1. Laser Doppler Velocimetry
Introduction to principles and applications
Dr. Arnold A. Fontaine
ARL / Bioengineering
Office: Water Tunnel Building
Ph:
Some Info compliments of Dantec Inc.

2. Characteristics of LDA
Invented by Yeh and Cummins in 1964
Velocity measurements in Fluid Dynamics (gas, liquid)
Up to 3 velocity components
Non-intrusive measurements (optical technique)
Absolute measurement technique (one calibration required)
Very high accuracy
Very high spatial resolution due to small measurement volume
Tracer particles are required

3. Applications of LDA Laminar and turbulent flows
Investigations on aerodynamics
Supersonic flows
Turbines, automotive etc.
Liquid flows
Surface velocity and vibration measurement
Hot environments (flames, plasma etc.)
Velocity of particles
...etc., etc., etc.

4. LDA - Optical principle
Photodetector
When a particle passes through the intersection volume formed by the two coherent laser beams, the scattered light, received by a detector, has components from both beams.
The components interfere on the surface of the detector.
Due to changes in the difference between the optical path lengths of the two components, this interference produces pulsating light intensity, as the particle moves through the measurement volume.
Direction of motion
Incident beams
Photodetector
Direction of motion
Incident beams

5. Frequency to velocity conversion
The Doppler shift model described above explains the origination of the so-called “Doppler burst.” The Doppler frequency is equal to the dot product of the particle velocity with the difference between the scattered and the incident wave vectors .
When observed at a single detector, the direction of the scattered wave vectors (causing both Doppler shifts) is the same. Therefore, the Doppler frequency created by the two Doppler shifts is equal to the dot product of the particle velocity and the difference of the incident wave vectors. Notice, this Doppler frequency is no longer a function of the angle of detection.
The relation obtained using the Doppler shift model yields the same result that was obtained using the interference model: the constant of proportionality between velocity and Doppler frequency is the calibration factor, C.

6. LDA - Fringe model
Focused laser beams intersect and form the measurement volume
Plane wave fronts: beam waist in the plane of intersection
Interference in the plane of intersection
Pattern of bright and dark stripes/planes

7. Velocity = distance/time
Flow with particles
t (measured)
Signal
Time
Processor
d (known)
Detector
measuring volume
Bragg
Cell
Laser
backscattered light

8. LDA - Fringe model
The fringe model assumes as a way of visualisation that the two intersecting beams form a fringe pattern of high and low intensity.
When the particle traverses this fringe pattern, the scattered light fluctuates in intensity with a frequency equal to the velocity of the particle divided by the fringe spacing.

9. Transmitting optics Basic modules: Beam splitter Achromatic lens
Options:
Frequency shift (Bragg cell)
low velocities
flow direction
Beam expanders
reduce measurement volume
increase power density BS
Laser
Lens
Bragg
cell
D E
 D  DL F

10. Measurement volume
Transmitting
system
The transmitting system generates the measurement volume
The measurement volume has a Gaussian intensity distribution in all 3 dimensions
The measurement volume is an ellipsoid
Dimensions/diameters x, y and z are given by the 1/e2 intensity points  Z DL F Y X 1
Intensity
distribution
1/e 2 z x Z
Measurement
volume y X Y

11. Measurement volume Length:       2 sin    2  Width: Height:z
Fringe separation:    f    2
sin    Z  2 
No. of fringes: x f X

12. Laser, characteristics and requirements
Monochrome
Coherent
Linearly polarised
Low divergence (collimator)
Gaussian intensity distribution
Laser
L-Diode
collimator
Laser

13. Principle of LDA, differential beam technique
Flow
Laser
Transmitting
optics
Receiving optics
with detector
HeNe
Ar-Ion
Nd:Yag
Diode
Beamsplitter
(Freq. Shift)
Achrom. Lens
Gas
Liquid
Particle
Achrom. Lens
Spatial Filter
Photomultiplier
Photodiode PC
Signal
processing
Signal
conditioner
Spectrum analyser
Correlator
Counter, Tracker
Amplifier
Filter

15. Signal characteristics
Sources of noise in the LDA signal:
Photo detection shot noise.
Secondary electronic noise, thermal noise from preamplifier circuit
Higher order laser modes (optical noise).
Light scattered from outside the measurement volume, dirt, scratched windows, ambient light, multiple particles, etc.
Unwanted reflections (windows, lenses, mirrors, etc).
Goal: Select laser power, seeding, optical parameters, etc. to maximise the SNR.
The goal of the LDA experimentalist is to create an environment in which accurate measurement results can be obtained with minimum cost and effort. Obtaining this goal requires a thorough understanding of the conflicting requirements previously described, along with an understanding of the capabilities of the LDA signal processor used.
The next table lists the most important considerations in evaluating the performance of an LDA signal processor.

16. Directional ambiguity / Frequency shift
Particles moving in either the forward or reverse direction will produce identical signals and frequencies. f
fmax
fshift
fmin u
umin
umax
shift
umin
umax
no shift
With frequency shift in one beam relative to the other, the interference fringes appear to move at the shift frequency.
With frequency shifting, negative velocities can be distinguished.

17. Frequency shift / Bragg cell
Acousto-optical modulator
Bragg cell requires a signal generator (typically: 40 MHz)
Frequency of laser light is increased by the shift frequency
Beam correction by means of additional prisms
fs40 MHz
Piezoelectric
transducer fL
wave front
fL + fS 
Laser
Absorber

18. System configurations
Forward scatter
and side scatter
(off-axis)
Difficult to align,
Vibration sensitive Backscatter
Easy to align
User friendly
Transmitting
optics
Receiving optics
with detector
Flow
Receiving optics
with Detector
Detector
Transmitting and receiving optics
Bragg
cell
Laser
Flow

19. Seeding: scattered light intensity
Polar plot of scattered light intensity versus scattering angle
The intensity is shown on a logarithmic scale

20. Seeding: ability to follow flow
Following Lumley (1976):
Typically: Particle should be small and near neutrally buoyant.
d < 50 microns

21. DATA PROCESSING What is a Signal Processor?
System Requirements: Accurate discrimination of burst.
High dynamic range.
Large frequency range.
High data rate capacity.
Can discriminate signal in low SNR.
Processor Types: Spectrum Analyzers.
Photon Correlators.
Trackers.
Counters.
Covariance processor.
Digital Signal processor.
A signal processor is a device designed to measure the instantaneous Doppler frequency and convert it into a velocity measurement.
Measuring individual burst as opposed to a mean burst averaged over several bursts is important, particularly in turbulent flows. It is very important to be able to measure this burst accurately.
Large dynamic range means the processor can measure velocities over a wide range from high speed flow to flow reversal with minimal change to system parameters.
Large frequency range implies that the processor does not have an inadequate floor or ceiling on the range of velocities that it can process. In other words, velocities ranging from mm/s to km/s can be processed.
Some flows have characteristically high data rates. In addition, high data rates are needed for spectral analysis. The processor must not limit the maximum data rate due to a data throughput bottleneck.
Must be able to identify and measure a burst in high background noise.
Processor Types:
Spectrum Analyzer: standard processor used to processor frequency domain signals. Good for average frequency but not for instantaneous frequency measurement.
Photon correlator: similar to spectrum analyzer but could be used for lower SNR.
Tracker: tracked the Doppler frequency as it changed from burst to burst. Good for high burst density (high data rate) signals. Did not work well in low data density situations (low data rate) due to the trackers inability to track large velocity changes with large time between data bursts.
Counter: used a high speed clock and logic circuits to measure the time between a fixed number of fringe crossings or cycles in the burst signal. The counter could not measure signals well in low SNR situations.
Covariance: poor accuracy.
Digital Signal Processors: Digitally sample the burst with a high frequency, accurate A-d and then perform a variety of signal processing techniques to determine the Doppler frequency. These are the state of the art in processing. These processors combine: High pass filters to remove low frequency components such as the signal pedestal and low frequency noise. Low pass filters to limit high frequency noise components. High speed A/D converter. Burst detection algorithms to help identify burst from background signal. Digital signal analyzer to estimate the frequency.

22. DIGITAL SIGNAL PROCESSORS
Digitally sample the burst with a high frequency, accurate A-D and then perform a variety of signal processing techniques to determine the Doppler frequency.
These are the state of the art in processing.
These processors combine:
High pass filters to remove low frequency components such as the signal pedestal and low frequency noise.
Low pass filters to limit high frequency noise components.
High speed A/D converter.
Burst detection algorithms to help identify burst from background signal. Digital signal analyzer to estimate the frequency.
Low pass filter reduces high frequency noise but also eliminates aliasing.
Burst Detector: Detects coherency in a signal. Searches the data for a pattern that looks like a burst and then only processes that portion of the signal while rejecting the rest of the signal. Greatly enhances the processors ability to measure a Doppler burst in a noisy signal.

23. LDV SIGNAL BIAS What is Bias? Examples? Types of bias in LDV signals:
1) Velocity bias.
2) Fringe bias.
3) Gradient bias.
Bias? An one way error in the calculation of a statistic caused by an identifiable but uncontrollable source causing an unrealistically high or low measure of that statistical quantity.
Examples: Having a fixed error in the measurement of a location due to a limitation of the measurement system. Typically, wall locations are determined by burying the LDV probe into a wall and watching the Doppler signal as the probe volume is slowly moved to the wall. Because the probe volume has a fixed dimension, one cannot usually measure the location of the wall to better than ½ the probe volume dimension. This is a bias in the location of the wall coordinate.
Type of bias in LDV signals:
Velocity bias – the statistics for LDV measured data are random arrival with poison distribution in time. That is, that there is a higher probability of getting more particles with a high velocity component crossing the probe volume in a given sampling time than particle with a lower velocity component. As a result, standard statistical methods such as ensemble averaging produces an averaged that is bias towards the higher velocities.
Fringe Bias: The LDV probe volume has a limited size and limited number of fringes. Most processors reguire a fixed number of fringes be crossed to validate the burst detectors. Particles moving through the outside edges of the measurement volume will cross fewer fringes than those crossing near the center. Thus, these particles may not get validated due insufficient fringe crossings. Also, particles crossing at a sharp angle to the fringe direction may not cross enough fringes. They may have crossed through the center but if their flow direction angle is too sharp compare to the fringe direction, they will not cross enough fringes. This is often called an angle bias.
Gradient bias: Since the LDV probe volume is a finite size with a length that is typically must longer than its diameter, it is not possible to accurately resolve velocity scales that are smaller than the length of the probe volume. This implies that sharp spatial gradients in the velocity field cannot be resolved. This results in an averaging over the length of the probe volume, and produces a resolution bias in the data.

24. Probe volume alignment for 3D velocity measurements
To measure three velocity components requires careful alignment.
The simplest method is by using a fine pinhole with an opening just large enough that the focused beam can pass through.
Fine adjustment can be made using a power meter behind the pinhole maximising the power of light passing through the pinhole for each beam.

25. REFERENCES
“The laser Doppler technique,” L.E. Drain, J Wiley and Sons Publishers, 1980.
“Report of the Special Panel on Statistical Particle Bias in Laser Anemometry,” R.V. Edwards, J. Fluids Engineering, Vol 109, pp89-93, 1987.