confirming the previous conclusion that no solution exists for Ecor = Ep. But with Ecor = Ep, a solution exists. This leads to the important general conclusion that aspheric surfaces on lenses, or separate plates, are useful parameters in combination with other lenses, or lens groups, from which they are axially separated. (This conclusion is, of course, identical with the basis of multi-plate correctors dealt with in § 4.2.1.) In other words, an aspheric on a lens is not useful for the correction of spherical aberration in its own function; but may be useful in combination with other elements with different E, the utility being principally in the relaxation of bending requirements as recognised by Paul [4.4]. The solution for a parabolic primary corrected by a thin afocal doublet and separated aspheric plate was already treated by Wynne in 1949 [4.23]. It was proposed also by Schulte [4.11] for an RC-telescope. According to Wynne [4.5], with the spherical aberration correction

liberated by the hyperbolic primary, it offers little advantage over the doublet-only type corrector with a hyperboloid proposed by Paul [4.4] and taken up in 1961 by Rosin [4.26], using a two-glass doublet design.

At this stage, we must introduce the reflector-corrector due to Baker [4.27]. This solves the problem of spherical aberration with a Ross-type doublet correcting a parabolic primary by adding into the incident beam, in roughly the same plane as the doublet, a Schmidt-type corrector plate -Fig. 4.8. This system is also discussed by Wynne [4.5]. The doublet corrects coma and astigmatism for the front stop and also field curvatureby appropriate residual positive power, giving somewhat more spherical aberration than that of a normal Ross doublet. This is corrected by the Schmidt-type plate, rather as in a Wright-Vaisala camera (see § 3.6.4.1), except that this latter cannot correct astigmatism and field curvature and works with a primary of oblate-spheroidal form. Since the stop is at the plate, it has no effect on other aberrations than ^ Si. This system has only half the length of the Schmidt telescope and gives in addition a flat field. The reflector-corrector can also be removed for naked use of the paraboloid. If this convertibility is of no consequence, the reflector-corrector can be used with a spherical primary as a compact modification of the Schmidt system.

We will now consider the case of an afocal corrector consisting of 2 spaced lenses, i.e. with different E-values. In fact, the same treatment applies to 2 spaced afocal doublets, since, as we saw above, the same formulae apply except for the precise form of the E-parameters in terms of physical dimensions in the system. For this case, Eqs. (4.47) can be written

Si = —f 'Z + (Si)cor 1 + (Si)cor 2 5ZSii = — 2 f' + (Sii)cor 1 + (Sii) cor 2 + E1(Si) cor 1 + E2(Si) cor 2

Siii = f' + (Siii)cor 1 + (Siii)cor 2 + 2E1(Sii)cor 1 + 2E2(Sii)cor 2 +E?(Si) cor 1 + E2(Si) cor 2

If the conditions Si = Sii = Siii = 0 are to be fulfilled with Z = 0 for a parabolic primary, these equations give:

(Sll)cor 2 = 1 /' — (Ei — E2)(Si)cor i — (Sll)cor i (4 63)

(SIII)cor 2 = — [ (SIII)cor i + 2(Ei — E2)(Sll)cor i

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