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giving

- (n' - 1)(n' + 2U dyf \ yf (WJ)GF,Bou ---,2- —3 ---„3 , (3.278)

8rJr2 7 32/

in which /', ri and r2 are negative, while d is positive, giving compensation between the first and second terms. This gives the Bouwers condition for the correction of third order spherical aberration as dBou - -ri

in which ri will be given some arbitrary value, usually as large as possible, taking account of the detector, to reduce higher order aberration.

In the Maksutov modification, the spherical aberration compensation must be maintained while the concentric meniscus form must be slightly modified to compensate its primary chromatic aberration. This arises from the dependence of its focal length /men on the index n'. Differentiating (3.276) gives d f' —dn'

Since the mirror images the virtual image of the object formed by the meniscus, shifts of its focus d/mer will be reproduced as longitudinal shifts of the final focus with wavelength. The Maksutov solution therefore requires a thick lens fulfilling the condition d/mer = 0 (3.281)

If (3.275) is inserted in (3.273), the "thick lens" formula converts to rir2

Differentiation and (3.281) give then as the Maksutov condition for achromatism of the primary aberration C1 in (3.222):

This gives a positive d for negative radii with the usual sign convention. The separation of the centres of curvature of the two surfaces of the Maksutov meniscus is

the minus sign indicating that the centre of curvature of surface 2 is closer to the mirror.

The final design of a Maksutov telescope requires an interactive process typical of optical design and implicit in modern optimization programs. Essentially, for a given thickness d, the three parameters power, "bending" (i.e. shape for a given power) and axial position must be optimized to give optimum correction of the three aberrations C1 (longitudinal chromatic aberration), Sj (spherical aberration) and Sjj (coma). It should be borne in mind that, once Sj and Sjj are corrected, the stop-shift formulae (3.22) and (3.213) show that, to the third order approximation, Sj, Sjj and Sjjj are independent of the stop position. The stop-shift term for C2, given in brackets in Eqs. (3.223), shows that this is also true of C2 because C 1 is corrected.

It follows that we can draw a very important conclusion for all such Maksutov-type systems: with Ci, Sj and Sjj corrected, the front stop position of Fig. 3.34 near the centre of curvature of the mirror ("long" Maksutov) can be abandoned in favour of a stop 'position at the meniscus without changing C1, C2, Sj, Sjj and Sjjj. Only Sv is influenced, from Eqs. (3.22), since Sjv = 0 (and by a small Sjjj residual), but this is of little practical consequence. This leads to the "short" Maksutov, a form which, with slight optimization, gives virtually the same image quality except for a minor increase in astigmatism. According to Maksutov [3.38], the optimum axial distance of the meniscus from the mirror is about 1.3/' to 1.4/'. Not only is the reduction in length of the "short" form of great significance, but also that of the diameters of the meniscus and mirror.

Table 3.11. Data for the "short" Maksutov telescope giving the results of Fig. 3.35 with D = 400 mm, f/3.0

r

d

(A = 486 nm)

Medium

(stop)

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