The above simple, approximate theory of atmospheric refraction is quite adequate for ADC systems because the match of real glasses to the atmospheric dispersion function is anyway only a rough approximation.

From (4.92), it follows immediately that the approximate formula for atmospheric dispersion for the wavelength range na1 to na2 is

For the same conditions, we can calculate the approximate value of firef from (4.91). Z = 70° gives firef = 164.2 arcsec. For the range 300-800 nm, (4.94) gives with (na - 1) = 0.000 289 8 as the effective value from (4.91) and (4.92) and the dispersion from Table 4.1

(5firef )z=7o° = 9.92 arcsec The corresponding values for Z = 45° are firef = 59.8 arcsec and

For a more modest range 400-800 nm, the equivalent dispersions are 4-65 arcsec and 1-69 arcsec. These values reveal how serious atmospheric dispersion is compared with modern image requirements of 0.5 arcsec or better, and the need for effective ADC.

Wallner and Wetherell [4.52] point out the practical value of zero-deviation solutions to avoid vignetting and pointing changes and suggest a Risley variable dispersion prism solution based on two zero-deviation prisms, each delivering finite dispersion from two different glasses, which are mutually rotated against each other to vary the dispersion and compensate the atmospheric dispersion for different values of Z. In fact, Wallner and Wetherell were not concerned with the general case of correcting a telescope image, but rather with the special case of speckle cameras. Such systems had already been described for this purpose by Beddoes et al. [4.57] and Breckenridge et al. [4.58]. It is possible for speckle purposes to mount the ADC in a parallel or nearly parallel beam, when prisms introduce no aberrations. The basic principles of ADC for a normal Cassegrain telescope, with a converging beam, were laid down in an admirable paper by Wynne [4.59].

Wallner and Wetherell investigated in detail the possibilities of glass pairs matching as closely as possible the dispersion - wavelength function of the atmosphere. Their aim was to achieve, for speckle purposes, diffraction limited ADC performance over a wide spectral band (350-1300 nm) for apertures up to 25 m! They achieve this for the Schott glass pairs LaF24/KF9 and (better) LaKN14/K11. The former pair gives serious absorption problems.

Wynne [4.59] demonstrates that the above approach has little relevance to the general problem of ADC at the Cassegrain focus. The converging beam will produce well-known aberrations due to the prism pairs as plane-parallel plates (see § and references [3.3] and [3.6] of Chap. 3) and other, more complex decentering aberrations if the surfaces are not normal to the telescope axis. If the individual prisms have the same refractive index for the central wavelength, then the zero-deviation requirement will give identical angles for the unit prisms and each prism pair will be, monochromatically, simply a plane-parallel plate perpendicular to the axis. Two such pairs in op-

Fig. 4.26. Dispersion variation by opposite rotation of two prism pairs posite directions will produce a zero resultant dispersion vector. If the pairs are rotated through an angle ±a in opposite directions about the telescope axis, the resultant vectors increase giving a maximum with rotations of ± 90° (Fig. 4.26). The effect is a vertical dispersion vector, variable between 0 and 2V where V is the dispersion of an individual pair. The necessary direction of the resultant vector will depend on the mount and attitude of the telescope and is achieved by a supplementary rotation of the entire unit. Two air-glass surfaces can effectively be economised by using an optical immersion oil between the pairs, as used by Breckenridge et al. [4.58]. The dispersions of the two glasses should be as different as possible to reduce the prism angles, since the inclined faces still produce chromatic variations of aberrations for wavelengths away from the central wavelength. Similarly, the ADC should be as far from the image as possible since this distance is the lever arm for it to produce transverse compensating dispersion: the necessary prism angles reduce linearly with this focal distance. However, a greater focal distance increases the size and hence the necessary thickness of the prisms: their effect as plane-parallel plates increases. Wynne [4.59] points out that the longitudinal chromatic aberration C1 is by far the most serious effect and that this can be entirely removed by arranging that the glasses in oiled contact have different dispersions and that the contact surfaces be given a slight curvature instead of being plane.

Wynne gives preliminary results for such an ADC for the William Her-schel 4.2 m telescope (f/11). The (Schott) glasses chosen were UBK7 and

LLF6 to give maximum dispersion difference with adequate transmission. The ADC was placed 2 m from the focus. Correction up to Z = 71.6°, giving an uncorrected lateral chromatic aberration of 5.8 arcsec between 340 and 800 nm, required prism angles of 1.506° and 1.454°. With single prism elements of central thickness 17 mm the contact surfaces had a radius of curvature of 50 m to correct C1. The residual aberrations over the whole spectral range are negligible, less than 0.05 arcsec, in the field centre, with very small changes over a field of 3.7 arcmin diameter. The limitation to optical quality is due to mismatch of the dispersion relative to the atmosphere, the problem considered by Wallner and Wetherell [4.52]. This amounts to about 7% of the atmospheric dispersion, i.e. about 0.4 arcsec for this spectral range at Z = 71.6°. This limitation is fundamental, unless the requirement of roughly equal central refractive indices is abandoned, as the work of Wallner and Wetherell showed, or more exotic materials are used (Fig. 4.27). Their preferred glass pairs had a very large index difference of about 0.2. It should be noted that tan 71.6° = 3. From (4.92) it follows that this 7% dispersion discrepancy reduces to only about 0.14 arcsec at Z = 45°.

300 365 500 700 900 1014

Wavelength (nm)

Fig. 4.27. Performance of the ADC designed by Wynne and Worswick for the William Herschel 4.2 m telescope with Z = 70o. Curve A shows the uncorrected atmospheric dispersion; curve B the correction achieved with the glasses used (UBK7 and LLF6); curve C what could be achieved with FK50 and Calcium Fluoride. (After Wynne and Worswick [4.60])

300 365 500 700 900 1014

Wavelength (nm)

Fig. 4.27. Performance of the ADC designed by Wynne and Worswick for the William Herschel 4.2 m telescope with Z = 70o. Curve A shows the uncorrected atmospheric dispersion; curve B the correction achieved with the glasses used (UBK7 and LLF6); curve C what could be achieved with FK50 and Calcium Fluoride. (After Wynne and Worswick [4.60])

In a later paper, Wynne and Worswick [4.60] give the complete aberration theory of such ADC for the Cassegrain focus, also spot-diagrams of the precise performance of the ADC (within 0.1 arcsec) for the 4.2 m telescope. Figure 4.27, reproduced from their paper, shows the correction relative to the uncorrected atmospheric dispersion at Z = 70° from 365-1014 nm.

As an independent Cassegrain ADC, the designs of Wynne and Worswick [4.60] appear to be the definitive solution. Their aberration analysis shows, moreover, that such simple systems are impracticable for typical PF focal ratios (f/3.5 or faster) because of unacceptable amounts of spherical aberration and coma arising from the thicknesses. Of course, this assumes the ADC is added to an existing telescope corrector. If the ADC is integrated in the corrector, as envisaged by Epps et al. [4.36], then compensations within the system may well be feasible.

Wynne [4.61] further analysed the possibilities of an independent ADC for the PF case. If the equivalent plane-parallel plates of the prism pairs are replaced by menisci, concentric to the focus, there will be no spherical aberration or longitudinal chromatic aberration. The sagittal field curvature is also zero but the tangential field curvature is twice the Petzval sum of the meniscus system, giving astigmatism. Wynne estimated this astigmatism to give about 0.5 arcsec aberration at the edge of a field diameter of 28 arcmin for the 3.6 m, f/3.2 PF of the Anglo-Australian Telescope (AAT). Logically, the ADC would be placed in front of the PF corrector. This aberration can easily be compensated in the corrector, with the disadvantage of limiting the corrector field if the ADC is removed for near-zenith observations. An oiled contact ADC has only two air-glass surfaces and may well be left in place. If a fully integrated design is envisaged, larger meniscus thicknesses become possible, so that sufficient dispersion may be available for a facility equivalent to an objective prism.

Wynne's work on ADC for prime focus correctors (PF) was reported more completely by Wynne and Worswick [4.62] with a detailed analysis of the aberration theory in this focus. Two cases were investigated, as shown in Fig. 4.28. It was found that the effective thick meniscus in front of a normal 3- or 4-lens PF corrector, if the whole system is re-designed, actually slightly

Fig. 4.28. Configurations of prisms for maximum dispersion setting, in cases 1 and 2 (angles exaggerated) for ADC in the prime focus (PF). (After Wynne and Worswick [4.62])
Fig. 4.29a. Spot-diagrams, reproduced from Wynne and Worswick [4.62], for their PF ADC for the 4.2 m, f/2.5 William Herschel Telescope. (a) Zero dispersion setting

improves the performance. This enables the use of a thicker meniscus with more powerful dispersions, giving an objective prism facility. In this case, the inclination angles are no longer negligible as they are for normal ADC, making Case 2 in Fig. 4.28 preferable. For the normal application limited to ADC, it is unimportant whether Case 1 or Case 2 is used.

Figure 4.29 gives the spot-diagrams for the ADC case of modest prism angles for 7 field positions and 5 wavelengths. (a) is for zero dispersion setting, (b) for ± 45° and (c) for maximum dispersion ± 90°. The field diameter is 40 arcmin.

Fig. 4.29b, c. Spot-diagrams, reproduced from Wynne and Worswick [4.62],for their PF ADC for the 4.2 m, f/2.5 William Herschel Telescope. (b) At± 45° and (c) maximum dispersion setting ± 90°

Bearing in mind the rotations of the spot-diagrams for different parts of the field, it is clear that the ADC causes negligible deterioration of the performance of the total corrector system. The glasses are UBK7 and LLF6, as in the Cassegrain case above. The authors also give spot-diagrams for a system some seven times more powerful for use as an objective prism. Inevitably, there is now appreciable effect of the prism system at ± 45°, but very little at ± 0° and ± 90°.

Another account of the above ADC-corrector systems has been given by Bingham [4.63], who shows the section through the finalised total system with an ADC prism arrangement as in Case 1 of Fig. 4.28. This is reproduced in Fig. 4.30. The ADC glasses are PSK3 and LLF1, and the contact layer is flat. The WHT primary is a paraboloid. Bingham also shows a similar ADC-corrector (the latter with 4 lenses) for an f/1.6 parabolic primary giving an f/2.0 final image. The image quality is similar over a somewhat reduced field of 30 arcmin diameter.

The PF systems described above use ADCs consisting of prisms with curved faces, that is combinations of lenses and prisms; or, putting it another way with spherical surfaces, off-axis sections of lenses.

In 1986 Su [4.64] proposed Cassegrain correctors in which the ADC feature is integrated into a doublet corrector. He called the lens-prism combinations "lensms". Figure 4.31 shows the form of his corrector, reproduced from his

Fig. 4.30. Section through the complete ADC-corrector systemfor the 4.2 m, f/2.5 PF of the WHT, reproduced from Bingham[4.63]

Fig. 4.30. Section through the complete ADC-corrector systemfor the 4.2 m, f/2.5 PF of the WHT, reproduced from Bingham[4.63]

Lensm I

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