o in which n0 is the refractive index at the central (correction) wavelength A0 and ni that for any other wavelength A i. The dispersion function

of the glass of the corrector is therefore the function determining the sphe-rochromatism for a constant (SWj*)0 resulting from the primary mirror of the Schmidt telescope. For a typical glass, e.g. Schott UBK7 chosen for favourable UV transmission, this dispersion curve is shown in Fig. 3.30. We shall profit from the excellent example of the achromatic Schmidt telescope to illustrate the dispersion properties of optical glasses, leading to the chromatic effects of "primary and secondary" spectrum.

The slope of the mean straight line of this function gives the primary spectrum effect. So-called "normal" glasses have a similar departure from the straight line called a "normal" secondary spectrum effect. The significance in the correction of achromatic doublets is dealt with by Bahner [3.5] and Welford [3.6]. The same physical situation as in Fig. 3.30 applies except that the ordinate is replaced by the back focal distance s' of the image as a function of wavelength. In both cases, the process of achromatisation combines a dispersion function with positive slope with another one of equal negative slope to give a resulting function of minimum slope over the wavelength

Fig. 3.31. The effect of achromatisation: the dispersion function is rotated to minimize its slope, giving desired zero points Ai and A2

range used, as shown in Fig. 3.31. If two "normal" glasses are combined, the resulting curvature of the dispersion function will be little changed, leaving a "normal" uncorrected secondary spectrum effect. This achromatisation process is only possible if the dispersion functions (vA)a and (va)r for the two elements a and 0 (glasses) are different: otherwise, the residual optical power in the case of a lens doublet, or the residual correction of <5Sf in the Schmidt plate case, would be zero. Fortunately, a wide variety of glasses with different dispersions and refractive indices n0 are available (Fig. 3.32). The larger the difference in 1/va, the easier the combination, in that the individual powers (achromatic doublet) or asphericities (achromatic Schmidt corrector) will be less extreme.

For simplicity, we will now omit the plate stop shift <5 of <5Sj, <5Wj etc., corresponding to Eq. (3.215), since the spherical aberration is independent of stop shift and <5Sj = Sj, <5Wj = W'. Then from (3.244), the conditions for achromatisation between A0 and A for the Schmidt corrector are

for the required total correction, giving

The asphericities are both proportional to 1/(vAa - var ). Note that the wavelengths A0 and A 1 used in (3.266) will not normally coincide with the conventional definition of va used in Fig. 3.32. The wavelengths and corresponding definitions of VAa and va^ must be adapted to the astronomical

requirements of the Schmidt telescope. For large sizes of the order of 1 m, the choice of glasses is limited by availability and considerations of absorption in the UV and blue. For the ESO 1m Schmidt telescope, the original singlet corrector was replaced by an achromat made from the glasses UBK7 and LLF6, the latter giving an adequate difference (vAa — va{3) together with acceptable transmission. Glasses further to the right in Fig. 3.32 than LLF6 contain increasing amounts of lead with unacceptable absorption in the blue.

The manufacture of such an achromatic plate is a very difficult technical undertaking. Apart from making the individual aspheric plates, the manufacturer must normally combine them in a total precision unit with optical cement between the elements. The cement should ideally have a refractive index intermediate between those of the plates in order to reduce light loss and, above all, ghost images at two extra reflecting surfaces. According to the law of Fresnel, the intensity of reflected light at the boundary between media of refractive indices n 1 and n2 is n2 + n 1

If n2 = 1.5 and n 1 = 1 for air, (3.269) gives the normal figure for (untreated) glass surfaces in air of I ~ 4%. If the cement reduces (n2 — n 1) by a factor of ten to 0.05, the reflections are reduced by a factor of 100.

Figure 3.33 shows the spot-diagrams of the (theoretical) ESO 1 m achromatic Schmidt in the same format as Fig. 3.29, but with a scale five times as large. The residual spherochromatism is small compared with the grain of the photographic plates. In practice, this gain must be offset by manufacturing errors of the corrector plates which produce a uniform degradation over the field. This is a matter to be defined by contractual tolerances.

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