Application of optical coherence interferometry to measure the spatial profile of fluid flow velocity

The spatial profile of fluid flow velocity in transparent glass conduits is measured using optical Doppler tomography (ODT). The flow velocity at any spatial location in the conduits is determined by measuring the Doppler shift of backscattered light from moving microspheres in the fluid. ODT is an accurate and inexpensive method for high resolution characterization of fluid flow velocity profile.


METHODOLOGY
Continuous near infrared light (=850 nm) emitted by a superluminescent diode (SLD) is coupled into a fiber optic Michelson interferometer and split into two beams by a 2x2 fiber coupler (Figure 1).SLD power in the input fiber of the interferometer is set at 1 mW.Optical power in the reference arm of the interferometer is attenuated to 2 tW to reduce intensity fluctuations and thus achieve higher signal to noise ratios  where çø is the angle between flow velocity and the optical axis of incoming light outside the conduit.

RESULTS AND ANALYSiS
Optical low coherence interferometry is often used to study static structures, such as biological tissues.8 By scanning the reference or probe arm across an empty glass conduit with square cross section, optical reflections from each surface in the conduit are detected (Figure 2).Since the coherent detection volume is small (5x5x1 0 .tm3),high spatial resolution is achieved.Four major peaks correspond to reflections from glass-air interfaces of the conduit.
If the conduit contains flowing fluid consisting of polymer microspheres, velocity of the microspheres can be obtained by measuring Doppler power spectra.

CONCLUSIONS
We have found that ODT is a simple and useful technique for high resolution measurement of fluid flow velocity profiles within conduits.Although flow is laminar in our experiments, when the direction is unknown (i.e., turbulence) and fluid velocity may be two-or threedimensional, multiple probes may be used.Specifically, such a provision for three (two) probes allows measurement of three (two) dimensional velocity flows.If the optical axes of the probes arbitrary are independent, flows of direction can be characterized.
The broad Doppler peaks (Figure 4) at lower frequencies (greater intensity) are consistent with the flow direction.
However, symmetrical peaks with respect to reference frequency (1000 Hz) at higher frequencies are simultaneously detected.Experiments are underway to clarify this effect.The frequency line shape is also under investigation When the optical properties of the test suspension and/or conduit can be controlled, a relationship may exist between the size and refractive index of the microspheres and their concentration for optimum SNR.When the size of the microsphere is small, in comparison to the optical wavelength, backscattered light intensity generally increases.Thus, in some applications, reducing the size of the microspheres may improve SNR.
The refractive indices of the solvent (n) and spheres (n') also affect data readings.When n'/n is near unity, signal is reduced.When the ratio is high, however, backscattered light intensity significantly increases.
The microsphere concentration can also be varied.A low concentration reduces backscattered light; a high concentration may cause multiple scatter and complicate signal analysis.
ODT has many potential scientific (e.g., medical) and industrial (e.g., mass transfer) applications, and provides a simple, effective and easily adapted technique for assessment of fluid or dry particle flow velocity within conduits.
The technique is noncontact and noninvasive, so that flow can be characterized without disturbing the stream.
flow velocity on the micro and macroscopic levels is valuable in both science and industry.Multi-gated ultrasound imaging' and laser Doppler velocimetry are among the most often used techniques.Although multi-gated ultrasound imaging can be used to resolve flow velocities at different locations within conduits, the mean Doppler frequency is easily altered by many factors and difficult to interpret.2In laser Doppler velocimetry, use of a highly coherent light source requires a specialized geometry (e.g., two light beams) or an invasive procedure to achieve useful spatial resolution.Optical Doppler tomography is a non-invasive technique that allows high spatial resolution (10 .tmaxial and 5 tm radial) determination of fluid flow velocity at discrete user-specified locations within the conduit.The method employs optical low coherence interferometry in combination with the Doppler effect.In our experiments, fluid flow velocity measurements are made in both circular and square glass conduits infused with a moving suspension of polymer microspheres in doubly de-ionized water.Measured velocity profiles within conduits compare well with calculated results.

Figure 2 .
Figure 2. Reflections from the interfaces of the glass conduit with square cross section (from left to right, air-glass, glass-air, air-glass, glass-air).

Figure 3 Figure 3 .
Figure3shows recorded interference fringe intensity as a single microsphere moves through the coherent detection volume.Microsphere concentration is very dilute (average spacing is 30 tm)

Figure 4 givesFigure 4 .
Figure 4 gives Doppler power spectra (circles) at different positions along a diameter (inner diameter, d = 400 tm) of a circular conduit.The solid lines represent best fit to a Lorentzian function; vertical lines show the reference phase modulation frequency (1000 Hz).Maximum velocity is found on the central axis of the conduit.The velocity decreases at positions near the wall.To deduce fluid flow velocity profile, Doppler shift (4f) was measured over a linear grid of points lying along a diameter of the circular conduit (Figure 5).The solid line represents a least squares fit based on solving the Navier-Stokes equation for laminar fluid

Figure 6
Figure 6 shows the flow velocity profile (circles) measured across a central axis perpendicular to the walls of a glass conduit with square cross section.The probed position in the conduit is computed from Eq. 1. Theoretical fit to the collected data is computed based on a Fourier series solution of the Navier-Stokes equation (solid line).'0Average flow velocity over the central axis calculated from our experiments is

Figure 5 . 0 Figure 6 .
Figure 5. Experimental (circles) and theoretical (solid line) fluid flow velocity profiles in a circular glass conduit.Band resolution of spectrum analyzer is 10 Hz.