Page 329 - Modern Optical Engineering The Design of Optical Systems

308 Chapter Thirteen

reflecting mirror M 2 . The angular position of one of the mirrors is
adjusted until both images coincide. In the rudimentary instrument
shown here, a pointer attached to mirror M 2 can be used to read the
value of /2; the distance to the object is found from
B
D (13.16)
tan
where B is the base length of the instrument. In actual rangefinders,
a telescope is often combined with the mirror system to increase the
accuracy of the reading, and any one of a number of devices may be used
to determine ; the distance is usually read directly from a suitable
range scale so that no calculation is necessary.
The accuracy of the value of D depends on how accurately can be
measured. For large ratios of D/B, we can write
B
D (13.17)

and differentiating with respect to , we get

dD B 2 d (13.18a)

Substituting B/D into Eq. 13.18a, we find that the error in D due to
a setting error of d is
D 2
dD d (13.18b)
B
Now d is primarily limited by how well the eye can determine when
the two images are in coincidence. This is essentially the vernier acuity
of the eye and is about 10 seconds of arc (0.00005 radians). If the mag-
nification of the rangefinder optical system is M, then d is 0.00005/M
radians, and the ranging error is
5
5 10 D 2
dD (13.18c)
MB
Thus, the greater the base B and the greater the magnification M, the
more accurate the value of the range D.
A few of the devices encountered in rangefinders are illustrated in
Fig. 13.14. In Fig. 13.14a the end mirrors are replaced by penta-prisms
(or “penta”-reflectors), which are constant-deviation devices, bending
the line of sight 90° regardless of their orientation. The reason for
their use is to remove a source of error, since no change in the relative
angular position of the two images is produced by misalignment of
the penta-prisms as would be the case with simple 45° mirrors. A double