Christian T. Lant

Ohio Aerospace Institute, Brook Park, Ohio

Doppler Global Velocimetry at NASA Glenn

Research Center: System Discussion

and Results

NASA/CR—2003-212179

February 2003

https://ntrs.nasa.gov/search.jsp?R=20030032406 2018-05-15T15:53:19+00:00Z
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

databases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
Christian T. Lant

Ohio Aerospace Institute, Brook Park, Ohio

Doppler Global Velocimetry at NASA Glenn

Research Center: System Discussion

and Results

NASA/CR—2003-212179

February 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Cooperative Agreement NCC3–861
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Trade names or manufacturers’ names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.

The Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/CR—2003-212179 iii 

TABLE OF CONTENTS 

INTRODUCTION........................................................................................................................... 1 

DGV TECHNIQUE ........................................................................................................................ 2 

EXPERIMENTAL SETUP.............................................................................................................3 

PROCEDURES............................................................................................................................... 6 

EQUIPMENT LIST ...................................................................................................................... 10 

FLOW VELOCITY RESULTS .................................................................................................... 11 

WHEEL VELOCITY RESULTS ................................................................................................. 19 

LFM WAVELENGTH CORRECTION & FIBER ILLUMINATION ........................................ 24 

Fiber Bundle Illumination ......................................................................................................... 27 

SPECKLE PATTERN MINIMIZATION..................................................................................... 29 

ERROR ANALYSIS..................................................................................................................... 32 

Possible wavelength calibration errors:..................................................................................... 34 

Calculated Velocity Error.......................................................................................................... 35 

Speckle Related Error................................................................................................................ 35 

CONCLUSIONS........................................................................................................................... 38 

REFERENCES.............................................................................................................................. 40 

APPENDIX—DIFFERENTIAL VELOCITY PROCESSING .................................................... 41 

NASA/CR—2003-212179 1 

INTRODUCTION 

The Doppler Global Velocimetry (DGV) measurement system at the NASA Glenn 

Research Center (GRC) has demonstrated very good quality one-dimensional flow data 

measurements. The GRC program is a part of a cooperative effort with Langley 

Research Center (LaRC) to develop a fiber-based beam delivery and image pickup 

capability for hypersonic propulsion system testing. The GRC effort to date has 

incorporated LaRC technology to develop and demonstrate the capability to make 

accurate velocity measurements at supersonic velocities using a fiber optic light sheet 

delivery system. This report documents the system design, processes, and techniques 

in an effort to guide future high quality data acquisition. 

The data sets highlighted in this report are dubbed “Flow7” and “Cal10” after the 

parent data directory names in which the image data are stored. The Flow7 data 

represent velocity measurements from an under-expanded free jet of cold, seeded air in 

a laboratory environment, where core velocities range from Mach 0.3 to Mach 1.1. The 

Cal10 data are for a spinning wheel target, which compares the performance of a new 

fiber bundle illumination beam delivery approach to that of a traditional laser beam 

propagating in freespace. 

Previous results at GRC incrementally improved data acquisition and calibration 

techniques, developed a robust processing approach, and highlighted both major and 

minor problems to avoid in the collection of the data. The initial velocity results, 

achieved taking data from a spinning wheel, were consistent and very useful in 

debugging the adopted LaRC processing software, but exhibited a proportional 

calibration error and speckle noise that reduced accuracy and spatial resolution. A 

simple linear calibration approach (see Appendix) was reasonable for the wheel series 

of tests, as the range of the Doppler shifts were tuned to fall within the linear region of 

the absorption line. 

An issue that obviated some previous flow test data was that the laser modehopping behavior changed since the iodine cell characterizations that were used with 

the wheel tests. After the wheel tests, the DGV equipment was moved to a different 

laboratory, and this possibly caused the laser to be disturbed in a way that caused a 

different number of modes to be skipped at a different region of the operating regime. 

The ultimate result was that the initial flow tests were conducted with the laser 

wavelength in a very low sensitivity region of the absorption curve and at a completely 

different absorption line than expected. In retrospect, some velocities are recoverable 

from the data, but with very low dynamic range (around 15% of the expected dynamic 

range). Instead, new data were acquired in which other improvements were 

implemented. 

These issues, and others, were overcome in the subsequent flow testing. The 

“Flow7” data set reported herein thus benefits from the incremental improvements 

gained through the learning curve, procedural corrections and improvements in the 

velocity calculations, and avoidances of unforeseen equipment performance problems. 
NASA/CR—2003-212179 2 

 DGV TECHNIQUE 

DGV measurement techniques for various applications have been reported in the 

literature by a number of researchers, but the GRC program is specifically based on the 

dynamic velocity measurement approach used by Meyers, et al. at LaRC.1

 In fact, most 

of the data acquisition system electronics and software used at GRC were designed at 

LaRC; conversely, the velocity component measurement heads and most of the 

processing routines reported herein were developed at GRC. 

In a simplified overview, the DGV technique is based on the measurement of 

Doppler shifted narrow band laser light scattered off particles seeding the flow being 

analyzed. The scattered light is detected by a CCD array camera after being filtered by 

an iodine vapor absorption cell. The iodine cell attenuates the light as a function of 

wavelength, which encodes one component of the flow velocity distribution (or Doppler 

shift distribution) according to light intensity on the camera array. The image is 

intensity-normalized by an identical camera system by being split before going through 

the iodine cell – the ratio of the iodine vapor modulated image divided by the 

unmodulated image gives an intensity-modulated coding of wavelength distributions, 

corrected for variations in the seed particle scattering cross-section. 

Corrections for jitter in the laser wavelength are also performed, by viewing a portion 

of the illuminating laser beam by an identical two-camera velocity component 

measurement head. Using four component heads (one for each velocity component 

and one to monitor the laser wavelength) the three components of velocity can be 

measured at each pixel over a planar slice of a flow distribution. 

The pixel values in each normalized image then represent calibrated optical 

frequency values converted to velocities in meters per second using the accepted 

Doppler relationship2 

( ) a l V

c

∆ = − • ν 0 ν (1) 

where ∆ν is the Doppler-shift frequency difference, ν 0 is the base laser frequency, 

determined by calibrating the seed laser offset voltage, c is the speed of light, a is the 

unit vector toward the Component camera, l is the unit vector of the Poynting vector, 

and V is the velocity vector. 

The current system uses two heads to measure one component of velocity, with the 

system capability to readily add two more components. The DGV measurement 

advantages are that the measurements are instantaneous over a nine-nanosecond 

exposure, and have high spatial resolution since each pixel contains all the encoded 

velocity information at that image location. 
NASA/CR—2003-212179 3 

EXPERIMENTAL SETUP 

The experimental apparatus used to acquire this data is generally the same as for all 

the flow velocity data runs, as opposed to the markedly different hardware used to 

generate the previous spinning wheel velocity data. Some changes were made 

incrementally to the hardware to improve various aspects of the data collection. Among 

these are: 1. To use an extended nozzle allowing the light sheet and image field of view 

to get closer to the nozzle exit port (reduces x/D to better understand the flow 

conditions), 2. to achieve better focusing of the laser light sheet at the test plane, in 

order to get a thinner planer section of flow data, and 3. to change to non-polarizing 

attenuators on the Component A head, to avoid scattering-dependent polarization 

effects. While all of these are thought to have contributed to better data, the successful 

advances over the flow data runs are primarily due to improvements in test parameter 

set points (image exposure levels and base laser wavelength selection relative to the 

absorption lines), iodine cell calibration accuracy, and specific processing algorithms. 

The general hardware setup is as follows. The laser light is delivered from the 

Continuum laser through a Newport high-energy beam attenuator (crossed GlanThompson polarizers) via two beamsteering mirrors into a non-imaging multi-mode 

optical fiber bundle. The fiber bundle output is focused into a light sheet with 

dimensions approximately 3 x 25 mm at the test section. Lower intensity marginal light 

is blocked with an 

adjustable slit 

aperture to provide 

better width 

definition to the 

sheet. See Figure 

1 for a picture of 

the test section. 

A 0.1% portion 

of the beam is split 

after the fiber to a 

ground screen, 

onto which the 

Laser Frequency 

Monitor (LFM) head 

is focused at nearnormal incidence. 

The split is 

accomplished with 

a custom beam 

sampling cube 

fabricated by CVI 

Laser Corp, whose 

specifications are shown in Figure 2. 

The two frequency measuring component heads are now of the same design, with 

the sole difference being the use of crossed polarizers in the LFM to adjust the signal 

Figure 1: Test section showing free jet nozzle, Component A and LFM heads, 

and fiber bundle/beam splitter/light sheet generator. Tapped holes in optical 

table are on 1" centers. 
NASA/CR—2003-212179 4 

levels between the reference and signal cameras. The overall signal level on the LFM 

cameras is adjusted by a stack of neutral density filters placed in front of the LFM 

beamsplitter. The 

Component A head has 

been retrofitted with 

neutral density filters to 

adjust the relative 

intensities between the 

reference and signal 

camera, on the caution 

that the scattering 

properties of the seed 

particles may change 

the calibrated ratios. 

Conversely, the LFM 

uses the same ground 

screen for both the 

calibration and the 

measurement runs, and 

is assumed not to be 

dependent on 

polarization. 

Previous tests 

showed no spatial 

dependence on 

frequency of the image 

ratios, so the LFM 

correction uses the 

average value of the 

pixel ratios to correct the 

Doppler shifted frequency measurement. Although there has been observed slight 

trends and noise on zero velocity images, these have also been observed in the flat 

field images at the same magnitude and thereby are not attributed to a spatial 

wavelength distribution in the laser beam. 

The flow that is being measured is generated by a converging nozzle of cold air 

seeded with an olive oil aerosol. The nozzle outlet diameter is 3/8”. The plenum 

pressure is monitored via a tap connecting the plenum to a TBD absolute pressure 

gauge. The flow is underexpanded, and is generated by plenum pressures ranging 

from 15 to 30.8 psia. 

The test geometry for this run can be seen in Figure 3. The light sheet is incident at 

59° from the flow direction toward the right of the page, and the Component A field of 

view is oriented at –55° from the flow direction. The velocity component measured is 

then about 2° off of the negative flow direction, along a unitless “sensitivity vector” R: 

R = (a-l) = - cos(59°)⋅cos(55°) (2) 

 = -1.09 

Figure 2: Specifications for custom beam sampler cube with ground 

screen. 
NASA/CR—2003-212179 5 

where a is the unit vector in the direction of the camera, and l is the unit vector from the 

laser. The laser sheet slices the flow at an x/D of about 1 to 2, and passes through the 

center of the core flow at about x/D = 1.7. 

The view of each data image 

shows the left boundary of the 

data, which is defined by the last 

column of dots visible before 

being occluded by the nozzle 

edge. Referring to the figure, 

the illuminated region of the flow 

is the intersection of the green 

laser sheet with the light gray 

FOV arrow for Component A. 

Starting from the left edge, the 

flow regions represented in the 

data images, therefore, integrate 

the velocities from: 1. The 

mixing region at around x/D=1.2; 

2. the core region at around 

x/D=1.7; and 3. the downstream mixing region at around 

x/D=2 to 2.5. The data 

boundaries of the mixing regions 

are determined by the signal 

level arising from the amount of 

seed that is drawn in from the 

core flow. The constant velocity 

core region is approximated by 

the cone drawn to converge at a 

point around four nozzle 

diameters from the nozzle exit. Figure 3: Scale diagram showing test geometry and flow 

measurement orientations. The nozzle diameter is 3/8”, and 

the sensitive velocity component is indicated by vector (a-l). 
NASA/CR—2003-212179 6 

PROCEDURES 

The iodine cells were set with the finger temperatures at 55 °C using the Iomega PID 

temperature controllers. This put the body temperature of the cells at around 71 °C. 

The transmission characteristics of the two cells were then measured after setting the 

camera attenuation levels to those needed during the laser exposure of the velocity 

tests. This exposure ratio setting is a compromise to maximize the dynamic range of 

the laser exposures without saturating pixels, while also guaranteeing successful 

centroid processing of the white light illuminated dot card images. The difficulty mostly 

comes from the need to use the reference/signal beamsplitter coating for both 532 nm 

and white light exposures, as the transmission/reflection ratio is different for each 

illumination source. In addition, the signal level from each target is different (ground 

glass, seeded flow, dot card), so adjustability, using stacks of various neutral density 

filters, is provided for each camera as well as for each component. 

Since the ratios are tuned to optimize the camera exposures at 532 nm, the proper 

exposure (brightness, flatness, and contrast) of the dot card images is achieved digitally 

off-line. This is important, as the success of the centroid processing is very sensitive to 

correct exposure and processing settings. However, the traditionally preferred 

approach of adjusting the exposure at the camera could not be done reliably without 

altering the calibration data. The current setup helps by using a wideband green 

transmission filter over the white light sources, but the camera image split ratio is still 

not near 50% (as with the 532 nm illumination) and digital adjustments are needed. 

To calibrate the I2 cells, the injection seed laser thermoelectric cooler’s drive voltage 

was varied between –4.0 to 10.0 volts for a coarse characterization. After observing 

different mode hopping behavior of the Nd:YAG laser than at the previous calibration, a 

finer calibration was done over the desired range of interest of –2.00 to 1.00 volts. The 

negative slope of the 18,789.98 cm-1 (532.1986 nm) I2 absorption line was then chosen 

for the current DGV test geometry for a number of reasons: 1. the negative slope 

compensates for the signal loss due to decreasing seed density at increasing velocities, 

by attenuating the red-shifted laser light less as the velocity increases; 2. the 

transmission dynamic range of this line for these I2 cells is greater than the neighboring 

lines; 3. no mode hopping behavior is observed in the laser operating region of this line. 

Figure 4 shows the I2 cells’ transmittance data over the selected absorption line, as 

a function of the seed laser’s wavelength control voltage. The calibration data were 

converted to a look-up table (LUT) for each component, which converted the normalized 

transmission ratios to absolute laser wavelengths. The LUTs were organized to 

associate gray scale values of 1 to 512 with wavelengths ranging over the negativeslope region of the absorption curve. Data points describing the absorption curve were 

interpolated using Origin 6.1 software to generate a final ASCII file of integer gray scale 

values and their associated wavelengths. These data sets are shown in Figure 5. 
NASA/CR—2003-212179 7 

Iodine Cell Transmittance - 7/16/02

Normalized to Ratio at -1.4 Volts

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

-1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7

Seed Voltage

Cell #3 (Comp A)

Cell #4 (LFM)

Normalized Iodine Calibration - 8/23/02

0

100

200

300

400

500

600

532.1995 532.1993 532.1991 532.1989 532.1987 532.1985

Wavelength (nm)

Interpolated CompA

Interpolated LFM

Figure 4: Transmittance data over the absorption line used to acquire the test data, 

normalized to the flat field ratio at -1.4 V. The primary seed laser offset voltage was 

-1.0 V. 

Figure 5: Iodine cell calibration data after convertion to LUT format. Integer values 

of 1 to 512 map to transmission values normalized to the flat field voltage ratio. 
NASA/CR—2003-212179 8 

The Flow7 data were processed using the absolute frequency measurement 

technique described below. This procedure to relate the velocity image ratio data to the 

calibration data involves normalizing the calibration data by the calibration flat field 

wavelength transmission ratio, and later normalizing the velocity data by the most 

recent test flat field transmission ratio. This partially corrects for environmental changes 

in the transmission characteristics since the last calibration. Each normalized pixel ratio 

value can then be assigned a calibrated wavelength, which can then be converted to 

velocity using the geometrical constants measured during the set up. 

The procedure to prepare the wavelength calibration LUTs follows: 

1. Acquire image pairs for each component head, sequentially over a range of 

seed laser offset voltages. Acquire twenty image pairs to average for each 

head at each offset voltage. 

2. Cross-correlate image pairs, correct offsets, calculate ratios according to the 

equation: 





 



 = ⋅ ( , )

( , ) ( , ) 512

reference i j

signal i j ratio i j (3) 

3. Perform averaging over a representative ROI for each component: 

a. Calculate ratio pixel means and s.d. over twenty images (temporal pixel 

means) 

b. Calculate spatial mean and s.d. of temporal pixel means over ROI 

c. Record a single spatial-temporal mean value for each component at each 

offset voltage. 

4. Normalize these ratios by the ratio (peak) found at the flat field voltage 

selected for this line, according to 





 



 = ⋅ FlatfieldRatio

Ratio i j Normalizedratio i j ( , ) ( , ) 512 (4) 

5. Interpolate these curves to generate wavelengths at integer values of gray 

scale from 1 to 512. 

6. Store in the format: (Gray Scale, CompA Wavelength, LFM Wavelength). 

This comprises the LUT for this calibration run. 

The procedure to measure velocity at each pixel is then to: 

1. Acquire all background, flat field, and velocity data. 

2. Subtract the average raw background image from each raw reference and 

signal image. 

3. Dewarp (and further align by correlation, if needed) each image pair for the 

LFM and CompA images. 

4. Take the image ratios using the IDL ratio script, according to Equation 3. 

5. Take flat field temporal and spatial mean for CompA and LFM. Store in 

velocity set file for calibration ratio normalization. 

6. Convert each array of pixel ratios to wavelengths using the calibration LUTs. 

7. Calculate the velocities at each pixel using the Doppler wavelength and LFM 

wavelength calculated in step 4, and the geometric sensitivity vector from 

Equation 2. 
NASA/CR—2003-212179 9 

The data were collected using version 5 of the LaRC DGVAck32.exe and the 

corresponding version of the DGVRec.exe software. The signal split between each pair 

of component cameras was adjusted by acquiring a set of image pairs and viewing 

them with a pixel-interrogating viewer (University of Texas’ ImageTool). The images 

were adjusted so that the relevant regions of interest were below saturation with the 

laser set at the flat field frequency. 
NASA/CR—2003-212179 10 

EQUIPMENT LIST 

The following lists major equipment used in the system. 

1. Pulsed, doubled, injection-seeded Nd:YAG laser; Continuum NY82S-10 

2. Fiber optic bundle with circular input and output apertures, 2 m; CeramOptek P/N 

PLGSS2/UV200/8.0MM/BPGS/2.0M/NASAG 

3. Custom beamsplitter cube with ground output face; CVI P/N PCB-532-0.1-150-SUV/FG 

4. Iodine cells #3 and #4 (CompA and LFM, respectively) 

5. 3/8” diameter free jet; NASA GRC fabrication, with protruding tip 

6. Seed generator with olive oil aerosol; TSI six jet atomizer 

7. CCD array cameras; Hitachi KP-F1, analog, 640 x 480 pixels 

8. 8-bit ADC framegrabbers; Matrox Pulsar 

9. DGVEMS timing generator; NASA LaRC fabrication 

10. Four Channel Delay/Pulse generator; Stanford Research Systems Model DG535 

11. Absolute gas pressure gauge; Heise Model 710B 

12. Dot card grids: LFM ⇒ 5/16” dot pitch; CompA ⇒ 1⁄2” dot pitch 

13. DGVAcq32 Acquisition and receiver software; NASA LaRC version 5 (Jan, 2000 

load) 
NASA/CR—2003-212179 11 

FLOW VELOCITY RESULTS 

Two runs of data were collected in the course of this flow test. The first one was 

collected with a seed laser offset voltage of –1.0 volts, and the second was collected 

with a seed laser offset voltage of –1.1 volts. For this test, the goal in selecting the 

offset voltage was to maximize the velocity range while not losing too much sensitivity 

near the lower-sloped ends of the absorption line. The base wavelength must not be at 

a maximum or a minimum of the absorption curve, even if all the measured velocities 

are expected to be non-zero, as the LFM always operates immediately around this base 

wavelength. The data set using an offset voltage of –1.1 volts was taken as a 

contingency, in case the data set using an offset voltage of –1.0 volt was found to have 

too much noise (in hindsight, it didn’t; but it did prove to be useful comparison data). 

Figure 6 shows an instantaneous image of color-coded velocity measurements for a 

pressure ratio of 0.937. The color scale was chosen to cover the velocity range in the 

series of images without saturation. The pixel values represent calibrated optical 

frequency values converted to velocities in meters-per-second, using the standard 

Doppler relationship given in Equation 1. The orange halo represents where the seed 

density and/or the illumination level falls off such that either the reference or signal 

image intensity is very low (also see the Error Analysis section). Since the flow was 

seeded in the core 

within the plenum, 

the transition 

boundary region is 

poorly seeded, with 

signal only available 

where seed has 

moved from the 

core. A vertical slice 

through any 

horizontal point in 

the image 

represents a 

constant x/D. 

The velocity 

images were 

subsequently 

masked by an image 

generated by a 

reference image 

thresholded at a 

gray scale value of 

10. This subjective 

threshold seems to 

eliminate most of 

what is considered 

noise in the following 

Figure 6: Instantaneous velocity map of flow at a pressure ratio of 0.937. 

Color coded velocities are in m/s. The core flow is centered approximately 

about pixel (65,244) 
NASA/CR—2003-212179 12 

data. A side effect is that the 

mask can also show where 

the core boundary is on the 

right side of the images. It is 

preferable to generate the 

mask based on the 

reference image, which give 

the best information on 

where the flow is well 

seeded (or illuminated) and 

where it is not. A drawback 

with this approach is that, 

depending on the signal 

level, this threshold will 

typically allow some noisy 

data to remain or, 

conversely, mask some 

meaningful data. Currently, a 

mask is generated from the 

first image in the series, 

which for turbulent flow has 

a unique seed boundary; 

averaging a series of 

images, in this simple 

algorithm, necessarily 

excludes regions having 

data in other images and 

includes regions that should 

be masked in other images. 

These overlapping mask 

regions are thus not 

weighted properly in the 

averaged images. 

Alternatives would be to 1. 

logically AND the masks to 

generate a common mask, 

or 2. normalize each pixel by 

the number of mask which 

include said pixel. 

Alternative ‘2’ would be 

preferable, as it includes the 

most data in the final result 

(albeit not all averaged 

resulting pixels would have 

undergone the same 

Figure 7: Same data as figure 6, but with a threshold of 10 applied 

to the reference image to mask the noise region. 

Figure 8: Flow data averaged over ten images, for Mach 0.3 core flow. 

The box outline represents core flow ROI in later plots. The green 

halo indicates the noise floor as the scattering intensity drops off. 
NASA/CR—2003-212179 13 

number of samples). 

Figure 7 shows the 

same data as in Figure 6, 

only being masked as 

initially described above. 

The image shows a central 

region having velocities 

ranging from 100 to 140 

m/s, with an average value 

of 121 m/s. 

A ten-image average of 

data taken at a pressure 

ratio of 0.937 is shown in 

Figure 8, with a 10 x 10 

pixel ROI shown as a black 

outline. This ROI is later 

used to calculate a 

representative core velocity. 

This ROI is centered around 

pixel (65,235), which is felt 

to be close to the flow 

centerline, based on image 

symmetry. A relatively large 

ROI previously extended 

across the core flow region 

to the mixing regions at the 

outer radii; although this 

larger ROI better 

represented the average 

velocity in the image, it did 

not represent the core 

velocity for which accurate 

comparison velocities can 

be calculated. The smaller 

core region was therefore 

used in the later comparison 

plots. 

Figure 9 shows an 

image of instantaneous 

velocities at a plenum 

pressure ratio of 0.474. As 

in Figure 6, the orange halo 

represents a region of very 

dim intensity and is 

considered noise. The 

core flow region seems to 

Figure 9: Instantaneous velocity map of flow at a pressure ratio of 

0.474. Core flow velocity is calculated to be Mach 1.1. The core flow 

is centered approximately about pixel (75,235) 

Figure 10: Same Mach 1.1 data as in Figure 9, but with a threshold of 

10 applied to the reference image to mask the noise region. The 

threshold appears to have removed some real low-signal data to the 

right of the core region. 
NASA/CR—2003-212179 14 

be centered around pixel (70,235) in this image. Figure 10 is the same data, but 

masked using an image generated by thresholding the reference image with a value of 

10; the two images show that the threshold value must be selected carefully so as not to 

mask possibly significant data. 

Figure 11 shows a ten-image average at a pressure ratio of 0.474, with an 80 x 60 

pixel ROI and a 10 x 10 pixel ROI shown as black outlines. Again, the smaller ROI is 

later used to calculate a representative average velocity. 

Figure 12 is a sequential view of the series of increasing velocity data. The images 

each represent an 

instantaneous map 

of velocities, 

masked to remove 

the noise 

background. The 

box outlines 

represent the same 

10 x 10 pixel regionof-interest used to 

determine the core 

velocities for 

subsequent plots. 

The same threshold 

value of ten is used 

on all the plots, 

which leads to 

variations in the 

usable data areas. 

The thresholds can 

be refined by hand, 

but has not been 

done here in the 

interest of uniformity. 

The data are 

averaged temporally 

and spatially to 

determine a 

representative velocity measured at each plenum pressure ratio. These local averages 

are calculated as follows. Each image is processed to yield pixel values of 

instantaneous velocity, and a series of ten such images taken at ten pulses of the laser 

yield the temporal velocity average at each pixel. A spatial average is then taken over a 

region of interest (ROI) in each of these average images, and plotted in Figure 13 for 

each set of data taken at a different pressure ratio. 

Figure 13 then shows plots of the measured velocities versus the expected 

velocities. The expected velocity is shown in green with a slope of unity, against which 

the measured velocities are compared. The calculated velocities came from a table 

generated by NASA Ames Research Center3

. The data taken at an offset voltage of 

Figure 11: Flow data averaged over ten images, for Mach 1.1 core flow. Box 

outlines represent core flow and image mean ROI data shown in later 

figures. The orange halo represents noise. 
NASA/CR—2003-212179 15 

-1.00 V, representing data sets “ex00” through “ex07”, are shown in blue; the data taken 

at an offset voltage of -1.10 V, representing data sets “ex10” through “ex16” are shown 

in red. The averages represented by the blue line and the red line use a very small ROI 

of 10 x 10 pixels, in order to sample the core region of the flow. Previous ROIs of 80 x 

60 (4,800) pixels, and 50 x 10 (500) pixels show very similar trends in the data and 

similar standard deviations, however, the slopes are lower (slightly higher than unity). 

Table 1 shows the statistics of these fits. 

The trends given by the core flow ROI averages give slopes of about 1.10 and 1.32, 

but with similar profiles. The last three data points on the red line show a flattening or 

clipping of the measured velocity, which is due to the Doppler shifts pushing the 

wavelength into the transmitting region of the absorption line. These three points are, 

therefore, not included in the linear fit. 
NASA/CR—2003-212179 16 

Figure 12: Series of eight instantaneous flow images for increasing pressure ratios (series ex00 through ex07). 

Mach number increases from left to right, and top to bottom. Box outline indicates ROI for core velocity plot. 
NASA/CR—2003-212179 17 

The core velocity should be constant over a converging cone reaching from the 

nozzle exit to a point roughly four nozzle diameters downstream. The ROI used in the 

above plots are ±5 x 5 pixels centered about pixel (65,235) for the core region. The 

agreement between the two runs at different seed voltages is excellent, up to the region 

where clipping occurred in the 1.1 V run; the error bars, representing Table 5, show that 

each velocity point agrees to within the theoretical resolution of the measurement, and 

all but one measurement point agrees to within the theoretical uncertainty with the 

expected velocity. The data above 200 m/s in both runs, however, seem to deviate 

much more from the theoretical velocity predicted by the nozzle pressure ratio. This 

profile is seen over a variety of different conditions, which tends to discount most 

systematic errors: different absorption region, slightly different nozzle pressure settings 

(pressure set points differed by 0.1 psi), and different spatial averaging ROIs (discounts 

local steady state flow variation). 

Measured DGV vs. Calculated Core Velocity 

Flow7 - 7/29/02

0

50

100

150

200

250

300

350

400

450

0 100 200 300 400

Calculated Peak Velocity (m/s)

Measured Core Velocity (m/s)

Expected Correlation

Seed Voltage = 1.00 V

Seed Voltage = 1.10 V

Fit of 1.00 V data

Figure 13: Comparison plots between measured and calculated core flow velocities. The blue line has a slope 

of 1.1 and an offset of 20 m/s. The black line is a linear fit with these coefficients. The green line is the 

expected correlation with a slope of unity. The error bars on the blue line show all but one data point to be 

within the theoretical uncertainty. The red line, which is included to show repeatability, is a second run 

through the same pressure ratios, but with a seed laser offset of 1.10 V, which puts the center wavelength 

more toward the middle of the iodine absorption line; the data was subsequently shifted into the flat 

transmitting region of the line, so the last three data points are invalid. 
NASA/CR—2003-212179 18 

A likely remaining error is in the plenum pressure measurement. For example, a 

leak in the pressure tap tubing may be come significant above a pressure of 20 psi, 

leading to higher actual velocities at the nozzle. A post-test calibration of the pressure 

gauge and tap indeed showed small leaks in the tubing and the swedge tubing fitting, 

but an accurate correction calibration was not possible, since the fittings were tightened 

prior to the calibration. 

Figure 14 shows slices of data taken across each velocity data average image, for 

each pressure ratio. The slices are taken at pixel row 240, which may be slightly higher 

than the flow axis around pixel 235. Referring to the geometry shown in Figure 3, each 

slice in Figure 14 consists of a central core region surrounded by mixing regions on the 

left and right; the plots cover flows from one to two nozzle diameters as the pixel 

number increases from left to right. The grayed-out box with the dashed outline 

indicates a region of low signal level due to low seed concentration for the higher 

velocity runs ex04, ex05, and ex06. 

The expected profile at each pressure ratio is a flat velocity profile in the core flow 

region included between pixels 60 to 80, which falls off to the ambient air velocity (zero, 

in this case) at each radial extreme (this extreme is well out of the range of the current 

data, as the data are limited to the seeded region). 

Mean Axial Velocity at Decreasing Pressure Ratios

0

50

100

150

200

250

300

350

400

450

20 40 60 80 100 120

Pixel along flow direction

Measured Velocity (m/s)

ex00 (r=0.937)

ex01 (r=0.813)

ex02 (r=0.711)

ex03 (r=0.629)

ex04 (r=0.569)

ex05 (r=0.517)

ex06 (r=0.474)

Figure 14: Mean velocity slices for increasing pressure ratios. Roll-offs at the ends indicate the transition flow 

regions. A slight asymmetry indicates the varying x/D and a restricted FOV on the left sides of the images. 

The core region is included between pixels 60 to 80. Significant signal drop-off is typically observed at pixel 

numbers above 110. The grayed-out region within the dashed outline indicates very low signal levels in the 

higher speed data. They are included here because they follow the expected trend, however, there seem to be 

discontinuous jumps in the ex04, ex05, and ex06 data.
NASA/CR—2003-212179 19 

WHEEL VELOCITY RESULTS 

A standard test application for DGV measurements has been to measure the 

velocity distribution on a spinning wheel covered in fine grit sandpaper. This test was 

performed at GRC with the two-fold goal of demonstrating basic velocity measurements 

and comparing results using wheel illumination via a fiber bundle versus freespace 

beam propagation. The following results were observed. 

Data were acquired using a 11.8” diameter wheel spinning at 3,000 RPM, as 

measured with a Hall effect sensor on the wheel mount. The setup was designed to 

measure the horizontal component of velocity. The data were processed according to 

the differential technique described in the Appendix. Taking into account the geometric 

sensitivity vector a-l, the calculated component of the measured wheel rim speed is 

±33.3 m/s. 

Figures 15 and 16 show 

masked single image results 

of the wheel velocity 

distributions, using a 

smoothing kernel of 1 and 

11, respectively. The 

velocities are color coded 

with an offset of 1000 m/s to 

avoid negative numbers in 

the scaling. The figures 

show a progressive 

horizontal velocity 

increasing from top to 

bottom of the wheel, which 

spins counter-clockwise. 

Figure 16 adds smoothing 

by an 11x11 kernel, to 

reduce noise from speckle 

variations. Slices of these 

two images are shown as 

the purple data in Figures 

18 and 20. 

A comparison between 

the fiber-delivered illumination and the freespace propagating illumination is seen in 

Figure 17. After spatially smoothing the image with an 11x11 kernel to compensate for 

speckle variations, the measured rim speed values range from 33 to –47 m/s for the 

fiber illumination data and 18 to –38 m/s for the freespace beam illumination data, and 

are plotted in red and yellow, respectively, in Figure 17. The green line indicates the 

calculated values expected for the given setup, and the red line is a linear fit of the fiber 

data. The standard deviation from a linear fit through each set of data is 4.1 m/s and 

9.4 m/s for the fiber and freespace illumination cases, respectively. Both data sets are 

a single pixel column from a spatially smoothed instantaneous image of velocity data, 

normal to the sensitive axis.

Figure 15: Single image of velocities measured for a wheel spinning 

at 3000 RPM. The wheel is fiber-illuminated, the reference and 

signal images are aligned by cross-correlation, and the ratios are 

not smoothed. 
NASA/CR—2003-212179 20 

The “random” noise visible 

in the data is lower than the 

system error of 10 m/s for 

the fiber data, and higher 

than the system error for the 

freespace data. There are 

scale factor errors in the 

slopes that are attributed to 

variations from the 

calibration conditions. The 

large deviations from the 

linear trend are attributed to 

overlying fringes in the 

freespace data that are not 

correlated between the 

reference and signal 

images. 

The prominent bumps in 

the data with widths of 

about 20 mm are thought to 

be decorrelated and offset 

speckles and fringes, and 

possibly centroid position 

errors in the dewarp 

algorithm. 

Wheel Data, 3000 RPM, Single Images Smoothed

-50

-30

-10

10

30

50

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Wheel Radius (mm)

Velocity (m/s)

Fiber, no correlation (s.d.=4.1 m/s)

Freespace, no correlation (s.d.=9.4 m/s)

Actual Velocity

Fit of Fiber Illuminated Data

Figure 17: Vertical velocity profile across a wheel spinning at 3000 

RPM. Red data indicate fiber bundle illuminated run, and the 

yellow data indicate freespace beam illuminated run. 

Figure 16: Single image of velocities measured for a wheel spinning 

at 3000 RPM. The wheel is fiber-illuminated, the reference and 

signal images are aligned by cross-correlation, and the ratios are 

smoothed by an 11x11-pixel kernel. 
NASA/CR—2003-212179 21 

The following series of 

graphs, Figures 18 through 21, 

show the effects of adding 

incremental improvements to 

the processing of the Cal10 

data, whose typical speckle 

size is larger than the pixel 

pitch. The first pair of graphs, 

Figures 18 and 19, compare 

the effect of image alignment 

prior to taking the ratios, for 

single images and then 

averaging over ten image ratio 

sequences. 

Figure 18 shows the 

difference between velocities 

calculated both with and 

without aligning the reference 

and signal images before 

taking their ratios. The plot 

shows vertical slices through 

single image ratios converted 

to velocities. The correlation 

shifts the reference image 5.7 

and –5.0 pixels in the x and y 

dimensions, respectively. 

Figure 19 shows a vertical 

slice of ten similar velocity 

images averaged over time. 

There is a statistical 

improvement in scatter 

between the plots in Figures 

18 and 19, since each image 

in the mean has a different 

speckle pattern. 

Figures 20 and 21 add 

spatial smoothing by an 11x11 

kernel to the data in Figures 

18 and 19. Figure 20 is a 

vertical slice through a single 

smoothed velocity image, and 

Figure 21 is a ten-image 

average of smoothed velocity 

images. An improvement is 

clearly seen as the pixels are 

Wheel Data, 3000 RPM, Single Images

-50

-30

-10

10

30

50

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Wheel Radius (mm)

Fiber, no correlation

Fiber, with correlation

Actual Velocity

Wheel Data, 3000 RPM, 10-image Mean

-50

-30

-10

10

30

50

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Wheel Radius (mm)

Velocity (m/s)

Fiber Mean, no correlation

Fiber Mean, with correlation

Actual Velocity

Linear (Fiber Mean, with correlation)

Figure 18: Single image velocity data slice, acquired using 

freespace beam propagation. Plots compare velocities from 

Signal/Reference image ratios calculated with and without 

alignment using 2-D cross-correlations. The high degree of scatter 

in the "aligned" correlated images indicate that that the intensity 

distributions being aligned do not represent any real-space image 

shifts. 

Figure 19: Velocities averaged over ten images, comparing aligned 

and unaligned image pairs. 
NASA/CR—2003-212179 22 

averaged over time and 

space. There is also clear 

indication of partial 

correlation of the speckle 

patterns between the 

reference and signal images, 

as image alignment prior to 

normalization flattens some 

of the features in the data. 

The lowest standard 

deviation is 1.83 m/s for the 

correlated images spatially 

smoothed and averaged 

over time. 

The calibration slope 

errors are consistent among 

the plots, and differ from the 

actual slope of 0.24 m/s/mm 

by about 17 to 23%. This 

slope error is due to iodine 

cell calibration errors 

caused by a linear 

approximation of the 

transmission curve and from 

errors reading graphically 

determined intercept values. 

Table 1 compares the 

standard deviations of the 

data in figures 18 through. 

In the table, the spatial 

standard deviations are 

given for four variations of 

smoothing and crosscorrelation. The standard 

deviations for both a single 

image and a series of ten 

images averaged over time 

show improvement from 

averaging noise. The 

measured improvements 

were 54% and 55% for the 

unsmoothed data, and 33% 

and 38% for the data that were already spatially smoothed. 

The average speckle size over 200 pixels in these f/4 CompA images is roughly 4 

pixels/speckle, showing that an improvement is expected when spatially smoothing the 

data. 

Wheel Data, 3000 RPM, Single Images Smoothed

-50

-30

-10

10

30

50

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Wheel Radius (mm)

Velocity (m/s)

Fiber, no correlation, k=11

Fiber, with correlation, k=11

Actual Velocity

Wheel Data, 3000 RPM, 10-image Mean Smoothed

-50

-30

-10

10

30

50

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Wheel Radius (mm)

Velocity (m/s)

Fiber Mean, no correlation, k=11

Fiber Mean, with correlation, k=11

Actual Velocity

Linear (Fiber Mean, with correlation, k=11)

Figure 20: Velocities smoothed by an 11x11 kernel prior to taking 

the image ratios. The plots show both an improvement from 

speckle smoothing and from image alignment. 

Figure 21: Velocities smoothed by an 11x11 kernel and averaged

over ten velocity images. Random noise has been reduced to about 

1.8 m/s. 
NASA/CR—2003-212179 23 

Standard Deviation Comparisons s.d. (m/s) 

k=1 Not Correlated Single image 17.5 

 Ave image 8.07 

 Improvement: 54% 

 Correlated Single image 12.7 

 Ave image 5.76 

 Improvement: 55% 

k=11 Not Correlated Single image 3.89 

 Ave image 2.61 

 Improvement: 33% 

 Correlated Single image 2.94 

 Ave image 1.83 

 Improvement: 38% 

Table 1: Comparison of standard deviations of data in Figures 18 

through 21. 
NASA/CR—2003-212179 24 

LFM WAVELENGTH CORRECTION AND FIBER ILLUMINATION 

The Doppler Global Velocimetry technique is based on the calibrated measurement 

of optical frequency (or wavelength). That is, the component image ratios are 

compared to a calibration between transmission ratio and optical wavelength, to assign 

a wavelength to each pixel in the image ratios. Any change in this wavelength from the 

fundamental laser wavelength is then attributed to a Doppler shift in the light scattered 

from the seed particles. However, the calibration is done over an average of many 

image pairs from a series of laser pulses, each of which varies slightly around the 

average wavelength (the variation is due to an active dithering of the cavity length 

required by the laser manufacturer to stabilize the laser). Therefore, the ability to 

accurately assign transmission ratios to Doppler wavelength shifts requires knowledge 

of the shot-to-shot laser wavelength variations; this is achieved with the Laser 

Frequency Monitor. So the laser wavelength is measured by the LFM and used in 

Equation 1 as the fundamental illumination wavelength. 

A concern in the GRC development is whether, in addition to a shot-to-shot variation 

in the average laser wavelength, there is a spatial variation in laser wavelength (either 

stable or varying from shot-to-shot). Previous tests showed no conclusive evidence of a 

spatial variation in wavelength using the GRC Continuum laser, and data supporting this 

are included here. An indication of such a variation of wavelength would be a difference 

in distributions or statistics visible between image ratios exposed by light inside and 

outside the absorbing region of the I2 curve; none were observed. 

The light emitted from the fiber bundle differs from the free space beam in that the 

spatial correlation with the beam out of the cavity is lost due to the intentionally random 

coherence between the input and output ends of the fiber bundle. That is, the fiber 

bundle is designed to randomize the intensity distribution on the free space beam, 

which also randomizes any wavelength distribution. This means that any wavelength 

distribution might be realized as an increase in RMS variation on the image ratios taken 

through the attenuating region of the I2 curve, compared to the flat field image ratios. 

Figures 22 and 23 compare image ratio data of fiber bundle-delivered light 

illuminating a ground glass screen, taken with the laser wavelength set inside and 

outside the I2 cell absorption band. The ground screen is angled slightly to cut across 

the beam, so that the illuminated region represents a cross-section of the laser beam 

stretched in the horizontal dimension. 

Figure 23 is an image ratio taken inside the absorption band, at the 33% 

transmission point, and Figure 22 is an image ratio taken in the flat field region, with a 

transmission coefficient of 94%. Since the in-band transmission ratio is 33%, the color 

scale on Figure 23 was divided by three to provide a comparative image representing 

any distribution differences between the two images. The images clearly show that the 

expected scale taken from the transmission curve maps the zero velocity data to the flat 

field data very effectively. Given that the scaling was successfully achieved, any 

difference in distribution may be attributed to either a spatial wavelength distribution on 

the beam or noise. 

The image ratios are masked in the same manner as Figure 7, using the thresholded 

reference image as the mask. Even so, the red boundaries seen on the top and bottom 

of the images may be considered noise, as their intensity is quite low. The red spot in 
NASA/CR—2003-212179 25 

the center is a blemish on 

the screen and is seen as a 

dim region on both 

reference and signal images 

[the gray scale value of the 

spot is roughly 20, which is 

about 20% of the peak data 

intensity]. This artifact 

highlights that there can be 

significant correlated noise 

present in the raw data, 

where in fact the velocity is 

zero. 

The wheel data set 

named Cal10 can be used 

to compare the fiber bundle 

results to the results from 

the beam propagating in 

free space. Table 2 shows 

the mean, standard 

deviation, and noise-tosignal ratio (NSR) for 

various image pair ratios. In 

the table, data sets ff00 and 

ex02 are the flat field and 

zero velocity data for the 

free space beam, and ff01 

and ex04 are the flat field 

and zero velocity data for 

the fiber bundle-delivered 

beam. Data labeled ic12 

and ic18 are the image 

ratios shown in Figures 22 

and 23. All the statistics are 

calculated over single image 

ratios, so no shot-to-shot 

averaging of speckle or 

wavelength is done. For the 

LFM images, the NSRs for 

the flat field and absorption 

band free space beam 

images are identical to two 

significant figures, and the 

NSRs for the fiber bundle 

images differ by 10%. A 

similar comparison of the 

Figure 23: Zero velocity image ratio in absorption region of iodine 

vapor cell. Color scale is matched to flat field data. 

Figure 22: Flat field image ratio outside of absorption region of the 

iodine vapor cell. A comparison of Figures 20 & 21 shows no 

statistical indication of wavelength variations. Color scale is the ratio 

* 1000.
NASA/CR—2003-212179 26 

Component A data shows the NSRs for the flat field and absorption band free space 

beam image ratios to differ by about 10% and 30%, respectively. Likewise, the NSRs 

for the I2Cal01 fiber data statistics show no trend that is attributable to a wavelength 

distribution. One unexplained anomaly in Table 2 is that the NSRs for the LFM are 

higher than for Component A; also, the LFM NSRs vary the most from run to run, 

whereas the Component A NSRs are quite consistent from run to run. The most likely 

explanation for this is a speckle size variation between the two LFM data sets; the fnumbers were used for the two runs were different, as were the image magnifications. 

The LFM camera lens f-numbers were f/11 and f/2.4 for the Cal10 and I2Cal01 data, 

respectively. Conversely, the Component A f-numbers were f/4 and f/2.4 for the two 

runs, but subsequent tests have suggested that the speckle sizes are smaller than the 

pixel size for f-numbers of f/4 and below. The scattering targets for both components 

change from 600 grit sandpaper to 200 grit ground glass between the Cal10 and the 

I2Cal01 runs, so this is not a differentiating factor. 

To verify that the Cal10 data, in fact, were taken at the calibrated transmission 

regions of the I2 curve, the LFM reference and signal image mean values were 

calculated and compared to the calibrated transmission ratios of the LFM iodine cell. 

The calibrated flat field transmission coefficient T at a seed laser offset voltage of 3.00 V 

is 94%, which compares well with the wheel-measured mean image ratio of 91%. 

Likewise, the transmission coefficients in the absorbing region with the seed laser offset 

voltage set to 4.12 V were 49% for both the calibrated and wheel-measured data. 

 CompA LFM 

Cal10 Mean s.d. NSR Mean s.d. NSR 

ff00 (freespace) 964 110 0.11 447 186 0.42 

ex02 (freespace) 421 49.4 0.12 620 261 0.42 

ff01 (fiber) 604 76.9 0.13 501 163 0.33 

ex04 (fiber) 283 26.9 0.10 260 78.6 0.30 

I2Cal01 (fiber) 

ic12nx00 (flat field) 481 57.7 0.12 550 135 0.25 

ic18nx00 (33% T) 136 20.1 0.15 262 63.3 0.24 

Table 2: Mean, standard deviation, and NSR (s.d. / mean) table for single image ratios of a wheel illuminated 

by beams delivered either via free space propagation or fiber bundle. For each component, the NSR does not 

change depending on whether the wavelength is in the attenuating region or not, for either the free space or 

the fiber bundle cases. This suggests that, in these data, there is no detectable wavelength variation over the 

beam. 
NASA/CR—2003-212179 27 

Fiber Bundle Illumination 

The optical fiber bundle approach to delivering the laser beam to the test section is a 

technically viable and experimentally convenient technique. Test comparisons for the 

Cal10 wheel data, shown in Figure 17, show similar velocity trends but with lower noise 

when using the fiber bundle. No Stimulated Brillouin Scattering (SBS) power density 

transmission limit is observed in the power transmission through the fiber bundles. 

The bundle is comprised of about 1,340 pure fused silica core multimode fibers, 

arranged in a random continuity between the input and output ends. The bundle ends 

are fused, rather than epoxied. The circular bundle ends are 8 mm in diameter, and the 

numerical aperture is about 0.37. Two progressively worse damage thresholds are then 

avoided by this approach to fiber coupling. The typical lower threshold to be avoided is 

burning of assembly epoxy via absorption, and the higher threshold is ablation of the 

glass fiber ends by an excessive power density causing thermal and acoustic shock. 

Eliminating the epoxy avoids the first threshold, and spreading the intensity over a large 

number of multimode fibers avoids the second threshold. A Teflon annulus is glued 

over the exposed end of the stainless steel ferrule surrounding the input end of the 

bundle, which protects stray light from the beam injection from ionizing and depositing 

metal on the face of the bundle. This bundle has been used to couple an input beam of 

up to 650 mJ/pulse without damage. 

Figure 24 shows the ratio 

of transmitted power to 

incident power as the incident 

power is increased. The 

transmission ratio in blue is 

relatively constant throughout 

the measured range; an 

indication of SBS would have 

been for the transmitted 

power to be clamped at some 

power level, with the balance 

of the incident power 

frequency shifted and 

backscattered toward the 

laser. Jeunhomme 

characterizes the BrillouinStokes frequency shift in 

silica fibers, such as those in 

the bundle, as –17/λ, or 32 

GHz, with a linewidth of 

29.6/λ2

, or 105 MHz, where 

λ is the wavelength of incident light in micrometers.5

 Even if SBS were to occur, 

however, any detrimental effect would be in limiting the delivered power rather than any 

real spectral broadening, as the frequency shifted portion would not be transmitted to 

the test section. 

When using the fiber delivered beam illumination, the standard LaRC cross 

correlation does not necessarily see enough structure in the beam to improve 

Fiber Bundle Power Transmission

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 2 4 6 8 10 12 14

Attenuator Rotation

Power (Watts)

Incident Power

Transmitted Power

Ratio (Trans/Incident)

Figure 24: Fiber bundle transmission coefficient as a function of 

attenuator position. 
NASA/CR—2003-212179 28 

alignment; in fact, it can destroy alignment and degrade the wheel measurement. 

Further, the cross correlation should not be needed if the dewarp process works, at 

least down to the pixel level of registration. Conversely, when using the freespace 

delivered beam illumination, the cross correlation seems to be necessary due to beam 

structure changes; that is, the beam fringes seem to shift between the signal and 

reference images. However, this fringe alignment does not necessarily represent 

velocity data registration, and use of it should assume that velocity gradients only occur 

over regions larger than the image shifts. See the Error Analysis section for more 

discussion. 

Advantages to the fiber bundle approach are that it reduces the number of 

components typically needed to deliver the beam, it reduces fringe noise on the raw 

beam and distributes the light intensity evenly across the emitting cone, and it makes 

the repositioning of the measurement plane more easily automated in a test 

environment. Disadvantages are that it reduces the delivered light intensity by about 

one-third (transmits 67%) and complicates the light sheet generation when using a 

circular output spot. A modification specified on the output end of the next fiber being 

purchased will produce a more rectangular output beam. This output geometry is 

expected to overcome the Lagrange Invariant constraint to the sheet thickness 

encountered with the circular output end; while the beam divergence will be similar, the 

beam thickness will be potentially improved by a factor of four (2 mm width versus 8 mm 

diameter). The elongated output beam should also reduce the weight and complexity of 

the laser sheet optics, which should be important to coming field applications. 

Generating a thin light sheet from the fiber bundle proved to be difficult, and believed 

to be caused by the LaGrange invariant and spherical aberration from the use of single 

element optics. Applying the LaGrange invariant to the current fiber bundle limits the 

theoretical sheet thickness to about 2.5 mm, assuming an output NA of 0.7 (full angle); 

this then is convolved with the point spread function expected from the single element, 

high NA optics used with the high energy laser beam to give a sheet thickness limit 

around 6±2 mm. This number is consistent with the observed sheet thickness of around 

6 to 8 mm. The Flow7 testing was done with a slit aperture at a conjugate plane in the 

sheet forming optics, giving a laser sheet waist of about 3 mm across. In order to 

eliminate the need for a slit aperture, a future fiber bundle termination with a rectangular 

fiber arrangement is proposed instead of a circular output termination. A reasonable 

bundle cross section is 2 x 50 mm. A fabrication compromise is that the output end 

must be epoxied rather than fused, as the jigging to fuse the fibers is not amenable to 

the rectangular geometry. However, this should be acceptable, with regard to the 

damage threshold, as the output face is comprised of a polished, bare fiber bundle 

rather than an epoxied cover glass. The only remaining assembly epoxy will be 

between the fibers, and only after a distance in the bundle where the leakage light is 

fully attenuated. 
NASA/CR—2003-212179 29 

SPECKLE PATTERN MINIMIZATION 

The Doppler Global Velocimetry technique is based on the calibrated measurements 

of two wavelengths – the instantaneous base laser wavelength illuminating the flow 

field, and the pixel-by-pixel Doppler shifted wavelengths scattered by the seeded flow. 

Since the wavelengths are encoded as intensity variations using a iodine vapor 

absorption filter, it is clear that any difference between the reference and signal nonvelocity related intensity patterns will result in a velocity error. Therefore, errors in the 

localized pixel velocities due to decorrelated speckle variations between the reference 

and signal cameras can potentially be significant. 

However, proper procedures can minimize this error, either by ensuring optically that 

the speckle size is sufficiently smaller than the pixel size, or by digitally smoothing with 

a low pass kernel prior to taking the image ratios. The preferred approach is to optically 

reduce the speckle size by opening the camera lens apertures, as long as the depth of 

field is sufficiently large to reasonably cover the imaged portion of the light sheet; this 

approach retains the spatial resolution of the measurement. Figures 18 through 21 and 

Table 1 show how spatial smoothing and image series averaging reduce the effects of 

speckles that are larger than the pixel size. 

The optical approach to reducing speckle size is opening up the camera aperture, 

according to the relationship described by Ennos6

 

σ ≈ 1.2( ) 1+ M λF (5) 

where σ is the diffraction-limited diameter of the speckle on the CCD array, M is the 

effective magnification of the lens, λ is the laser wavelength, and F is the f/number of 

the lens. The factor 1.2 arises due to the circular aperture symmetry, and comes from 

the location of the first zero in the first-order Bessel function. Note that the speckle size, 

or spacing, definition is somewhat arbitrary, and is only an approximation. Smith 

defines the noise to signal ratio (NSR) as 1 m , where m is the number of speckle 

correlation cells within the pixel region7

. Then the NSR is defined as the speckle size 

divided by the pixel size ∆x, or 

( )

x

M F NSR

∆

+ ≈ 1.2 1 λ . (6) 

Table 3 and Figure 25 suggest that the speckle size is becoming sufficiently reduced 

at an aperture around f/4, for the Component A magnification used in the setup 

described in this report. Images were acquired over a range of lens apertures and the 

pixel-to-pixel noise to signal ratios were calculated at each aperture, in order to observe 

the point at which the NSR became independent of aperture or speckle size. In Figure 

25, f-stops read off the lens were converted to f/numbers using the relation f-number 

= f-stop⋅(1+M). The correction is slight, as the magnification M in this setup is about 

0.017. 
NASA/CR—2003-212179 30 

 Speckle2 Data Set 

f-stop Mean s.d. NSR 

f/22 (ex00) 156 54.8 0.35 

f/16 (ex01) 101 31.9 0.32 

f/11 (ex02) 175 49.7 0.28 

f/8 (ex03) 196 46.6 0.24 

f/5.6 (ex04) 77 16.5 0.21 

f/4 (ex05) 62 11.4 0.18 

f/2.8 (ex06) 156 27.4 0.18 

Table 3: Noise to signal (NSR) for single images, calculated for a range of Component A lens 

apertures; statistics are calculated over 20,000 pixels. At f/4 the NSR decreases less rapidly 

with larger aperture, suggesting that the speckle size is close to the pixel size and pixel 

smoothing occurs. The f-number corrections use magnification M=0.017. 

The Table 3 statistics are for the worst-case of a single image containing speckles; 

the image is not dewarped and is not normalized by the reference image. An analysis 

could also be done between the ratio of signal/reference image pairs, cross-correlated 

for best alignment, to the partial speckle correlation behavior described by McKenzie 

and Reinath.8

 McKenzie multiplies the NSR by an experimentally-determined speckle 

correlation constant, with values between zero and one, that decreases the NSR when 

the speckle patterns in the image pairs are correlated. 
NASA/CR—2003-212179 31 

Figure 25 shows the 

measured NSR in images as 

a function of lens aperture, 

and compares this to an 

image acquired at f/22 and 

repeatedly smoothed with a 

range of kernel sizes. The 

smoothing kernels range from 

1x1 to 11x11, and have been 

converted to the equivalent 

aperture by dividing f/22 by 

the number of pixels 

smoothed in one dimension. 

The optical and smoothed 

results compare quite well 

over the measured range. 

The data in Figure 25 also 

compare well with the 

speckle NSR results 

published by McKenzie et 

al.8

 Interestingly, the trends 

of these and the McKenzie 

results seem to flatten 

slightly below f/4 and above 

f/16. Figure 26 adds to 

Figure 25, on a different 

scale, the NSR calculated 

from Equation 6 in order to 

compare measurements to 

theory. The predicted values 

are much higher than the 

measured values. This may 

be due to differences in the 

parameter definitions; in fact, 

Smith’s and McKenzie’s 

calculations differ in that 

Smith uses the Ennos 

speckle diameter as the 

average spacing and 

McKenzie uses the Rayleigh 

criterion9,10 for resolution limit 

as the average speckle 

spacing. 

NSR vs. Lens and Equivalent Kernel Apertures

22

16

11

8

5.6

4 2.8

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20 22 24

Equivalent Aperture

Noise-to-Signal Ratio

Optical Aperture NSR

Smoothed f/22 NSR

Figure 25: Plots of measured NSR over a range of lens apertures, 

compared to an f/22 image filtered over a range of kernel sizes. The 

kernel sizes are converted to equivalent apertures for ease of 

comparison. 

NSR vs. Lens Apertures and Theory

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 2 4 6 8 10 12 14 16 18 20 22 24

Equivalent Aperture

Noise-to-Signal Ratio

Optical Aperture NSR

Smoothed f/22 NSR

Speckle Theory

Figure 26: Adds to the data in Figure 23, on a different scale, the 

NSR calculated from Equation 6 in order to compare 

measurements to theory. 
NASA/CR—2003-212179 32 

ERROR ANALYSIS 

The measured data show very good correlation and agreement with the expected 

values, however, a repeatable slope error indicates a possible calibration error exists. A 

linear fit of the –1.00 V data in blue gives a slope of 1.10, a standard deviation of 7.9 

m/s, an intercept of 19 m/s, and a correlation coefficient of 0.997. The largest error 

trend in the data appears to be an offset in the intercept. Forcing the fit through the 

origin alters the fit statistics, as shown in Table 4. 

A similar fit of the –1.10 V data in red, excluding the three clipped data points, shows 

worse slopes and standard deviations. The data averaged over a larger ROI show a 

lower standard deviation, as expected. Table 4 shows the slope, intercept, and 

standard deviation for the various cases discussed above. 

Linear Fit Results 

No constraints to fit: Slope Intercept (m/s) S.D. (m/s) 

ex00-07, core ROI 1.04 18.3 11.1 

ex10-16, core ROI 1.25 -26 10.6 

Force fit through origin: 

ex00-07, core ROI 1.10 0 11.9 

ex10-16, core ROI 1.12 0 12.8 

Table 4: Fit coefficients for Figure 13 plots. The regressions were calculated both with and without 

forcing the fit through the origin. A scale error, possibly from a calibration drift, is suspected to lead to 

the higher slopes. 

Primary sources of random error include laser speckle decorrelation between 

reference and signal images, registration errors between reference and signal images, 

and uncertainty in the calibrations. Systematic errors include geometric errors in the 

optical orientations, and calibration errors in the flat field correction, measuring the 

transmission function, and performing the polynomial fits and interpolation of the data 

into the LUTs. The decorrelated speckle error is minimized by using a lens aperture of 

f/2.8 on both the LFM and CompA cameras. 

The sensitivity of the velocities to error in various measured parameters can be 

described as a total differential equation of the velocity equation based on Equation 4. 

This can be solved for velocity U as 















 − ⋅ =

1 0

0 1 1

cosθ λ λ

λ

R

c U (7) 
NASA/CR—2003-212179 33 

so that the total differential of Equation 7, defined as 

1

1

0

0

λ

λ

λ

λ

θ

θ

∆

∂

∂ ∆ +

∂

∂ ∆ +

∂

∂ ∆ +

∂

∂ = U U U R

R

U dU (8) 

becomes 

[ ] 2 1

1

0

0

1 cos cos

tan λ

λ θ

λ λ

λ θ

θ θ ∆



 



 ∆ − 



 



 ∆ + ⋅ ∆ + 



 



− = R

c

R

c R U

R

U dU . (9) 

Normalizing this by velocity, we get 

[ ] ( )



 





−

∆  −



 





−

∆

+ ∆ ⋅ + 



 



− ∆ =

1 0 1

0 1

0 1

0 tan

λ λ λ

λ λ

λ λ

λ θ θ

R

R

U

dU . (10) 

In the equations, U is the Doppler velocity component measured, R is the magnitude of 

the vector difference a-l, θ is the included angle between R and the flow direction, and 

λ0 and λ1 are the base laser wavelength and Doppler shifted wavelengths, respectively. 

Equation 9 then shows the contribution of velocity error for given errors in parameters 

R, θ, λ0, and λ1. Representative values for these parameters are discussed below. 

The geometrical uncertainties are estimated from angular errors in aligning the light 

sheet, Component A head, and flow nozzle axis. Each of these uncertainties is 

estimated to be ±2°, which lead to uncertainties in R and θ of ±0.06 and ±2°. Although 

these uncertainties could certainly be reduced further in subsequent setups, they do 

represent the current setup and what are believed to be typical field based setup 

uncertainties. Note that the first two terms in Equation 9 are proportional to U 

(geometrical errors) and the last two are absolute errors. These absolute wavelength 

errors are the crux of the art of the measurement technique, and are where most of the 

potential pitfalls in the technique lie. 

Conversely, the form of Equation 10 highlights that the velocity uncertainty due to 

the error in measuring the wavelengths decreases with higher velocity; the proportional 

errors in R and θ are systematic, and can be reduced readily. The following error 

estimate includes the aforementioned parametric errors, but does not include errors in 

the signal/reference ratios due to decorrelated speckle patterns. 

Substituting the values and uncertainties from Table 3 into Equation 9 leads to 

dU = ±0.09U ± 10 m/s (11) 

and 

dU = ±0.06U ± 7 RMS m/s (12) 
NASA/CR—2003-212179 34 

The total differential dU gives a worst-case estimate, and the RMS result dURMS takes 

into account that the errors are not always additive. These results are summarized in 

Table 5. 

Parameter Value Uncertainty 

R 1.09 0.06 

θ 0° ±2°

λ0 532.19888 nm ±10–5 nm 

λ1 532.19888 nm ±10–5 nm 

Velocity Error ±10 m/s ±9% 

Table 5: Error estimates for parameters in the velocity equation. Does not 

include decorrelated speckle modulation error.

 

The largest contribution to the scale error is the angular positioning of the light sheet 

and the Component head; the coincidence of the flow axis with the component’s 

sensitive axis is relatively insensitive. The precision of most of the values reported 

herein is based on the estimated precision of the gray scale values from which they 

stem. 

Possible Wavelength Calibration Errors: 

• A possible reason for the slope errors in the pressure ratio trends is in the 

calibration data. Looking at the LFM data here, in order to eliminate Doppler 

effects due to flow a comparison was made between LFM transmission ratios 

from the calibration run and the Flow7 run. If the calibration data are accurate 

during the run, then it seems that the following relationship should be observed 

between the mean ratio values: 

ROIave

ROIave

ROIave

ROIave

ex dx

ff dx

ic dx

ic dx

00

00

20

12 = (11) 

where the constants ic12dx and ic20dx are averages (temporal, then over the 

ROI) of image ratios at seed laser offset voltages –1.40 V and –1.00 V (recorded 

during the calibration run), and ff00dx and ex00dx are the corresponding flat field 

and velocity averages (recorded during the velocity run). That is, ic12 and ff00 

data are both taken at seed laser offset voltages of –1.40 V, and ic20 and ex00 

are both taken at seed laser offset voltages of –1.00 V. The actual values for the 

relationships in Equation 11 are 5.6 and 17, which differ by a factor of three. 

The wavelength correction algorithm automatically corrects part of this 

discrepancy, by using the flat field data to normalize the peak transmission; 

however, a correction is not done to the minimum in the transmission curve, so 

there would still remain an error in slope in the calibration curve. 
NASA/CR—2003-212179 35 

Therefore, there is thought to remain a small scale factor error in the LFM 

wavelength calibration LUT, and, presumably, a similar calibration error remains 

in the CompA LUT. While the magnitude of this error is not yet known, it appears 

to be less than the 9% geometric error, when comparing the measured slope 

error to known slope uncertainties. 

• Divide-by-zero errors were avoided algorithmically by setting reference pixel 

values of zero to one before the ratio step; if this happens to divide, say, a zero 

or one in the signal image, the result is a large ratio (high velocity) when in fact 

the signal levels were merely in the noise. This is compensated for by the 

thresholding procedure shown later in this report, but could be improved at this 

wavelength calculation stage instead. 

• Calibration image pairs are not dewarped as in the velocity data. Rather, a 

spatial correlation is performed. The reasoning was that only a spatial average 

would be used in the calibration, but a better approach would be to low pass filter 

(to a resolution below that of any warping shifts) before taking the ratios, and 

then perform the temporal and spatial averages. 

Calculated Velocity Error 

The accuracy of the pressure gauge was calibrated after the data acquisition to be 

±0.2 psia, and the resolution was observed to be about ±0.01 psia. Based on the 

accuracy, the pressure data is recorded with three significant figures, which gives a 

resolution comparable to the Mach table resolution. 

The proportional error was measured to be about 0.3%. The calculated Mach 

number table resolution is 0.01, or about 3 m/s. Therefore, the baseline errors in the 

calculated velocities are estimated to be around 4 m/s absolute error plus a proportional 

error of 0.3%. 

However, a possible cause for the deviation from linear of the velocity data in Figure 

13 is explained by verified pressure leaks in the tap from the nozzle plenum. Such 

leaks occurring above some minimum pressure could indicate lower core velocities than 

actually measured at the higher pressures, which is consistent with the measured 

velocities. There are two splices and four couplings in the tubing between the tap and 

the gauge. 

Speckle Related Error 

The use of the correlation approach to improve pixel registration deserves close 

inspection. It is important to consider that every test situation can produce images with 

more or less sensitivity to speckle effects. However, in general, the images in each 

component head can be thought of as a superposition of an image intensity distribution 

and a speckle/fringe pattern. The typical approach to implementing subpixel registration 

is to perform a bulk image cross-correlation between each dewarped reference and 

signal image, possibly in two stages (course and fine shifts), and then shift the signal 

image by the two-dimensional displacement indicated by the correlation peak position. 
NASA/CR—2003-212179 36 

The LaRC software calculates the average shift over the image series, which should 

have the effect of reducing the speckle sensitivity. The cross-correlation approach finds 

the largest pixel-by-pixel integrated product over a range of shifts between the two 

intensity patterns. This approach has shown improvement in the RMS deviations 

across an image ratio, but it is believed to be due, at least in part, to speckle field 

alignment rather than real image registration. While that may reduce RMS variations, it 

does not improve the accuracy of the velocity contribution to the intensity 

measurements when the velocity varies spatially over a region smaller than the shift 

amount. 

Consider that each camera image is a real image of the test location modulated by a 

speckle pattern formed by the aperture of the camera lens (while other apertures do 

exist in the optical system, the lens aperture is the dominant one determining the 

speckle statistics in the standard application). The Doppler encoded velocity 

information is indisputably correlated to the image location from where the light was 

scattered, in both the reference and signal cameras; the goal is to have each of these 

scattering image points as closely registered as possible between the reference and 

signal images. However, the speckle pattern modulating each image is a interference 

effect subject to global and local phase objects in the imaging paths to which the image 

positions are not susceptible. Therefore, it is reasonable that an intensity distribution on 

the CCD arrays may have independent components from physical objects and speckle 

patterns. 

The degree to which the speckle pattern correlation dominates the real image 

correlation is a function of the degree of correlation between the two speckle patterns in 

the reference and signal images. When the speckle patterns are highly correlated, the 

calculated peak image shift position may be entirely due to the speckle pattern. In the 

case of extreme decorrelation between the speckle patterns, the contribution of the real 

image to the shift position will increase relative to the speckle pattern contribution. 

However, even in the case where the speckle patterns are decorrelated, there will be a 

clear correlation peak representing the best alignment of the decorrelated speckle 

patterns, since the imaging parameters defining the average speckle sizes present in 

the distributions are the same. 

Two aspects of the image data can be used to judge the possibility of speckleinduced misalignment: 1. if spatial velocity variations in the image are on a length scale 

larger than the speckle pattern shifts, then the correlation shifts should on average 

improve the image ratio accuracy; an alternative way of characterizing this is to test for 

when the noise from speckle mismatch exceeds that from other random errors (that is, 

aligning the images or velocities may add more random noise by misregistering 

speckles; 2. when real image contrast dominates speckle contrast. 

However, the preceding dewarping process relies on dots having vague boundaries. 

That is, it is expected that the dewarping process actually introduces localized distortion 

errors with magnitude of 1-3 pixels, while the subsequent bulk image shift only repairs a 

net global fraction of this. The speckle mottling seen on the GRC data may be due to 

mis-registered pixel normalization due to residual local distortions. It may also be due 
NASA/CR—2003-212179 37 

to the two speckle patterns (Reference and Signal) being uncorrelated to some degree. 

An analyses on speckle decorrelation is done by McKenzie,8 and uncertainty estimates 

due to pixel registration is done by Morrison and Gaharan.11 

A preferable alternative to the current cross-correlation approach is proposed for test 

situations where spatial resolution of the velocity is smaller than the speckle-induced 

shift. The images can be aligned manually by physical features in the images, such as 

bright seed particles and rigid fixtures in the setup. It may be beneficial to enhance the 

contrast of the alignment images to bring out poorly illuminated fixtures. It could also be 

beneficial to add an appropriate target in the camera field of view during the test, 

expressly for registering the images. These approaches would best be combined with 

the maximum optical speckle reduction allowable by the test hardware. 
NASA/CR—2003-212179 38 

CONCLUSIONS 

Many incremental improvements have been integrated into the data acquisition and 

processing procedures for the DGV measurements at GRC. As is typical, most of these 

techniques and procedures go well beyond the level of detail reported in the literature, 

and represent a significant advancement in the learning curve needed to successfully 

implement the DGV technique in facilities at GRC. 

The velocity distributions and trends agree well with those expected from the flow 

that was generated, with deviations close to those expected from the error analysis. 

The images show the velocity distributions clearly, and the core region is discernable in 

both the 2-D image maps and the row slices taken at each pressure distribution. An 

improvement in future testing would be to seed the ambient air to better discern the 

outer flow boundaries. 

The slope, and offset errors indicate that a calibration adjustment, possibly of either 

the velocity measurement or the pressure ratio measurement, may improve the data. It 

is not yet clear whether these residual errors are due to the velocity calculation 

algorithm, a frequency calibration drift, or leaks in the pressure tap. Even so, the 

agreement with expected error indicates that the procedures and data are credible and 

realistic. 

The slopes given by the core velocity comparisons with calculated velocities are 

about 10% higher than expected, but have very good correlations with fits to a linear 

equation (R>0.996); therefore, the slope error is thought to be a calibration error or 

other systematic error. The offset errors in the trend are around the absolute error of 10 

m/s expected in the technique. Again, since this does not appear to be a random error 

from test run to test run, it may be correctable as the calibration is refined. 

The LFM corrections show no need for a spatially resolved wavelength correction for 

either the free space beam or fiber bundle beam delivery techniques. Ratio images for 

both beam delivery techniques comparing flat field data and attenuation region data 

show neither meaningful spatial distributions nor statistical differences between the two 

wavelength-discriminated cases. While other lasers may have shown a spatial 

distribution, or there may actually be a very low-level distribution on the GRC 

Continuum laser, there are two reasons a wavelength distribution does not need to be 

measured at GRC: 1. any distribution is below the noise floor of the current hardware; 2. 

the fiber bundle would spatially flatten any distribution in the same way it flattens the 

intensity distribution, which would tend to desensitize the measurements rather than 

add error. 

The optical fiber bundle approach to delivering the laser beam to the test section is a 

technically viable and experimentally convenient technique. Test comparisons with 

freespace beam propagation data show similar velocity trends but with lower noise 

when using the fiber bundle. No Stimulated Brillouin Scattering threshold is observed in 

the power transmission through the fiber bundles. 

When using the fiber delivered beam illumination, the standard LaRC cross 

correlation does not necessarily see enough structure in the beam to improve 

alignment; care should be taken to understand why any image shifts are implemented. 

When using the freespace delivered beam illumination of a wheel, the cross correlation 

seems to be necessary due to beam structure changes; that is, the beam fringes seem 
NASA/CR—2003-212179 39 

to shift between the signal and reference images. However, this fringe alignment does 

not necessarily represent velocity data registration, and should assume velocity 

gradients only occur over regions larger than the image shifts (this requirement proves 

to be true for the wheel data). 

Advantages to the fiber bundle approach are that it reduces the number of 

components typically needed to deliver the beam, it reduces fringe noise on the raw 

beam and distributes the light intensity evenly across the emitting cone, and it makes 

the repositioning of the measurement plane more easily automated in a test 

environment. Disadvantages are that it reduces the delivered light intensity by about 

one-third (transmits 67%) and complicates the light sheet generation when using a 

circular output spot. An elongated output profile is preferable, and will be incorporated 

into the next flow testing phase. 

The transition from wheel measurements to flow measurements required very 

different approaches to both acquisition and processing. Signal level complications 

encountered with the wheel tests became intolerable with the greater dynamic range 

required of the supersonic flow tests; while the scattering cross-section in the former 

case didn’t change as a function of wheel velocity, it did indeed change with velocity in 

the latter case that used an aerosol to seed the flow. As the flow increased, the seed 

density decreased and the signal level dropped. At the same time, the greater red-shift 

induced in the scattered light caused greater attenuation by the iodine vapor, further 

reducing the signal level. In addition to these practical issues, a software conflict in the 

data acquisition code had the effect of recording lower gray scale values than are 

observed using the monitoring software during the signal level adjustments. Once 

these issues were found, they were corrected for in subsequent tests. The processing 

software used for wheel data and flow data are also very different, due to differences in 

the image geometry and an improvement to the laser frequency correction approach 

used for the flow data processing. 

The absolute frequency conversion approach required a procedural change that 

greatly increased the accuracy of the calibration between intensity ratios and optical 

wavelength. The approach was driven by the large range of Doppler shifts typical of 

high speed flow measurements, and required a constant split between the reference 

and signal cameras between performance of the iodine cell calibration and the velocity 

data collection procedures. In addition, a non-linear mapping of the absorption curve is 

required to avoid large errors at the endpoints of the curve. The initial processing 

approach corrected for a variable ratio, in contrast to the traditional single-point flat field 

procedure that only corrects for an offset, not a scale factor in the calibration. The 

approach was changed to the traditional absolute wavelength measurement technique, 

however, which uses an intensity-to-wavelength look-up-table to improve accuracy and 

to extend the Doppler shift band to the non-linear regions of the absorption line. This 

improvement had the side effect of slightly reducing the dynamic range previously 

available, as the fine exposure adjustment built into the system to maximize the signal 

in each camera for each test could no longer be used (it has been observed that the 

ideal flat field ratio split is not necessarily constant during the time between the 

calibration and the velocity data acquisition, possibly due to polarization sensitivity). 

However, this was more than compensated for by the increased accuracy of the data 

near the flatter endpoints of the iodine absorption line. It is believed that a multi-point 
NASA/CR—2003-212179 40 

flat field correction can be developed to better correct the non-linear absorption curve at 

the time of the test (e.g. measure both endpoints of the absorption line rather than just 

the transmission peak, to fit both the scale and offsets to the I2 cell characterization). 

Refer to the Error Analysis section for more discussion on this topic. 

REFERENCES 

1. Yeh, Y., Cummins, H., “Localized Fluid Flow Measurements with a He-Ne Laser 

Spectrometer,” Applied Physics Letters, Vol. 4, No. 99, 1964, pp. 176–178. 

2. Komine, H., Brosnan, S., Litton, A.B., Stappaerts, E.A., “Real-Time Doppler Global 

Velocimetry,” AIAA 29th Aerospace Sciences Meeting, Reno, NV, AIAA 91–0337, 

Jan. 1991. 

3. “Equations, Tables, and Charts for Compressible Flow,” NASA Ames Research 

Center Staff, 1953. 

4. Clancy, P.S., Samimy, M., “Two-Component Planar Doppler Velocimetry in High 

Speed Flows,” AIAA Journal Vol.35, No. 11, November 1997. 

5. Jeunhomme, L.B., “Single-mode Fiber Optics, Principles and Applications,” 2nd

Edition, Marcel Dekker, Inc., 1990, pp. 324–325. 

6. Ennos, A.E., “Speckle Interferometry,” in Topics in Applied Physics, Vol. 9, “Laser 

Speckle and Related Phenomena,” J.C. Dainty, ed., Springer-Verlag, 1975, p. 207. 

7. Smith, M.W., “The Reduction of Laser Speckle Noise in Planar Doppler Velocimetry 

Systems,” 20th AIAA Advanced Measurement and Ground Testing Technology 

Conference, 15–18 June 1998, Albuquerque, NM, AIAA 98–2607. 

8. McKenzie, R.L., Reinath, M.S., “Planar Doppler Velocimetry Capabilities at Low 

Speeds and Its Application to a Full-Scale Rotor Flow (Invited),” 21st AIAA 

Aerodynamic Measurement Technology and Ground Testing Conference, 19–22 

June 2000, Denver, CO, AIAA 2000–2292. 

9. Born, M., Wolf, E., “Principles of Optics,” 6th Edition, Peramon Press, 1980, p. 333. 

10. Hecht, E., “Optics”, 3rd Edition, Addison Wesley Longman, Inc., 1998, pp. 461–465. 

11. Morrison, G.L., Gaharan, C.A. Jr., “Uncertainty Estimates in DGV Systems Due to 

Pixel Location and Velocity Gradients,” Meas. Sci. Technol. 12 (2001) 369–377. 
NASA/CR—2003-212179 41 

APPENDIX—DIFFERENTIAL VELOCITY PROCESSING 

Two velocity processing approaches were developed for the GRC DGV system; one 

is a differential frequency conversion and the other is an absolute frequency conversion. 

The differential velocity processing approach used for the narrow-band wheel data 

relies on a linear approximation of the desired region of the iodine absorption curve. It 

relies on a differential LFM correction and a two-point normalization of the iodine 

absorption curve. The differential technique is described below, and the absolute 

technique is described in the body of the CR. 

The differential approach corrects both endpoints of the calibration curve to the test 

data values, using the flat field and the zero velocity ratio averages. The LFM 

correction to each velocity image ratio is then a normalized offset from the CompA ratio, 

rather than an absolute frequency measurement. While this technique is not usually 

more accurate than a more direct absolute frequency measurement, it allows for 

intensity drifts in the absorption curves prior to the velocity data acquisition. The 

absolute approach assumes that the calibration curve represents the current image ratio 

split between the components cameras, and is potentially more accurate since it uses 

interpolation of a high order fit LUT, rather than a linear approximation currently used in 

the differential approach. 

The following diagram is a schematic representation of the differential approach. 
NASA/CR—2003-212179 42 

GRC DGV Velocity Processing Procedure

Differential Linear Approximation

Component Signal Image

[ex02as00.dgx]

Component Ref. Image

[ex02ar00.dgx]

LFM Signal Image

[ex01dsnn.dgx]

LFM Ref. Image

[ex01drnn.dgx]

[ ]

[ ] ji

ji

R

Sig

,

,

ef

×128

Key:

i,j ≡ pixel indices

k ≡ time series

[ ] ≡ array

ex01 ≡ vel=0 data

ex02 ≡ vel data

ff01 ≡ data in I2 T region

00 ≡ use one image

nn ≡ use all k

LFM Signal Image

[ex02ds00.dgx]

LFM Ref. Image

[ex02dr00.dgx]

Σ

Σ

–

[ ]k [ ]i,j

slope

II vel vji

ji

0,

,

− = =

CTL – 3/14/02

Component Signal Image

[ff01asnn.ffx]

Component Ref. Image

[ff01arnn.ffx]

[ ]k [ ]i,j

Component Signal Image

[ex01asnn.dgx]

Component Ref. Image

[ex01arnn.dgx]

–

[ ]k [ ]i,j

Σ =dy

[ ]

[ ] ji

ji

R

Sig

,

,

ef

×128

[ ]

[ ] ji

ji

R

Sig

,

,

ef

×128

[ ]

[ ] ji

ji

R

Sig

,

,

ef

×128

[ ]

[ ] ji

ji

R

Sig

,

,

ef

×128















 − ⋅ =

−=

−=

=

−=

+=

==

01

0

12.432.4

00

11

coscos2

.01.01

/

φ θ λ λ

cλ

velveldx

rataxavexrataxavffdy

dxdym

mvIb

bmxy

VV

vv

Where (for Cal10 data)

θ =vector correction angle=53°

φ =magnitude correction angle=9°

=offset Transmission Slope:

Wheel Calibration: (Use 0 m/s velocity intensity.) 

Follows the above state diagram and assumes the following data have been acquired: 

• Dot card images of Components A and D 

• Flat field images in transmitting region of iodine cell; also record seed laser 

voltage 

• Velocity images with wheel RPM=0 (or very slowly rotating); also record seed 

laser voltage set to mid-point of transmission line 

• Velocity images at full wheel speed, with seed laser voltage at 1⁄2 transmission 

point. 

Process data by the following steps: 

1. Modify raw *.dtr images to increase contrast and brighten background: 

a. Import image into ImageTool 

b. Click “show Contrast Control” button – drag contrast bar up until dot field 

looks good... 

c. Copy image to clipboard; paste into Photoshop. 

d. Click on foreground selector; pick color between dots with eyedropper. 
NASA/CR—2003-212179 43 

e. Select with “magic wand” the dark background which will be converted to 

the picked color; change background color by selecting paint bucket and 

clicking on selected region. 

f. Save as raw file & exit; rename raw file to *.dtr. 

2. Process all LFM and CompA data through Wheel03, to get dewarped, lowpassed, and aligned 16-bit Reference & Signal images. Check whether the 

alignment gives image feature registration or speckle pattern registration. 

3. Ratio LFM and CompA Ref & Signal image pairs using DGVratio16.exe. 

4. Calculate mean pixel value of the mean LFM and CompA ratio images using 

ImageStats_mean16.exe. [ImageStats_mean16 also generates statistics for one 

image as a byproduct; if run for a single image, mean and s.d. over the image 

are stored in a text file and printed to the CRT.] That is, calculate the mean over 

i,j and then over k. Every subsequent zero velocity CompA image mean should 

have the same offset to its LFM mean [tests show an actual variation of 3-4 pixel 

values – see notes 2/14/02]. Therefore, every non-zero velocity CompA ratio 

pixel should be offset by the offset found here. 

5. Cal10/ex04a mean,mean from step 4 can be used as the zero-velocity value 

(process through programs: DGVratio16 and ImageStats _mean16 (can use 

appropriate versions of dgvratio16.bat and Stats.bat). 

6. Process Cal10/ff01a & d as in step 5: DGVratio16 and ImageStats _mean16 [1st

call to ImageStats_mean16 prints mean to the CRT]. [This gives the gray scale 

value at the flat field point, corresponding to the graphically-determined velocity.] 

7. Compute linear equation for I vs. λ... [from calibration steps 5 & 6 above]: 

y=mx+b , where m = dy/dx = [FlatFieldA.ratmean,mean- ZeroVelAmean,mean]/ 

Corresponding velocity in gray levels / m/s, and b = 301 – 2.021 * 0. Enter slope 

and intercept into last two parameters of each velocity data set’s vela.set file. 

Velocity Calculation: (Use 3000 RPM data.)

1. Take 3000 RPM data as per LaRC procedure. 

2. Process LFM and CompA data through Wheel03, to get dewarped, low-passed, 

and aligned 16-bit Reference & Signal images. 

3. Ratio LFM and CompA Ref & Signal image pairs. 

4. Calculate mean pixel value of the LFM and CompA ratio images using 

ImageStats16.

5. Compute intensity offset of CompA (ex03a) pixel values from LFM (ex03d) pixel 

values. (offset, since ∆λ shifts the transmission curve.) Use this relationship: 

CompAxnn.rat ν-corrected = 500+ex03axnn.rat + [ex03dnn.ratmean - ex04d.ratmean,mean] 

where values are offset by 500 to avoid negative numbers 

Enter ZeroVelocityD.ratmean,mean into each velocity data set’s freqa.set file; run 

freqa.bat. 

These are now arrays of pixel intensities corrected for laser intensity and 

frequency variations. They now need to be converted to velocity by using step 6. 

6. Run each I- and λ-corrected CompA image through program 

Intensity_to_Velocity.exe to convert grey levels to velocities in m/s (run vela.bat). 
NASA/CR—2003-212179 44 

The above steps are condensed into batch files or called as DOS commands. An 

example using Cal10 data sets follows (after processing through LaRC routines 

wheel01, wheel02, and wheel03): 

• d:\dgvprocessing\cal10\dgvratio_ex04a.bat 

• d:\dgvprocessing\cal10\dgvratio_ex04d.bat 

• d:\dgvprocessing\cal10\dgvratio_ex03a.bat 

• d:\dgvprocessing\cal10\dgvratio_ex03d.bat 

• d:\dgvprocessing\cal10\dgvratio_ff01a.bat 

• d:\dgvprocessing\cal10\dgvratio_ff01d.bat 

• d:\dgvprocessing\ImageStats_mean16.exe 

d:\dgvprocessing\cal10\statsratio_ex04d.set 

• d:\dgvprocessing\ImageStats_mean16.exe 

d:\dgvprocessing\cal10\statsratio_ex04a.set 

• d:\dgvprocessing\ImageStats_mean16.exe 

d:\dgvprocessing\cal10\statsratio_ff01a.set 

• d:\dgvprocessing\Freq_correction.exe d:\dgvprocessing\Cal10\ex03\freqa.set 

• d:\dgvprocessing\Intensity_to_Velocity.exe d:\dgvprocessing\Cal10\ex03\vela.set 

(Note: these iconized programs can be called in Windows98 by dragging the 

appropriate set file onto them.) 

File name conventions: 

xnn.rat => raw ratio image in /raw directory 

cnn.rat => freq-corrected raw ratio image in /frq directory 

cnn.vel => cnn.rat converted to raw velocities in /vel directory 

vnn.tif => cnn.rat converted to TIF velocity image in /vel directory 

Mean => image array series averaged over each pixel’s time series; output is an 

average array 

Mean,mean => spatial average of a single average array; output is a single mean 

and standard deviation. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Final Contractor Report

Unclassified

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

February 2003

NASA CR—2003-212179

E–13780

WBS–22–708–73–26

NCC3–861

51

Doppler Global Velocimetry at NASA Glenn Research Center: System Discussion

and Results

Christian T. Lant

Doppler Global Velocimetry; Planar Doppler Velocimetry; Supersonic velocity

measurement; Fiber optic laser beam delivery

Unclassified -Unlimited

Subject Category: 35 Distribution: Nonstandard

Ohio Aerospace Institute

22800 Cedar Point Road

Brook Park, Ohio 44142

Project Manager, Mark P. Wernet, Optical Instrumentation Technology Branch, NASA Glenn Research Center,

organization code 5520, 216–433–3752.

A ruggedized Doppler Global Velocimetry system has been built and tested at NASA Glenn Research Center. One

component of planar velocity measurements of subsonic and supersonic flows from an under-expanded free jet are

reported, which agree well with predicted values. An error analysis evaluates geometric and spectral error terms, and

characterizes speckle noise in isotropic data. A multimode, fused fiber optic bundle is demonstrated to couple up to

650 mJ/pulse of laser light without burning or fiber ablation, and without evidence of Stimulated Brillouin Scattering

or other spectral-broadening problems. Comparisons are made between spinning wheel data using illumination by

freespace beam propagation and fiber optic beam delivery. The fiber bundle illumination is found to provide more

spatially even and stable illumination than is typically available from pulsed Nd:YAG laser beams. The fiber bundle

beam delivery is also a step toward making remote measurements and automatic real-time plume sectioning feasible

in wind tunnel environments.