BSA Flow Software Installation and User's Guide - CSI

Doppler effect
d0
R(z)
Figure 7-1 Laser beam with Gaussian intensity distribution.
With a known wavelength λ of the laser light, the laser beam is uniquely
described by the size d 0 and position of the beam waist as shown in
Figure 7-1.
With z describing the distance from the beam waist, the following formulas
apply:
Beam divergence
λ
Beam diameter ( ) = + α for
π
⎛ 4 z⎞
dz d0
1 ⎜ ⎟ → z z→
∞
2
⎝ d ⎠
Wave front radius
4 λ
α =
π d
0
π
( ) = +
λ
⎛ ⎡
2
d ⎞ 0
Rz z⎢1
⎜ ⎟
⎣⎢
⎝ 4 z⎠
0
2
2
⎤
⎥
⎦⎥
α
⎧→∞
for z →0
⎨
⎩→
z for z→
∞
The beam divergence α is much smaller than indicated in Figure 7-1, and
visually the laser beam appear to be straight and of constant thickness. It is
important however to understand, that this is not the case, since
measurements should take place in the beam waist to get optimal
performance of any LDA-equipment. This is due to the wave fronts being
straight in the beam waist, and curved elsewhere, and will be explained in
more detail later. For now you should just note that the wave front radius
approach infinity for z approaching zero, meaning that the wave fronts are
approximately straight in the immediate vicinity of the beam waist. This
means that the theory of plane waves can be used here, greatly simplifying
calculations.
I(r)
z
(7-1)
As indicated by the name Laser Doppler Anemometry, the Doppler effect
plays an important role in LDA, since the technique is based on Doppler
shift of the light reflected (and/or refracted) from a moving seeding particle.
BSA Flow Software:Reference guide 7-3