1. Laser Doppler Velocimetry: Introduction
TSI LDV/PDPA Spring Workshop & Training
Presented by Joseph Shakal Ph.D.
Copyright© 2005 TSI Incorporated

2. Laser Doppler Velocimetry
Light Scattering Principles
Fringe Formation
Characteristics of Scattered Light
Doppler Signals
Properties of the Measurement Volume (Beam Waist)
System Optics
Conclusion
We will begin with a review of the light scattering principles of the LDV technique, and then talk about how fringes are formed. Then we will look at properties of the scattered light. Next we will look at resulting Doppler signals, and then spend some time looking at beam waist characteristics – diameter, length, and fringe spacing. We’ll then look at the optical hardware in an LDV system.
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3. Laser Doppler Velocimetry
Photodetector (PMT)
i(t)
Signal is a Time
Varying Current
Flow
Scattered Light
The LDV technique relies on the light scattered by scattering centers in the fluid to measure flow velocity. We will refer to the scattering centers as “particles,” with the understanding that bubbles or anything else that has a relative refractive index (compared to the fluid) different from unity could be the source of scattered light. The particles, whose velocities are measured, must be small enough (generally in the micron range) to follow the flow and large enough to provide adequate signal strength for the processor to give velocity measurements. It should be noted that the signal exists only when a detectable particle is in the measuring volume and, hence, is discontinuous.
Some of the key aspects of this non-contact flow measuring technique are:
Light scattered by “particles” in the flow contains information about the scatterer (particle)
Generally, measurement is independent of the properties of the medium
Can measure the desired component of velocity by suitably orienting the system
Direct measurement of velocity
Scattered light contains information other than velocity
Illuminating
Beams
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4. LDV Hardware Components
Signal
Processor
FSA
Laser
Photo-detector
Receiving Optics
Transmitting Optics
The above schematic shows the basic components of a complete LDV system for velocity measurements.
To optimize a measurement, one must have:
1. Particles that follow the flow and provide an adequate signal.
2. Laser, optics and photodetector.
3. A signal processor that extracts the frequency from the burst signal.
4. Software that fully interfaces with the signal processor to provide the needed flow information.
With LDV, results can be obtained that are simply not available by any other technique.
Components of system:
Argon-ion (usually) Laser – Source of Monochromatic, Collimated, Coherent light
Color Separation Optics, Bragg Cell, Beam Launching Optics (Contained in Fiberlight)
Beam Polarization, Collimation, Steering Optics, Focusing lens (Contained in fiber probe)
Collecting lens, Aperture, Receiving fiber (Contained in fiber probe)
Photodetector, Signal processor, Data Analysis system (Contained in PDM and FSA, FlowSizer Software)
Particles moving
with the fluid
No Probe in the Flow Small Measuring Volume
No Velocity Calibration Large Dynamic Range
Desired Velocity Components High Frequency Response
measured Directly
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5. Copyright© 2005 TSI Incorporated
Fringe Description
Actual Fringes
Transmitting Optics df
The fringe spacing, df depends only on the wavelength of light, L, and half angle, K. With lasers, the wavelength is known accurately (0.01% or better). Therefore, an accurate measurement of beam angle gives the value of df that relates the particle velocity to the frequency of the signal. d u f x D    2
sin
 = Wavelength of incident light
= Frequency detected at PMT f D
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6. Copyright© 2005 TSI Incorporated
Fringe Description ux
Focal Length = f
Focal Distance  f
Particle crosses a fringe
Pedestal  d f 
We can consider that each peak in the burst signal corresponds to the seeding particle crossing a fringe, and the pedestal due to the fact that the fringes are brighter in the center of the waist.
It should be noted that the fringe description does not involve a “Doppler shift” and is, in fact, not always appropriate.
“Differential Doppler” is another term applied to the LDV technique. This correctly implies Doppler shifted scattered light signals from a particle illuminated by two beams. This scattered light mixes at the photodetector surface to give the “difference” signal.
However, the fringe description is convenient and gives the correct frequency. It may not predict the correct signal shape or quality.
In either case, the amplitude variation of the signal reflects the Gaussian intensity distribution across the laser beam.
2 sin K d f u  f d f x D
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7. Collection Optics Location
Receiver
Off-axis
Forward Scatter
Off-axis
Backscatter
Not Here
Receiver
Receiver 
The measured LDV velocity is independent of the location of the scattered light collection system.
The backscatter mode is a very convenient arrangement since all the optics are on one side of the measuring point, requiring only one window and provides easier traversing arrangement of the LDV system. In this case, the same lens is used for both focusing the two beams and collecting and collimating the scattered light.
If direct backscatter is not used, then a separate receiving system, appropriately positioned, to collect the scattered light is used.
Notice the banner.
As we will see in the next slide, the signal strength is not the same for all receiver angles.
Once the receiving optics is separate from the transmitting optics, forward scatter locations provide stronger signal.
Transceiver
Receiver
Backscatter

Forward scatter

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8. Scattered Light Intensity Variation
Log Scale
Linear Scale
The figure shows the variation of the scattered light intensity as a function of receiver position. The intensity values are obtained from Mie scattering calculations. Forward scatter has very high power, but levels dip very low between 90 and 120 deg. Recall the banner note on the previous slide.
Note the immense variation in intensity with angle in the linear plot.
The curve has no small ripples, which is the case for very small particles like the PSL shown here.
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9. Typical Frequency vs. Velocity Curves
 = nm
nm
= 140
100000
1000
14
Frequency, MHz
 = 0.140 10
Typ. Frequencies
14
Typ. Velocities
Shown here is are generic response curves for an LDV system. Please note the following:
It is plotted on log scales, showing an immense range of values
Velocity dynamic range of over 108 is generally achieved by LDV systems
For most common flows, the corresponding Doppler frequencies are in the 100kHz to 10MHz range (green arrows).
The value of k= 14° represents a lens with an f/# (focal length/diameter) of 2. This would correspond to a 120mm FL lens on our TR 60 series probes, or a 100mm FL lens on our TM 50 series probes.
At k = 0.14°, the f/# would be about 200, corresponding to an extremely long focal length lens.
The absolute minimum fringe spacing, df , is the laser wavelength divided by 2 (i.e., when sin k = 1). This gives frequencies of about 4 MHz per m/s of velocity.
A “typical” fringe spacing is 5um.
A “large” fringe spacing would be 25um.
In practice, measurements from 1 µm/sec to over 1,000 m/sec have been made, which corresponds to a dynamic range of over 109.
0.1
0.001
1.0 E-06
1.0 E-04
0.01
1.0
100
10,000
Velocity (m/sec)
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10. Spectrum of Doppler Signal and Filtering
Pedestal
Sum
Frequency
HPF
Doppler
LPF
Power
Noise
Frequency
The light scattered by a particle passing through the intersection region of the two focused laser beams is collected and focused onto a multimode fiber and transmitted to a photomultiplier tube (PMT). The PMT converts this light flux into an electrical voltage. Variations in this voltage – the Doppler burst - are subsequently analyzed to determine the velocity of the particle.
The “continuous” signal from the photodetector at high light flux has, at the minimum, the following components:
Low frequency “pedestal” caused by the particle passing through the beam waist.
Doppler frequency, superimposed on the pedestal and “oscillates” at the fringe crossing frequency, fD.
Wide bandwidth noise generated in the PMT and downstream electronics.
Optical shift to enable velocity measurements in both directions.
The PMT output signal therefore has unneeded bandwidth that must be removed. So the incoming signal is first high-pass filtered to remove the Pedestal – this is at 20MHz or 5MHz for FSA systems. Next, the signal is downmixed to remove all or part of the 40MHz shift. The low pass filter removes noise and the downmixer’s ‘sum’ frequency.
Then the FSA’s bandpass filter setting is chosen to encompass the range of Doppler frequencies present (indicated above by “Doppler”) and extract the velocity of the particle.
Signal
After high pass filter (HPF)
After low pass
filter (LPF)
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11. Copyright© 2005 TSI Incorporated
Measurement Volume 1
Intensity
1/e2
The effective diameter of the measurement region, dm , is defined as shown above.
One way to interpret the effective diameter is as follows.
The light scattered by a particle passing through the beam but outside the effective diameter will be so low that it would not produce a signal that can be processed to get a reliable velocity measurement. dm dm
dm is the diameter of the measurement volume, or in other words, the 1/e2 waist diameter
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12. Measurement Volume Dimensions
Fringes
Beams are in plane of page  x
1/e2 Contour S D e -2 y 
De-2
 Beam Diameter 
de2
 Focused Beam Dia. z l m d m
The volume is the ellipsoidal surface shown above, and it corresponds to the surface on which the amplitude of the fringes is 1/e2 of the maximum amplitude, which occurs at the center of the measurement volume.
De-2 is the diameter of the unfocused Gaussian laser beam measured at 1/e2 of the centerline intensity. A larger De-2 results in smaller de2 , due to Gaussian beam optics.
de2 is the corresponding diameter at the focal spot (beam crossing point) for each beam. The resulting waist diameter is slightly larger.
dm is the resulting diameter at the measurement volume, accounting for the fact that two beams cross and overlap to get this spot size. It is basically the projection of the de2 diameter onto the vertical plane. That is why the resulting waist diameter is slightly larger than de2.
lm is the resulting length at the measurement volume, accounting for the fact that two beams cross and overlap. It is basically the projection of the de2 diameter onto the horizontal plane. y
de2 = 4 f l / p De-2
dm = de2 / cos 
de2 = diameter here
lm = de2 / sin  x V 
6 cos2  sin  3  / (
de2 z
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13. Measurement Volume Parameters
Diameter of Measuring Volume:
de2 = f 4   e D 2 
and
dm = de2 / cos 
(from previous slide)
dm ~ de2 / 1
since  is small
dm ~ f l / 2 since De2 ~ 2.5mm
dm ~ f / 4 since l ~ 0.5mm
Units: Dm will be in mm, if l in mm, f in mm, De2 in mm
f = focal length of the lens, l = laser wavelength, , 0.488, , or 0.532um
De2= beam diameter, dm = waist diameter
The diameter of the measuring volume (or waist) dm is given by
dm = de2 /cos k
Since k is small, cos k ~ 1, and dm = de2
We can simplify by assuming a 2.5mm beam diameter and 0.5um wavelength:
Focal Length of 120mm gives 120/4 = 30um waist
Focal Length of 250mm gives 250/4 = 60um waist
Focal Length of 350mm gives 350/4 = 90um waist
Focal Length of 500mm gives 500/4 = 125um waist
The laser beam diameter depends on the type of fiber probe and can range from 0.9 mm to 4.5 mm.
Example:
f = 120mm
Measurement Volume Diameter dm 30mm, → “small”
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14. Measurement Volume Parameters
Length of Measuring Volume
lm = dm / sin 
(from previous slide)
tan  ~ sin k ~ (S/2) / f e D -2  f S
so lm = 2 f dm / S = f dm / 25
Fringe Spacing df
f  S  f  
2 sin K ~
0.5
Generally, half angle k is small and hence sin k ~ tan k ~ k
From the angles here, tan k = (S/2)/f or S/2f
For a beam spacing S = 50mm like in the TR 60 series probes, lm = f dm / 25
Often, the length is approximated as 10x the diameter of the waist.
Smaller measuring volume sizes are obtained for larger half angles k.
With a 120mm lens on a TR 60 series probe, the half angle is 12deg
The fringe spacing is 0.5 * 120/50 = 1.2um
The measurement volume diameter is ~ f/4 = 30um
The measurement volume length is ~ 10 dm = 300um
Example : TR-260 probe, f = 250 mm, S = 50 mm
lm = 10 dm = 620 m and df = 2.5 m
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15. Measuring Volume Parameters
Number of Fringes dm
4 fl / pDe2
4 S
NFR    df
fl / S  e D 2 
Note: NFR is independent of focal length ( f) and beam expansion
NFR ~ S / 2 if S is in mm, since De2 ~ 2.5mm
The number of fringes may have been more important in the early days of analog processors, and inflexible downmixing (shift). It is still important for high speed flows, and when selecting custom beam diameters.
S is the beam spacing
The beam diameter is approximately 2.5 mm
Notice what happens if we use an optional 4.5mm beam diameter.
The number of fringes is independent of focal length and beam expansion.
Example
for S = 50 mm, NFR = (for = 2.6 mm) e D 2 
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16. Copyright© 2005 TSI Incorporated
System Parameters
Many of these parameters are found in the FlowSizer Run Setup -> Optics tab.
The FlowSizer Optics Setup Screen has all the important parameters automatically calculated and shown.
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17. Total System Parameters
All these parameters and many more are found in the PDPA LDV performance spreadsheet
The TSI system performance spreadsheet has all these parameters, and more. Please ask for one if you would like to upgrade your system and see a performance summary for various lenses and beam expansion options.
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18. Copyright© 2005 TSI Incorporated
Considerations in LDV
Optimize Optics and Seeding for:
Physical Limits of Experiment
Flow Media
Laser Power Required for Good Signals (SNR)
Adequate Spatial Resolution
Required Data Density
Select Signal Processor Based on:
Frequency Range Required (Maximum Flow Velocity)
Bandwidth (Dynamic Range)
Required Flow Information
When establishing the specifications for a LDV system, we look at the size of measured flow, what fluid is being measured (air, water, oil, etc), the presence of windows, factors that make a high laser power necessary, and seeding requirements for adequate data density.
We must also look at stand-off requirements, measurement room size constraints, and the range of velocities that need to be measured.
In selecting the FSA signal processor, we must look at the range of velocities present, whether they are steady or represent a large dynamic range. We also seek the requirements now or at a future point for size measurement (PDPA).
Next we look at some applications
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19. Turbulence Characteristics of a Swirling Jet
3D LDV set up in a “tent” to enclose the particle cloud.
Courtesy of Courtesy of Prof. J. Naughton and R. Semaan, Dept. of Mechanical Engineering, Univ. Wyoming.
Full turbulence statistics measured with a 3D LDV system.
See AIAA paper number for details.
Copyright© 2005 TSI Incorporated

20. Turbulence Characteristics of a Swirling Jet
Data taken with a traverse can be interpolated and plotted with high-level software.
Black dots indicate measurement locations.
Courtesy of Courtesy of Prof. J. Naughton and R. Semaan, Dept. of Mechanical Engineering, Univ. Wyoming.
Axial normalized turbulent stress distribution (uu/U2o) for a swirl number of 0.39, Reynolds number of 100,000, and solid body type swirl.
See AIAA paper number for details.
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21. Copyright© 2005 TSI Incorporated
High Speed Flow
This slide shows data from an aerated liquid jet in a supersonic cross-flow from Dr. Steven Lin at AFRL-Wright Patterson Air Force Base. The injected liquid was water, the freestream gas was air.
The liquid injector diameter was 0.5mm, the Jet-to-freestream momentum flux ratio was 7, the injector gas-to-liquid mass ratio was 5%, and measurements here are at 100mm downstream.
The statistics speak for themselves.
Notice the data rates, validation rates, and mean gate time.
Next slide shows a composite of many measurements in the test section of this wind tunnel.
Vmean = 595m/s
Freqmean = 118.8MHz
Valid Vel = 100%
Valid Dia = 91.7%
Gate Timemean = 110ns
Data Rate: Ch 1 = 55.8kHz, Ch 2 = 26kHz
Copyright© 2005 TSI Incorporated
Courtesy of Dr. Steven Lin, TaiTech Inc.

22. Analysis of a Fluttering Flow
Power spectrum can provide details of the energy content of a flow. This in turn can indicate whether the turbulence present is coherent or repeatable in some way, such as that due to a wire or body in the flow. This slide shows velocity data with a periodic fluctuation, at about 210Hz. It could be due to vortex shedding, slug formation/blow-out in a pipe, or another similar process. The lower plot shows the power spectrum of this data, clearly indicating the peak at 210Hz. Although our data rate was quite high (40kHz) only 2500 samples were obtained.
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23. Aircraft Turbine Combustor
Cold Flow
Lean Low NOx Combustor (GE CFM 56 Engine)
Combustion
Courtesy of Jonathan Colby, Georgia Institute of Technology
This slide shows data from a premixed pre-vaporized lean (PPL) type aircraft combustor. Here, fuel efficiency and NOx emissions are the main concern. This translates into how to burn the fuel in a short amount of time, in spite of overall lean and low temperature conditions. Turbulence is the answer, and TSI’s LDV system can measure turbulence in this combustor, even with the flame present.
Fuel Rate = 0.75g/s
Eq. Ratio = 0.4
Tair = 380K
Twall = 540K
Copyright© 2005 TSI Incorporated
Courtesy of Jonathan Colby, Georgia Institute of Technology

24. Phase Discriminated LDV
Use a single probe, Ar ion wavelengths
NO dyes, NO wavelength filtering, NO expensive spherical particles required
Uses ordinary seeding particles and ordinary sand
Wave Machine
Tracers in the Water (Continuous Phase)
Sand is Transported off the Crests (Dispersed Phase)
An LDV system can be used to measure phase discriminated velocities. The following few slides show results from a wave tank, measuring the velocities of sand particles and the free stream.
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25. Phase Discriminated LDV
We do not expect the typical Iscatter ~ d2 to hold for irregular particles
However, regardless of particle shape, surface texture, etc. larger particles are expected to scatter more light than smaller particles
“Borrow” burst intensity measurement capability from PDPA*
Measured burst intensity histogram:
Sand
Tracers
This slide shows data from a seeded wave channel flow, for the Crest Region - a location where both sand and freestream interact, thus we see both peaks.
* US Patent
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26. Phase Discriminated LDV
Compare intensity distribution for various measurement locations
On the bed (sand only)
In the free stream (tracers only)
This slide shows data from a seeded wave channel flow, for three measurement locations: On the Bed is very close to the sand bed, capturing predominantly sand particles. These are measured as a peak at about 150mV. In the Freestream is far from the bed, thus detecting only tracer particles. Here we see only the lower intensity peak. In the Crest Region is at a location where both sand and freestream interact, thus we see both peaks.
flowSizer software’s Sub-Range feature can be used to separate the data according to the intensity level. We would place the tracer/sand cutoff around 90mV. All values corresponding to intensities below 90mV would then be sorted out and displayed. The same is then done for intensities 90mV and above.
Sand
Tracers
In the crest region (both sand and tracers)
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27. Phase Discriminated LDV
Sediment (Dispersed Phase)
0.5Hz
30cm/s
Tracers (Continuous Phase)
0.5Hz
1Hz
34cm/s
This slide shows data separated by intensity.
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28. Probes for Underwater LDV
Sealed Stainless Steel Probes
Prism Attachments
This slide shows sealed stainless steel underwater LDV probes (1D on right, 2D on left).
Underwater prism attachments makes it easy to set the beam overlap, and also easy to adjust the beam steering for measuring through walls, etc.
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29. Copyright© 2005 TSI Incorporated
Conclusions
Special properties of laser beams allow us to generate fringe patterns
Particles are added to flow, their velocity is measured
Light is scattered in all directions, but not uniformly
Different lens focal lengths give different fringe spacings
Fringe crossing rate of particle generates Doppler frequency
Velocity is determined directly from Doppler frequency
Multitude of applications
In this section we have seen the following:
Special properties of laser beams – collimated monochromatic coherent light source - allow us to generate fringe patterns
Particles are added to flow, their velocity is measured rather than the gas velocity
Light is scattered in all directions, but not uniformly, as given by Mie scattering theory (in the most complete form)
Different lens focal lengths give different fringe spacings
Fringe crossing rate of particle generates Doppler frequency
Velocity depends directly upon the Doppler frequency, via the fringe spacing
Multitude of applications in air and water measurement
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