SSf = 8(n' - n)ay4 , where a is a constant and n = 1 for the normal case of a glass plate in air. If a virtual plate in the object space is calculated as described above, the profile constant a in (3.221) must be multiplied by rnpl, where rnpi is the magnification of the plate imagery back into object space.

In ยง 3.6, we shall see the direct application of Eqs. (3.219) and (3.220) to wide-field telescopes, and in Chap. 4 to field correctors.

3.5 The role of refracting elements in modern telescopes: chromatic variations of first order and third order aberrations

Although the refracting telescope and oculars are not considered as belonging to the domain of modern telescope optics and are not treated in this book (older books such as Konig-Kohler [3.30] or Bahner [3.5] deal excellently with this material), this does not mean that chromatic aberrations no longer play an important role in modern telescope systems. This role is generally that of correcting aberrations without contributing significantly to the optical power of the system. The optical power is essentially provided by the mirror system. This does not mean that lenses with significant power will not be used: it means that powered lenses will normally be used in a corrective combination which has a small total power. Since, for thin lenses, primary chromatic aberration (the variation of longitudinal focus with wavelength for a simple lens) is dependent on the total power, the main curse of lenses is thus avoided. Of course, different materials may also be used to produce achromatism, but the effects of secondary spectrum, longitudinal aberration residues due to the different dispersions of the materials, remain. Such effects can only be reduced by the use of "special glasses" or crystal materials which may have other design limitations or limitations of availability (diameter).

Refractive corrector elements can produce not only simple longitudinal chromatic aberration but also other chromatic effects. The general theory is given by Hopkins [3.3] and Welford [3.6]. By analogy with Eq. (3.21) for the monochromatic aberrations, the wavefront form for the chromatic aberrations of the first and third orders can be expressed by

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