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Optical System Layout 291

where s 2 and s 1 are the erector conjugates as indicated in Fig. 13.1c. For
a scope as shown, f o , f e , and s 2 are positive signed quantities and s 1 is
negative. The resulting MP is thus positive, indicating an erect image.
An afocal system is the basis of the laser beam expander. The beam
diameter of a laser is enlarged by a factor equal to the MP when the
laser beam is sent into the eyepiece end of the telescope. Expansion of
the beam reduces the beam divergence. The Galilean form (Fig. 13.1b)
is usually preferred because there is no focus (which can cause a break-
down of the air if the laser is powerful) and the optical design charac-
teristics are more favorable. However, the Keplerian form (Fig. 13.1a)
is used when a spatial filter (a pinhole at the focus) is necessary.
An afocal system can also be used to change the power, focal length,
and/or the field of view of another system by inserting it in a space in
the system where the light is collimated (i.e., where the object or image
is at infinity.) (See Sec. 17.4 and Fig. 17.34.)
Note that an afocal system can be used to image objects which are not
at an infinite distance. For example, the exit pupil of a telescope is the
image of the aperture stop, which is usually at the objective lens. Again,
a consideration of the rays diagramed in Fig. 13.1 will indicate that the
linear magnification m is the same, regardless of where the object and
image are located. The magnification m h′/h is equal to the recipro-
cal of the angular magnification, MP. Thus, m h′/h 1/MP. Note that
if the aperture stop is placed at the internal focus, then an afocal system
becomes telecentric in both object and image space.

13.2 Field Lenses and Relay Systems

In a simple two-element telescope as shown in Fig 13.2a, the field of
view is limited by the diameter of the eyelens (as was discussed at
greater length in Chap. 9). In the sketch, the solid rays indicate the
largest field angle that a bundle may have and still pass through the
telescope without vignetting; for the bundle represented by the dashed
rays, only the ray through the upper rim of the objective gets through,
and vignetting is effectively complete.
The function of a field lens is indicated in Fig. 13.2b. If the field lens
is placed exactly at the internal image, it has no effect on the power of
the telescope, but it bends the ray bundles (which would otherwise miss
the eyelens) back toward the axis so that they pass through the eyelens.
In this way the field of view may be increased without increasing the
diameter of the eyelens. Note that the exit pupil is shifted to the left,
closer to the eyelens, by the introduction of a positive field lens. The
distance from the vertex of the eyelens to the exit pupil is called the
“eye relief” (since the eye must be placed at the pupil to see the full field
of view). The necessity for a positive eye relief obviously limits the