Page 314 - Modern Optical Engineering The Design of Optical Systems

Optical System Layout 293

system without vignetting. The dashed rays emerging from lens A will
indicate the large diameters which would otherwise be necessary to
cover the same field of view. This type of system is used in periscopes
and endoscopes.
An optimum arrangement for most optical systems is often the layout
with the least total amount of lens power. In a periscope system the
minimum power system is simple to design. Given the maximum lens
diameter (which is determined by the available space) the image at the
field lenses is arranged to fill this diameter, and the clear aperture of
the relay lens is filled with the beam. Thus, with reference to Fig. 13.3,
the focal length of the objective is set equal to the field lens CA divided
by the total field of view, and the distance from A to B is the product of
the relay lens CA times the f-number of the objective lens. Lenses B, C,
D, etc., all have the same focal length, which is half the distance from
A to B, and lenses B, C, D, etc., are all working at unit magnification
(m 1). This arrangement yields the minimum lens power for the
system; this is the best layout for a periscope system.
An endoscope is a miniature periscope used to examine the inside of
a cavity through a small orifice; they are widely used in medical appli-
cations. The size of the optics in a medical endoscope is on the order of
2 or 3 mm in diameter. The equivalent air path is the actual physical
path divided by the index of refraction. In an endoscope or periscope,
the number of relay stages is determined by the length of the instru-
ment. If the airspaces are filled with glass, the equivalent air path is
shortened by a factor equal to the index of the glass, and the number
of relay stages is thereby reduced. Rather than simply fill the spaces
with rods of glass, the relay lenses are typically made as cemented
doublets, with the flint (negative) element made thick enough to fill the
space. The outer surface of the flint is made convex so that it functions
as the field lens. This is often referred to as a rod-lens endoscope. The
reduction in the number of relay components both reduces the cost of
the endoscope and improves the image quality (especially by reducing
the secondary spectrum and the Petzval field curvature).

13.3 Exit Pupils, the Eye, and Resolution
Since almost all telescopes are visual instruments, they must be
designed to be compatible with the characteristics of the human eye.
In Chap. 8, we saw that the pupil of the eye varied in diameter from
2 mm to about 8 mm, depending on the age of the viewer and the
brightness of the scene being viewed. Since the pupil of the eye is, in
effect, a stop of a telescopic system, its effect must be considered. For
ordinary use, an exit pupil of 3-mm diameter will fill the pupil of the
eye and no increase in retinal illumination will be obtained by providing