giving, with /' = 1, y1 = 1/20 for f/10, and upr 1 = 0.01 rad for a field diameter of 1.15°,
VSm = — [-0.1501 f= -3.75 ■ 10-^ 222 400 J V1007
400 J V100 J
a modest value. This can be converted into angular aberration at best focus using Eq.(3.208):
Then the angular astigmatism at best focus is, setting n' = 1 for the image space,
(Sup)ast,m = +0.155 arcsec , an excellent value. With slight defocus of the detector, astigmatic lines of length 0.31 arcsec would appear. We must remember, from Table 3.1, that this grows with the square of the field upr1.
Because of the high secondary magnification m2 and telephoto effect T, the only serious aberration is the field curvature. This is given from Table 3.5, with H2 = 1 for a normalized system, by
The effective field curvature is (see Table3.3 and Eq. (3.203)), for the normalized system
2Sjjj + Sty = 2(-0.150) + 11 = +10.70 , giving a radius of curvature of the optimum image surface rc(oPt) = -/'/10.70
With an aperture of 400 mm, /' = 4000 mm and rc(opt) = -373.8 mm. For visual use, this is of little consequence, but for photography a field flattener would be used. Since the image surface is concave towards the light, the field flattener must be a negative lens (see § 220.127.116.11 concerning field flatteners). We saw above that the asphericity required on the correcting plate is
SS| = -24.0625, a very high value compared with -0.25 (Eq. 3.229) for a basic Schmidt telescope. This is the price for the steep (f/2) primary and the short constructional length. The determination of the plate form from the value SS| was given in detail in § 18.104.22.168. A singlet plate is limited by chromatic effects, above all spherochromatism. However, it is still better than a refractor of similar size using classical glasses. An achromatic plate gives better performance, but is a major manufacturing complication. A singlet plate is already a difficult element to manufacture, particularly as fifth order correction will also be necessary with an f/2 primary, but such a design gives a very powerful and compact design for amateur use.
Figure 3.46 shows the spot-diagrams of the above design, somewhat modified by optimization, with an achromatic corrector plate. The quality is excellent: the field of ±1° could be increased.
It is instructive to consider the evolution of such an aplanatic Schmidt-Cassegrain design as the plate is moved further from the primary. The plate asphericity SSff weakens and bs2 becomes more positive, passing through the Slevogt solution (see below) in which both primary and secondary are spherical. With a doubled plate distance (sp¡ = 2/), the secondary is already an oblate spheroid with bs2 = + 0.75 and ¿Sf = — 19.25. If the plate distance is increased by a factor of five (sp¡ = —/'),then bs2 = +2.555 and SSff = —12.03. In the limit case with sp¡ = — ro, its lever arm is infinite and SSff ^ 0, i.e. the plate is non-existent and we have from Eqs. (3.220) the same result as the 2-mirror SP telescope without coma correction. From Eq. (3.137), the secondary then has the extreme form bs2 = + 5.56.
Reference has been made here and above to the Slevogt system [3.44] [3.46], in which both primary and secondary of a Schmidt-Cassegrain have a spherical form. In this respect, it resembles the monocentric Schmidt-Cassegrain of Linfoot (Fig. 3.43). However, in the Slevogt design they are not monocentric: the curvatures are nearly identical, giving only a small Petz-val sum residual. The design is therefore nearer to the Baker-types shown in Fig. 3.42, also from the point of view of the constructional length relative to the equivalent focal length which is about 1.38/'. However, it is formally an aplanatic Schmidt-Cassegrain, not an anastigmat, because the astigmatism is not fully corrected. This small residual is balanced against the residual Petzval curvature so that E Siv = —2 E Siii to give an effectively flat field. Because of the weak curvature of the secondary, the final image is placed just in front of the primary, as in the Baker systems, to give reasonable obstruction. The value of the secondary magnification |m2| is bound to be low, giving typically f/2 - f/3.25. With a singlet corrector plate, as with the Baker designs, the image quality is entirely limited by the large spherochromatism, but becomes excellent with an achromatic plate. The quality is then fully comparable with the aplanatic Schmidt-Cassegrain of Fig. 3.46, also equipped with an achromatic plate. Figure 3.47 shows the spot-diagrams for such a Slevogt system of aperture 400 mm, f/2.0 - f/3.25.
The Slevogt system has the advantages of the spherical secondary and a flat field and is fast because of its low |m2|; but its increased length, high obstruction and final image position are much less favourable than the geometry of Fig. 3.45.
File : C:\ZEMAX-EE\BAKER.RAY
Date : Fri Mar 03 1995
GENERAL LENS DATA:
Surfaces Stop System Aperture Ray aining Gaussian Factor Eff. Focal Len. Total Track Image Space F/# Working F/# Ohj. Space N.A. Stop Radius Parax.Ima. Hgt. Parax. Mag. Entr. Pup. Dia. Entr. Pup. Pos. Exit Pupil Dia. Exit Pupil Pos. Maximum Field Primary Wave Lens Units Angular Mag.
Field Type: Angle # X-Value
1 0.000000 2 0.000000 3 0.000000
i degrees Y-value 1.000000 0.700000
Weight 1.000000 1.000000
Was this article helpful?