BSA Flow Software Installation and User's Guide - CSI

The fringe model
The beat-frequency, also called the Doppler-frequency fD, is much lower
than the frequency of the light itself, and it can be measured as fluctuations
in the intensity of the light reflected from the seeding particle. As shown in
Equation (7-5) the Doppler-frequency is directly proportional to the
x-component of the particle velocity, and the velocity can thus be calculated
directly from fD:
λ
u = f
2sin 2
( θ )
x D
(7-6)
Although the above description of LDA is accurate, it may be intuitively
difficult to quantify. To handle this, the fringe model is commonly used in
LDA as a reasonably simple visualisation producing the correct results.
Interference fringes When two coherent laser beams intersect, they will interfere in the volume of
intersection. If the beams intersect in their respective beam waists, the wave
fronts are approximately plane, and consequently the interference produce
parallel planes of light and darkness as shown in Figure 7-4.
Figure 7-4 Fringes form where two coherent laser beams cross.
The interference planes are known as fringes, and the distance δf between
them depend on the wavelength and the angle between the incident beams:
λ
δ f =
2 sin 2
( θ )
x
z
(7-7)
The fringes are oriented normal to the x-axis, so the intensity of light
reflected from a particle moving through the measuring volume will vary
with a frequency proportional to the x-component ux of the particle velocity:
f
D
( θ )
u 2sin 2
x = =
δ λ
f
–which is identical to the result in (7-5).
u
Beam alignment If the two laser beams do not intersect in the beam waists but elsewhere in
the beams, the wave fronts will be curved rather than plane, and as a result
the fringe spacing will not be constant but depend on the position within the
intersection volume. As a consequence the measured Doppler frequency will
also depend on the particle position, and as such it will no longer be directly
7-6 BSA Flow Software: Reference guide
x
(7-8)