Page 315 - Modern Optical Engineering The Design of Optical Systems

294 Chapter Thirteen

a larger exit pupil. From Eq. 13.5, it is apparent that the maximum
effective clear aperture for an ordinary telescope objective is thus limited
to a diameter of about 3-mm times the magnification. In practice, this
is, however, a fairly flexible situation. In surveying instruments exit
pupils of 1.0 to 1.5 mm are common, since size and weight are at a
premium and resolution is the most desired characteristic. In ordinary
binoculars, a 5-mm pupil is usually provided; the added pupil diameter
makes it much easier to align the binocular with the eyes. For the
same reason, rifle scopes usually have exit pupils ranging in size from
5 to 10 mm. Telescopes and binoculars designed for use at low light
levels (such as night glasses) usually have 7- or 8-mm exit pupils in
order to obtain the maximum retinal illumination possible when the
pupil of the eye is large.
In Chap. 8, it was indicated that the resolution of the eye was at best
about one minute of arc; Chap. 9 indicated that the angular resolution
of a perfect optical system was (5.5/D) seconds of arc when the clear
aperture of the system (D) was expressed in inches. One or both of
these limitations will govern the effective performance of any tele-
scope, and for the most efficient design of a telescope, both should be
taken into account. If two objects which are to be resolved are sepa-
rated by an angle , after magnification by a telescope their images
will be separated by (MP) . If (MP) exceeds one minute of arc, the eye
will be able to separate the two images; if (MP) is less than one
minute, the two objects will not be seen as separate and distinct. Thus,
the magnification of a telescope should be chosen so that

1
MP ( in minutes)

0.0003
( in radians) (13.8)

where is the angle to be resolved. For critical work, a magnification
value considerably larger than indicated in Eq. 13.8 is often selected
in order to minimize the visual fatigue of the viewer.
From the opposite point of view, since the resolution of a telescope
(in object space) is limited to (5.5/D) seconds, it is apparent that the
smallest resolved detail in the image presented to the eye will subtend
an angle of (MP) (5.5/D) seconds, and if this angle equals or exceeds one
minute, the eye can discern all of the resolved details. Equating this
angle to one minute (60 seconds), we find that the maximum “useful”
power for a telescope is

MP 11D (13.9)