This article is based on a newsgroup contribution by the author in response to the question: "What is a Schiefspiegler ?"
The name "Schiefspiegler" (spell "sheef-speeg-ler"; "ee" as in "sheep") is German and means "skew" or "oblique reflector." There are various types of Schiefs which have been constructed, and even more are constructable. They have in common that they are reflecting telescopes without the obstruction by secondary mirrors which otherwise effects the images of stars and makes them less sharp (i.e., diminishes the "image definition", as the Schief pioneer Anton Kutter put it). This is achieved by inclining the primary mirror against the symmetry line of the image, thus allowing to move the secondary mirror (e.g., of a Cassegrain) out of the viewing line of the primary. By doing so, there occur imaging defects at first, namely coma and astigmatism, which can be influenced by inclining the secondary mirror also. These defects stay managable for large focal ratios, therefore most Schiefs have f:20 or higher. They can be managed by carefully choosing inclination angles for the mirrors in small Schiefs; the Belgian manufacturer Lichtenknecker has their optics in this form for up to 5-inch. Higher apertures and/or shorter focal ratios require additional corrections (more acurately, additional optical errors with opposite sign so that they compensate); this may be achieved by adding a correcting lense (Lichtenknecker does this "catadioptric" solution for Schiefs of 6 to 16- inch aperture).
These simple possibilities lead to Schiefspiegler telescopes of Kutter type; they consist of a primary about double as large as the secondary, and the eyepiece/photo end. One common construction is to put the secondary mirror and the eyepiece in quite a long but thin tube, which has an oval hole in one side for letting in the light from the primary, which sits in a separate thick tube mounted aside the eyepiece. This is the "open" construction which leads to handy light-weight scopes.
Alternatively, one can build a larger case which "packs" the two mirrors and has only an aperture hole at the "front end" (near the secondary mirror), of about the same diameter as the primary mirror. This "closed" construction is more massive and less handy then the open, but has the advantage of less air turbulence, better light and dew protection, and, e.g., a "simpler" possible use of full-aperture Solar filters.
There are other types of schiefs, one more notable being the Yolo: Here, the mirrors are deformed by mechaincal forces to achieve an error-free optical image. Others use three or four mirrors ("Tri" and "Tetra" Schiefs), however they are not so common because patents prohibit a low-cost production (at least this was written), and the scopes get more and more complicated.
As the Schiefs have a full obstruction-free aperture, their power is equal to that of refractors of same size (even better than that of refractors not well corrected for chromatic effects, as they are reflectors). This means that they (as refractors of same aperture) are, from construction, as "good" for the observation of planets, multiple stars, the Moon and the Sun as Newtons and Cassegrains of notably larger aperture, the exact value depending on the amount of obstruction. Basically, the instruments must have the same "free diameter" aperture: As discussed e.g. in our obstruction page, "sharpness" (image definition or image contrast) is related to an "effective" telescope diameter, which, for cirular aperture of diameter D and circular obstruction of diameter d, is given by
For small secondary mirrors obstrucing 20-25 percent, this is a factor 1.25-1.33, for the "usual" ~40 percent SCs it is 1.67, and approaches a factor 2 as the secondary goes to 50 percent of the primary's free aperture - so the common 11-cm Kutter about as sharp as a 14-15 cm Newton or a 7-8 inch (17-20 cm) SC, provided the optical quality is about equal.
For deep-sky objects, this effect is less important, and they only profit from their a bit larger free aperture: Here, light gathering power is the more important issue, and for it the effective diameter would be given by D_eff^2 = D^2 - d^2. Therefore, for faint deepsky objects, unobstructed telescopes are about as powerful as 20-percent obstructed Newtons or Cassegrains of 1.12 times their aperture, or 40-percent obstructed SCs of 1.3 times their free diameter (so above 11-cm Schief corresponds to a 12.4-13 cm Newton or a 14-15 cm SC with respect to light gathering power).
From their price, Schiefs are far below a refractor of same size, and because they are lighter, they need a less expensive mount.