¤ Basic 2-beam Schematic for In-plane Sensing ...

VELOCIMETERSfrom: 'Electro-Optical Instrumentation' by S.Donati, 2004, © Prentice Hall (USA)

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¤ Basic 2-beam Schematic for In-plane Sensing◊ fringe pattern◊ the velocimeter as an interferometer

¤ Performance Parameters◊ scale-factor accuracy ◊ accuracy of Doppler frequency◊ size of sensing region ◊ alignment/positioning errors◊ sign discriminination ◊ particle seeding

¤ Electronic Processing of Doppler Signal◊ time-domain ◊ frequency-domain

¤ Optical configurations ◊ forward ◊ backward◊ two-color ◊ with fiber bundle

Laser Laser DopplerDoppler VelocimetersVelocimeters

Summary


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¤ horizontal fringes are produced at the beam crossover ¤ a particle crossing fringes scatters a field replicating the fringe pattern¤ period of scattered signal is then T=D/v

Basics operation of a LDV

He-Ne laser

BS

mirror

photodetectorθθ

R

R

w m

D

D 2sin θ = λ

θ

A

BC

O

k1

k 2

θθ

θ

v

M

L

D

particle

w m

sin θ

wL

wL

L1

θ

θ

¤ with beamsplitterBS and mirror M, we get twocollimated beamswith offset R¤ lens L focusesbeams to cross the axis at F, with anangle tanθ =R/F


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fringe spacing D is found by setting pathlength AB+AC equal to λ,this gives 2sin θ D = λ, or a fringe spacing

D= λ/ 2sin θ

a particle crossing fringes scatters a field replicating the fringe patternIf period of scattered signal is then T=D/v, then the frequency content is

fD= v/D

Basics operation of a LDV 2

D

D 2sin θ = λ

θ

A

B

C

O

k 1

k 2

θ

θ

θ

v

D

particle

θ

θ


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¤ the envelope of the oscillation signal replicatesthe Gaussian beam profile.¤ particle A, crossing the superposition region at the midpoint, develops the largest number of periods, and is the ideal response.¤ particle B gives fewerperiods and its signal hasless contrast. ¤ particle C outside the superposition region, onlysamples the beam profileand its waveform carriesno information

fringe-crossing signals in a LDV

2 θ

transversal mode profile (along OB or OC)

A B

C

x or y

time

particle in A with a speed v

time

particle in A, but with v'<v

time time

particle in B particle in C

v

v

xy

v D/v

D/v'


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¤ In a LDV, velocity measurement is brought to frequencymeasurement on an electrical signal, with a scale factor R = fD/v= 1/Tv= 1/D= 2sinθ /λ [Hz/(m/s)] example: for θ=30°, λ=1μm → D=1μm, hence R=1/1μm= 1MHz/(m/s)

¤ This is very favorable, as frequency measurement is the best we can perform in electronics, covering e.g. 9 to 12 decades, from mHz...μHzto GHz and above. With a single counter, we may readily make a frequency measurement on 8 decades, for example from 1 Hz to 100 MHz. ¤ as a frequency meter is easily traced to standards of frequency, ourmeasurement has also a precision, with typical ΔfD/fD≈10-6 and better. ¤ taking R =1 MHz/(m/s) as a reference value, we can go from verysmall velocity, ≈μm/s, in the low range (Hz’s) to very high velocity, up to ≈100m/s, in the high range (100MHz’s).

measurement range in an LDV


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the following descriptions of the LDV are equivalent: • fringe crossing• the Doppler frequency deviation ΔfD of a source moving with speed v respect to the observer is ΔfD/f=v/c, or ΔfD=v/λ; accounting for the obliquity factor sinθ, we get for the two beams: ΔfD = ±v sinθ/λ, or, the total frequency difference is Δf = 2v sinθ /λ.

• field E0 impinges on particle from k

the LDVas an interferometer

1 and we look itfrom direction k0: we get E0 exp i(k1-k0)⋅s [generaliza-tion of the usual term E0 exp i2ks]. Then, field is: E= E0 exp i (k1-k0)⋅s + E0 exp i (k2-k0)⋅s and photocurrent I = 2E0

2 [1+ cos (k1-k2)⋅s]. Now, k1-k2 is parallel to the y-axis and has modulus is ⎟k1-k2 ⎟ =2k sin θ. By time-differentiating the phase shift φ we obtain once again: f = (2π)-1(dφ/dt) = (2π)-12k(ds/dt) sinθ = 2 sinθ v/λ

• Doppler effect • interferometric phase shift

k2

k1

k -1k

2

θ

θ


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(top): a ‘referenced’ LDV schematic, with the detector positioned tocollect one beam for use as local oscillator in homodyne detection; (bottom): another referenced LDV uses a beam deviated from the laser to detector. Fringes are not formed, yet kill-kobs determines the axis of sensitivity to the speed component

other configurations of LDV

BS

mirrorM

kill

kobs

v

BS1

v

PDL1

PDL1

2θ

2θ

BS2

M1 M2

laser source

laser source

k illk

obs


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◊ Scale Factor Relative Error: R = f/v= 2sinθ/λ has a relative error sum of the errors in angle, Δθ/θ, where θ=atan R/F and in wavelength, Δλ/λ. (typ. they are 10-3 to 10-4)◊ Accuracy of Doppler frequency fD: detected signal replicates the Gaussian distribution of laser spot: s(t) = (sin 2πfDt) exp -t2/2σt

2 , where σt=wm/v and wm is spot size. By a Fourier transform of s(t) we get s(f) = exp-[(f-fD)2(2πσt)2/2] where the rms error of frequencyis σf =1/(2πσt). Substituting σt=wm/v gives σf= [2π wm/(fDD)]-1, and by rearranging:

σf /fD = 1/(2πNf) where Nf =wm/D is the number of fringes contained in wm

◊ the same result holds for the relative accuracy of the speedmeasurement,

σv /v = 1/(2π Nf)

LDV accuracy performance


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¤ the sensing region is defined by the longitudinal and transversalsizes, wm, and wl. These depend on beam size wL and offset radius Ros¤ they are found from acceptance aω=πwf

2 π(wL/F)2 =λ2 that giveswf =λF/πwL, and considering the obliquity factors (cosθ and sinθ) connecting to wm, and wl . Thus we get

wm = (π cosθ)-1 λF/wL, wl = (π sinθ)-1 λF/wL

¤ number of fringes is then NF = (2/π)Ros/wL

Size of the Sensing Region

θθ

wf

R

F

aω

θos

wf

wm

wl

wL


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At the focusing objective, errors of the incidence angle or of the lateral offset of the two beams result in fringes with unequalspacing (bottom left) or with a tilt with respect to the optical axis(bottom right).

alignment and positioning errors1

1

2

2

1 2

beam waists

optical axis

off-axis imbalance

incidence angle error

a

aa

a

b

b

b

b

correct alignment

off-axis beam waist

tilted beam waist


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alignment /positioning errors 2

¤ Using a beamsplitter prism BS and the folding prisms P1-3 asmirrors (left), we obtain a splittingschematic much more stable and easily trimmed compared to basic schematic. Even better, we can employ Dove prisms to minimizeparts count and improve stabilityfurther (right)

R

R

wL

beamsplitterBS

folding prism

P1

P2

P3

optical axis

objective

b1

b2

BS

Dove prism

Dove prism

¤ The Doppler waveform has100% modulation (or V=1) ifsuperposed beams have a path-length difference less much thanthe coherence length (top). ¤ if coherence is less, or beamsare unequal intensity, wave-forms have a pedestal (bottom)

time

time


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Light scattered byparticle in the measurement regionis collected byphotodetector lookingat the forwardscattering (top) or at the backwardscattering (bottom).Signal is larger in forward scattering forlarge particles, (> 5μm). Is the same asbackward for smallparticles (<0.1μm)

Placement of the photodetector

photodetector

laser I ph

photodetector

laser

I ph

fluid

fluid

mirror

Ω

Ω

L

L'

L

L'

m'


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By adding a frequency shifter on the path of one of the beams of the velocimeter, we generate a moving fringepattern in the measurement region and are able todiscriminate the direction of velocity v

direction discrimination

M1b1

b2

Bragg Cell

k1

k2

fringes move upward at v=f D

f

f+ Δf

f

v= Δf D


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According to the average number N=fT of particles in the measurement volume, the waveform is best processed in the time domain (top) or in the frequency domain (bottom)

Processing of the Doppler Signal

1 2 3 10 11 time (arb. units)

N = f T-0.1

-0.3

- 1

1 2 3 10 11

1 2 3 10 11

time

time


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¤ In time-domain processing, the Doppler signal is time-differentiatedand then squared by a discriminator with a zero-crossing threshold. ¤ Another discriminator works on the signal-envelope to check signal pre-sence and enable counters, one for Doppler signal, the other is for clock.¤ When the signal ends, an inspection circuit checks counter content. If itis high, the result is validated to calculate velocity, if low, is discarded

time-domain processing

fro

m th

e ph

otod

etec

tor

low-noise amplifier

-A

time differentiator

S(t)

S'(t)

clock

S level discriminator

0low-pass filter (smoother)

gatepulse shaper

enable

zero

main counter

zero aux countergate

enable

end of pulse detector

monostable multi

min

content check and gate

divider

<N >Nmax

outv

Nc

fNSSW

@ fc

Senv

enablS

timeout

start out

S level discriminator

0

-A


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¤ (top): Doppler signal S(t) at photodetector output. ¤ (2nd line): computing the time derivative S’(t), we cancel out pedestal and drift and Dopplersignal is in form of zero-crossings. ¤ (3rd line): after discrimination at threshold S0, we get Nf pulses in time Tc. ¤ (4th line): envelope detector finds the signal-end, yielding a gate square wave lasting time Tc.¤ when signal is over, Nf isvalidated by an inspection circuit.¤ clock pulses (Nc) are countedduring Tc. By computing the ratio Nf/Nc, velocity is obtained

waveforms in time-domain processing

time

S(t)

S'(t)

time

S0

discriminator output

gated clock

Tc

SSW

S0

S , envelope of S(t)

env

envelope detector output S enabl


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When particle concentration is high, the number of counts Nf per period Tc is affected by a large error. Then, we look directly at the frequency content of the signal S(t), by two approaches: - autocorrelation: we compute the autocorrelation functionc(τ) = ∫0-∞ S(t)S(t+τ) dt, by first converting the signal S(t) to digital, with an ADC, then acquiring the data and computing c(τ).The ADC may have a 8 bit resolution,because the round-off error issmall respect to that of waveform noise, but it and the acquisitioninterface need to be fast to cover the high-velocity range allowed bythe LDV instrument. [For example, if we get 100 kHz of conversion and acquisition rate, we are then bound to a maximum velocityv≈1μm⋅100kHz= 0.1 m/s].- phase-locked loop When velocity is very high and the frequencycontent too high for the ADC, we use an approach based on the PLL technique.

Frequency-domain processing


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The Doppler signal of an LDV can be filtered for fD extraction by a simple PPL (phase locked loop) arrangement. Signal S(t) iscompared to the oscillation of a Voltage Controlled Oscillator(VCO), and the phase error is used to correct the frequency until itis dynamically locked to the frequency contained in S(t). The gain and filter sections act as the feedback loop of the frequency-trackingoperation. With them, we filter signal S(t), while frequencychanges, yet keeping a narrow band around the average frequency.

PLL approach to frequency-domain

fro

m th

e ph

otod

etec

tor

low-noise amplifier

S(t)

VCO

phase comparator

freq. control

filter

hi-pass filter

out

out

gain


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If the fluid is murky and/or the scattering volume is large, we use particles already there.If the fluid is clean and the scattering volume very small, we may require seeding. Best particle radius is 0.5-0.8λ.

Particle seeding

PMMA spheres1

0.5

0.5 1 r/λ00

averaging response

scatter efficiency


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Common LDV opticalconfigurations incorporatedinto products are:(i) forward-lookingconfiguration ending on a PMT (ii) backward configuration(iii) two-components LDV using a two-line Ar-ion laser(iv) fiber optics configurationto connect laser and receiver tothe measuring volume

LDV opticalLDV optical configurationsconfigurations


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A LDV system is developed for use on practical gas-turbine engines. The system measures inlet and exhaust velocities on an F-100 EMD engine from an F-15 airplane. Plots below show axial speeds in inlet and exhaust flows as measured by use of the LDV system during a transient from idle to full military power then back to idle.

LDV applicationsLDV applications

from: Dryden Flight Research Center


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The LDA technique is ideal for 1D, 2D and 3D point measurement of velocity components and turbulence distribution in both free flows and internal flows. Results of measurement are important steps in fine-tuning product designs to improve aerodynamic efficiency, quality and safety. Application here is an example of measurement of external flow patterns around car’ hulls,to optimize the CX

LDV applicationsLDV applications

Dantec Dynamics’ LDA systems


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Hot-wire Anemometry (HWA) is a point-measuring technique appropriate for measurement of flows with high turbulence and the study of microstructures, where we need to resolve small flow eddies down to the order of tenths of a mm.HWA is often applied in wind tunnel during the design phase of buildings and structures located both on land and in the sea, when they must be optimised to withstand wind and/or wave forces. Typical applications include flows around tall buildings, bridges, offshore oil rigs and research inaerodynamics and turbulence

…… and other approaches: 1and other approaches: 1-- HWAHWA

courtesy of Dantec Dynamics


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courest

PIV is a whole-flow-field technique providing velocity vector measurements in a cross-section of a flow. Two axes are usually measured, but with a stereoscopic approach all 3 are recorded, resulting in instantaneous 3D velocity vectors for the entire image. The use of CCD cameras and dedicated computing hardware, results in real-time velocity maps.

…… and other approaches: 2and other approaches: 2-- Particle Image Velocimetry (PIV)Particle Image Velocimetry (PIV)

courtesy of Dantec, DK


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◊ LDV is a non-contact, powerful technique for velocitymasurements and diagnostics in fluids

◊ it measures the velocity component perpendicular to the optical axis of the projection lens

◊ key parameter is fringe spacing, D=λ/2 sinθ, and is tailoredby the projection angle θ

◊ as velocity is converted to frequency, LDV offers a very wide, unparalleled dynamic range of measurement , from μm/s to over 100 m/s

◊ sampling size is small transversally (wm=λF/πcosθ wL, typ. mm’s), and can be adjusted by setup parameters wm, F, θ.

◊ longitudinal sampling size (wl= wm/tanθ) can be clipped by an a-posteriori signal processing

Summary and Conclusions


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◊ detector can be placed on the same side as source, exceptfor very opaque fluids (optical density >2)

◊ resolution Δv/v=Δf/f is typically % or better, as determined bythe number of fringes N in the sampling region - it can betraded-off for sampling size

◊ clean fluids shall be seeded with small spheres (typ. 1μm dia.)

◊ both time-domain and frequency-domain signal processingare used, for clean and opaque fluids, respectively

◊ drawbacks: 2D extension possible but 3D difficult, image LDV not easily implemented

◊ alternatives to LDV are: the HWA and the PIV, but they haven’tgained the same acceptance, yet

Summary and Conclusions

¤ Basic 2-beam Schematic for In-plane Sensing ...

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