Page 320 - Modern Optical Engineering The Design of Optical Systems

Optical System Layout 299

Figure 13.7 In a Galilean tele-
scope, the field of view is deter-
mined by the diameter of the
objective lens and the location of
the exit pupil, which is usually
the pupil of the observer’s eye.

the ray through, then scaling the ray data by an appropriate constant
(as indicated in Chap. 9) to make the ray height at the objective equal to
one-half its clear aperture. To simplify matters, we will assume here
that the pupil is coincident with the eyelens; thus, u e is equal to half
the objective diameter divided by the spacing between the lenses, or
0.05 radians in this instance. Since MP u e /u o per Eq. 13.4, we can
solve for u o 0.05/4 0.0125 radians. The total real field is 0.025 radians
(about 1.5°), considerably less than that of the inverting telescope dis-
cussed above. Note that the same type of field vignetting considera-
tions as discussed related to the eyelens of the astronomical telescope
may be applied to the objective of the Galilean telescope. One must
also bear in mind that the direction of the Galilean field of view can be
changed by a lateral shift of the viewer’s eye; this is not true for a tele-
scope with a real internal image when the field stop is located at the
image.
For the erecting telescope example, we will lay out a telescopic rifle
sight, with a magnification of 4 , a length of 10 in, and a maximum
lens diameter of 1 in, as before. For small-caliber (.22) rifles, a 2-in eye
relief is acceptable; for heavier guns, eye reliefs of 3 to 5 in are common.
Let us assume that we desire an eye relief of 4 in and design the tele-
scope accordingly. The entrance pupil (at the objective) has a diameter
of 1 in; by Eq. 13.7, the exit pupil diameter is thus 0.25 in. Again by
Eq. 13.6, the apparent field at the eyepiece (u e ) is equal to 4u o , where
u o is the real field. With reference to Fig. 13.8, it is apparent that u e is
limited by the diameter of the eyelens and that for an unvignetted

Figure 13.8 Optics of a simple erecting telescope.