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98
Revision 00 EN - 01/2021
HP-MSM-HB
35,0(6
23.1.1
Rotationally symmetric beams
According to ISO 11145 as well as ISO 11146 three beam parameters are necessary for the characterization
of a rotationally symmetric beam:
• the z-position of the beam waist (focus) z
0
• the diameter of the beam waist d
σ
F
• the far field divergence angle
Θ
By means of these three values it is possible to determine the beam diameter at every spot along the propa-
gation direction. The following restriction is applicable: The divergence angle has to be smaller than 0.8 rad
and the focus diameter and the divergence angle were determined with the 2. moment method.
(1.1)
Furthermore, the beam propagation is described by means of the so called beam propagation ratio K.
(1.2)
with:
K
= beam propagation ratio
M²
= beam propagation factor
λ
= wavelength in a medium with the refractive index n
Θ
σ
= divergence angle
d
σ
0
= beam waist diameter
The derived beam parameter product, is a constant size as long as image defect free and aperture free com-
ponents are used.
(1.3)
An important beam parameter is the Rayleigh length:
The Rayleigh length is the distance towards the propagation in which the laser beam has increased by
. It
can be calculated by means of the following formula:
(1.4)
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