BSA Flow Software Installation and User's Guide - CSI

-This will usually differ from the fringe count calculated from (7-10), which
apply only when a seeding particle move straight through the centre of a set
of stationary fringes. (i.e. no frequency shift).
If for example the diameter of the focused laser beam is df = 100 µm,
the laser wavelength is λ = 500 nm,
and the beam intersection angle is θ = 20º,
equation (7-10) predicts, that a seeding particle passing the measuring
volume along the x-axis will cross 70 fringes irrespective of its velocity.
This is sufficient to determine the absolute velocity of the particle, but the
direction will be unknown. To resolve the directional ambiguity, a frequency
shift of f0=40MHz can be applied, allowing for detection of velocities
ux > ux,min = -57.6 m/s, according to the previous example.
Since the frequency shift cause the fringes to move, the number of fringes
crossed by the particle will also change. In the limit ux = -57.6 m/s the
particle moves with the same speed as the fringes, and consequently there
are no fringe-crossings, and the particle will not be detected at all. It can be
shown that for ux = ½·ux,min = -28.8 m/s, the number of fringe crossings will
be identical to the case of no frequency shift; Nf = 70. For lower velocities
the fringe count will be smaller, and for higher velocities it will be bigger. In
the special case ux = 0, the fringe count will in principle approach infinity,
since the seeding particle remain in the measuring volume. In practice no
particle is ever completely immobile, and even if ux equals 0, uy or uz
probably don’t, and as such ensure that the seeding particle leaves the
measuring volume “sideways”, thereby limiting the number of fringecrossings.
Nonzero velocity components uy and/or uz will generally reduce
the fringe count, since they mean that the seeding particle does not pass the
measuring volume along the x-axis.
If you are certain that all velocities are bigger than ½·ux,min, the frequency
shift may also help you to increase the effective fringe count in cases, where
the number of fringes according to (7-10) might otherwise be too small.
Fringe tilt In principle the frequency shift will also tilt the fringes slightly, so they are
no longer exactly normal to the x-axis, but in practice this can be ignored,
since the typical frequency shift of 40 Mhz is several orders of magnitude
smaller than the frequency of light. This means that the difference in
wavelength between the shifted and the unshifted beam will also be several
orders of magnitude smaller than the laser wavelength itself, and
consequently the tilt angle of the fringes get negligible.
In the example above (fI = c/λ= 3·10 8 /5·10 -7 = 6·10 14 Hz, f0 = 40 Mhz
and θ = 20°), the tilt angle would be approximately 10 -5 degrees.
7-14 BSA Flow Software: Reference guide