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f ' (Ni)

2.2.5.2 Basic compound telescopes with two powered mirrors. The two most important telescope forms with two powered mirrors are those invented early in the history of the reflector, the Gregory and Cassegrain forms, shown in Figs. 2.11 and 2.12 respectively. We shall establish a number of paraxial relationships which are common to both these forms and are of great importance, not only for the Gaussian layout of telescopes but also in the general aberration theory of Chap. 3.

Gaussian Beam Telescope

As stated in ยง 2.2.4 above, the Gregory form is the equivalent of a defo-cused Kepler-type refractor, the Cassegrain of a defocused Galileo-type. The image side principal planes P are constructed as shown, the Gregory form having then a negative focal length f , the Cassegrain form a positive f . The object side principal planes P, constructed by tracing a parallel beam backwards into the system from the right, lie well to the left of the system and to the left of the image principal planes P in both cases. If the telescopes are made afocal, with I1 at the focal point of M2, the principal planes are at infinity.

Although the operation may at first sight seem trivial, it is very instructive to trace the paraxial ray through the system using Eqs. (2.36) - (2.38) step by step, for example with the normalized data of Cases 3 and 7 of Table 3.3 in Chap. 3 where the paraxial parameters are used for calculating the third order aberrations. The ray trace for the first surface (prime focus) is common to both Gregory and Cassegrain. Table 2.2 shows the signs of the paraxial quantities, the most important aspect being the sign reversals in certain cases between the Gregory and Cassegrain forms.

The strong shifts of the principal planes with the analogy of the defocused refracting telescopes indicate the most important property of the Gregory and Cassegrain forms: they are strong telephoto systems because the power of the

Spherical Aberration Telescope

primary is largely annulled by the secondary. This situation is expressed by the equivalent relationship to Eq. (2.52) for the total residual power of two separated mirrors, which can be written [2.3]:

where d x/n 1 is the effective optical separation of the mirrors. If all the refractive indices are set to +1, this reduces to the lens formula of (2.52). For our 2-mirror case and with our sign convention of Table 2.2, n 1 = n2 = n = +1 and n1 = -1 in the normal case in air. The separation d1 is negative in both cases as is /1 = r1/2; while /2 = r2/2 is positive in the Gregory and negative in the Cassegrain case. Eq. (2.53) reduces to

In both the Gregory and the Cassegrain case, |d1| is slightly greater than for the afocal case, giving an |/ | far larger than |/1|. / is then negative for Gregory and positive for Cassegrain. The strong telephoto effect is evident from the construction of Figs. 2.11 and 2.12.

Another obvious way of interpreting the telephoto effect is to consider the secondary as a magnifier increasing the effective focal length without increasing the length of the system. This brings up the important question of the definition of the magnification m2 of the secondary.1 For an optical

1 I am deeply grateful to Dr. Daniel Schroeder for querying this matter, leading to an excellent discussion by correspondence. As a result, a more detailed justification of the definition I chose in this book is now given here for the 2nd. edition.

Table 2.2. Gregory and Cassegrain telescope forms: sign of paraxial ray trace quantities (*denotes sign inversion between Gregory and Cassegrain)

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