Co

Fig. 3.37. Spot-diagrams for a "short" Maksutov telescope with aperture 400mm and f/3.0 optimized with an achromatic field flattener (Table 3.12)

timized with such a field flattener. The extra degrees of freedom enable C2 to be reduced to about one quarter and the residual Sj jj to about one third. Fig. 3.37 shows the spot-diagrams to twice the scale of Fig. 3.35. If the relative aperture is reduced from f/3.0 to f/3.5, a further significant improvement is achieved by reduction of fifth order aberrations.

The residual C2 shown in the spot-diagrams of Fig. 3.37 is largely due to the secondary spectrum of the "normal" glasses BK7 and F2 composing the field flattener. This leads to a curvature of the locus of the centres of gravity of the spot-diagrams in the field. The curvature is convex to the axis abcissa, corresponding to overcorrection of C2 in the blue, undercorrection in the red, compared with the uncorrected C2 of the meniscus shown in Fig. 3.35.

3.6.4 More complex variants of telescopes derived from the principles of the Schmidt, Bouwers and Maksutov systems

The telescope forms dealt with so far have consisted of one element or two separated elements. As we have seen, the analytical theory of the 2-element telescope is by no means trivial and was only initiated and completed in the first half of this century through the pioneer work of Schwarzschild, Chretien, Schmidt, Bouwers and Maksutov.

The analytical theory of sophisticated forms containing more than three elements inevitably grows rapidly in complexity. Third order theory is still of utmost value in understanding the potential and limitations of any given system type, but the final layout and optimized design will be performed with one of the many programs available for a wide range of computers, including PCs. However, for the systems dealt with in § 3.6.4.1 below consisting of an aspheric plate and one or two mirrors (aspheric in the general case), the analytical equations derived in the general theory above provide a simple and powerful basis for complete understanding of their optical properties.

A complete treatment of the systems proposed and investigated in the past 50 years would itself require a whole book. The purpose of the account given in this section is to describe the characteristics of the basic types and refer to the literature for further detail. The books referred to are all excellent in their way and give a rich diversity of treatment reflecting the particular interests or style of the author.

3.6.4.1 Further developments of Schmidt-type systems. Solid and semi-solid Schmidt cameras: This form is really only of interest for spectro-graph cameras rather than telescopes but I include it here for completeness and because it is instructive optically. I follow the brief but excellent account by Schroeder [3.22]. Fig. 3.38(a) shows the basic optical property of the solid Schmidt and is to be compared with Fig. 3.36(b) for the Maksutov form. The solid Schmidt consists of a glass block with the aspheric form (front surface) at the centre of curvature of the spherical concave back. In glass with refractive index n', therefore, the Schmidt geometry is fully maintained. The essential feature is the single refraction of the principal ray with the semi-field angle upr, giving a refracted angle of upr = upr /n'. Clearly, the image height at the spherical focal surface is reduced by the factor 1/n'. In other words, the effective focal length fsol = f '/n', where f' is the equivalent focal length of a normal Schmidt in air of the same physical length. The "speed" of the system as a camera is therefore (n')2 higher, an important advantage in spectrographs. Alternatively, one can interpret the effect as an increase in the field coverage in object space.

The image height is given by

from Fig. 3.38(a). Differentiating with respect to n' gives

Schroeder quotes the application of this equation to the case of a solid Schmidt made of SiO2 for the wavelength range 400-700 nm and f' = 500 mm at an angle upr = 1°, giving dn = 61 ^m. Since the scale is f '/206 265 n' ~ 1.66 ^m/arcsec, this transverse colour aberration amounts to about 37 arcsec, a value which excludes use for direct imagery unless very narrow band filters are used. Transverse colour aberration is of no consequence in a spectrograph camera because it only produces a slight distortion in the spectrum.

A conventional Schmidt plate, even if it is thick, produces no transverse colour because a plane parallel plate produces no change of angle of an incident beam, irrespective of wavelength. For a Maksutov telescope with its stop at the meniscus (Fig. 3.36(b)), the refraction at its first surface is the same as in the solid Schmidt; but this huge error is almost entirely removed by the refraction at the second surface.

Fig. 3.38. The solid Schmidt camera in the direct form (a) and folded form (b), with effective focal length fjn'

Schroeder shows that the solid Schmidt reduces the field aberrations by a factor (n')2 compared with the normal Schmidt in air.

The focal surface can be made accessible by drilling a cylindrical hole into the block towards the primary mirror from the corrector face to the image surface, but the access remains inconvenient. Figure 3.38(b) shows how this problem can be solved by including a plane mirror in the block, a device first proposed (according to Riekher [3.39(a)]) by Hendrix in 1939.

A semi-solid Schmidt is shown in Fig. 3.39. Its advantage is that the focal surface is accessible without an additional reflection but is still rigidly attached to the mirror by a single glass block. The focal length is f'/n' as with the solid Schmidt; the aberration characteristics are also similar.

Wright-Vaisala system: This was the first important modification [3.40] [3.41] of the basic invention by Schmidt. Accounts are also given by Bahner [3.5], Baker [3.23(b)] and Konig-Kohler [3.30]. Essentially, the aim was to overcome the major weakness of the classical Schmidt, its excessive length. Wright and Vaisala independently discovered the important property that the conditions for the correction of spherical aberration (S ) and field coma (S ) can be fulfilled for any position of the corrector plate along the axis, if the mirror is given a suitable aspheric form. In fact, this is simply a further application of the important law discussed above as a consequence of Schwarzschild's theory [3.1] that, in any telescope consisting of two elements, the two conditions S j = Sjj = 0 can be fulfilled for any (significant) axial separation by appropriate aspherics on the elements (see Eqs. (3.219)). The third condition fulfilled by the classical Schmidt (Sjjj = 0) cannot be satisfied, the price to be paid for the more compact form. The Wright-Vaaisaalaa solution places the correcting plate at the focus, halving the length of the classical Schmidt (Fig. 3.40).

Fig. 3.39. The semi-solid Schmidt camera with effective focal length f '/n'

The third order aberrations of such systems can be derived at once from the general equations (3.219) for an aspheric mirror and an aspheric plate. Since, by definition of the Wright-Vaisala telescope, the plate is effectively at the focus, we have spi written:

fi with fi negative. Eqs. (3.219) can then be esi = E Si i = esi i i =

y 1

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