Windspeed and Flow Angle Measurement by Tracking of a

Laser-Induced Breakdown Spark

R. Mark Rennie1, Minh Nguyen

2, Stanislav Gordeyev

3, Eric J. Jumper

4

University of Notre Dame, Notre Dame, Indiana, 46545

Alan B. Cain5

Innovative Technology Applications Co., Chesterfield, MO, 63006

Timothy E. Hayden6

U.S. Air Force Academy, Colorado Springs, Colorado 80840

An experimental measurement of three components of velocity and associated flow angles

by optical tracking of the light emitted by a laser-induced breakdown (LIB) spark is

described. The measurements were performed in a blowdown wind tunnel at a nominal flow

Mach number of 4.38. The tests showed that flow velocity could be accurately measured

using the technique, with a demonstrated flow-angle uncertainty of less than ± 0.2o at the

Mach 4.38 test condition. Wavefront measurements through the shock of a 20o wedge were

also performed, and indicated that the measurements could also be performed through a

shock with negligible effect on spark formation due to the much smaller aperture of the LIB

laser beam in relation to the wavelength of the shock aero-optical effect.

Nomenclature

= flow pitch angle

= flow yaw angle

CX ,CY = image centroid coordinates

DAP = laser beam aperture diameter

tf = time separation between camera frames

= laser pulse energy

f = frequency

I = image pixel intensity

KGD = Gladstone-Dale constant

= wavelength

n = index of refraction

12 = stereoscopic viewing angles

= density

si = image scale

u = measurement uncertainty

V∞ = freestream velocity

VX,Y,Z = velocity components

VX1,VZ1 = velocity components in 1st view

VX2,VZ2 = velocity components in 2nd

view

I. Introduction

EVERAL development programs for new hypersonic flight vehicles are currently underway, as described in

Refs. [1-3]. To facilitate these development programs, hypersonic test programs [4-6] are being conducted to

enhance understanding of high-speed flows so as to enable improved prediction and design capabilities. This kind of

fluid-mechanic understanding cannot be obtained from ground-test and computational fluid dynamics (CFD) efforts

1 Research Associate Professor, Department of Mechanical and Aerospace Engineering, Hessert Laboratory for

Aerospace Research, Notre Dame, IN 46556, Senior Member AIAA. 2 Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, Hessert Laboratory for

Aerospace Research, Notre Dame, IN 46556, Student Member AIAA. 3 Research Associate Professor, Department of Mechanical and Aerospace Engineering, Hessert Laboratory for

Aerospace Research, Notre Dame, IN 46556, Senior Member AIAA. 4 Professor, Department of Mechanical and Aerospace Engineering, Hessert Laboratory for Aerospace Research,

Notre Dame, IN 46556, Fellow AIAA. 5 President, Innovative Technology Applications Company, Chesterfield, MO 63006, Associate Fellow AIAA.

6Aerospace Engineer, Department of Aeronautics, Senior Member AIAA.

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33rd AIAA Applied Aerodynamics Conference

22-26 June 2015, Dallas, TX

AIAA 2015-2574

Copyright © 2015 by R.M.Rennie, M.Nguyen, S.Gordeyev, E.J.Jumper, A.B.Cain, T.E.Hayden. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA Aviation

alone, since ground-test facilities are not capable of achieving all points in the flight envelope of realistic flight-

vehicle designs, while CFD simulations require validation data.

One of the difficulties associated with hypersonic flight-test measurements is a lack of reliable instrumentation

for the accurate measurement of fundamental flight-path data, including windspeed, pitch and yaw. These

measurements are critical for the correct interpretation of data acquired during the test. In this paper, a novel “air-

data probe” is described in which three components of freestream velocity are measured by tracking the motion of a

laser-induced breakdown (LIB) spark that is created in the freestream flow outside of the vehicle shock. A schematic

of the instrument concept is shown in Fig.1.

Fig. 1: Basic concept for air data probe to measure 3-components of freestream velocity.

II. Experiment

Testing of the measurement concept was performed in the Trisonic Wind Tunnel (TWT) at the US Air Force

Academy. This tunnel is a blowdown configuration with test-section dimensions of 1 ft x 1 ft, maximum Mach

number of 4.38, and maximum test-section total pressure of 1.7 MPa. Air storage consists of six 25.5 m3 tanks that

can be pumped to a pressure of 4 MPa, giving up to 7 min of total run time depending on test conditions. The stored

air is first dried to -45oC dewpoint and then heated to around 38

oC in order to prevent water condensation, ice

formation and/or liquefaction in the test section.

All tests were performed at a target Mach number of 4.38 and test-section total pressure of 1.5 MPa. The test-

section windspeed at these test conditions, computed assuming isentropic expansion from the stagnation conditions

in the wind-tunnel settling chamber, was approximately 697 ± 2 m/s. The test-section density was 0.31 kg/m3, which

corresponds to a standard-atmosphere altitude of 12000 m.

A. Wind-Speed Measurements using LIB Spark

A schematic of the optical setup for the wind-speed measurements is shown in Fig. 2. The experiments were

performed with an empty test section. A LIB spark was formed near the center of the test section by focusing a

Nd:YAG pulsed laser with a wavelength of 1064 nm through a fused-silica window with broad transmission

bandwidth into the center of the wind-tunnel test section.

As shown in Fig. 2, a plate beamsplitter was used to merge two sight lines of the LIB spark onto the camera

images to enable stereoscopic measurement of the three components of motion of the spark. Note that in a deployed

instrument, the stereoscopic measurements could be made using multiple cameras (see Fig. 1); however, the optical

setup of Fig. 2 was used to enable the measurements using a single high-speed camera. Lenses with 500 mm focal

length were used to accomplish simultaneous focusing of both sight paths onto the camera images, while at the same

time providing an optimum level of magnification of the LIB spark. The field of view of each sight line was

calibrated prior to the tests using a ruler with minimum 1/100 in divisions that was mounted in the test section at the

location of the LIB spark, and aligned with the flow direction. Both sight lines were aligned with the horizontal

plane of the test section, but were offset by 46o around a vertical axis through the spark, see Fig. 2. A photograph of

the optical setup in the TWT test section is shown in Fig. 3.

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Fig. 2: Schematic of experiment to measure three components of motion of LIB spark using high-

speed camera.

Fig. 3: Photograph of optical setup installed in TWT test section.

The motion of the spark was measured using a high-speed camera with a frame size of 128 x 64 pixels and a

frame rate fC of 390 kHz. A telephoto lens was used to increase the resolution of the spark images. The streamwise

field of view of the camera images was approximately 13 mm, giving a pixel resolution of 0.1 mm/pixel. For these

tests, the maximum possible shutter time of 1/fC was used, on the order of 2 s, in order to increase the spark

brightness in the images and hence maximize the number of frames that showed a spark.

B. Evaluation of Shock Effect on LIB Spark Formation

As shown in Fig. 1, the LIB spark is focused outside of the vehicle shock wave in order to measure the

freestream velocity components. Measurements were also performed in the TWT to evaluate the aero-optical effect

of the flight-vehicle shock on the formation of a LIB spark.

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Fig. 4: Diagram of measurements to evaluate shock effect on formation of LIB spark.

Measurements of the aero-optical effect of a shock were performed in the TWT at a test-section Mach number

of M∞ = 3. For these tests, a 20o wedge model was installed in the middle of the test section, with one side of the

wedge parallel to the incoming flow, see Fig. 4. A collimated, continuous (CW) laser beam was reflected from a

mirror mounted in the wedge face approximately 125 mm downstream of the leading edge of the wedge. As shown

in Fig. 4, two tests were performed: for the first test (Fig. 4 left), the wedge was aligned to produce a shock through

the interrogating CW beam. A second test with wedge aligned to produce no shock through the beam (Fig. 4 right)

was also performed to evaluate the effect of the wedge on the wall boundary layer, which also imposed an aero-

optical effect on the CW beam. A detailed description and the results of this test are presented in a companion paper

[8].

After exiting the test section, the reflected beam from the wedge was passed through a beam reducer and into a

high-speed Shack-Hartmann wavefront sensor using the optical setup shown in Fig. 5. The wavefront sensor

consisted of a 38 mm focal-length, 70 x 60 lenslet array that divided the CW beam into an array of focused dots that

were recorded using a high-speed camera. In order to resolve any potential high-frequency optical effects of the

shock, the wavefront measurements were performed by sampling a small region of the CCD array containing just a

few focused dots from the lenslet array, at a sampling rate of approximately 650 kHz, see Fig. 6. Additional

description of the wedge measurements is also given in Ref. [8].

Fig. 5: Schematic of experimental setup for CW measurements of the aero-optical effect of shock.

Fig. 6: Single image of a small number of wavefront-sensor dot images captured at high sampling rate (650

kHz) using the CCD camera.

III. Results

An example of a sequence of camera frames acquired using the high-speed camera is shown in Fig. 7. The

motion of the spark with the flow from left to right can be seen in the frames. Note that the top spark image in each

frame was recorded by the line of sight at 34o with respect to the flow direction (see Fig. 2) while the bottom images

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correspond to the 12o line of sight; as such, the frame-to-frame displacement of the bottom spark image appears

greater than the top spark image due to the 12o upstream line of sight being more perpendicular to the actual

streamwise motion of the spark.

Fig. 7: Typical sequence of images of LIB spark acquired using high-speed camera, with flow from left to

right, E ~ 100 mJ, = 1064 nm.

The apparent location of the spark for each sight line in each frame was computed using simple first-order

centroiding equations:

i i

Xi

i

x I dxC

I dx

, i i

Yi

i

y I dyC

I dy

(1)

where the integrations of Eqs. (1) were performed over the pixels of each spark image, (x,y) are the coordinates of

the pixels, and I is the image intensity of the pixels. In Eq. (1), the index i refers to the two viewing angles. It is

assumed that in a deployed instrument, wind-speed data would be calculated from only two camera images

separated by a time tf , so that the apparent streamwise and vertical velocity components in the image plane of each

camera are therefore:

i Xi Xi

Xi

f

s C CV

t

2 1 , i Zi Zi

Zi

f

s C CV

t

2 1 (2)

In Eq.(2), si is the image scale, which was measured in wind-off conditions to be si = 0.100 ± 0.002 mm/pixel using

a ruler aligned with the flow direction of the wind tunnel.

For calculation of velocity components, a coordinate system was defined with the two camera sight lines aligned

with the X-Y plane (see Fig. 2). With the viewing angles 1, 2 defined with respect to the Y axis (see Fig. 2), then

the flow velocity components Vx, Vy, Vz, can be determined from the apparent velocities measured in the two camera

image planes (VX1, VZ1 and VX2, VZ2) by simultaneous solution of:

cos( )

cos( )X XV V

1

1 (3)

cos( )

cos( )X XV V

2

2 (4)

atan Z

X

V

V

(5)

atan Y

X

V

V

(6)

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Z Z ZV V V 1 2 (7)

where , are the flow pitch and yaw angles. In effect, due to the geometrical arrangement of the optical setup, a

direct measurement of the flow velocity component Vz is produced by both cameras, while each camera records an

apparent horizontal velocity that is the projection of the true VX and VY components along the sight line of the

camera. Furthermore, since the coordinate system was set up with the X-axis aligned with the wind-tunnel flow

direction, VX is a direct measurement of the wind-tunnel flow speed.

In general, the measured image sequences of the spark contained four useable images, since some of the images

were too dim while others were over-saturated. In future work, methods of expanding the dynamic range of the

camera to obtain more useable frames will be investigated. With four useable images, velocity components for a

maximum tf corresponding to the time separation between four images could be computed, or maximum tf ~

7.5 s; however, velocity components were also computed for images spaced by shorter time separations to evaluate

the effect of tf on the measurement accuracy. The mean and uncertainty of the measured velocity components as a

function of tf, determined using Eqs. (1) – (7) are summarized in Figs. 8 and 9 for a total of 180 separate

measurements. The uncertainties plotted in Fig. 9 are shown as 2x the standard deviation of the velocity results

(95% confidence).

Fig. 8: Calculated mean velocity components as a function of time separation between frames.

Fig. 9: Uncertainties of velocity components as a function of time separation between frames.

A. Discussion of Measurement Errors

Uncertainty analysis of the measurement technique is an important part of the instrument development since it

can be assumed that the air data probe will be required to meet defined accuracy targets. The uncertainty analysis

can also identify key components of the measurement and analysis process that would most benefit from further

refinement. Assuming that the camera frame rate is accurate, then Eqs. (1) – (7) show that measurement uncertainty

arises primarily from the image scaling si, the determination of the viewing angles 1 and 2, and the accuracy of the

centroiding calculations.

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1. Absolute Errors

Of the three sources of error mentioned above, errors in the image scaling or viewing angles generally produce

absolute errors or offsets in the measured velocity components VX, VY and VZ. Specifically, an error in si uniformly

increases or decreases all three measured velocity components via Eq. (2). Similarly, errors in 1 and 2 produce

offsets in both in VX and VY that are related through Eqs. (3), (4), and (6).

For the experimental data acquired in the TWT, the mean VX results shown in Fig. 8 range from 690 m/s

(tf = 2.5 s) to 684 m/s (tf = 7.5 s). These results are within 1% to 2% of the nominal test-section wind speed of

Vi = 697 ± 2 m/s computed from an isentropic-flow analysis of the blowdown wind-tunnel stagnation conditions.

Although the isentropic assumption behind the calculation of Vi may have additional inaccuracies in itself, the

difference between the measured VX and Vi can be almost entirely attributed to the uncertainty of the image scaling

si, such that a closer comparison between VX and Vi could most likely be obtained using an improved evaluation of

image scaling or instrument calibration. The fact that the mean VY and VZ (Fig. 8 right) results are nonzero indicates

either a flow angularity in the TWT test-section flow or, more likely, a slight misalignment between the coordinate

system of the instrument and the wind-tunnel centerline. However, the absolute magnitude of the measured velocity

(VX2 + VY

2 + VZ

2)

0.5 is still 1% to 2% less than the isentropic wind speed, indicating that a scaling or calibration error

would still exist even if the instrument were more carefully aligned.

2. Random Errors

On the other hand, errors produced by the image centroiding calculations are generally random in nature.

Specifically, variations in spark shape or intensity distribution would interact with the centroiding routine to produce

errors that are effectively random in nature and cannot be corrected by more-careful or improved scaling, alignment,

or calibration methods. In this regard, the image centroiding calculations have an important impact on the minimum

uncertainty that can be achieved by the measurement technique.

If the centroiding calculations have an uncertainty uC, then from Eq.(2):

i CV

f

s uu

t

2 (8)

An analysis of spot centroiding routines for use in Shack-Hartman wavefront calculations [7] shows that the

centroiding error depends upon the spot size, mean noise level (ratio of the average image background noise to the

maximum image brightness) and signal-to-noise ratio (SNR). However, in general, average spot centroiding errors

as low as 0.05 pixels are achievable for simple first-moment centroiding routines for typical SNR’s [7]. In Fig. 9

left, the velocity uncertainty computed using Eq. (8) for a 0.2 pixel centroiding uncertainty (uC = 0.2 pixels) is

shown to produce reasonably-good agreement with the measurement uncertainty of the TWT experimental data.

This relatively-large pixel uncertainty suggests that there is room to improve the measurements either by improved

centroiding methods, better optical conditioning, and/or improved post-processing of the camera images. Note that,

for the TWT wind-tunnel tests, the measurement uncertainty may also have been unrealistically increased by wind-

on vibrations of the optical setup.

An uncertainty analysis of Eqs. (1) to (7) also shows how the ratio of the VY to VX uncertainties, uVY / uVX, depends on the total angle between the two cameras, 1 + 2, and is plotted in Fig. 10. This result shows that the

uncertainty of the velocity components determined by the stereoscopic analysis is minimized if the angular

separation of the sight lines is 90o. Figure 10 also shows the ratio uVY / uVX for the experimental data for all tf. For

the 46o total angle between the two camera sight lines (see Fig. 2), Fig. 11 shows that the measured ratio uVY / uVX is

only slightly greater than the prediction of Fig. 10.

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Fig. 11: Measured ratio of uncertainties of

VY to VX

.

Fig. 10: Predicted ratio of uncertainties of VY to

VX as a function of total angle between cameras,

determined from uncertainty analysis.

.

B. Flow-Angle Uncertainty

Figure 9 shows that uVZ ~ 4 m/s was achieved in the TWT tests for all tf, while uVX ~ 4 m/s was also obtained

for tf = 7.5 s. Furthermore, as shown in Fig. 10, uVY = uVX for a total viewing-angle separation of 90o which in this

case would give a measurement uncertainty of ~ ± 4 m/s for all three velocity components. Using these results as a

benchmark for the instrument performance, the flow-angle uncertainty of the instrument can therefore be estimated

using:

4 m/s,u u

V

(9)

Table 1 shows the resulting uncertainty of the flow-angle measurements for flight at different Mach numbers,

computed using Eq. (9) for standard-atmosphere conditions at a flight altitude of 20 km. The table shows that flow

angles can be measured to within approximately ±0.5o for flight Mach numbers greater than 2, and within ±0.2

o for

flight Mach numbers greater than 4. However, as mentioned above, some of the scatter in the wind-speed

measurements may also have been caused by wind-on vibrations of the optical setup, so that the results shown in

Table 1 should be considered to be conservative.

Mach

number

V∞ (m/s) u, u

(deg)

1 295 0.78

2 590 0.39

3 885 0.26

4 1180 0.19

5 1475 0.16

Table 1: Flow-angle uncertainties computed using Equation (9), for flight at 20 km altitude.

C. Aero-Optical Effect of Shock

A standard method of evaluating the frequency content of aero-optical data is to compute the jitter angle J

corresponding to the motion of the focused dots on the wavefront-sensor CCD array (see Fig. 6) [9]:

J

L

d

f (10)

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where fL is the lenslet focal length. The jitter angle corresponds to the local slope of the wavefront at the particular

lenslet that produced the dot under consideration.

Figure 12 shows three spectra computed from the jitter data measured using the wavefront sensor. The blue

curve in Fig. 12 shows the measured spectrum with no wedge installed in the test section, and therefore represents

the aero-optical effect of the test-section wall boundary layer. The green curve was measured using the setup of

Fig. 4 right; since the CW beam did not pass through a shock wave in this case, the green curve therefore gives an

evaluation of the effect of the wedge model on the test-section wall boundary-layer aero-optical effect. Finally, the

spectrum acquired with the CW beam passing through the shock wave as shown in Fig. 4 left is plotted in red in

Fig. 12. The top axis of Fig. 12 shows the equivalent wavelength of the convecting aero-optical structures

computed using:

V

f (11)

where the freestream velocity V∞ of the flow was computed to be 620 ± 2 m/s from an isentropic-flow analysis of

the measured flow stagnation conditions.

Fig. 12: Jitter spectra for empty test section (blue curve), wedge (green), and wedge with shock passing

through CW beam (red).

Figure 12 clearly shows that the aero-optical effect of the shock occurs primarily at comparatively low

frequencies, below 10 kHz, and at long wavelengths between ~0.12 m to 0.63 m. Figure 12 also shows some

discrepancy between the high-frequency part of the spectra for the “BL with shock” and “BL only” cases; however,

since this discrepancy also occurred with the wedge orientated so that a shock did not form in the beam, it is

assumed that the discrepancy in this high-frequency region was caused by the effect of the wedge on the wall

boundary-layer flow, and not because of the shock.

For typical instrument deployments, it is anticipated that the optical aperture for the LIB laser would be on the

order of 25 mm in diameter or less, in order to minimize space requirements in the flight vehicle. Furthermore, as

the LIB laser focuses towards the LIB spark, the diameter of the LIB laser will be even smaller than 25 mm by the

time it passes through the vehicle shock wave. As such, the diameter of the LIB laser beam will be much smaller

than the wavelength of the shock aero-optical disturbances, so that the aero-optical effect of the shock will be greatly

reduced by the “aperture filtering” effect described in [10]; specifically, for optical apertures that are much smaller

than the wavelength of the optical aberration, the optical aperture behaves as a high-pass filter that strongly filters

out the effects of optical disturbances with wavelengths longer than the beam diameter.

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Fig. 13: Gain of aero-optical disturbances of wavelength due to aperture of diameter DAP (taken from [10])

The effect of a beam with circular aperture diameter DAP on aero-optical disturbances with wavelength is

shown in Fig. 13 [10]. From Fig. 12, the shortest-wavelength component of the shock aero-optical effect is ~

0.12 m; for a beam diameter of DAP ~ 25 mm this gives StAP = DAP / . As shown in Fig. 13, the 25 mm

aperture for the LIB laser would therefore filter this shortest-wavelength component by over 20 dB, so that the aero-

optical effect of the shock would be reduced by over 99%. For smaller apertures, or longer-wavelength frequency

components of the shock, the amount of attenuation of the shock aero-optical effect would be even greater. As such,

the adverse effect of the shock on the ability to focus the LIB laser and create a breakdown spark is expected to be

negligible.

1. Tip/Tilt effect of shock

In addition to the higher-order aberrations that the shock may impose on the LIB laser beam described above,

the shock may also impose a low-order tilt effect that would deflect the LIB laser beam without otherwise aberrating

it. This kind of refraction of the LIB laser beam would shift the location of the formation of the LIB spark, without

degrading the ability to form the LIB spark.

Refraction through the shock is produced as light passes through the large density gradient across the shock. A

diagram showing the refraction of light beams across the shock is shown in Fig. 14, where the angles and are

related by Snell’s law:

1 2

2 1

sin

sin

n

n

(12)

In Eq. (12), the local refractive indices n1 and n2 can be determined using the Gladstone-Dale relation:

1 GDn K (13)

where KGD ~ 2.25 x 10-4

kg/m3 for visible and near-IR wavelength radiation in air. Due to the very small

value of the Gladstone Dale constant for air, the change in refractive index across the shock is very small, on the

order ~10-4

or smaller. This means that refraction effects by the shock would have a negligible effect over the very

short distances in which the LIB laser would be focused.

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Figure 14: Refraction of light by vehicle shock wave.

IV. Concluding Remarks

The experiments performed in the TWT have validated the basic concept of determining three components of

wind-speed and flow angle by optical tracking of a LIB spark. The tests performed at M∞ = 4.38 demonstrated an

achievable measurement uncertainty of ± 4 m/s for all three velocity components, corresponding to flow-angle

uncertainties less than ± 0.5o for flight Mach numbers greater than 2, and less than ± 0.2

o for Mach numbers greater

than 4. Optical wavefront measurements were also performed through the shock of a 20o wedge, which showed that

the aero-optical effect of the shock occurred at wavelengths that are much longer than the expected beam diameter

of the LIB laser used in a deployed system. The aero-optical effect of the shock on focusing of the LIB laser is

therefore expected to be negligible due to the filtering effect of the small beam size as the LIB laser passes through

the shock. Furthermore, tip/tilt effects of the shock are also expected to be negligible due to the very short focusing

distance for the LIB laser.

Acknowledgments

This work has been supported by the United States Air Force Office of Scientific Research Contract Number

FA9550-13-C-0010. The U.S. Government is authorized to reproduce and distribute reprints for governmental

purposes notwithstanding any copyright notation thereon. Any opinions, findings and conclusions or

recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the

AFOSR.

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