BSA Flow Software Installation and User's Guide - CSI

An alternative geometry of a 3D LDA system is presented in Figure 5-74:
2-D Probe
1-D Probe
Figure 5-74 Alternative geometry of a 3D LDA system.
– the 2D-probe still measures the velocity components u1 and u2, while the
1D-probe measures the velocity component u3.
The optical axes of both probes still lie in the v-w plane, and u1 still
correspond to the desired vertical velocity component u exactly, but
horisontal velocity-components are now measured differently:
In the example in Figure 5-73, only the 1D probe measured off-axis, while
the 2D probe was aligned with the optical axis parallel to the w-direction,
yielding u2=v. In the example in Figure 5-74, both probes measure off-axis,
being aligned symmetrically on either side of the w-axis, requiring a
somewhat different transformation matrix.
Assuming that both probes has an off-axis angle of α=15º this becomes:
⎡
⎢
⎢
C = ⎢
⎢
⎢
⎣⎢
u3
u2
⎤
1 0 0
⎥ ⎡ 1000 . 0. 000 0. 000 ⎤
1 1 ⎥ ⎢
⎥
0
⎥ = ⎢ 0. 000 0518 . 0518 . ⎥
2cosα
2 cosα
⎥ ⎢
⎥
1 −1
0
⎥ ⎣⎢
0. 000 1932 . −1932
. ⎦⎥
2sin
α 2sinα
⎦⎥
5.15.2 Co-ordinate transformation of mean velocities from Moments object
In special cases where only mean velocities are of interest, co-ordinate
transformation of mean velocities is faster than transformation of all
coincident samples.
In cases where coincidence filtering removes too much information due to
poor overlap of measurement volumes, this is a way to extract useful
information of the data.
BSA Flow Software: Project explorer objects 5-81
v
u1
u
w
α
α