Richard G. Seasholtz

Glenn Research Center, Cleveland, Ohio

Jayanta Panda

Ohio Aerospace Institute, Brook Park, Ohio

Kristie A. Elam

Akima Corporation, Fairview Park, Ohio

Rayleigh Scattering Diagnostic for Dynamic

Measurement of Velocity Fluctuations in

High Speed Jets

NASA/TM—2001-210821

April 2001

AIAA–2001–0847
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NASA/TM—2001-210821

April 2001

National Aeronautics and

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Glenn Research Center

Prepared for the

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Reno, Nevada, January 8–11, 2001

AIAA–2001–0847

Richard G. Seasholtz

Glenn Research Center, Cleveland, Ohio

Jayanta Panda

Ohio Aerospace Institute, Brook Park, Ohio

Kristie A. Elam

Akima Corporation, Fairview Park, Ohio

Rayleigh Scattering Diagnostic for Dynamic

Measurement of Velocity Fluctuations in

High Speed Jets
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7121 Standard Drive

Hanover, MD 21076

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Available electronically at http://gltrs.grc.nasa.gov/GLTRS
NASA/TM—2001-210821 1 

RAYLEIGH SCATTERING DIAGNOSTIC FOR DYNAMIC MEASUREMENT OF VELOCITY 

FLUCTUATIONS IN HIGH SPEED JETS 

Richard G. Seasholtz 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Jayanta Panda 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Kristie A. Elam 

Akima Corporation 

Fairview Park, Ohio 44126 

ABSTRACT

 A flow diagnostic technique based on the molecular 

Rayleigh scattering of laser light is used to obtain 

dynamic density and velocity data in a high speed flow. 

The technique is based on analyzing the Rayleigh 

scattered light with a Fabry-Perot interferometer used in 

the static, imaging mode. An analysis is presented that 

established a lower bound for measurement uncertainty of 

about 20 m/sec for individual velocity measurements 

obtained in a 100 μsec time interval. Software and 

hardware interfaces were developed to allow computer 

control of all aspects of the experiment and data 

acquisition. The signals from three photomultiplier tubes 

were simultaneously recorded using photon counting at a 

10 kHz sampling rate and 10 second recording periods. 

Density and velocity data, including distribution functions 

and power spectra, taken in a Mach 0.8 free jet are 

presented. 

 

INTRODUCTION

 In this paper we describe a flow diagnostic based 

on the molecular Rayleigh scattering of laser light for 

use in NASA test facilities. This diagnostic will provide 

dynamic aerothermodynamic data that are not presently 

available. These data will be important in studies such 

as the investigation of growth and decay of turbulent 

fluctuations. The effort is part of the non-intrusive 

instrumentation development program supporting 

propulsion research at the NASA Glenn Research 

Center. This work is directed to the measurement of 

fluctuations in flow velocity, density, and temperature 

for jet noise studies. One of the main objectives in jet 

noise research is to identify noise sources in the jet and 

to determine their contribution to noise generation. In 

particular, researchers have focused on the correlation 

of fluctuations in flow parameters with far field noise1

. 

 A variety of nonintrusive, laser based flow 

diagnostics (Rayleigh scattering, Laser Doppler 

Velocimetry (LDV), Particle Imaging Velocimetry (PIV), 

Laser Induced Fluorescence (LIF)) are routinely being 

applied for time average and instantaneous planar 

measurements of velocity, density, temperature, and 

species concentrations. However, an important class of 

measurements, high frequency response dynamic 

measurements of flow parameters, is not addressed by 

current laser diagnostics. This type of time history data is 

needed to determine, for example, density and velocity 

spectra, density-velocity correlations, and two-point 

correlations. Although LDV can typically achieve data 

rates of a few tens of kHz, it is difficult to achieve much 

higher rates without introducing larger amounts of seed 

material into the flow. In practice, LDV normally 

provides mean velocity and a measure of turbulence 

intensity. Furthermore, the measurements are random 

in time, which makes it difficult to obtain time history 

data needed for power spectra. In turbulent flows, LDV 

measurements are beset by a variety of so-called biasing 

errors, caused by correlations between the measurement 

rate and flow properties. Planar techniques, such as PIV 

and planar Rayleigh scattering, provide a large number of 

simultaneous measurements in a plane, but are generally 

limited to low sampling rates, determined by the pulse 

repetition rate of the laser and by the time needed to 

transfer image data from the camera. New techniques 

are needed to provide nonintrusive, dynamic 

measurements that can provide data similar to that 

provided by hot wire anemometers. Since it is unrealistic 

to expect (at least at the present time) to make 

measurements at a large number of locations and at a high 
NASA/TM—2001-210821 2 

sampling rate, it seems prudent to develop a laser 

diagnostic capable of point measurements at high 

sampling rates. 

 Because the Rayleigh scattering technique under 

study is based on molecular scattering rather than particle 

scattering, no seed material need be injected into the flow. 

One difficulty with LDV and PIV is that they require the 

flow to be "seeded" with micron size seed particles to 

provide a sufficient concentration of scattering centers. 

The reliance on seed particles presents a number of 

difficulties, such as difficulty injecting a uniform cloud of 

seed, and providing seed material that can withstand the 

flow environment. For high temperatures, refractory seed 

materials are necessary. In addition, seed material can 

contaminate the facility, coating surfaces and windows. 

Facility engineers are often wary of the introduction of 

this foreign, often abrasive material, into their equipment. 

A further limitation of particle scattering methods is that 

the particles, although small, may not be able to follow 

large flow accelerations, thus introducing inaccuracy in 

the prediction of the gas velocity. 

 These problems associated with particle scattering 

measurements are eliminated if molecular scattering is 

used, since the gas molecules that constitute the flow 

under study are used as the scattering centers. The 

simplest molecular scattering based diagnostic is 

Rayleigh scattering. The frequency spectrum of Rayleigh 

scattering is closely related to the velocity distribution of 

the scattering gas. The spectrum may be analyzed to 

determine temperature, density, and velocity. Density is 

simply proportional to the total scattered light; 

temperature is related to the width of the Rayleigh 

spectrum; and one component of velocity is proportional 

to the shift of the spectral peak from the frequency of the 

incident light. Because the spectral width is also a 

function of the molecular weight of the gases in the flow, 

knowledge of the gas composition is generally required; 

however, this is not a concern in the proposed work, 

which is directed toward air flows where the composition 

is well defined. In any case, velocity measurements, 

because they are determined from the frequency of the 

peak of the spectrum, are independent of the gas 

composition. Rayleigh scattering is particularly suitable 

for measurement of supersonic and hypersonic velocity 

where the mean molecular velocity (flow velocity) is 

larger than the random molecular velocity (temperature). 

 Because of the relative simplicity of Rayleigh 

scattering based gas density measurements, they have 

been more widely used than velocity and temperature 

measurements. In our work, for example, time and phase 

averaged density measurements have been made in an 

underexpanded supersonic free jet in support of jet noise 

studies2

. We have also demonstrated simultaneous 

multiple point density measurements for determining gas 

density fluctuation spectra, cross-spectra, and cross 

correlation functions in a low speed heated jet3

. The 

more difficult problem of dynamic velocity and 

temperature measurements was addressed in two previous 

papers. The first paper4

 used direct imaging of the 

Rayleigh scattered light through a Fabry-Perot 

interferometer. One photomultiplier tube (PMT) was 

used to detect the total Rayleigh scattered light for density 

measurements (as is done in the present paper). Two 

additional PMT’s were used to determine the velocity and 

temperature. A disadvantage of this method, however, is 

that it required the detection system, including the 

sensitive Fabry-Perot interferometer, to be located close 

to the experiment. A second paper5

 described a system 

that used an optical fiber to transmit scattered light from 

the experiment to the Fabry-Perot Interferometer (FPI), 

which could be located at some distance from the 

experiment. This allowed the interferometer to be located 

in a controlled environment, where the temperature can 

be held constant and where acoustic noise and vibration 

can be minimized. This system also incorporated an 8x8 

multiple anode PMT that was used to detect the 

interference pattern formed by the FPI. However, the 

quantum efficiency of the 8x8 multiple anode 

photomultiplier was only about 5 %. This is low 

compared with the quantum efficiency of about 25 % that 

can be achieved with single PMT’s. In addition, both 

these systems used analog data acquisition equipment, 

which resulted in relatively high noise levels in the 

detected signals. 

 In this paper we present an improved version of 

these systems. The present system uses three 25% 

quantum efficiency PMT’s to improve the detection 

efficiency. A new photon counting data acquisition 

system is used, which improves the signal to noise ratio of 

the detected signals by reducing the amount of noise due 

to electrical interference. Also, new computer software 

and hardware have been incorporated that greatly 

simplify the system operation. Some basic background 

material related to molecular Rayleigh scattering based 

diagnostic systems is first presented. The lower bounds 

for measurement of density, temperature, and velocity are 

given, assuming errors result only from Poisson noise 

generated in the photo detection process. This establishes 

the best possible measurements that could only be 

approached by use of an ideal instrument. We then 

describe the scheme used to measure dynamic velocity 

based on a Fabry-Perot interferometer and three PMTs. 

The lower bounds for velocity measurement uncertainties 

are calculated for this particular system. 

 An experiment conducted to evaluate the technique 

on a subsonic flow (up to about 300 m/sec) is then 

described. Results are given for data sampled at a 10 kHz 
NASA/TM—2001-210821 3 

rate. Examples of velocity time history and power 

spectrum of velocity fluctuations are given. 

THEORY

Rayleigh scattering 

 The spectrum for Rayleigh scattering from a low 

density gas has a Gaussian profile given by 

S f f df aK

f f

aK df o

o ( ) exp ( ) −= − − −⋅



 









	




	





	




	

2 2 2

π π K u (1) 

where fo is the laser frequency and u is the mean gas 

velocity. The interaction wave vector is K = ks-ko (with 

ko and ks being the wave vectors of the incident and 

scattered light), and a = (2κT/m)

1/2 is the most probable 

molecular speed (with κ being Boltzmann's constant, m 

the molecular mass, and T the gas temperature). Note 

that the spectral peak is shifted by a frequency 

proportional to the component of the bulk velocity in 

the K direction. The spectral width is proportional to 

the square root of the gas temperature. It is convenient 

to introduce the velocity component uK = K· u/K, 

which represents the measured velocity component. 

 The assumption of a Gaussian shaped Rayleigh 

scattering spectrum is only valid if 

y p

Ka

= <<

η

1

where p is the gas pressure and η is the shear viscosity. 

Collective effects of the molecular motions become 

important for higher density gases (y ∼ 1) and a more 

detailed kinetic theory model, such as the Tenti S6 

model6

, is required to describe the Rayleigh scattering 

spectrum. Although the Tenti spectrum does differ 

significantly from a Gaussian spectrum for the flows we 

are studying, similar results are obtained for the 

uncertainty analysis we conducted. We, therefore, used 

the Gaussian spectral model to reduce the 

computational time. 

Lower bounds for ideal measurements

Since Rayleigh scattering is a relatively weak 

process, the uncertainty in the measurements often is set 

by the photon statistical noise (shot noise), which 

determines the lower bound on measurement 

uncertainty. For example, the variance in the number of 

photoelectron counts for a Poisson process is equal to 

the mean number of counts. Thus the lower bound for 

the relative uncertainty in the measurement of gas 

density ρ, is equal to the square root of the variance 

divided by the mean counts NR. The lower bounds for 

temperature and velocity uncertainties have also been 

evaluated for a low-density, one-component gas. The 

relative uncertainties caused by photon statistics for this 

case can be written 7,8. 

σ ρ

ρ

σ σ       = 



 



 = 



 



 = 1 2

2

12 12

1 2 N

T

T N u a

R R N K

R

/ /

/ , , (2) 

These relations provide a lower bound for the 

measurement uncertainties, which can only be attained 

if the shot noise is the dominant noise and if an ideal 

instrument is used. 

 Consider an experiment with the following 

parameters: a laser (532 nm) with output power Po = 

5 W, air at STP (T = 293 K, p = 1 atm), probe volume 

length Lx = 1 mm, f/4 collecting optics (i.e., solid 

collection angle Ω = 0.05 sr), and efficiency factor ε = 

5 %. The rate of detected photons, given by 

N P nL

hc R

o x = 

  =

ε λ σ

χ

Ω

Ω

d

d

million counts / sec

sin2

50

 (3) 

In this equation, n is the gas number density, dσ/dΩ is 

the differential scattering cross section (6.13x10-32 m2

/sr 

for air at 532 nm), χ is the angle between the electric 

field vector of the (linearly polarized) incident light and 

the direction of the scattered light, h is Planck’s 

constant, and c is the velocity of light. If we wish to 

obtain independent measurements at a 10 kHz rate, the 

total number of detectable photons in each period would 

be 5000. Equation 2 gives the lower bound for 

measurement of density, temperature and velocity for 

each period: 

σ ρ

ρ

σ

σ     == = 1 20 41 .4 %, . % , .   T

T uK m/sec 

This shows that high sampling rate Rayleigh scattering 

measurements are at least feasible. It must be 

emphasized, however, that these values represent the 

best possible measurements given an ideal instrument. 

In practice, we are limited to instruments, such as the 

Fabry-Perot interferometer used here, which result in 

significantly higher uncertainties, as described below. 

Lower bounds for practical instrument

 Estimates of the measurement uncertainty for the 

technique described here, where the Rayleigh scattered 

light is analyzed with a planar mirror Fabry-Perot 

interferometer, are obtained by numerically calculating 

the Cramer-Rao lower bound9

. The variance of the 

estimate of a parameter αi (e.g., temperature or 

velocity) is given by 
NASA/TM—2001-210821 4 

V i ii ( ) α = − Γ 1 (4) 

where no summation over repeated indices is implied. 

For Poisson statistics, Γ is the Fisher information matrix 

with elements 

Γij

D q

D

i

D

N j

N N

q

q q

= ∑ 1 ∂

∂α

∂

∂α

 (5) 

where <NDq>is the expected number of counts from the 

qth photodetector. The summation is over the number of 

photodetectors, and the quantities <NDq>depend on the 

details of the optical system and the flow parameters, as 

presented below in the Uncertainty analysis section. 

Optical configuration

 In order to perform an uncertainty analysis, we 

first describe the setup (fig. 1) used for the experimental 

work. Light from a 5W, 532 nm, single-frequency, 

Nd:Vanadate CW laser was focused by lens L1 

(350 mm focal length) to a 150 μm diameter beam at 

the probe volume. The laser beam was terminated in 

light trap LT. Rayleigh scattered light is collected at a 

90° scattering angle and focused by L2 (two 160 mm 

focal length lenses) into a 1 mm core diameter, 20 m 

long optical fiber. The light exiting the fiber is 

collimated by lens L3 (145 mm focal length) and split 

into two paths with an uncoated optical flat (BS1). 

About 10% of the light is reflected and focused by lens 

L4 (85 mm focal length) onto PMT 1 (quantum 

efficiency ~ 25 %). This signal is proportional to gas 

density. The light transmitted by the beamsplitter is 

directed through a planar mirror Fabry-Perot 

interferometer (70 mm dia. mirrors, 90 % reflectivity, 

10 GHz free spectral range (FSR), finesse ~ 15). The 

light exiting the interferometer is focused by the fringe 

forming lens, L6. This lens consists of a pair of lenses 

(f/2 135 mm focal length and f/1.2 50 mm focal length) 

that has an effective focal length of 1600 mm. 

At the focal plane of the fringe pattern, the 

light is divided into two parts by a pair of mirrors 

(image dissector). A small mirror (6 mm dia.) is 

centered on the fringe pattern and directs light from the 

central part of the fringe through lens L7 (100 mm focal 

length) to PMT 2. This small mirror is mounted on a 

larger mirror (25 mm dia.) that directs light from the 

outer part of the fringe through L8 (100 mm focal 

length) to PMT 3. The mirrors are tilted ±3° with 

respect to the optical axis. A typical calculated image 

of the inner fringe of Rayleigh scattered light is shown 

in figure 2. Note that a flow in the direction of the K

vector, which here is in the jet flow direction (fig. 1), 

results in a positive frequency shift and increasing 

fringe diameter, while a flow in the direction opposite 

the K vector results in a negative frequency shift and 

decreasing fringe diameter. Thus, as the frequency of 

the Rayleigh scattered light increases, less light is 

detected by PMT 2 and more light is detected by PMT 

3. At the mirror location, the diameter of the image of 

the optical fiber is 11 mm. Additional optics were 

included to provide a reference image of light at the 

unshifted laser frequency. To accomplish this, several 

components could be placed in the optical path using 

remotely controlled pneumatic actuators. When placed 

in the beam path, mirror M directed laser light onto the 

diffuser (D) that scattered light into the optical fiber. 

Also, a prism assembly (PA) could be placed in the 

light path between the Fabry-Perot interferometer and 

the fringe forming lens. This served to direct light into 

a standard video camera. The video signal from this 

camera was digitized by a PC frame grabber card. A 

computer program analyzed this image and generated 

signals to control the Fabry-Perot mirror alignment. 

Uncertainty analysis

 We can now calculate the Cramer-Rao lower 

bounds given by equation 4 for velocity measurements 

based on the optical configuration described in the 

previous section. This allows us to conduct parametric 

studies to determine the optimum configuration for the 

Fabry-Perot interferometer and for the light detection 

system. The expected number of photons detected in 

time interval ∆t by detector 1 (PMT 1) is simply RBNR∆t 

where RB is the reflectivity of the beamsplitter BS and 

NR is given by equation 3. The expected number of 

photons detected by PMT 2 and PMT 3 are 

< >= −  N R N t S f I f f df dA Dq B R R FP r L ( ) () (, ) 1 2 ∆ θ (6) 

where the integrations are over frequency and the area 

of the qth detector (i.e., PMT 2 or 3), fL is the focal 

length of the fringe forming lens, and IFP is the FabryPerot instrument function given by10

I F FP ψ ψ   = + 



 



 



 





−

1

2

2

1

sin (7) 

where ψ is the phase change (neglecting any phase 

change on reflection) of the light between successive 

reflections given by 

ψ θ π μ θ (, ) cos f f d

c r

r = 4 (8) 
NASA/TM—2001-210821 5 

Here, μ is the refractive index of the medium in the 

Fabry-Perot cavity, d is the Fabry-Perot mirror spacing, 

θr is the angle between the ray and the optic axis, and 

F=1/(sin2

(π/2NE) where NE is the effective finesse. In 

general, the image of a monochromatic extended source 

located in the object plane consists of a series of 

unequally spaced concentric rings. In this work, 

however, the field of view is restricted by the diameter 

of the optical fiber and includes only the inner fringe as 

shown in figure 2. 

We can readily calculate the lower bounds for 

density, velocity, and temperature measurement 

uncertainties based on the detected light using three 

PMT’s as shown in figure 1. The uncertainties are 

evaluated as a function of the zero velocity fringe order 

no and the flow velocity. 

It is convenient to describe the fringe location in 

terms of the fringe order rather than fringe radius because 

of the nonlinear nature of the spectral response of the 

Fabry-Perot. For example, if there is a bright fringe on 

axis, concentric bright fringes occur at integral values of 

lower orders, but the change in fringe radius decreases 

with decreasing fringe order. 

Here we define the fractional order of the fringe 

with radius r as 2

L

d r n λ f

  =    

 (9) 

For example, at the location of the image dissector, the 

fringe order of the 6 mm diameter mirror is 0.10. 

Likewise, the fringe order corresponding to the diameter 

of the image of the optical fiber is 0.33. And, if unshifted 

laser light generates a bright fringe with radius ro, we 

refer to this as order no. Note that here we are using the 

term “fringe order” to denote change of the fringe order 

from the actual fringe order on the optical axis, which is 

2d/λ.

The change in fringe order with optical 

frequency is 

f n FSR

∆ ∆ = (10) 

so the change of fringe order ∆n with change of velocity 

∆V is given by 

( sin( /2) 2/ ) s n V

FSR

λ θ ∆= ∆ (11) 

where θs is the scattering angle. For example, with a 

velocity of 100 m/sec, a FSR of 10 GHz and 90° degree 

scattering, the change in the fringe order ∆n is 0.0266. 

 The lower bound for velocity uncertainty was 

numerically evaluated as a function of the fringe order 

no and the velocity using equations 1, 3, 4, and 6. For 

these calculations, either two or three unknown 

parameters were assumed (i.e., the αi in eq. 5 were NR, 

and uk, or NR, uk, and T). The results are shown in 

figure 3 for the optical system described above for a 

single measurement using 0.5 mJ of laser energy (i.e, a 

measurement made in a 100 μsec time interval using a 

5 W laser). Note that the minimum uncertainty for 

velocity measurements depends on the fringe order no

and velocity. Thus, the fringe order should be set to 

minimize the velocity uncertainty for the range of 

velocities to be measured. The mean number of 

photoelectron counts in a 100 μsec time interval for the 

three PMT’s are shown in figure 3a. Two cases of the 

lower bound of velocity uncertainty are shown for 

temperatures ranging from 150 to 300 K, where the 

density is fixed. One is for a flow with unknown 

temperature (fig. 3b), and one is for a flow with known 

temperature (fig. 3c). Note that, as expected, the 

measurement uncertainty is lower for colder gas. Also, 

in general, knowing the temperature significantly 

decreases the predicted measurement uncertainty. In 

this example, the uncertainty for a flow with known 

temperature is about 25 m/sec for a 300 K gas. As 

discussed above, an ideal measurement taken for a 

100 μsec time interval would have an uncertainty of 

about 4 m/sec. Thus, for our FPI based measurement 

system, the expected velocity uncertainty is about a 

factor of six larger than the uncertainty that would be 

obtained with an ideal instrument. Finally, an important 

observation is that a low velocity measurement 

uncertainty can be expected over a 600 m/sec velocity 

range (for the more general case of unknown 

temperature). 

EXPERIMENT

Setup

 The optical system described above and shown in 

figure 1 (with the laser output power equal 5 W) was 

used to measure the flow in a subsonic free jet (8.8 mm 

exit diameter). The probe volume was located in the 

potential core of the jet to avoid any dust particles in the 

ambient air. The laboratory compressed air supply used 

for the jet was passed through a three-stage filter to 

remove particles and oil vapor. As shown in figure 1, 

the jet axis bisected the incident and scattered light 

directions. With this configuration, the measured 

velocity component was the jet axial component. Since 

the flow velocity was in the same direction as the K

vector, the frequency shift was positive. Thus the 

Fabry-Perot interferometer fringe diameter of the 

Rayleigh scattered light increased as the flow velocity 

increased. An electronic pressure gauge was used to 

measure the total pressure in the nozzle plenum. These 

pressure measurements were used to calculate the flow 

velocity and temperature using the isentropic flow 

relations. A high precision electronic thermometer was 
NASA/TM—2001-210821 6 

used to monitor the temperature within the FPI 

enclosure to correlate interferometer stability with 

temperature. 

Data Acquisition 

A flow chart and block diagram of the PC 

based control and data acquisition system developed for 

this work is shown in figure 4. 

 The photoelectron pulses from the three PMT’s 

were amplified (Gain = 5) and sent to constant fraction 

discriminators (CFD). The CFD’s output 10 ns wide 

TTL level pulses that were counted by a PC countertimer board. Pulses could be simultaneously counted on 

the three channels at rates to 80 MHz for indefinite 

times. Typical photoelectron count rates for this work 

were on the order of 5 MHz. The accumulated counts 

on each channel were recorded at preset time intervals, 

typically 100 μsec, and stored on the computer hard 

disk. The number of counts in each time interval was 

given by the difference between adjacent values of the 

accumulated counts. 

 The flow chart of the software used to control all 

aspects of the instrument system operation is shown in 

figure 4a and the block diagram of the hardware is 

shown in figure 4b. The system had two modes of 

operation: (a) the Reference mode, where the automatic 

Fabry-Perot interferometer stabilization is active; and 

(b) the Rayleigh mode, where the Rayleigh scattering 

data is acquired. When the program is run, the 

sequence of operations shown in figure 4a is executed. 

The operator has the option of either switching to the 

Reference mode between each data set or taking 

sequential data sets without switching to the reference 

mode. The advantage of using the Reference mode 

between data sets is that any drift in the interferometer 

is minimized. 

Data processing

The gas density can be obtained in a 

straightforward manner, since it is proportional to the 

total Rayleigh scattered light measured by PMT 1. 

Calibration constants (slope and intercept) are found 

from a linear least squares fit (shown on fig. 5) of the 

PMT 1 counts plotted as a function of the gas density. 

One approach to processing the PMT signals 

in order to obtain the velocity would be to use 

parameter estimation techniques based on the model 

developed for the calculation of the lower bounds of 

measurement uncertainty. This would entail doing a 

nonlinear fit of the data to the model function given by 

equation 6. However, because of the large quantity of 

data (acquired at a 10 kHz rate for the three PMT’s) a 

simpler procedure was used. This procedure took 

advantage of the fact that the temperature only varied 

over a small range, from about 295 K for low flow to 

about 255 K for the maximum flow velocity of about 

280 m/sec. The operating region was selected so the 

count rate for the inner and outer regions were 

approximately linear with respect to velocity. The first 

step was to obtain a set of mean data for the velocity 

range of interest, where the velocity was calculated 

from the total temperature and pressure ratio using 

isentropic flow relations. A linear fit was then done to 

obtain the four constants A1, B1, A2, and B2 as shown 

for a typical data set on figure 6. 

11 2 2 I A BV O A BV =+ =+ , (12)

These are solved to find the velocity as a function of the 

ratio R = O/I . 

2 1

1 2

A AR V

BR B

− = − (13)

This rational function of V = V(R) could also have been 

obtained by directly doing a nonlinear fit, but this would 

have required an iterative algorithm. 

 After the calibration constants are obtained, the 

data may be processed by using equation 13 for each 

data point to obtain a velocity time history. The power 

spectrum of the velocity fluctuations can also be 

calculated. Because of the high noise levels, it is 

necessary to use relatively long data records and 

process them using a technique such as described in the 

following section. 

Welch method of modified periodograms

 We used the Welch method of modified 

periodograms11 to calculate an estimate of the power 

spectrum of the velocity fluctuations. In this procedure, 

a long data record sampled at rate fs for time T (total 

samples = N = Tfs ) is subdivided into a number Kr of 

smaller records (which may be overlapping), each of 

length L samples. The modified periodograms of each 

sub-record are calculated using a data window; these 

individual periodograms are then averaged to obtain the 

estimate of the power spectrum. The frequency 

resolution of the resulting spectrum is thus fs /L. By 

overlapping the segments by one half of their length, a 

near maximum reduction in the variance in the spectral 

estimate is achieved; the variance in the estimated 

spectrum is reduced by a factor of 11/9Kr compared to 

the variance of the spectral estimate calculated directly 

from the original long data record. 

RESULTS

 Although the eventual application of this 

technique is the study of turbulent flows, the 

measurements reported here were all taken in the 

potential core of the subsonic free jet where the 

turbulence level should be quite low. This initial work 
NASA/TM—2001-210821 7 

in the free jet allowed the system to be evaluated for 

known flow conditions, where the flow velocity, 

density, and temperature could easily be determined 

using isentropic flow relations. 

An example of a set of mean velocity 

measurements (each calculated using 100,000 samples 

taken at a 10 kHz rate) is shown in figure 7. The solid 

line is the velocity calculated from the measured total 

and ambient pressures using isentropic flow relations. 

The calibration constants described in the data 

processing section were obtained from data taken five 

days earlier. The rms deviation of the mean velocities 

from the isentropic values is 7.7 m/sec. This plot shows 

that the Fabry-Perot stabilization system is able to 

reproduce the correct interferometer alignment (locking 

to a preset fringe diameter before each measurement). 

The distribution function of the counts from 

PMT 1, which are proportional to density, is shown for 

two flow velocities (22 and 284 m/sec) in figure 8. The 

square of the standard deviation of the distribution (the 

variance) is very close to the mean, as expected for the 

Poisson statistics of the photoelectron counts. Also 

note that at the higher velocity, the density is greater 

because the temperature is reduced by the isentropic 

expansion. 

The velocity distributions of two time history 

records are shown in figure 9 along with Gaussian fits. 

Since the measurements were taken in the potential core 

of the jet, the actual turbulence intensity is low and the 

fluctuation in the velocity is due almost entirely to the 

shot-noise. The measured values of velocity standard 

deviation, about 20-30 m/sec, agree with the predictions 

of the lower bounds calculations shown earlier. The use 

of the standard deviation as a measure of turbulence 

intensity can only be done for velocity fluctuations on 

the order of, or larger than the standard deviation due to 

the shot-noise. In this situation, since the shot-noise 

and velocity fluctuations are independent and add in 

quadrature, one can subtract the contribution of the 

shot-noise. However, we can see that this is much more 

attractive for higher velocity flows. 

 Finally, two examples of velocity power spectra 

calculated using the Welch method of modified 

periodograms described above (with K = 195 

overlapping segments of length L = 1024) are shown in 

figure 10. For the low velocity flow (22 m/sec) shown 

in Figure 10a, the spectrum is relatively flat, except for 

very low frequencies. For the higher velocity flow 

(284 m/sec) shown in Figure 10b, the spectrum shows 

significant power in the frequency range 200-800 Hz. 

This is most likely caused by flow fluctuations 

generated in the nozzle air supply line. 

 

CONCLUDING REMARKS

An improved technique for obtaining dynamic 

gas density velocity measurements using molecular 

Rayleigh scattering was described. An analysis was 

presented that established a lower bound for 

measurement uncertainty of about 20 m/sec for 

individual velocity measurements. The velocity was 

determined by analyzing the scattered light with a 

Fabry-Perot interferometer. The signals from three 

photomultiplier tubes were simultaneously recorded 

using photon counting at a 10 kHz sampling rate and 10 

second recording periods. Software and hardware 

interfaces were developed to allow computer control of 

all aspects of the experiment and data acquisition. 

Density and velocity measurements taken in a subsonic 

free jet were presented. The measured velocity 

standard deviation was close to the lower bound 

prediction. Velocity and density power spectra were 

obtained using the Welch method of modified 

periodograms. The stabilization system used for the 

Fabry-Perot interferometer allowed calibration data 

obtained one day to be used for data acquired five days 

later. This technique, which simultaneously measures 

time history of density and velocity, will be an 

important new tool for study of noise generation in 

turbulent flows. 

REFERENCES

1

 Schaffar, M., “Direct measurements of the correlation 

between axial in-jet velocity fluctuations and farfield noise near the axis of a cold jet”, J. Sound 

and Vibration, 64, pp. 73-83, 1979. 2

 Panda, J., and Seasholtz, R.G., “Measurements of 

shock structure and shock-vortex interaction in 

underexpanded jets using Rayleigh scattering”, 

Phys. Fluids, 11, pp. 3761-3777, 1999. 3

 Seasholtz, R., and Panda, J., “Multiple point dynamic 

gas density measurements using molecular 

Rayleigh scattering”, 18th International Congress 

on Instrumentation in Aerospace Simulation 

Facilities Conference, Toulouse, France, June 14-

17, 1999. [also NASA TM-1999—209295]. 4

 Seasholtz, R.G., and J. Panda, “Rayleigh Scattering 

Diagnostic for Simultaneous Measurements of 

Dynamic Density and Velocity”, AIAA 38th

Aerospace Sciences Meeting, Reno, NV, AIAA2000-0642, 2000. 

5

 Seasholtz, R.G., and J. Panda, “Rayleigh scattering 

diagnostic for dynamic measurement of velocity 

and temperature”, AIAA 37th Aerospace Sciences 

Meeting, Reno, NV, AIAA-99-0641, 1999. 
NASA/TM—2001-210821 8 

6

 Tenti, G., Boley, C.D. and Desai, R.C., “On the 

kinetic model description of Rayleigh Brillouin 

scattering from molecular gases”, Can. J. Phys. 

52, pp. 285-290, 1974. 7

 Seasholtz, R.G., “High-speed anemometry based on 

spectrally resolved Rayleigh scattering”, Fourth 

International Conference on Laser Anemometry, 

Cleveland, Ohio, 1991 [also NASA TM-104522]. 8

 Seasholtz R.G. and Lock, J.A., “Gas temperature and 

density measurements based on spectrally resolved 

Rayleigh-Brillouin scattering”, NASA Langley 

Measurement Technology Conference, Hampton, 

VA, 1992. 

9

 Whalen, A.D., Detection of Signals in Noise, 

Academic Press, New York, pp. 324-231, 1971. 10 Vaughan, J.M., The Fabry Perot Interferometer, 

History, Theory, Practice and Applications, Adam 

Hilger, Bristol, pp. 89-112, 1989. 11 Welch, P.D., “The use of fast Fourier transform for 

the estimation of power spectra: A method based 

on time averaging over short, modified 

periodograms”, IEEE Trans. on Audio and 

Electroacoustics, AU-15, pp. 70-73, 1967. 
NASA/TM—2001-210821 9 

NOZZLE 20 m , 1 m m fiber

Nd Vanadate Laser

M

M

LT

D

BS 1

PA

 VIDEO

CAMERA

FPI

L1

L2

L3

L4

L5

L6

PMT 3

PMT1

L8

L7

 IMAGE

DISSECTOR

PMT 2

K

Fig. 1 - Layout of Rayleigh scattering system 
NASA/TM—2001-210821 10 

PMT 2

PMT 3

Fig. 2 – Fabry-Perot interferometer fringe showing two 

regions where light is directed to PMT 2 (INNER) and PMT 

3 (OUTER). 

-1000 -800 -600 -400 -200 0 200 40

0

100

200

300

400

500

600

700

800

900

1000

1100

PMT 1

PMT 2 (INNER)

PMT 3 (OUTER)

Counts

Velocity, m/sec

-1000 -800 -600 -400 -200 0 200 400

0

10

20

30

40

50

60

70

80

90

100

Velocity, m/sec

Velocity Uncertainty, m/sec

-1000 -800 -600 -400 -200 0 200 400

12

14

16

18

20

22

24

26

28

T = 300 K

T = 150 K

Velocity, m/sec

Velocity Uncertainty, m/sec

Fig. 3 (a) Number of counts for PMT 1, PMT 2 

(INNER), and PMT 3 (OUTER) as function of 

velocity for zero velocity fringe order no = 0.10; 

(b) Lower bound for velocity uncertainty for 

unknown temperature; (c) Lower bound for 

velocity uncertainty for known temperature. 

(a)

(b) 

(c) 
NASA/TM—2001-210821 11 

(a) 

290 300 310 320 330 340 350

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

Y = A + B * X

Parameter Value Error

-------------------------------------------------

A -0.01335 0.00653

B 0.00342 2.07821E-5

-------------------------------------------------

ρ ρ/ amb

PMT 1 COUNTS

Fig. 5 – Calibration plot for gas density . 

50 100 150 200 250 300

250

300

350

400

450

500

I = A1 + B1 * V

Parameter Value Error

-----------------------------------------------

A1

 510.20572 5.15344

B1 -0.8551 0.02843

-----------------------------------------------

INNER COUNTS

Velocity, m/sec

(a) 

(b)

50 100 150 200 250 300

300

320

340

360

380

400

420

O = A2 + B2 * V

Parameter Value Error

-----------------------------------------------

A2 287.166 1.322

B2 0.41484 0.0073

-----------------------------------------------

OUTER COUNTS

Velocity, m/sec

Fig. 6 – Linear fit of INNER (a) and OUTER (b) counts 

as function of velocity 

FPI PRISM

 ACT.

PMT

 0

PMT

 1

PMT

 2

HV

 A

HV

 B

HV

 C

5 5 5

D

0

D

1

D

2

ACTUATOR

CONTROL

DIF

ACT.

IEEE

D/A

 VID

CCD

OPTICAL

 FIBER

CT DO

DO PC 1

PC 2

TFP

(b) 

Fig. 4 – Experiment control and data acquisition system (a) Flow 

chart of system operation; (b) Block diagram 

(a)

DISABLE STABILIZATION SYSTEM

SWITCH PA AND DIF

TURN ON PMT HV

DELAY 10 SECONDS

RECORD TOTAL PRESSURE

 AND FPI TEMPERATURE

COUNT 3 PMT CHANNELS

CALCULATE MEAN AND STD DEV

WRITE DATA TO DISK

TURN OFF PMT HV

SWITCH PA AND DIF

ENABLE STABILIZATION SYSTEM

 GO TO

REF MODE NO YES

NO

YES

IN REF

MODE

(a)
NASA/TM—2001-210821 12 

0 50 100 150 200 250 300

0

50

100

150

200

250

300

Velocity, m/sec

Velocity, m/sec

 RAYLEIGH

 ISENTROPIC

Fig. 7 – Velocity obtained from Rayleigh 

scattering measurements and from isentropic flow 

relations. 

200 220 240 260 280 300 320 340 360 380 40

0

1000

2000

3000

4000

5000

6000

7000

Gaussian Fit

 

mean 297.2

std dev 17.44

PMT 1 COUNTS

200 220 240 260 280 300 320 340 360 380 40

0

1000

2000

3000

4000

5000

6000

7000

Gaussian Fit

 

mean 342.03

std dev 18.45

PMT 1 Counts

Fig. 8 – Distribution of PMT 1 counts (representing 

density) for mean flow velocity of 22 m/sec (a) and 

284 m/sec (b). 

0 1000 2000 3000 4000 5000

0.1

1

Velocity Power Spectral Density, m2\sec

Frequency, Hz

0 1000 2000 3000 4000 5000

0.1

1

Velocity Power Spectral Density, m2/sec

Frequency, Hz

Fig. 10 – Power spectrum of velocity 

fluctuations for mean velocity = 22 m/sec (a) 

and 284 m/sec (b). 

(a)

(b)

-100 -50 0 50 100 150

0

1000

2000

3000

4000

5000

Gaussian Fit

 

mean 14.21 m/sec

std dev 25.85 m/sec

Velocity, m/sec

180 200 220 240 260 280 300 320 340 360 380

0

1000

2000

3000

4000

5000

6000

Gaussian Fit

mean 281.0 m/sec

std dev 22.4 m/sec

Velocity, m/sec

Fig. 9 - Velocity distribution function of mean 

flow 22 m/sec (a) and 284 m/sec (b). 

(a)

(b)
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NASA TM—2001-210821

AIAA–2001–0847

E–12739

WU–704–20–53–00

18

A03

Rayleigh Scattering Diagnostic for Dynamic Measurement of Velocity

Fluctuations in High Speed Jets

Richard G. Seasholtz, Jayanta Panda, and Kristie A. Elam

Rayleigh scattering; Fabry-Perot interferometers

Unclassified -Unlimited

Subject Category: 35 Distribution: Nonstandard

Prepared for the 39th Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and

Astronautics, Reno, Nevada, January 8–11, 2001. Richard G. Seasholtz, NASA Glenn Research Center; Jayanta Panda,

Ohio Aerospace Institute, 22800 Cedar Point Road, Brook Park, Ohio 44142; and Kristie A. Elam, Akima Corporation,

Fairview Park, Ohio 44126. Responsible person, Richard G. Seasholtz, organization code 5520, 216–433–3754.

A flow diagnostic technique based on the molecular Rayleigh scattering of laser light is used to obtain dynamic density

and velocity data in a high speed flow. The technique is based on analyzing the Rayleigh scattered light with a FabryPerot interferometer used in the static, imaging mode. An analysis is presented that established a lower bound for

measurement uncertainty of about 20 m/sec for individual velocity measurements obtained in a 100 μsec time interval.

Software and hardware interfaces were developed to allow computer control of all aspects of the experiment and data

acquisition. The signals from three photomultiplier tubes were simultaneously recorded using photon counting at a

10 kHz sampling rate and 10 second recording periods. Density and velocity data, including distribution functions and

power spectra, taken in a Mach 0.8 free jet are presented.