## F21

while, for the field, the supplement (ypr)2 given by

is required, for an object at infinity. The total diameter (Dtot)2 is then given by

The position of the exit pupil in the normal case of entrance pupil at the primary is determined by tracing a paraxial ray from the primary to the secondary. If this is turned round and the ray traced from left to right in the normal way, Eq. (2.35) gives

in which (s2)e is the exit pupil distance from the secondary, (s2)e the entrance pupil distance and (r2)s the radius of curvature of the secondary in the reversed ray trace. Now (r2)s is 'positive in the Cassegrain form (Fig. 2.13) and (s2)e is negative, i.e. -|di|. Therefore, in the Cassegrain form, (s2)e is always positive, i.e. the exit pupil always lies behind the secondary, somewhat nearer than the prime focus Ii if b > 0. In the Gregory form, (s2)e is always negative, so the exit pupil lies in front of the secondary, again somewhat nearer than the prime focus if b > 0.

In spite of the advantages of efficient use of the primary in the conventional choice of the entrance pupil E at Mi, the increasing importance of infra-red observation in astronomy often forces the decision to place the aperture stop of the telescope at the secondary. Since there is no subsequent element with

Fig. 2.13. Exit pupil position E in the Cassegrain form with the entrance pupil E at the primary

optical power, the secondary then becomes the exit pupil E . The paraxial image of the secondary in the primary is then the entrance pupil E. Tracing from E at M2 to Mi gives from Fig. 2.14

Now (ri)g and (si)e are both negative. In the Cassegrain form |(ri)g| > 2|di|, so the denominator is always positive, as is also the numerator. Therefore, (si)e is always positive, giving a virtual entrance pupil to the right of the primary. With the geometry of Case 3 in Table 3.3 (Chap. 3), the distance MiE is +3.44|fi|. In the Gregory form 2|di| > |(ri)g|, so that the denominator of (2.Q5) is always negative, the numerator always positive. The entrance pupil E is therefore real and in front of the primary. With the geometry of Case 7 of Table 3.3, MiE _ —5.44|fi |. In both Cassegrain and Gregory forms, a supplement will have to be added to the diameter of Mi if vignetting of the field is to be avoided. The supplement is 2|(ypr)i| where (ypr)i is given by

The reader is reminded of the remarks in § 2.2.3 concerning the means of fixing the aperture stop in an optical system. If, in a telescope laid out to have its stop at the primary without vignetting at the secondary, a stop is laid over the secondary such that the axial beam at the primary is reduced to the extent required to accommodate the required field surplus according to (2.Q6) with its actual diameter, then the exit pupil is at the secondary and no vignetting takes place. This conversion process represents an elegant solution to the problem of switching between the aperture stop at the primary and the secondary. However, the diaphragm over the secondary has to be designed to give an acceptable level of IR emissivity.

In Tables 2.1 and 2.2 above, we gave a list of the paraxial ray trace quantities to indicate the signs for use in the Gregory and Cassegrain forms in the numerous relations derived. These relations also include some derived quantities. Since correct use of the signs is essential, these are given in Table 2.3.

Fig. 2.14. Entrance pupil position E in the Cassegrain form with the exit pupil E at the secondary
 * Sign Gregory form Cassegrain form inver Positive Negative Positive Negative sion quantities quantities quantities quantities

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