Rami Arieli: "The
Laser Adventure" Chapter 8 Section 1, page 11a
Mathematical formulas
of beam expander:
The relation between the beam diameters and the beam divergence
angles is:
f1 = Focal length [m] of the input
lens - ocular.
f2 = Focal length [m] of the output
lens - objective.
d1 = Diameter of the input beam [m].
d2 = Diameter of the output beam
[m].
q1 = Divergence
angle (Rad) of the beam at the input to the beam expander.
q2 = Divergence
angle (Rad) of the beam at the output to the beam expander.
From the equation it is clear that the
ratio between the beam diameters is directly related to the ratio of the
focal lengths of the lenses.