## F Z S L

Taking again the data of Table 3.2 and f/g = 35, the values are d1 = -0.19375/', L = +0.225/'

S = -0.00418133/' Z = +0.729 015 £ = +3.258 650 From Table 3.5 with m2 = -4: bs1 = -1.045 563 bs2 = -3.260 541

Comparing with the values for the RC system of Table 3.2, we see that bs1 has increased by 0.89% which is negligible from a manufacturing viewpoint. However, the increase in (1 + bs1) is 25.6% which is very advantageous for prime focus correctors. The increase in bs2 is 3.18%, again negligible from a manufacturing viewpoint.

We now note a very important property which is common to most Cassegrain correctors: the value of S above must be similar to that calculated above for a Gascoigne plate for a strict RC system, in fact it is 2.82% larger than that value. This effect on the spherical aberration was only 0.026 arcsec, completely negligible. So the corrector can be removed without any effect on the axial image quality. However, it does affect the coma: this was the reason for liberating the mirror constants. We have for the contribution of the plate

and E has the same value taken for the strict RC case. So the coma on removing the plate is also 2.82% more than the value calculated above, which gives a tangential coma for our quasi-RC on removing the plate of 0.4434 arcsec at a semi-field of 15 arcmin.

Since all three conditions are fulfilled, this quasi-RC system with an as-pheric plate is the theoretical equivalent of a system of 3 aspheric mirrors with the third (plane) mirror near the focus. Such systems have been studied in detail by Schulte [4.17] and Bowen and Vaughan [4.18]. According to Gascoigne [4.9], several such telescopes had been built by 1973. Schulte [4.17] discusses the corrector for the 1.52 m quasi-RC design at Cerro Tololo, including a field-flattener, and gives a quality of less than 0.5 arcsec for a semi-field of upr = 0.75° for the wavelength range 660 nm to 340 nm. The plate is of fused silica and has a diameter of 380 mm. Gascoigne [4.9] also pointed out that a flat field of 3° diameter was realised for a 1 m telescope by using equal radii on primary and secondary and correcting with such a plate to a monochromatic quality within 0.2 arcsec.

As in the PF case, the limits will be set here by the higher order chromatic aberrations, above all chromatic differences of coma and astigmatism. These can be considerably reduced if large amounts of lateral chromatic aberration (C2) and chromatic difference of distortion are tolerated; but this is only acceptable if the use is confined to narrow spectral bands with interference filters. Normally, all of these aberrations must be reasonably balanced against each other. Figure 4.6 gives spot-diagrams for such a system based on the Cassegrain geometry of the ESO 3.6 m telescope and including a field flattener.

In view of the favourable ghost images of such correctors (see above in the introduction to this chapter) and the robust and favourable position tolerances of plate correctors, there is no doubt that such a plate corrector with a quasi-RC solution represents a very attractive design. Furthermore, the increased eccentricity of the primary in the quasi-RC solution favours the design of PF correctors in general and the Gascoigne plate for the PF in particular.

Although the effect on the spherical aberration is negligible, this does not mean that the asphericity over the whole plate diameter is small. The

File : C:\ZEMAX-EE\CAGASC.RAY Title: ESO 3.6M CASS. GASC. Date : Tue Apr 11 1995

GENERAL LENS DATA:

### Surfaces Stop

System Aperture Ray aining Gaussian Factor Eff. Focal Len. Total Track Image Space F/# Working F/# Obj . Space N.A. Stop Radius Parax.Ima. Hgt. Parax. Mag. Entr. Pup. Dia. Entr. Pup. Pos. Esit Pupil Dia. Exit Pupil Pos. Maximum Field Primary Wave Lens Units Angular Mag.

Fields :

Field Type: Angle # X-Value

1 0.000000 2 0.000000 3 0.000000

Wavelenghts :

Entrance Pupil Diameter Off

0.000000 28784.1 8943.55 7.99559 7.99533 l.Be-007 1800 376.805 0

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