Specifications

Beam Propagation
33
optical design. The Rayleigh range is the difference in distance
between the beam waist location and the point at which the beam is
1.4 times larger.
The beam waist diameter can be for a focused beam in this issue but
it could also be any other beam waist and the equation is still appli-
cable. For the same focused beam in the previous example, the
Rayleigh range or depth of focus is:
Z
r
= (3.14 x(0.245 mm)
2
) /(4 x 0.0106 mm x 1.2)
Z
r
= (0.188 mm
2
) /(0.051 mm) = 3.7 mm
It should be noted that reducing the spot size will reduce the depth
of focus more rapidly than the spot size is reduced. Thus when
reducing spot size the process can become much more intolerant to
variability in the distance between the focusing lens and the work
piece. The Rayleigh range provides a guide to the range of accept-
able working distances but the actual value will depend on the
process, the equipment, and dynamics between the two factors.
Beam Expansion
As noted above, an increase in the beam diameter on a focusing lens
can produce smaller focused spot size. The other issue that beam
expansion addresses is variation in the focused spot size on gantry
based system. In these later systems, the beam size on the focusing
lens will vary as the distance between the laser and the focusing lens
is moved which in turn causes the focused spot size to change as well
as the distance to the beam waist. Beam expansion will reduce the
change in the focused spot size and changes in focal point. The
simplest beam expanders use two lenses with different focal lengths
(see figure 14). The ratio of the focal lengths gives the magnification
of the beam. Galilean beam expanders use a negative lens followed
by a positive lens for expansion.
Using the simple beam expander as an example, the combination of
a 2.5 inch and 5 inch lenses will magnify the beam by a factor of
two. The proper separation of the two lenses is the sum of their focal
lengths. Small adjustment of the separation is required to correct for
the effect of the distance from the first lens to the beam waist. As a
general guide line for design keep the ratio of the focal length
Z
r
πD
o
2
4λM
2
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=