Measurement of Gas Properties by Incoherent and Coherent Rayleigh Scattering Richard B. Miles Princeton University Dept. of Mechanical

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Measurement of Gas Properties by Incoherent and
Coherent Rayleigh ScatteringRichard B.
MilesPrinceton UniversityDept. of Mechanical
Aerospace Engineering
The Ohio State University Frontiers in
Spectroscopy Feb 16-18, 2005
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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

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Field Surrounding a Dipole
k?/c2p/? 107 m-1. For rgtgt ?
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The Dipole Field
For Rayleigh scattering, the dipole is driven by
an incident field that creates the polarization.
since
we have
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The Induced Dipole
The induced polarization is proportional to the
incident field. In the case of an atomic gas,
the polarizability is a scalar.
and
For molecular gases, the polarizability is a
tensor
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Scattering Cross Section
Total Scattering Power integrate over a sphere
surrounding the dipole
The differential scattering cross section is
The total scattering cross section is
so
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Polarizability
The polarizability can be written in terms of the
index of refraction
Note that this comes from
with the 3/(n22) Lorentz-Lorenz factor added to
account for the local field correction
This gives
(Air is 1.00027)
If as in a gas
and
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Power Collectedfrom a single dipole
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
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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

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Incoherent Scattering
n of molecules in the observed volume
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
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Rayleigh Signal

• N the number of dipoles per unit volume
• Vthe illuminated volume of the sample
• ?Othe collection solid angle
• ?the detector and optical system efficiency
• IIthe incident laser intensity

Laser
detector




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Filtered Rayleigh Scattering

Narrow linewidth laser

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

Camera

Test
Molecular or atomic vapor Cell

Section


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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
  NdYAG are tunable over many iodine lines
• Maximum attenuation is 105 because of weak
  continuum absorption

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Absorption Spectrum of Iodinein Doubled YAG
region
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Optically Thick Iodine Absorption
Spectrum (measured and modeled 3 Torr) Forkey
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500,000 Frame per Second Imaging of Supersonic
Air withCO2 Nanoparticles and an Iodine Filter
Particles in the Rayleigh range (2prltlt?) have a
large cross section so they can be used for flow
visualization
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Shock-Wave/Boundary-Layer Interaction in Mach 3
Wind Tunnel
Box Car
PC
I2 Cell
Lens
PD1
Pulse-Burst Laser
?0.532mm
PD2
Optics
y
Flow
x
z
Laser Sheet Orientation x-ystreamwise x-zplanfo
rm
I2 Cell
MHz Camera
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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

Mach 2.5 FLOW
240 ANGLE RAMP

• 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

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Mach 3 core flow Flow velocity 600 m/s 0.053
cm-1 shift
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Visualization of Mach 8 Flow over Three
Dimensional Body
41 Elliptic Cone
X-33 Space Vehicle Model
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Mach 8 Flow Over 41 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
Laser Sheet Orientations Streamwise (X-Y)
Planform (X-Z) Spanwise (Y-Z)
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Simultaneous Imaging of Two Planes 500 kHz,
Rex1.6106
Spanwise View
Planform View
Flow
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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

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3-D Reconstruction of 41 Centerline
Region(Rex1.57 million)
FLOW
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Boundary Layer Structure over 21 Elliptic Cone
(Rex1.3 million)
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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

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Rayleigh Scattering Spectrum(of Nitrogen)
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Cabannes Line Broadening

• Y scattering length / mean free path

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Kinetic Regime

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

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Cabannes (central Rayleigh) Line in Air Showing
the Y parameter effect
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Cabannes Line of Air at standard conditions with
doubled YAG laser with detection at 90o Y 0.7
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Mach 2 Underexpanded Supersonic Air Jet
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Temperature, pressure and velocity of a Mach 2
free jet with weak crossing shocks
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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

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Coherent Rayleigh-Brillouin ScatteringPhysical
process
z
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The optical dipole force produces the density
fluctuations. Polarizable molecules feel a force
toward the region of high field
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Coherent Rayleigh Scattering in Weakly Ionized
GasesHow 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.

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Coherent Rayleigh-Brillouin Scattering in
molecular gasesTheory

• 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

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Coherent Rayleigh-Brillouin Scattering in
molecular gasesTheory Wang-Chang-Uhlenbeck
equation
fi is the space velocity-time distribution
function for molecules in state i.
At equilibrium, fi has a Gaussian distribution of
velocities and a Boltzmann distribution of states.
The forcing term is from the laser interaction
and accelerates along the z axis
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Perturbation Approach
At equilibrium, the distribution function is
,
,
and
where
The distribution function is assumed to be
perturbed and the equations are solved for the
dimensionless parameter,
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Gas parameters needed

• Mass
• Shear viscosity
• Bulk viscosity
• Thermal conductivity
• Dimensionless internal specific heat capacity (1
  for O2 and N2, 2 for CO2)

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

• Argon plasma at 50mb
• Pump laser is Frequency doubled NdYAG
• 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 NdYAG
• 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

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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

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Coherent Rayleigh-Brillouin ScatteringExperiment
setup
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Experiment setup photo in Weakly Ionized Gases
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Coherent Rayleigh Scattering in Weakly Ionized
GasesData shows the mode structure of the pump
laser
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Coherent Rayleigh Scattering in Weakly Ionized
GasesA sample result in argon gas
(Tthermocouple 293 K /- 1 K)
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Coherent Rayleigh Scattering in Weakly Ionized
GasesA sample result in argon glow discharge
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Coherent Rayleigh-Brillouin Scattering in atomic
gases?b0
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Data and model for nitrogenN2 ?b0.73 ?, agrees
with previous measurements
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Data and model for oxygen at 292 K?b1.0 ?,
differs from previous measurements (0.4 ?)
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Data and model for oxygenO2 Sensitivity of the
measurement
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CO2 Bulk Viscosity Sensitivity
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CO2 Measurement and fit?0.25 (frozen ?1.4)
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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

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Acknowledgments

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

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RELIEF ENERGY LEVEL DIAGRAM
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Thermal Diffusion RELIEF Lines in Static Dry Air
at 362 K
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Thermal Diffusion of RELIEF Lines in Static Air 1
pixel 20.33 mm
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Linear Fit to Thermal Diffusion of RELIEF Line D
0.26 cm2/sec
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Maximum Time Between Tagging and Interrogation
for Moist Air
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RELIEF Line at the Tagging Position and After 7
msec Delay in 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.
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RELIEF Velocity measurement in the 1 meter
diameter R1D Test Facility at AEDC An X was
written into the air and the displacement
measured and compared with a pitot probe
measurement
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Simultaneous Tagging (Rayleigh Scattering) and
Interrogation (RELIEF) Image in the R1D Facility
at AEDC
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Horizontal Displacement for AEDC Velocity
Measurement Velocity is 202.4 /- 0.25 m/sec
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Comparison of Pitot and RELIEF Velocity
Measurements at AEDC
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RELIEF for Supersonic Mixing (Glenn Diskin,
NASA) The core helium jet is seeded with 1 oxygen
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Helium core jet is seeded with 1 O2 so it can
be tracked
18 mm
28 mm
43 mm