46
An Introduction to Beam Physics
FIGURE 2.10: Sketch of a parallel–to–point system.
FIGURE 2.11: Sketch of a point–to–parallel system.
This is an example of parallel–to–point systems as illustrated in Fig. 2.10.
A parallel–to–point system requires that
(x|x) = 0.
If we look at the eye as a DLD system, this requires
(x|x) = 1 − l 2 /f = 0 =⇒ l 2 = f,
while l 1 is arbitrary. Thus the retina has to be exactly at the focal length;
almost as important is that the distance to the object is arbitrary since we
cannot change our distance to the stars significantly. Another important
parallel–to–point system is the photographic camera.
2.3.3 Point–to–Parallel (• •) Systems
Another important class of systems is the point–to–parallel systems. In
these systems, the final slope depends only on the initial position, but not on
the initial slope as illustrated in Fig. 2.11. So we have
(a|a) = 0.
Examples include the flashlight, the microscope, and laser and particle beam
transports over long distances such as those considered for the SDI Transport
(Strategic Defense Initiative) considered by the US government in the 1980s.
As an example, let us try to achieve a point–to–parallel system with a DLD
combination. We obtain
(a|a) = 1 − l 1 /f = 0 =⇒ l 1 = f,