Download Presentation

Doppler spectra broadening depending
on absolute value of flow velocity
Petrov D.A., Ghaleb K. E. S., Abdulkareem S.N.,
Proskurin S.G.
Biomedical engineering,
TSTU, Russia
http://bmt.tstu.ru/
http://spros.tamb.ru/
[email protected]
Saratov Fall Meeting 2015
Objectives
Described method of direct measuring of flow velocity and Doppler angle
using Doppler Optical Coherence tomography.
The key feature of the technique is use of Doppler spectrum broadening,
carrier frequency and measured transversal and longitudinal velocities for
calculation of Doppler angle.
It is shown that after a complex procedure of computer processing, this
method allows determining the value of the Doppler angle and velocity
with great precision.
Doppler shift of interference
signal
Doppler shift of the interference signal usually expressed as
follows:
f D  2vs cos( d ) / 

is the Doppler angle
vs
is the flow velocity
Measurement of the Doppler angle
Exact definition of the Doppler angle is quite complex and difficult procedure.
Inaccurate measurement of it leads to errors in fluid velocity determination. We
are using the technique what can avoid this limitation. The power spectrum of the
signal can be described using this formula:
2

Ar
 f  f0  
P( f ) 
exp  
   An exp( i 2ft n )

  n
  
- amplitude of light coming from reference arm,
-amplitude of reflected light,
- Doppler shift,
- current frequency,
- spectrum bandwidth
Doppler spectrum bandwidth can be determined by transverse velocity and
wavelength dispersion as:
 
and
Vt
2 0

f 0 
0
0
can be determined from data processing.
So, transverse and longitudinal velocities are:



Vt  2t0   f 0
  0 ;
0


Vl  f 0
0
2
It is possible to calculate flow velocity vector as:
V  V0 exp( i ),
And Doppler angle:
where
V  Vt  Vl
2
 Vt
  arctan 
 Vl




2
Experiment
Probe beam geometry in the sample
arm of the OCT system.
The effectiveness of this technique was tested using the experimental
setup. Optical characteristics were chosen such that they correspond to
those of the blood. Series of experiments were performed to test
method for different flow velocities and Doppler angles.
Spectrogram
a)
b)
Spectrograms of the measured signal.
Doppler angle is set to 84º (a) and 90º (b), perpendicular scanning.
Averaging
a)
b)
Spectrogram before averaging (a), and after averaging by 5 adjacent A-scans (b)
Technique errors
Additive noise at 3.5-4.5kHz. Deleted by spectral subtraction of mean value at
corresponding frequencies
1
M 
n
n
A,
i 1
i
Ai  Ai  M
Reflected signal
At some angles of scanning there is a reflected signal appearing on the
spectrogram. It has the same amplitude and width as the true signal, but lower
intensity and it is shifted by the distance of half width of the signal. Also it
intersects the main signal. It is possible to get rid of it by subtracting signal part
from the area of the spectrogram where the reflected part appears.
Spectrograms before (left) and after (right) noise removal
Transverse and longitudinal
velocities
Experimental results
Preset values
Angle (deg)
90
84
Velocity
(mm/s)
Estimated Values
Angle (deg)
Velocity
(mm/s)
38.2
89.89
39.31
27.0
89.56
28.42
17.4
89.20
19.27
38.2
83.71
39.09
27.0
83.43
28.62
17.4
83.35
19.63
Conclusion
Knowing the value of the broadening of spectral lines, it is
possible to determine the flow rate of the moving particles.
Broadening of the Doppler spectra carries important information.
By using it, its possible to determine the velocity of the flow of
particles.
Presented results demonstrate not functional, but statistical
relation of the velocity value with the spectral broadening.
In some cases it is possible to obtain very accurate information.