Measurement of Gas Properties by

Incoherent and Coherent Rayleigh

Scattering

Richard B. MilesPrinceton University

Dept. of Mechanical & Aerospace Engineering

The Ohio State UniversityFrontiers in Spectroscopy

Feb 16-18, 2005

Two approaches to the measurement of local neutral gas temperature in a weakly ionized plasma

• Filtered Rayleigh Scattering (Joe Forkey, Walt Lempert, Pingfan Wu, Rene Tolboom)

– Uses an optically thick atomic cell for filtering the Rayleigh signal to reject background scattering

– Requires a tunable, narrow linewidth laser and an atomic or molecular vapor filter

– Yields a single point, line, or cross sectional plane measurement

– A single pulse (10 nsec) measurement possible if pressure is known

• Coherent Rayleigh Brillouin Scattering (Xinggau Pan, Mikhail Shneyder, Jay Grinstead, Peter Barker)

– Four wave nonlinear effect similar to CARS

– Gives very strong background rejection and high signal strength

– Requires one broad band laser and one narrow line tunable laser

– Yields a single point measurement, but a line measurement possible

Field Surrounding a Dipole

eR 2 cos

o

ik

r

1

r2

x ()e it ikr

4r

e sino

1

r2 ik

r k 2

x ( )e it ikr

4r

e k 2 sin x( )e it ikr

4ro

k=ω/c=2π/λ ~107 m-1. For r>> λ

0Re

x

y

z

r

a

ra

x��������������

The Dipole Field

2

sin,s

o

pE r

r

2

0 ,,

2s

s

c E rI r t

2 2 2

4 2

sin

2so

cpI

r

For Rayleigh scattering, the dipole is driven by an incident field that creates the polarization.

since

we have

p ����������������������������

The Induced Dipole

IEp

2 22

2 4 2sins I

o

I Ir

The induced polarization is proportional to the incident field. In the case of an atomic gas, the polarizability is a scalar.

and

IzzzIyzyz

IzyzIyyyy

IzxzIyxyx

EEp

EEp

EEp

For molecular gases, the polarizability is a tensor

Scattering Cross Section

Iss

s Ir

I2

1

2 22

2 4sinss

o

I

o

IP42

23

3

8

Iss I

P

42

23

3

8

o

ss

The differential scattering cross section is

Total Scattering Power integrate over a sphere surrounding the dipole

The total scattering cross section is

soss

ss d

Polarizability

2

132

2

n

n

No

2

2

2

24

3

2

124

n

n

Nss

2

4

3 1

3

32

N

nss

22

24

4 1sinss n

N

The polarizability can be written in terms of the index of refraction

Note that this comes from 20 0 0D E P E N E n E

with the 3/(n2+2) Lorentz-Lorenz factor added to account for the local field correction

This gives

If as in a gas 1n

and

(Air is ~1.00027)

Power Collectedfrom a single dipole

I

ss IP

ss

IIP

The optical system can only collect light from a small fraction of the sphere into which the light is scattered. The differential detected power per steradian is

The power collected from one dipole is that differential power integrated over the collector solid angle

Coherent vs Incoherent Scattering

•For coherent dipoles, the peak intensity is n2 times the single dipole intensity, but that only occurs where all the phases add. For many dipoles, this corresponds to a very small angle. At other angles, the intensity is low.

•For incoherent scattering, the interference washes out, so the intensity increases as n, i.e. linearly with the number of dipoles and the scattering is not well collimated

Incoherent Scattering

I 1

2En

n 2

I nI1

For Rayleigh scattering, the density fluctuations in the air cause the interference to be washed out in all but the forward direction, where all the path lengths are the same because there is no scattering delay, so the phase of the scattered light matches the phase of the propagating light. In this direction Rayleigh scattering is suppressed and the effect reduces to the index of refraction

n= # of molecules in the observed volume

Rayleigh Signal

dNVIP ssIDET

detector

Laser

•N = the number of dipoles per unit volume•V=the illuminated volume of the sample•ΔΩ=the collection solid angle•η=the detector and optical system efficiency•II=the incident laser intensity

Narrow linewidth laser

Test Section

Camera

Molecularor atomic vapor

Cell

Filtered Rayleigh Scattering

Rayleigh scattering is very weak•High power laser is needed•Exclusion of background scattering

Iodine

• Simple to build - cell is close to room temperature

• Overlaps both doubled YAG and argon ion lasers– Note that with injection locking, both Ar++ and

Nd:YAG are tunable over many iodine lines

• Maximum attenuation is 105 because of weak continuum absorption

Absorption Spectrum of Iodinein Doubled YAG region

Optically Thick Iodine Absorption Spectrum(measured and modeled: 3 Torr) Forkey

500,000 Frame per Second Imaging of Supersonic Air withCO2 Nanoparticles and an Iodine Filter

3 22 6

2 4

8

3ss

o

V r

3particles V r

Particles in the Rayleigh range (2πr<<λ) have a large cross section so they can be used for flow visualization

Shock-Wave/Boundary-Layer Interaction in Mach 3 Wind Tunnel

Pulse-Burst Laser

Box Car

Flow

MHz Camera

I2 Cell

I2 CellLensPD1

PD2 Optics=0.532m

PC

x

y

z

Laser Sheet Orientation:x-y:streamwisex-z:planform

CO2 as a Seed Material• ~1% CO2 is added to the air upstream of the

supersonic wind tunnel plenum chamber

• As the flow expands through the nozzle, CO2 condenses into clusters as temperature drops

• In the thermal boundary layer, the temperature recovers to close to the plenum temperature and CO2 clusters sublime

Upper limit of the average CO2 cluster size is estimated around 10 nm.

Models predicted that the CO2 clusters rapidly condense or sublime so they accurately mark the temperature discontinuity in the boundary layer

Mach 2.5 FLOW

240 ANGLE RAMP

Mach 3 core flowFlow velocity ~600 m/s0.053 cm-1 shift

Laser tuned tohighlighthigh velocity

Laser tuned toobservelower velocity

Visualization of Mach 8 Flow over Three Dimensional Body

X-33 Space Vehicle Model 4:1 Elliptic Cone

Mach 8 Flow Over 4:1 Elliptic Cone

Three Dimensional Unsteady Boundary Layer:• Pressure gradient between major and minor axis generates crossflow along circumferential direction• Crossflow vortices are predicted to cause early boundary layer transition

Y-Z

X-Z

FLOW

X-Y

Laser Sheet Orientations• Streamwise (X-Y)• Planform (X-Z)• Spanwise (Y-Z)

Simultaneous Imaging of Two Planes 500 kHz, Rex=1.6×106

Spanwise View

Planform ViewFlow

Flow

Volumetric Imaging of Boundary Layer at Mach 8 Using Sequential Spanwise Images

•Pulse-burst imaging of centerline boundary layer in planform orientation revealed slowly-evolving structures• 3-dimensional image of transitional boundary layer is reconstructed under “frozen flow” assumption

Planform Single-shottaken at 16 µs

Flow

16 s

12 s

8 s

4 s

0 s

37.7 mm

8.8 mm20 s

Flow moving out of plane

Spanwise sequential slicestaken by pulse-burst laser

3-D Reconstruction of 4:1 Centerline Region(Rex=1.57 million)FLOW

Boundary Layer Structure over 2:1 Elliptic Cone (Rex=1.3 million)

Pressure, Temperature and Velocity Images in Air by Filtered Molecular

Scattering

• Mach 2 vertical supersonic jet is observed

• The laser is expanded to a sheet and frequency tuned

• Multiple images give the local, frequency shifted Cabannes line convolved with the iodine filter line at each pixel

• Deconvolution knowing the iodine filter shape gives the Cabannes line shape at each pixel

• Pixel by pixel curve fitting to theory gives T, v, P

Rayleigh Scattering Spectrum(of Nitrogen)

Rotational Raman 12 cm-1

Vibrational Raman

2331 cm-1

Cabannes 0.03 cm-1

Y = scattering length / mean free path

Cabannes Line Broadening

Scattering length, Λ

k1 k2

1 2

2k k K

max / 2laser

observerLasersource

Kinetic Regime

• If Y < 1, then in the Knudsen Regime – no collective effects. The Cabannes line is Gaussian in this regime

• If Y > 1, then in the hydrodynamic regime – collective effects dominate – Acoustic waves are important– In this regime there are three peaks, a central peak

associated with non propagating entropy fluctuations and two side Brillouin peaks associated with propagating sound waves

Cabannes (central Rayleigh) Line in AirShowing the Y parameter effect

-6 -4 -2 0 2 4 6

0.0

0.1

0.2

0.3

0.4

0.5

Re

lati

ve

In

ten

sity

(A

.U.)

Frequency (GHz)

Cabannes Line of Air at standard conditions with doubled YAG laser with detection at 90o

Y = 0.7

Mach 2 Underexpanded Supersonic Air Jet

Average image Single shot image

Temperature, pressure and velocity of a Mach 2 free jetwith weak crossing shocks

Coherent Rayleigh Brillouin Scattering (CRBS)

• Two pump beams create moving gratings• Ponderomotive forces drive moving, grating like density

fluctuations in the synchronized velocity groups• Coupling is to the polarizability of the molecule – force

occurs for monatomic as well as polyatomic molecules• The density of gratings created reflects the thermal

velocity distribution• Probe laser Bragg scatters off the density gratings• Temperature is found from the spectral profile of the

coherent signal beam observed ~10 meters from the sample volume

Coherent Rayleigh-Brillouin Scattering

Physical process

z

The optical dipole force produces the density fluctuations. Polarizable molecules feel a force toward the region of high field

Coherent Rayleigh Scattering in Weakly Ionized Gases

How is the intensity spectrum related to temperature?

• The molecules with velocity close to the wave phase velocity will be reorganized by the ponderomotive force leading to a moving density grating

• I() is then related to f(v=/k).

• Conclusion is: The width of the intensity spectrum depends on (T/m)1/2. The spectrum is closely Gaussian, about 10% wider than the spontaneous Rayleigh spectrum.

v = /k

f(v)

v

• Theory based on the Wang-Chang-Uhlenbeck Equation

• Internal energy modes considered• Perturbative method, linearized equation, model

collision term• Gas density perturbation waves: generation by the

optical dipole force and relaxation through particle collisions

Coherent Rayleigh-Brillouin Scattering in molecular gases

Theory

Coherent Rayleigh-Brillouin Scattering in molecular gases

Theory: Wang-Chang-Uhlenbeck equation

i ii v i

coll

f fv f a f

t t

( . ) ( , , )i in r t f v r t dv

1 2 sin( )z

k E EFa a kz t

m m

The forcing term is from the laser interaction and accelerates along the z axis:

At equilibrium, fi has a Gaussian distribution of velocities

and a Boltzmann distribution of states.

fi is the space –velocity-time distribution function for

molecules in state i.

Perturbation Approach

0( , , ) ( )i if v r t n x v3/ 2 2

2 20 0

1( ) exp( )

vv

v v

i

b

j

b

E

k Ti

i E

k Tj

j

g ex

g e

At equilibrium, the distribution function is

0( , , ) ( ) 1 ( , , )i i if v r t n x v h v r t

where and

The distribution function is assumed to be perturbed and the equations are solved for the dimensionless parameter, ih

1ih

, , 0 2 /bv k T M

Gas parameters needed

• Mass

• Shear viscosity

• Bulk viscosity

• Thermal conductivity

• Dimensionless internal specific heat capacity (1 for O2 and N2, 2 for CO2)

Yip & Nelkin (1964) theory for monatomic gases Pan, Shneider & Miles, PRL, 2002

The Experiment• Argon plasma at 50mb

• Pump laser is Frequency doubled Nd:YAG– 24.8 GHz (FWHM) with 250 MHz longitudinal mode structure

– Split and intersected in the gas at 1780 crossing angle

– Focal diameter is 200 μm diameter

– 6 mJ per pulse

– Polarized out of plane

• Probe laser is injection locked and tunable frequency doubled Nd:YAG– 150 MHz linewidth

– ~1 mJ per pulse

– Polarized in plane

• Fabry Perot Etalon– 99.6% mirror reflectivity at 532 nm

– Finesse of 215

– Free Spectral Range of 11.85 GHz

• Wavelength Monitoring Etalon FSR = 900 +/- 0.2 MHz

Experimental Details

• The pump beams produce a spectrum of interference patterns

– The patterns only couple to the gas over the region of kinetic motion

– The pump line width is broad compared to the kinetic spectrum, so it is considered constant

– The 250 MHz beat frequency is removed by Fourier transforming, filtering, and then back transforming the data

• The probe laser is scanned and the intensity of the scattering is monitored by a fixed etalon

– The intensity of the shifted scattering is a measure of the number of molecules in the kinetic (velocity) state that produces that shift.

– The probe is polarized orthogonal to the pump to eliminate background noise

Coherent Rayleigh-Brillouin Scattering

Experiment setup

Experiment setup photo in Weakly Ionized Gases

Coherent Rayleigh Scattering in Weakly Ionized Gases

Data shows the mode structure of the pump laser

Coherent Rayleigh Scattering in Weakly Ionized Gases

A sample result in argon gas (Tthermocouple = 293 K +/- 1 K)

Coherent Rayleigh Scattering in Weakly Ionized Gases

A sample result in argon glow discharge

Coherent Rayleigh-Brillouin Scattering in atomic gases

b=0

Data and model for nitrogen

N2 b=0.73 , agrees with previous measurements

Data and model for oxygen at 292 K

b=1.0 , differs from previous measurements (0.4 )

Data and model for oxygen

O2 Sensitivity of the measurement

CO2 Bulk Viscosity Sensitivity

CO2 Measurement and fitη=0.25 (frozen: γ=1.4)

Summary

Developed an alternative optical method to measure bulk viscosity.

New frequency regime, ~GHz. High frequency wave phenomena: ~1.

Convenient for measuring gas mixtures (Martian and other planetary atmospheres)

Convenient for measurements over a wide range of temperatures

Acknowledgments

This work was supported by the Air Force Office of Scientific Research under the Plasma Rampart Program.

Raman Excitation (RE)Tagging step

Interrogation step

Oxygen X (ground) State

Oxygen B State

Laser Induced Electronic Fluorescence (LIEF)

RELIEF ENERGY LEVEL DIAGRAM

Thermal Diffusion RELIEF Lines in Static Dry Air at 362 K

1 s

100 s

200 s

300 s

400 s

Thermal Diffusion of RELIEF Lines in Static Air1 pixel = 20.33 m

Linear Fit to Thermal Diffusion of RELIEF LineD = 0.26 cm2/sec

Maximum Time Between Tagging and Interrogation for Moist Air

RELIEF Line at the Tagging Position and After 7 sec Delayin Turbulent Subsonic Free Air Jet

A. Noullez, G. Wallace, W. Lempert, R.B. Miles, and U. Frisch, "Transverse Velocity Increments in Turbulent Flow Using the RELIEF Technique," J. Fluid Mechanics 339, 1997, pp. 287-307.

RELIEF Velocity measurement in the 1 meter diameter R1D Test Facility at AEDCAn X was written into the air and the displacement measured and compared with a

pitot probe measurement

flow direction

RELIEF(displaced)

Rayleigh(initial)

Region averaged in vertical dimension

3.6 mm

Simultaneous Tagging (Rayleigh Scattering) and Interrogation (RELIEF)Image in the R1D Facility at AEDC

Horizontal Displacement for AEDC Velocity MeasurementVelocity is 202.4 +/- 0.25 m/sec

Comparison of Pitot and RELIEF Velocity Measurements at AEDC

RELIEF for Supersonic Mixing (Glenn Diskin, NASA)The core helium jet is seeded with 1% oxygen

Helium core jet is seeded with ~1% O2 so it can be tracked

18 mm

28 mm

43 mm