BSA Flow Software Installation and User's Guide - CSI

As long as the particle velocity does not introduce a negative frequency shift
numerically larger than f0, the Bragg cell will thus ensure a measurable
positive Doppler frequency fD.
-u
f0
fD
+u
ux
( )
2sin θ 2
f = f0+ u
λ
D x
Figure 7-10 Resolving directional ambiguity using frequency shift.
In other words the frequency shift f0 allows measurement of velocities down
to
u
x >−
λ f0
2sin 2
( θ )
-without directional ambiguity.
Typical values might be λ = 500 nm, f 0 = 40 MHz, θ = 20°, allowing for
measurement of negative velocity components down to
u
x >−
500⋅10 m⋅40⋅10 s
2sin 20 2
−9 6 −1
( ° )
=−57.
6 m/ s
(7-13)
Upwards the maximum measurable velocity is limited only by the responsetime
of the photo-multiplier and the following signal-conditioning
electronics. In modern Dantec equipment this allows measurement well into
supersonic velocities.
Fringe model To get an intuitive understanding of the frequency shift, we use the fringe
model once more. Introducing a fixed frequency shift f0 in one of the beams
will cause the fringe pattern itself to roll along the x-axis with constant
velocity. This means that even a stationary particle will scatter light with an
intensity pulsating at a frequency equal to f0. A seeding particle moving
towards the fringes will produce a Doppler burst of higher frequency, while
particles moving in the same direction as the fringes will produce a lower
frequency. The lower velocity limit in equation (7-13) correspond to a
seeding particle moving with exactly the same speed as the fringes.
The key issue here is the number of fringes crossed by the seeding particle
while it is in the measuring volume. If ∆t is the particle’s residence time
within the measuring volume, and fD is the measurable Doppler frequency
according to (7-12), the fringe count Nf is simply calculated as:
Nf = fD · ∆t (7-14)
BSA Flow Software:Reference guide 7-13