlow lens) a few cm before the eyepiece. With some designs, a Barlow plus eyepiece in a sliding holder gives a variable-magnification or zoom eyepiece. For those eyepiece designs that place the focal surface in a physically accessible point (outside the eyepiece), a reticle may be inserted and perhaps illuminated. These are useful for guiding, location, offsetting to a reference point, and measuring separations on the sky (as in a filar micrometer). Note that the optically best eyepieces aren't always the best in real life. Eyepieces that should give awful performance may, for example, just happen to cancel 90% of the chromatic aberration of a particular refractor.

In order to produce the brightest image the telescope can produce, the dark-adapted eye must be able to intercept all the light coming out of the eyepiece, through the exit pupil (generally a few cm behind the last lens). This pupil is smaller than the objective diameter by the factor of the magnification, so for large telescopes there is a lower limit to the magnification that avoids light loss (though you can still apply lower powers in a "finder" mode). For a typical eye, the exit pupil should not exceed 7-8 mm in diameter, for a minimum magnification of about 125 for a 1-meter telescope (for example).

When changing eyepieces, one must in general refocus the telescope (usually by moving the eyepiece). Sometimes sets of similar eyepieces of different focal length are manufactured to be parfocal, so that the focal surface falls in the same mechanical place for each (i.e. in principle, they are in focus at the same position).

Refractors: (also known as dioptric telescopes). These are fairly rugged, require relatively little maintenance, and are excellent in convenience for small diameters. Chromatic aberration and sagging of the objective limit the practical (and economical) size of refractors; several with apertures up to 1m (even a 1.2m stationary one) were built a century ago, but have never been superseded. Wide-field astrometric versions have been their most recent use in moderately large apertures (0.5m or so). They are widely used as finders and guide telescopes. Chromatic aberration means that better performance required large f-ratios until new multielement and exotic-glass designs came into use.

Refractors, chromatic aberration aside, can deliver crisp images with no diffraction spikes or structure due to central obscurations. Most designs produce an inverted real image; the Galilean produces an erect virtual image, accounting for its popularity among really cheap applications like opera glasses. When an erect image is really necessary, binocular-style prisms or a chain of lenses can turn it around.

Reflectors: (catoptric telescopes). There are numerous flavors.

Prime focus: just the primary mirror and the detector, perhaps with additional elements to correct aberrations and increase the useful field of view. This works only for fairly large apertures, since the detector can block light. Paraboloidal primaries give small fields (50mm or so in diameter) before significant aberrations (primarily coma) set in. Larger fields are possible through the use of correcting lenses (generally achromatic doublets). Like all on-axis reflectors, their images have diffraction spikes produced by the supports for the prime-focus equipment protruding into the incoming beam. Various arrangements of curved supports are possible, which spread the same amount of diffracted light in a more diffuse pattern. Herschel experimented with an off-axis prime focus to avoid the diffraction and light loss at a secondary mirror.

Newtonian: basically a folded prime focus, with a flat mirror folding the beam through 90 degrees to put the focus just outside the upper edge of the tube. The image quality is essentially that of a prime-focus arrangement. The Newtonian is very convenient to build and test optically in small sizes, but for larger apertures the height of the detectors and unbalanced tube are grave disadvantages. Further folded versions also exist, using additional flat mirrors to put the focal positions at the bottom of the tube or the lower side.

Cassegrain and Ritchey-Chretien: here a primary mirror (paraboloidal or hyperboloidal respectively) of short focal ratio is paired with a convex hyperboloidal secondary, directing the beam (at a longer effective focal length) back through a hole in the primary. The R-C form has an especially wide field with good third-order aberration correction for both coma and spherical aberration. Both forms have excellent stability due to the short tube structure for given focal length, and offer convenient and well-balanced mounting points for instruments and detectors. These are the most common designs for large reflectors (including HST). For specialized applications, there is also a Gregorian form, with a concave secondary placed beyond the prime focus.

Specialized applications may need alterations. Matching a detector or sampling to the typical seeing disk may require a focal reducer, which must be carefully designed and aligned to avoid dreadful coma. Large secondary mirrors may block unacceptable amounts of light, and infrared applications dictate the smallest practical secondary mirror, since the mirror gives off thermal radiation at the relevant wavelengths and field chopping requires the least moving mass. Light baffling may be needed below the secondary and above the hole in the primary to prevent stray light being scattered into the beam.

Coude: the ultimately folded system. Here a series of 3-5 mirrors sends the beam to a fixed point below the telescope mounting, traditionally where large stable spectrographs are kept. Some of its functions have been taken over by echelle spectrographs compact enough to mount at the Cassegrain focus, and by optical fibers feeding a fixed instrument from any desired focal station.

Nasmyth focus: for an altazimuth mount, a folded Cassegrain focus exists along the elevation axis, this moving only horizontally and nearly as stable as a coude focus. These have been used at the Russian 6-meter (BTA) (see especially here) and 4.2m Herschel telescopes, and more recently in the whole array of 8-10m telescopes built since 1990.

Siderostats and Heliostats: sets of moving mirrors that feed a fixed telescope with light from any desired direction. Such mirrors can be used to get double duty from large coude' spectrographs, by feeding light into moderate-sized fixed telescopes and thence into the spectrograph when the main telescope is otherwise occupied. This view shows such an arrangement at the KPNO 2.1-m telescope, with the moving flat mirror in the foreground feeding the fixed parabolic primary mirror atop the tower.

Catadioptric systems:

Schmidt cameras: using a spherical primary mirror eliminates coma, while a thin refractive corrector reduces spherical aberration. Schmidts can give nearly diffraction-limited performance over a field several degrees wide, and have been the only practical instruments for sky surveys. They cannot be used visually, as the focus is in the middle of the tube. The plates must be curved to match a spherical focal surface. Variants (the Baker-Schmidt) use correcting lenses to put the focus in the middle of the corrector, and can be used as Cassegrains as well by installing a secondary mirror.

Schmidt-Cassegrain: puts a secondary mirror just inside the corrector, for a wide-field Cassegrain focus. Very popular in amateur sizes up to 30 cm or so. A related, very clever, design, is the Maksutov, where the corrector and secondary are one element. Details on many flavors of these and their construction and testing can be found in the the 3 volumes of Amateur Telescope Making.

Giant telescopes: New advances are making possible designs for telescopes of 10-16 meter effective aperture. These fall into a few basic categories:

  • Thin meniscus primaries, where active mirror support is needed.
  • Segmented primaries (like the Kecks), again with active measurement and control.
  • Multiple-mirror telescopes, with attendant problems of field and beam combination, plus active alignment.
  • Multiple telescope telescopes (like the ESO VLT), where either coherent or incoherent signal addition is possible. All the elements may be used together or separately, and for most optical applications, one adds the data from separate identical instruments (with no noise penalty in the sky-noise-limited regime).
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