Page 316 - Modern Optical Engineering The Design of Optical Systems

Optical System Layout 295

(when D is in inches). Magnification in excess of this power is termed
empty magnification, since it produces no increase in resolution. How-
ever, it is not unusual to utilize magnifications two or three times this
amount to minimize visual effort. The upper limit on effective magni-
fication usually occurs at the point when the diffraction blurring of
the image becomes a distraction sufficient to offset the gain in visual
facility.

Example 13.1
As numerical examples to illustrate the preceding sections, we will
determine the necessary powers and spacings to produce a telescope
with the following characteristics: a magnification of 4 and a length
of 10 in. We will do this in turn for an inverting telescope, a Galilean
telescope, and an erecting telescope, and will discuss the effects of
arbitrarily limiting the element diameters to 1 in.
For a telescope with only two components, it is apparent that Eqs. 13.1
and 13.4 together determine the powers of the objective and eyelens.
Thus, we have
D f f 10 in
o e
and
f o
MP 4
f e
where the sign of the magnification will determine whether the final
image is erect ( ) or inverted ( ). Combining the two expressions and
solving for the focal lengths, we get
(MP) D
f
o (MP) 1
D
f
e 1 (MP)
For the inverting telescope, we simply substitute MP 4 and D
10 in, to find that the required focal length for the objective is 8 in; for
the eyelens, it is 2 in. Since the lens diameters are to be 1 in, the exit
pupil diameter is 0.25 in (from Eq. 13.5). The position of the exit pupil
can be determined by tracing a ray from the center of the objective
through the edge of the eyelens or by use of the thin-lens equation
(Eq. 2.4), as follows:
1 1 1 1 1 1 1
0.4
s′ f s f ( D) 2 10
e
s′ 2.5 in