from (2.55). Combining (2.83) with (2.82) gives finally with L/s2 = m2
This is probably the most useful of all the paraxial formulae for Gregory and Cassegrain telescopes, for the following reason. In setting up the telescope design parameters it is normal to start with the diameter and the f/no of the primary, thereby defining f1. Also, the position of the final image I2 behind the primary is defined by technical considerations. This defines P. Usually a final f/no for the emergent beam is envisaged, which defines m2 from (2.55). Then Eq. (2.84) gives f2 = r2/2. The fundamental parameter remaining, which is dependent, is Ra. From (2.58) and (2.82), we have
These forms are useful, but a clearer indication of the driving parameters is given by substituting for P from (2.81) to give
A f1 (m2 - 1) m2 - 1 where b = b = L +(1 - Ra) , (2.87)
Equation (2.86) makes it clear what must be changed if Ra is too high (assuming b ^ |). m2 must be increased. So either f must be increased or f1 reduced. If the latter is preferred, to maintain the Light Transmission Power, the primary will be steeper and more difficult to make, but T will be increased giving a more compact solution. The denominator of (2.86) reveals the superiority of the Cassegrain form again since it is larger, m2 being negative in the Cassegrain form, if |m2| is the same for Gregory and Cassegrain solutions.
If f2 and P are given parameters, Eq. (2.84) gives for m2:
Finally, there are useful relations linking f2,L and m2. From (2.55) and (2.81) we have
Substitution in (2.84) gives the simple relation f2 = = £2 (mm+1) , (2.90)
from (2.55), a result which is also given directly by the reflection equation (2.35). We shall see in Chap. 3 that this is one of the most important paraxial relations in the aberration theory of 2-mirror telescopes.
The 'position of the entrance pupil has no influence on the Gaussian parameters of these telescope systems, but it does affect the diameters of the mirrors required. Conventionally, the entrance pupil is placed at the primary for the simple reason that the primary is the most difficult and expensive element in the system and is most efficiently used in this way. In this case, a supplement in diameter at the secondary is required if vignetting in the field is to be avoided. For the axial beam at the secondary, we have from (2.72)
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