Sky & Telescope, August, 1981, page 166-168.

Conducted by Roger W. Sinnott

Most mirror makers, given a choice, would prefer a telescope design in wich the primary mirror is spherical. Such a surface is easiest to figure and test. But the standart Newtonian or Cassegrain telescope requires a paraboloidal primary mirror, and many alternative designs, using a spherical mirror, have been explored.

Normally, the primary can be left spherical only if the aberration thereby introduced is compensated in some other part of the system. Sometimes, as in the Maksutov and Schmidt-Cassegrain variations, a full-aperture correcting lens is placed at the sky end of the telescope. But this approach significantly increases the cost of glass and the work involved.
Various subaperture correctors have also been suggested. In Sky and Telescope for September, 1957, page 548, Robert T. Jones described what amounts to a Newtonian configuration, with a negative two-element correcting lens placed between the primary and diagonal mirrors (much closer to the latter). He computed curves for the doublet so that it would correct the aberration of the spherical primary while also serving as an achromatic Barlow lens. Another example is the design by Robert Magee described in Scientific American for August, 1972, page 110, in which a two-element Mangin secondary mirror serves in a Cassegrain arrangement.

Australian amateur Ralph W. Field, after completing the design calculations presented in this article, begins to grind the small meniscus corrector for a working telescope.

Both of these designs suffer from the inevitable secondary spectrum of crown and flint glasses. While not large, this effect may be avoided by using the self-achromatic meniscus principle proposed by D. D. Maksutov in 1944.

Instead of using the meniscus as a full-aperture corrector, my design presented here use a small meniscus located in the convergent beam of light from the spherical primary mirror. After passing through the corrector again before reaching the Cassegrain focus.

I have calculated two alternative designs with the aid of a Texas Instruments TI-59 programmable calculator. Both use the same 6-inch primary mirror, so one telescope can be converted to the other by simply replacing the secondary-corrector unit. Both are specified completely in the table on this page. The f/9.6 design has a focal length of 47.5 inches and excellent images across a 1.8 degrees field of view; it would serve nicely for photography of deep-sky objects. The f/15.7 design, with a focal length of 86.2 inches, is more suitable for lunar and planetary work.

Both designs are corrected to within 0.001 inch for both color and spherical aberration. The "offense against the sine condition" is 0.0016 for the faster system and 0.0024 for the slower. Both of these values are below the maximum of 0.0025 recommended by the famous English lens designer A.E. Conrady early in this century (see p.395 of Conrady's book, Applied Optics and Optical Design, vol.I, Dover, 1957).

Although the surface of best definition is not quite flat, being slightly concave to the sky, the resolution at the edge of a 1.5-inch-diameter flat photographic plate should be no worse than 30 lines per millimeter. The same is true of the f/15.7 design at the edge of a 1-inch-diameter circle.

Diffraction effects should not interfere with visual performance of the f/15.7 design at high magnification, because the central obstruction is slightly less than 30 percent of the aperture. However, it is important to have antireflection coatings on the corrector surfaces, because the double passage of rays means there are effectively four air-glass surfaces.

The aperture stop of these designs is not at the primary mirror (as it would be in an ordinary Cassegrain), but near the open end of the tube instead. This location was chosen to give the best balance between astigmatism and curvature of field.

As in all Maksutov design, the difference between the radii of curvature of the two corrector surfaces is the most critical part of the speifications. In the f/9.6 design, this difference should be held to within 0.004 inch, although the individual radii may depart together from the specifications by as much as 0.05 inch in either direction. The f/15.7 design is more sensitive to errors because of the greater amplification and shorter radii; accordingly, for this design the tolerances are halved.

As compared with a full-aperture Maksutov corrector, there is a great saving in glass, abrasive, and labor by going to the subaperture corrector of these designs. The sagitta of the concave side of either it is over 0.75 inch in an f/15 Gregory-Maksutov of similar aperture.

Although the subaperture designs no longer have the closed-tube feature that automatically seals the tube of a conventional Maksutov from dust and thermal air currents, it is fairly common practice nowadays to mount a secondary mirror on an optical window. This would not only close the tube but also avoid the diffraction spikes that are produced on bright star images when spider vanes support the secondary.

Ralph W. Field, Australia