BSA Flow Software Installation and User's Guide - CSI

es
e2
e1
U
Figure 7-3 Scattering of two incoming laser beams.
In this way both incoming laser beams are scattered towards the receiver, but
with slightly different frequencies due to the different angles of the two laser
beams.
⎡ U ⎤
fs, 1 = f1
1+
⋅( s − 1)
⎣
⎢
e e
c ⎦
⎥
⎡ U ⎤
fs, 2 = f2
1+
⋅( s − 2)
⎣
⎢
e e
c ⎦
⎥
Doppler frequency When two wave trains of slightly different frequency are super-imposed, we
get the well-known phenomenon of a beat frequency due to the two waves
intermittently interfering with each other constructively and destructively.
The beat frequency correspond to the difference between the two wavefrequencies,
and since the two incoming waves originate from the same
laser, they also have the same frequency, f1=f2=fI, where subscript I refer to
incident light:
fD = fs, 2 − fs,
1
⎡ U
= f2
+ ⋅ s −
⎣
⎢
1 e e2
c
⎤
⎦
⎥
⎡
1
⎣
⎢
1
U
c
es e
⎡U
⎤
= fI
⋅( − )
⎣
⎢
e1 e2
c ⎦
⎥
fI
= [ e1−e2 ⋅U ⋅cos(
ϕ)
]
c
1 2sin( θ 2)
= ⋅2sin( θ 2)
⋅ ux = ux
λ
λ
( ) − f + ⋅( − )
1
⎤
⎦
⎥
(7-4)
(7-5)
-Where θ is the angle between the incoming laser beams and ϕ is the angle
between the velocity vector U and the direction of measurement.
Note that the unit vector es has dropped out of the calculation, meaning that
the position of the receiver has no direct influence on the frequency
measured. (According to the Lorenz-Mie light scattering theory, the position
of the receiver will however have considerable influence on signal strength).
BSA Flow Software:Reference guide 7-5