Page 311 - Modern Optical Engineering The Design of Optical Systems

290 Chapter Thirteen

From Chap. 9 we recall that the exit pupil of a system is the image
(formed by the system) of the entrance pupil. In most telescopes the objec-
tive clear aperture is the entrance pupil and the exit pupil is the image
of the objective as formed by the eyelens. Using the newtonian expres-
sion relating object and image sizes (h′ hf/x), and substituting CA e
(the exit pupil diameter) and CA o (the entrance pupil diameter) for h′
and h, f e for f, and f o for x, we get

CA o
f o
MP (13.5)
CA e f e
While the above derivation has assumed the entrance pupil to be at the
objective, Eq. 13.5 is valid regardless of the pupil location, as is obvious
from the rays sketched in Fig. 13.1.
We also can get a simple expression for the eye relief of the Kepler
telescope as follows:

R (MP 1) f /MP
e
The amount of motion of the eyepiece needed to focus the telescope
for someone who is nearsighted or farsighted is given by

2
Df e /1000
where is in millimeters and D is in diopters.
Equations 13.4 and 13.5 can be combined to relate the external charac-
teristics (magnifications, fields of view, and pupils) of any afocal system,
regardless of its internal construction

u e
CA o
MP (13.6)
u o CA e
The erecting telescope, Fig. 13.1c, consists of positive objective and
eyelenses with an erecting lens between the two. The erector reimages
the image formed by the objective into the focal plane of the eyelens.
Since it inverts the image in the process, the final image presented to the
eye is erect. This is the form of telescope ordinarily used for observing
terrestrial objects, where considerable confusion can result from an
inverted image. (An erect image may also be obtained by the use of an
erecting prism as discussed in Chap. 7.) The magnification of a terres-
trial telescope is simply the magnification that the telescope would
have without the erector, multiplied by the linear magnification of the
erector system
s 2
f o
MP (13.7)
f e s 1