THE EFFECT OF MEASUREMENT VOLUME SIZE ON 

PHASE DOPPLER ANEMOMETER MEASUREMENTS 

OF GLASS MICROSPHERES†

John M. Davis 

UC-FEST, Department of Aerospace Engineering, University of Cincinnati 

Cincinnati, Ohio 45221-0070, USA 

davisjh@email.uc.edu 

Peter J. Disimile 

USAF 46 Test Wing, Aerospace Survivability and Safety Flight 

Wright-Patterson AFB, Ohio 45433-7605, USA 

peter.disimile@wpafb.af.mil 

937-255-6823 ext. 212 

ABSTRACT 

Phase Doppler Anemometry (PDA) is a widely used measurement technique capable of nonintrusively measuring a droplet diameter and up to three components of its velocity, 

simultaneously. PDA systems are frequently used to characterize spray nozzles and suppressant 

transport phenomena, which may be further used in model validation. It has been shown that the 

optical configuration can have a considerable effect on PDA diameter measurements. The 

current paper is part of an ongoing effort toward the development of a procedure to properly 

configure a PDA system for the best drop size measurement accuracy and reports on backscatter 

diameter measurements of glass microspheres using four separate measurement volume sizes. 

The presented data covers approximate particle to measurement volume diameter ratios from 

1/25 to 1/3 which will be useful in providing guidance for the minimum ratio required to acquire 

backscatter diameter measurements free of errors due to measurement volume effects. 

 

†

 This research is part of the Department of Defense's Next Generation Fire Suppression Technology Program, 

funded by the DoD Strategic Environmental Research and Development Program 
INTRODUCTION 

Phase Doppler Anemometry (PDA) is a widely used measurement technique capable of nonintrusively measuring a droplet diameter and up to three components of its velocity, 

simultaneously. Since the PDA technique is heavily based of light scattering theories, earlier

PDA diameter measurements were reported without any indication of the measurement 

uncertainty. Due to the recent demand for error analysis reporting, researchers began 

investigating several effects that could cause a bias in PDA diameter measurements. 

The current paper is part of an ongoing effort focused on the effect on PDA measurements due to 

varying optical parameters. Three previous works by Davis and Disimile1-3

 have reported on the 

effects of optical configuration on PDA diameter measurements. The first two works1-2

 showed 

up to a 70% difference in the arithmetic mean diameters (66% in Sauter mean diameters)

between the various optical configurations evaluated and proposed an experimental selection 

method for choosing an optimum optical configuration. Since the proposed selection method 

was based off of air/water spray measurements of an unknown size, a third paper3

 was presented 

supporting the optical configuration selection method with measurements of glass microspheres 

of a known size range. However, these earlier results also showed that investigation into the 

effect of the ratio of particle diameter to the measurement volume diameter for back-scatter 

measurements was needed to further support the proposed selection method. 

The ratio of the particle diameter to the measurement volume diameter is an important parameter 

due to the trajectory ambiguity effect (TAE), or measurement volume effect (MVE). This effect 

is due to the Gaussian intensity distribution of the intersecting laser beams in the measurement 

volume and has been investigated by a number of researchers.4-6

 Naqwi and Menon7 presented a 

three step procedure for determining the important parameters of a PDA system, but these were 

never tested experimentally and require apriori knowledge of the diameter range to be measured. 

A recently published text8

 on phase Doppler measurement techniques gives insight into the 

maximum allowable particle-to-measurement volume diameter ratio required to avoid MVE. In 

this text the authors propose a 1/3 or 1/5 ratio (particle/measurement volume) as a general ruleof-thumb in order to avoid MVE, however, stated that the required ratio is specific to the 

experimental conditions. In addition, Araneo et al.9

 experimentally investigated the MVE in

detail and found that a 1/3 ratio was sufficient for a forward-scatter measurement configuration. 

As part of a PDA system commissioning test, Mulpuru et al.10 presented PDA measurements of 

glass microspheres of known sizes. Although they showed excellent agreement between the 

measured diameters and the known microsphere sizes, their experimental data was all measured 

in a forward-scatter mode, and not the back-scattering mode. 

The back-scattering mode is commonly used when attempting measurements in facilities with 

limited optical access and is distinctly different than the forward-scatter mode. Back-scatter

measurements are acquired using light from the second-order refraction scattering mode. Light 

scattered from this mode is typically lower in intensity than forward-scattered light (reflection or 

refraction modes). The lowered intensity can increase the difficultly in separating second-order 

refraction signals from light scattered in another mode (i.e. reflection), thereby increasing the 

sensitivity to MVE. Therefore the need exists for data measured in the back-scatter mode with

Page 2 
several particle-to-measurement volume diameter ratios. This data will be used to determine the 

ratio needed to avoid MVE for back-scatter measurements. 

The current work reports on PDA diameter measurements of glass microspheres using four 

measurement volume diameters. Using two separate sizes of glass microspheres with each of the 

four measurement volume diameters, particle to measurement volume diameter ratios of 

approximately 1/30 to 1/3 were examined. 

PHASE 2 EXPERIMENTAL STRATEGY 

To allow a direct comparison of data, the general PDA setup and strategy used previously3

, was

repeated for this study. With the current study focusing on the measurement volume size effects 

on the diameter measurements, two additional measurement volume sizes were investigated with

the recent acquisition of a new 2500 focal length lens and beam expander. 

A standard three-dimensional Phase Doppler Anemometry system was used to measure the

diameter distribution of two separate sizes of solid glass microspheres suspended in distilled 

water. The glass microspheres were of a known size band classified by sieve fractions provided 

by the manufacturer. The upper and lower limits of the glass microsphere sieve fractions used 

are 25-32 μm and 45-53 μm. These size ranges will be discussed in further detail in the results

section. The microspheres were constantly mixed to maintain suspension in distilled water in a

rectangular glass walled test cell. The test cell can be seen in Figure 1 along with the 

transmitting and receiving optics. 

Receiving Optic Transmitting Optic Test Cell 

Figure 1. PDA Setup. 

Page 3 
A 98 degree off-axis scattering angle was chosen between the transmitting and receiving optics.

This angle was chosen as optimal for second-order refracted light by examination of light

scattering charts for glass in water. For each measurement, 20,000 samples were acquired and

diameter statistics computed. Diameter measurements were acquired for the two microsphere

sizes, using four optical configurations, providing four separate measurement volume diameters. 

The four optical configurations utilized during experimentation can be seen in Table 1. The 

measurement volume diameter is a function of the focal length of the transmitting optic, the

wavelength of the transmitted beams, and the transmitted beam diameter directly after expansion. 

For all optical configurations, a wavelength of 514.5 nm was maintained for the transmitting

beams. Therefore, the measurement volume was only varied by changing the focal length of the 

transmitting lens and the transmitted beam diameter. The transmitted beam diameter was varied 

through the use of different beam expanders. Three transmitting lenses were used with four

beam expansion ratios to yield measurement volume diameters of 196, 260, 408, and 809 μm. 

Table 1. Optical Configurations. 

Transmitting 

Lens 

Receiving 

Lens 

Beam Expansion 

Ratio 

Measurement Volume

Diameter (μm)

402.5 mm 310 mm 1.00 196 

1000 mm 1000 mm 1.98 260 

2500 mm 310 mm 2.97 408 

2500 mm 310 mm 1.50 809 

Aperture masks change the diameter dynamic range of the PDA system by effectively changing 

the spacing between the receiving fibers in the receiving optic. Since these masks are installed in

the receiving optic they only affect the received signal and therefore do not change the 

measurement volume diameter. However, since the aperture mask can affect the diameter 

measurements, each of three available masks (namely Mask A, B, and C) were utilized with the 

four optical configurations described above. All three masks are shown in Figure 2. Mask A

had the largest aperture thus providing a smaller depth of field while Mask C has the smallest 

aperture, which provided a larger depth of field. Mask B’s aperture fell between that of Masks A

and C. 

Mask A Mask B Mask C

Figure 2. Aperture Masks. 

The test matrix for the present study is shown in Table 2. The test number (first column) 

indicates the test order. The configuration number (shown in column 2 of Table 2) is an arbitrary 

label given to each unique optical configuration tested. Using three aperture masks with four 

lens combinations, 12 optical configurations could be tested. Configuration 12, corresponding to 

mask C with the optic configuration yielding the 809 μm measurement volume diameter, was 

omitted from testing. The reasoning for the omission of configuration 12 is explained below in 

Page 4 
the results section. Columns 3 - 6 of Table 2 show the optical parameters for each of the 11 

optical configurations utilized. 

Table 2. Test Matrix. 

Test 

No. 

Conf. 

No. 

Transmitting 

Lens (mm)

Receiving 

Lens (mm)

Beam

Expansion 

Ratio 

Aperture 

Mask 

M.V. 

Diam. 

(μm)

Microsphere 

Size (μm)

Particle 

to M.V. 

Diam. 

Ratio 

1 1 402.5 310 1.00 A 196 25 - 32 0.145 

2 2 402.5 310 1.00 B 196 25 - 32 0.145 

3 3 402.5 310 1.00 C 196 25 - 32 0.145 

4 1 402.5 310 1.00 A 196 45 - 53 0.250 

5 2 402.5 310 1.00 B 196 45 - 53 0.250 

6 3 402.5 310 1.00 C 196 45 - 53 0.250 

7 4 1000 1000 1.98 A 260 25 - 32 0.110 

8 5 1000 1000 1.98 B 260 25 - 32 0.110 

9 6 1000 1000 1.98 C 260 25 - 32 0.110 

10 4 1000 1000 1.98 A 260 45 - 53 0.188 

11 5 1000 1000 1.98 B 260 45 - 53 0.188 

12 6 1000 1000 1.98 C 260 45 - 53 0.188 

13 7 2500 310 2.97 A 408 25 - 32 0.070 

14 8 2500 310 2.97 B 408 25 - 32 0.070 

15 9 2500 310 2.97 C 408 25 - 32 0.070 

16 7 2500 310 2.97 A 408 45 - 53 0.120 

17 8 2500 310 2.97 B 408 45 - 53 0.120 

18 9 2500 310 2.97 C 408 45 - 53 0.120 

19 10 2500 310 1.50 A 809 25 - 32 0.035 

20 11 2500 310 1.50 B 809 25 - 32 0.035 

21 10 2500 310 1.50 A 809 45 - 53 0.061 

22 11 2500 310 1.50 B 809 45 - 53 0.061 

The measurement volume diameter, microsphere size, and particle to measurement volume

diameter ratio are shown in columns 7, 8, and 9 of Table 2, respectively. The particle to 

measurement volume ratio shown is approximate and was calculated by dividing the mean value 

of the microsphere size range by the measurement volume diameter. 

RESULTS 

The measurements of the two microsphere sizes using the 11 optical configurations shown above

are presented herein. Configuration 12 was omitted, as stated earlier, due to the fact that aperture

mask C cuts a large amount of light in the received signal. In addition, the overall light intensity 

in the measurement volume is decreased as the measurement volume size is increased. If the 

measurement volume is not sufficiently powered, diameter measurements could be biased toward

larger particles (larger particles reflect and refract more light than smaller particles). Combining 

the decreased light intensity in the measurement volume for configuration 12 with the decrease 

Page 5 
in the received signal using mask C, configuration 12 required the use of a higher powered laser 

to sufficiently illuminate the measurement volume. Attempted tests using configuration 12 

confirmed that with the maximum available laser power was not sufficient and thus the 

measurements were biased towards the upper range of the sieve fraction. A higher powered laser 

was not available for this investigation thus configuration 12 was omitted.

It should also be noted that based on the sieving procedure used to separate the microspheres, an 

error band of ±15% of the sieve fraction was specified by the manufacturer. Therefore, the 

arithmetic mean diameter (D10) of the measurements should fall within the 21.25 - 36.80 μm

range for the smaller microspheres and 38.25 - 60.95 μm for the larger microspheres. 

25 μm to 32 μm Microsphere Measurements 

The measured arithmetic mean diameter (D10) for the 25-32 μm microspheres using the 11 

optical configurations (described in Table 2) are plotted in Figure 3. From the microsphere

manufacturer’s suggestion, the arithmetic mean diameter measurements of the 25-32 μm

microspheres are expected to fall in the 21.25 - 36.80 μm range. The limits of this range are 

shown in Figure 3 as red dashed lines. The red solid lines in Figure 3 represent the upper and 

lower sieve fraction limits, however, these are shown for comparison purposes only as any 

diameter measured between the dashed red lines must be deemed acceptable. Repeated 

measurements for configurations 1, 2, 4, and 7 are also shown in Figure 3. The repeated

measurements provide insight into the measurement repeatability. 

Arithmetic Mean Diameter

25 - 32 μm Sieve Fraction

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10 11 12

Optical Configuration

Arithmetic Mean Diameter (μm)

Lower Sieve Fraction - 15% 

Upper Sieve Fraction 

Lower Sieve Fraction 

Upper Sieve Fraction + 15%

Figure 3. 25 μm to 32 μm Microsphere D10 Measurements, All Configurations.

Page 6 
It can be seen that the measurements for all configurations except 1 and 2 fall within the 

expected limits (red dashed lines). Therefore, configurations 3 - 11 can be said to be acceptable 

configurations for the given measurement condition, based solely on the data shown in Figure 3. 

Recall that configurations 1, 2, and 3 all have the smallest measurement volume diameter. It 

could be initially thought that since the data measured with configuration 3 is within the

acceptance band and configurations 1 and 2 share the same measurement volume size as 

configuration 3, the measurement volume size is not the main parameter causing the discrepancy 

in the D10 measurements. However, mask C cuts the most light of the three receiving aperture

masks. Since larger particles scatter more light than smaller particles it is possible that the data

acquired using configuration 3 is biased towards the larger particles thus giving the impression 

that configuration 3 is an acceptable configuration. Inspection of the diameter distributions (not 

shown) provides evidence of a bias toward the larger particles for configuration 3. Thus the 

change in the measurement volume size could still be a main factor in the difference between the

diameters measured with configurations 1 and 2 and those measured with configurations 4-11. 

The effect of the measurement volume diameter on the diameter measurements is better 

illustrated by plotting the measured D10 diameters against the measurement volume diameter for

each aperture mask separately. This is shown in Figure 4 and Figure 5 for masks A and B, 

respectively. The particle to measurement volume ratio plotted on the abscissa was calculated by 

dividing the median value of the given sieve fraction by the measurement volume diameter. This 

is an approximate value since the actual microsphere sizes can fall anywhere in the provided 

range. Due to the biasing effect with mask C (described above), only the data for configurations 

using masks A and B will be examined. 

Arithmetic Mean Diameter

25 - 32 μm Sieve Fraction, Mask A

0

5

10

15

20

25

30

35

40

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Particle to M.V. Diameter Ratio

Arithmetic Mean Diameter (μm)

Lower Sieve Fraction - 15% 

Upper Sieve Fraction 

Lower Sieve Fraction 

Upper Sieve Fraction + 15% 

Figure 4. 25 μm to 32 μm Microsphere D10 Measurements, Mask A. 

Page 7 
Examination of Figure 4 shows that the data measured with a particle to measurement volume 

diameter ratio of 0.145 (approximately a 1:7 ratio) was not within the acceptable limits for the 

25-32 μm microspheres. The diameters measured for the three configurations at or below a ratio 

of 0.110 all fall within expected limits. This suggests that the measurement volume size is 

affecting the data. Although it cannot be confirmed at this time, it seems a maximum particle to 

measurement volume diameter for minimal error exists between 0.110 and 0.135 for the given

measurement condition. The data for mask B (see Figure 5) shows a similar trend which further 

suggests that a maximum ratio likely exists in the range of 0.110 to 0.135. 

Arithmetic Mean Diameter

25 - 32 μm Sieve Fraction, Mask B

0

5

10

15

20

25

30

35

40

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Particle to M.V. Diameter Ratio

Arithmetic Mean Dia

meter (μm) 

Lower Sieve Fraction - 15%

Upper Sieve Fraction

Lower Sieve Fraction 

Upper Sieve Fraction + 15%

Figure 5. 25 - 32 μm Microsphere D10 Measurements, Masks B. 

45 μm to 53 μm Microsphere Measurements 

Figure 6 is similar to Figure 3 except plotted for the 45-53 μm microsphere measurements. It 

can be seen that all configurations except configurations 1, 3, and 4 are measuring diameters 

within the expected range. However, the measurement repeatability shown in configurations 7 

and 10 indicates the measurements close to the lower expected limit (dashed blue line) cannot 

accurately be concluded to be either acceptable or unacceptable. However, Figure 6 clearly 

shows that the diameter measurements are affected by the optical configuration utilized. 

Page 8 
Arithmetic Mean Diameter

45 - 52 μm Sieve Fraction

0

10

20

30

40

50

60

70

0 1 2 3 4 567 8 9 10 11 12

Optical Configuration

Arithmetic 

Mean Diameter (μm)

Lower Sieve Fraction - 15%

Upper Sieve Fraction

Lower Sieve Fraction 

Upper Sieve Fraction + 15%

Figure 6. 45 μm to 53 μm Microsphere D10 Measurements, All Configurations.

A better indication of the affect of the measurement volume diameter on the diameter 

measurements is shown by again plotting the measured diameters against the ratio of the particle 

to measurement volume diameter for each mask separately (see Figure 7 and Figure 8). The data 

in Figure 7 suggest a maximum particle to measurement volume diameter ratio for minimal error 

might exist between approximately 0.120 and 0.180. However, the data in Figure 8 does not 

support this assumption with all the measurements falling within the expected range. Again, due 

to repeatability, the points close to the lower limit of the expected range cannot be determined to 

be acceptable or unacceptable. Thus, although it appears that a maximum ratio needed to 

minimize error possibly exists in the range of 0.120 - 0.180, this cannot be concluded due to the 

wide acceptance band in which the measurements could fall.

Page 9 
Arithmetic Mean Diameter

45 - 52 μm Sieve Fraction, Mask A

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

Particle to M.V. Diameter Ratio

Arithmetic 

Mean Diameter (μm)

Lower Sieve Fraction - 15%

Upper Sieve Fraction 

Lower Sieve Fraction

Upper Sieve Fraction + 15%

Figure 7. 45 μm to.53 μm Microsphere D10 Measurements, Mask A 

Arithmetic Mean Diameter

45 - 52 μm Sieve Fraction, Mask B

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

Particle to M.V. Diameter Ratio

Arithmetic 

Mean Diameter (μm)

Lower Sieve Fraction - 15% 

Upper Sieve Fraction 

Lower Sieve Fraction

Upper Sieve Fraction + 15%

Figure 8. 45 μm to 53 μm Microsphere D10 Measurements, Mask B. 

Page 10 
Combined Particle to Measurement Volume Diameter 

Since the above data indicated that a maximum ratio between the particle and measurement 

volume diameter needed to minimize diameter measurement error might exist, additional data

was acquired using microspheres of a 75-90 μm sieve fraction. These measurements were

combined with the two sets of measurements described above. Individual plots of the 75-90 μm 

microsphere measurements did not provide any further insight and thus are not presented. 

The combination of the 75-90 μm microsphere measurements with the 25-32 μm and 45-53 μm 

measurements is shown plotted against the particle to measurement volume diameter ratio in 

Figure 9 for configurations using mask A only. To allow a direct comparison of the data from

different size microspheres, the arithmetic mean diameters were normalized by the median value

of the sieve fraction range. Thus a normalized arithmetic mean of 1 represents a D10 diameter

measured at the median value of the sieve fraction range. 

Norm. Arithmetic Mean Diameter vs. Particle Diameter/M.V. Diameter Ratio

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Particle to M.V. Diameter Ratio

Norm. Arithmetic Mean

Mask A

Figure 9. Normalized D10 Measurements, Mask A. 

Assuming that the D10 diameter should ideally be close to the median value of the sieve fraction 

(normalized values close to 1) the data in Figure 9 suggests that a maximum ratio needed to 

minimize error occurs around 0.11. Data measured with a configuration providing a ratio lower 

than 0.11 appears to level off close to a normalized mean diameter value of 1. Above the 0.11 

ratio the data appears to level off to a normalized value of closer to 0.80. A similar plot showing 

the data for masks B and C is shown in Figure 10. Again it appears that a maximum ratio for 

minimized error possibly occurs around 0.11. This corresponds to an approximate ratio of 1:9 

between the particle size and the measurement volume diameter. 

Page 11 
Norm. Arithmetic Mean Diameter vs. Particle Diameter/M.V. Diameter Ratio

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Particle to M.V. Diameter Ratio

Norm. Arithmetic Mean

Mask B Mask C

Figure 10. Normalized D10 Measurements, Mask B and C. 

Figure 9 and Figure 10 are the result of a preliminary method pf representing the data. Since the

D10 diameters could fall in a relatively large range, it cannot be confirmed that the measurement

volume should be 9 times greater in size that the expected measured particle size to minimize

error in the diameter measurements (as suggested above by a 1:9 ratio). However, the data is 

showing signs that a ratio between the particle diameter and measurement volume diameter

possibly exists to allow diameter measurements with minimal error. 

SUMMARY 

It was shown that that the chosen measurement volume diameter, more importantly the ratio 

between the particle and measurement volume diameter, affects the arithmetic mean diameter

measurements. Previous literature suggested that a maximum ratio of 1/3 to 1/5 be kept for 

forward-scatter scenarios to minimize error in the diameter measurements due to MVE. The data 

presented herein is suggesting that a maximum ratio also exists in a back-scatter arrangement. 

This ratio for back-scatter configurations appears to occur at approximately 1/9, which would 

require that the measurement volume diameter be maintained at a size 9 times greater than the 

expected maximum particle size to be measured. However, with the broad range in which the 

diameter measurements were deemed acceptable, further investigation using microspheres with a

tighter range is needed to confirm the suggestion of a 1/9 ratio for back-scatter measurements. 

Page 12 
REFERENCES 

1. Davis, J. M., and Disimile, P. J., “The Effect of Optical Configuration Selection on Phase

Doppler Anemometer Fire Suppressant Nozzle Characterizations”, 14th Halon Options 

Technical Working Conference, May, 2004 

2. Davis, J. M., and Disimile, P. J., “The Effect of Lens/Aperture Selection on Phase Doppler 

Anemometer Measurements,” 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, 

NV, 2004, AIAA Paper No. 2004-604. 

3. Davis, J. M., and Disimile, P. J., “Optical Configuration Selection Effects on Phase

Doppler Anemometer Measurements of Glass Microspheres,” 43rd AIAA Aerospace 

Sciences Meeting and Exhibit, Reno, NV, 2005, AIAA Paper No. 2005-1410. 

4. Qui, H., and Chin, T. H., “Method of Phase-Doppler Anemometry Free from the

Measurement-Volume Effect,” Applied Optics, Vol. 38, No. 13, 1999, pp. 2737 – 2742. 

5. Gouesbet, G., and Grehan, G., “Gaussian Beam Errors in Phase-Doppler Anemometry and 

Their Elimination,” Developments in Laser Techniques and Applications to Fluid 

Mechanics, Proceedings of the Seventh International Symposium, edited by R. J. Adrian,

D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, and J. Whitelaw, Springer-Verlag. New 

York, 1996, pp. 243 - 259. 

6. Sankar, S. V., and Bachalo W. D., “Response Characteristics of the Phase Doppler Particle

Analyzer for Sizing Spherical Particles Larger than the Light Wavelength,” Applied 

Optics, Vol. 30, No. 12, 1991, pp.1487 – 1496. 

7. Naqwi, A., and Menon, R., “A Rigorous Procedure for Design and Response 

Determination of Phase Doppler Systems,” Developments in Laser Techniques and 

Applications to Fluid Mechanics, Proceedings of the Seventh International Symposium, 

edited by R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, and J. Whitelaw, 

Springer-Verlag. New York, 1996, pp. 340 – 353. 

8. Albrecht, H.-E., Borys, M., Damaschke, N., and Tropea, C., Laser Doppler and Phase 

Doppler Measurement Techniques, Springer-Verlag, New York, NY, 2003. 

9. Araneo, L., Damaschke, N., Tropea, C., “Measurement and Prediction of the Gaussian 

Beam Effect in the Phase Doppler Technique,” Tenth International Symposium on 

Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2000, Paper No. 

20.6. 

10. Mulpuru, S. R., Balachandar, R., Ungurian, M.H., “Phase Doppler Anemometer: 

Commissioning Test for Measurements of Water Aerosol Sizes and Velocities in Flashing 

Jets,” Nuclear Engineering and Design, Vol. 166, pp. 443 - 452. 

Page 13