BSA Flow Software Installation and User's Guide - CSI

Transducer
Travelling
wave front
Laser
fI
f0=40 MHz
θB
fI
fI+f0
Absorber Glass cell
Figure 7-9 Bragg cell.
Direct beam
First order
diffraction
The incident light beam hits a series of travelling wave fronts which act as a
thick diffraction grating. Interference of the light scattered by each acoustic
wave front causes intensity maxima to be emitted in a series of directions.
By adjusting the acoustic signal intensity and the tilt angle θB of the Bragg
cell, the intensity balance between the direct beam and the first order of
diffraction can be adjusted. In modern LDA-equipment this is exploited,
using the Bragg cell itself as beam splitter. Not only does this eliminate the
need for a separate beam splitter, but it also improves the overall efficiency
of the light transmitting optics, since more than 90% of the lasing energy can
be made to reach the measuring volume, effectively increasing signal
strength.
The Bragg cell adds a fixed frequency shift f0 to the diffracted beam, and
including this in the equations (7-5) yield:
U
f f f e e f f f f
c
U
⎡
⎤
, 2 = + 0 ⎢ + ⋅ − 2 ⎥ 0 0
⎣
⎦
c
( ) 1 ( ) = + + ( + ) ⋅( e −e
)
s I s I I s
U
f f ( e e ) f f ( )
c
( ) ( ) ( )
U
e e
c
f f f f f f U
e e f
c
U
e e
c
f f U
e e e e f
c
U
c
f f U
e e f
c
U
⎡
⎤
s, 1 = I⎢1+ ⋅ s − 1 ⎥ = I + I ⋅ s − 1
⎣
⎦
D = s, 2 − s, 1 = 0 + I + 0 ⋅ s − 2 − I ⋅ s − 1
= 0 + I ⋅ s − 2 − s + 1 + 0 ⋅ s −
= 0 + I ⋅ 1 − 2 + 0 ⋅ s − 2
2sin 2
= f0
+ + 0
λ
c 12 4 34
{ ≤2
≤1
≤10−5
144 424444 3
Negligible
⇓
( )
2sin θ 2
f ≅ f0+ u
λ
D x
( ) ( e e )
( ) ( e e )
c
( θ )
u f ( − 2 ) cos
{
ϕ
U
x es e
2
2
(7-12)
7-12 BSA Flow Software: Reference guide