Page 317 - Modern Optical Engineering The Design of Optical Systems
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296 Chapter Thirteen
Figure 13.4 The inverting telescope of Example 13.1.
1
Thus, the eye relief of our simple telescope is 2
in.
2
The field of view of this telescope is not clearly defined, since it is
determined by vignetting at the eyelens, as consideration of Fig. 13.4
will indicate. The aperture will be 50 percent vignetted at a field angle
such that the principal (or chief) ray passes through the rim of the
eyelens. Under these conditions
dia. eyelens 1
u 0.05 radians
o
2D 2 10
and the real* field of view totals 0.1 radians, or about 5.7°.
This is a poor representation of what the eye will see, however, since
the vignetted exit pupil at this angle closely approximates a semicircle
0.25 in in diameter and can thus completely fill a 3-mm eye pupil. The field
angle at which no rays get through the telescope is a somewhat more
representative value for the field of view. If we visualize the size of u o
in Fig. 13.4 as being slowly increased, it is apparent that the ray from
the bottom of the objective will be the first to miss the eyelens and the
ray from the top of the objective will be the last to be vignetted out. For
the example we have chosen, with both lenses 1 in in diameter, it is
apparent that the limiting diameter of the internal image will also be
1 in. (For differing lens diameters, it is a simple exercise in proportion
to determine the height at which this ray strikes the internal focal
plane.) The half field of view for 100 percent vignetting is then the
quotient of the semidiameter of the image divided by the objective
focal length, or 0.0625 radians; the total real field is 0.125 radians,
or about 7.1°.
Thus, for an exit pupil of 0.25 in, the field of view is totally vignetted
at 0.125 rad, 50 percent vignetted at 0.1 rad, and unvignetted at
0.075 rad. These three conditions are illustrated in Fig. 13.5, and it is
*The real field of a telescope is the (angular) field in the object space. The apparent
field is the (angular) field in the image (i.e., eye) space.
