Page 194 - Modern Optical Engineering The Design of Optical Systems

Stops, Apertures, Pupils and Diffraction 177

Notice that the initial and final intersections of the dashed principal
ray with the axis locate the pupils, and that the diameter of the axial
cone of rays at the pupils indicates the pupil diameters. It can be seen
that, for any point on the object, the amount of radiation accepted by,
and emitted from, the system is determined by the size and location
of the pupils. Note that any image of the aperture stop is a pupil. In
Fig. 9.2 there is a pupil at diaphragm #1.

9.3 The Field Stop
By following the path of the principal ray in Fig. 9.2, it can be seen that
another principal ray starting from a point in the object which is farther
from the axis would be prevented from passing through the system by
diaphragm #2. Thus, diaphragm #2 is the field stop of this system.
The images of the field stop in object and image space are called
the entrance and exit windows, respectively. In the system of Fig. 9.2, the
entrance window is coincident with the object and the exit window is at
infinity (which is coincident with the image). Note that the windows of a
system do not coincide with the object and image unless the field stop
lies in the plane of a real image formed by the system.
The angular field of view is determined by the size of the field stop,
and is the angle which the entrance or exit window subtends from the
entrance or exit pupil, respectively. The angular field in object space is
frequently different from that in image space. (Alternate definition:
the angular field of view is the angle subtended by the object or image
from the first or second nodal point of the system, respectively. Thus,
for nontelescopic systems in air, object and image field angles are
equal according to this definition. Note that this definition cannot be
applied to an afocal system, which has no nodal or principal points.)

9.4 Vignetting
The optical system of Fig. 9.2 was deliberately chosen as an ideal case
in which the roles played by the various elements of the system are
definite and clear-cut. This is not usually the situation in real optical
systems, since the diaphragms and lens apertures often play dual roles.
Consider the system shown in Fig. 9.3, consisting of two positive
lenses, A and B. For the axial bundle of rays, the situation is clear; the
aperture stop is the clear aperture of lens A, the entrance pupil is at
A, and the exit pupil is the image, formed by lens B, of the diameter of
lens A.
Some distance off the axis, however, the situation is markedly diffe-
rent. The cone of energy accepted from point D is limited on its lower
edge by the lower rim of lens A and on its upper edge by the upper rim