Download Coherent Rayleigh-Brillouin Scattering

Measurement of Gas
Properties by
Incoherent and
Coherent Rayleigh
Scattering
Richard B. Miles
Princeton University
Dept. of Mechanical & Aerospace
Engineering
The Ohio State University
Frontiers 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
x
2 cos  ik 1 x ( )e
eR 
 2

o
r r 
4r
 it ikr

x
it ikr
sin  1 ik
2  x ( )e
e 
k
2 

 o r
r
4r
k=ω/c=2π/λ
~107
m-1.
For r>> λ
k 2 sin   x ( )e it  ikr
e 
4r o
eR  0
ar
a
r

y
z
The Dipole Field
For Rayleigh scattering, the dipole is driven by an
incident field that creates the polarization.   p
Es  r ,   
since
we have
 p sin 
 o 2r
Is
 r, t  
 0c Es
 2cp 2 sin 2 
Is 
2 o  4 r 2
 r , 
2
2
The Induced Dipole
The induced polarization is proportional to the
incident field. In the case of an atomic gas, the


polarizability is a scalar. p  EI
and
 2 2
I s  2 4 2 I I sin 2 
o  r
For molecular gases, the polarizability is a tensor
p x   xy E Iy   xz E Iz
p y   yy E Iy   yz E Iz
p z   zy E Iy   zz E Iz
Scattering Cross Section
The differential scattering
cross section is
Total Scattering Power
integrate over a sphere
surrounding the dipole
P
 ss  2 2
 2 4 sin 2 
  o 
 ss 1
Is 
I
2 I
 r
 ss 

 ss
d

8 3 2
3 o 
2
4
II
The total scattering cross
section is   P
ss
so
II
8 3 2
 ss 
2
3 o 4
Polarizability
The polarizability can be written2 in terms of the
3
n 1
 o
index of refraction
2
n 2
N
D   0 E  P   0 E  N E   0 n 2 E
Note that this comes from
with the 3/(n2+2) Lorentz-Lorenz factor added to
account for the local field correction
This gives
 ss 


If n  1 as in a gas
 ss
2
2
32 3  n  1 

34  N 
 ss 4 2  n  1 
2
 4 
 sin 

  N 
2
and


24  n  1 
4 N 2  n 2  2 
3
2
(Air is ~1.00027)
Power Collected
from 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
P 
 ss
I I 

The power collected from one dipole is that
differential power integrated over the collector
solid angle
 ss
P  I I




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
1
2
I
En

2 n
I  nI1
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
Rayleigh Signal
PDET
 ss
  I I NV 
d

•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
Laser

detector
Filtered Rayleigh Scattering
Narrow linewidth laser
Rayleigh scattering is very weak
•High power laser is needed
•Exclusion of background scattering
Camera
Test
Section
Molecular
or atomic vapor
Cell
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 Iodine
in Doubled YAG region
Optically Thick Iodine Absorption Spectrum
(measured and modeled: 3 Torr) Forkey
500,000 Frame per Second
Imaging of Supersonic Air with
CO2 Nanoparticles and an Iodine
Filter
Particles in the Rayleigh range (2πr<<λ) have a large cross
section so they can be used for flow visualization
 particles  V  r
3
8 3 2
 ss  2 4  V 2  r 6
3 o 
Shock-Wave/Boundary-Layer Interaction in
Mach 3 Wind Tunnel
Box Car
PD1
PD2
PC
Lens I2 Cell
Optics
=0.532mm
Pulse-Burst Laser
y
Flow
x
I2 Cell
MHz Camera
Laser Sheet Orientation:
x-y:streamwise
x-z:planform
CO2 as a Seed Material
Mach 2.5 FLOW
• ~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
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
Laser tuned to
highlight
high velocity
Laser tuned to
observe
lower velocity
Mach 3 core flow
Flow velocity ~600 m/s
0.053 cm-1 shift
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
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
Flow
Planform View
Flow
Volumetric Imaging of Boundary Layer at
Mach 8 Using Sequential Spanwise Images
Spanwise sequential slices
taken by pulse-burst laser
•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-shot
taken at 16 µs
20 ms
8.8 mm
16 ms
12 ms
8 ms
4 ms
0 ms
Flow moving out of plane
Flow
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)
Vibrational Raman
-1
2331 cm
Rotational Raman
-1
12 cm
Cabannes
-1
0.03 cm
Cabannes Line Broadening
Y = scattering length / mean free path
Laser
source
k1
k2
observer
Scattering length, Λ
2
k1  k2  K 

 max  laser / 2
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 Air
Showing the Y parameter effect
Cabannes Line of Air at standard conditions
with doubled YAG laser with detection at 90o
Y = 0.7
0.5
Relative Intensity (A.U.)
0.4
0.3
0.2
0.1
0.0
-6
-4
-2
0
2
Frequency (GHz)
4
6
Mach 2 Underexpanded Supersonic Air Jet
Average image
Single shot image
Temperature, pressure and velocity of a Mach 2 free jet
with 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
f(v)
• 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
v = /k
Coherent Rayleigh-Brillouin Scattering in molecular gases
Theory
• 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: Wang-Chang-Uhlenbeck equation
fi is the space –velocity-time distribution function for
molecules in state i.
fi
 fi 
 v fi  a v fi    
t
 t  coll

ni (r.t ) 

fi (v, r , t )dv

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:
a  az 
 k E1E2
F

sin(kz   t )
m
m
Perturbation Approach
At equilibrium, the distribution function is
fi (v, r , t )  n0 xi (v)

gi e
where xi 
Ei
kb T
g e

Ej
kb T
,
 1 
 (v )   2 
  v0 
3/ 2
v2
exp( 2 )
v0
, and v0  2kbT / M
j
j
The distribution function is assumed to be perturbed
and the equations are solved for the dimensionless parameter, hi
fi (v, r, t )  n0 xi (v) 1  hi (v, r, t )
hi  1
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 fit
η=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.
RELIEF ENERGY LEVEL DIAGRAM
Oxygen B State
Laser Induced Electronic
Fluorescence (LIEF)
Interrogation step
Raman Excitation (RE)
Tagging step
Oxygen X (ground) State
Thermal Diffusion RELIEF Lines in Static Dry Air at 362 K
1 ms
100 ms
200 ms
300 ms
400 ms
Thermal Diffusion of RELIEF Lines in Static Air
1 pixel = 20.33 mm
Linear Fit to Thermal Diffusion of RELIEF Line
D = 0.26 cm2/sec
Maximum Time Between Tagging and Interrogation
for Moist Air
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.
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
Simultaneous Tagging (Rayleigh Scattering) and Interrogation (RELIEF)
Image in the R1D Facility at AEDC
flow direction
3.6 mm
RELIEF
(displaced)
Rayleigh
(initial)
Region averaged in vertical dimension
Horizontal Displacement for AEDC Velocity Measurement
Velocity 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