Beam Profiling Algorithm
The following figure illustrates the case when both beam radius measurements (W1 and W2, or σ1 and σ2)
are taken on the same side of the beam waist (W0 or σ0). Given W1 and W2, or σ1 and σ2 and the
separation ∆z between the two measurement locations along beam axis, we can find the profiling
parameters of the beam using the following algorithm.
Geometrical illustration:
Based on the basic geometrical properties of beamline diagram (that is, the axial distance from the beam
waist is proportional to the beamline distance along the beam line and the proportional factor is kσ0). We
can write:
101
zka
σ
= and 202
zka
σ
=
therefore, 21 0
zz z kd
σ
∆= − =
From the area of triangle OPQ, we have: 01
zkdka
σ
σ
∆
==, then we can have:
1
z
QE a k
σ
∆
==
Further more, in triangle OQE, 22
2
OE AQ l a
σ
=== −
22
12 1
PE QD c l a
σ
σσ
===−= −− and therefore in Triangle PQE, we can have: 22
dca=+
Thus, 022
zz
kd kc a
σ
∆∆
==
+
22
110
a
σ
σ
=− , and 101
zka
σ
=
22
220
a
σ
σ
=− and 202
zka
σ
=
2
00
zk
σ
=
