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Fig. 9.9 Anastigmatic Littrow mounting spectrograph with a double-pass single lens and corrector plate. The mounting is telecentric if the grating is at the distance fL from the lens

Fig. 9.9 Anastigmatic Littrow mounting spectrograph with a double-pass single lens and corrector plate. The mounting is telecentric if the grating is at the distance fL from the lens

In this design the transverse magnification is M = -1 for the central wavelength. The amount of Sphe 3 to be corrected by the aspherical plate can be derived from (9.5a). Setting c2 = 0, i.e. B = 1 for a convexo-plane lens, and u'2 = 0 i.e. C = 1 for an image at infinity, this amount simply reduces to x4

From (1.68), Sphe 3 of a concave and spherical mirror for an object at infinity is expressed by x4

where its focal length f is negative.

Let us denote OLens = fL/D = fL/2xmax and Omit = -fM/D = -fM/2xmax the focal ratios of the lens and of the mirror. The above expressions become

64^Lens

If their amount of Sphe3 are the same, i.e. SI|Lens = SI|Mir, and also their clear apertures D, we obtain a relation between the focal length of the lens and that of the mirror. Considering their focal ratios, this relation is

Hence we may compare the f-ratio of a lens-and-plate design with that of a plate-and-mirror Schmidt when they both use the same aspherical plate:

^ If the refractive index of a lens isn = 3/2, then an aspherical plate correcting a spherical mirror at f/3-03 also corrects a convexo-plane lens at f/(62/3 x 3-03) = f/10.

For instance, the single lens and corrector plate design was used in cross-dispersion spectrographs with white pupil transfer for high spectral resolutions (cf. Coravel-Ohp and Cashawec-Cfht, Baranne et al. [11]).

References

1. W.T. Welford, Aberrations of Optical Systems, Adam Hilgeredt., England, 4th edition (2002) 465, 466,467

2. H. Chretien, Calcul des Combinaisons Optiques, Masson edt., Paris, 5th issue (1980) 465,473

3. M. Born, E. Wolf, Principles of Optics, Cambridge Univ. Press, New York (1999) 465, 473

4. H. Coddington, A Treatise on the Reflexion and Refraction of Light, London (1829) 465

5. R. Descartes, La Geometrie LivreII, and La Dioptrique, in Discours de la Méthode, Adam & Tannery edt., 389-441 (1637), reissue Vrin edt., Paris (1996) 468

6. C. Zeiss, Photographic Objectives, Palmos Hand Cameras, Jena (1902). Facsimile edition of this catalog by N.J. Clifton, The Zeiss Historica Society edt., Toronto (1990) 473

7. R. Kingslake, A History of the Photographic Lens, Academic Press, San Diego 4th issue (1989) 473

8. M. Laikin, Lens Design, Marcel Dekker edt., New York, 2nd issue (1995) 473

9. S.P. Timoshenko, Theory of Elasticity, McGraw-Hill edt., New York, 299 (1970) 476,486

10. G. Lemaitre, Elasticité et Optique Astronomique, Doctoral thesis dissertation, Universite de Provence, Aix-Marseille I (1974) 476, 479

11. A. Baranne, M. Mayor M., J-L. Poncet, CORAVEL - A new tool for radial velocity measurements, Vistas Astron., 23, 279 (1979) 489

Chapter 10

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