Page 200 - Instrumentation Reference Book 3E

184 Fiber optics in sensor instrumentation --

Mirror with Central
Ap;rtp ing Objec; /,/, ~
I HeNe Laser

Optical Fiber
Analyzer
Focusing Lens
Back-Scattering
Photo-Detector Particle
Figure 12.17 Illustration of an optical configuration of the fiber optic Doppleranemometer (FODA) used for particle-size
analysis (Dyott 1978).
fiber is introduced into the liquid medium contain- Doppler anemometry relates the velocity v of a
ing the particles, and laser light is directed down the moving scattering surface to the induced Doppler
fiber such that it is both partially reflected from the frequency shift fd by the relationship:
fiber elid face and also backscattered from the 2 v7z 1
particles in suspension (Figure 12.17). The penetra- fa = --cos0 (1 2.22)
tion depth of the radiation into the liquid will A3
depend upon the concentration of particles and where 121 is the refractive index of the liquid medium.
the absorbency of the mediuni. Due to the numer- Due to the numerical aperture (NA = sin&,) of
ical aperture of the fiber the emitted cone of light the optical fiber there will be a range of angles up
will have a maximum distance of penetration to which the light can enter the fiber given
before the backscattered captured light falls off by 0,. Consequently, there will be a spread in the
appreciably. For a clear liquid this is about 2mm Doppler frequency Afd of:
for a 90 percent reduction in capture efficiency.
For higher attenuating solutions this distance falls ~ Afd = 1 - cos [sin-' (e)] (12.23)
to 100 pm or less. The application of optical fiber .fd
anemometry to Brownian motion is significant For an NA of 0.15 and when operating in a water
since there is no net flow of the fluid medium. medium (n = 1.33), the normalized frequency
In contrast, when using such techniques in fluid spread is 0.0065.
flow applications there is the additional compli- When considering the sizing of particles in the
cation that the fiber end face disturbs the flow region of 5-2000nm diameter suspended in a
velocities about the fiber tip, producing a stagna- liquid medium, the frequency spectrum produced
tion region and thus giving erroneous results. from the motion of the particles under the action
When measuring, for example, fluid flow rates of Brownian motion can be monitored through
such as arterial blood flow, methods of overcom- the Doppler frequency spectrum observations.
ing this problem need to be addressed; these are A typical power spectrum for such particle
discussed further later on. motion is illustrated in Figure 12.18. The diffusion
1 .o
Normalized noise

Normalized moddied power
spectrum from suspended
5
Lorentzian high frequency
tail used to determine
particle radius by
graphical method

V ' I
Frequency (Hz) 4000
Figure 12.18 Illustration of a FODA output signal showing a Lorentzian power spectrum from suspended particles moving
under the action of Brownian motion (Ross et al. 1978).