1

THE EFFECT OF OPTICAL CONFIGURATION SELECTION ON 

PHASE DOPPLER ANEMOMETER FIRE SUPPRESANT NOZZLE 

CHARACTERIZATIONS†

John M. Davis 

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

Cincinnati, Ohio 45221-0070, USA 

Peter J. Disimile

USAF 46 Test Wing, Aerospace Survivability and Safety Flight 

2700 D Street, Bldg 1661 

Wright-Patterson AFB, Ohio 45433-7605, USA 

peter.disimile@wpafb.af.mil 

937-255-6823 ext. 212 

ABSTRACT 

Phase Doppler Anemometry is widely used to characterize spray nozzles, and is currently being 

used to aid in the validation of suppressant transport modeling. For these purposes, absolute 

diameter and velocity of the suppressant droplets must be measured. During the characterization 

of a two-phase suppressant nozzle it was found that the droplet diameters measured by PDA are 

very sensitive to the specific optical configuration utilized. This can cause major setbacks since 

most PDA systems are used as turnkey, and the optical configurations are chosen for physical 

reasons, other than the diameter dynamic range of the PDA system. The current work presents 

an investigation into the effects of using a less than optimum optical configuration for PDA 

measurements. A standard three dimensional fiber optic PDA system was configured with 

several transmitting/receiving lens and receiving aperture combinations and used to acquire 

velocity and drop diameter data downstream of an air/water fire suppressant spray nozzle. 

Experimental results show that velocity measurements are relatively unaffected by the optical 

configuration while the diameter measurements can have a considerable bias depending on the 

optical configuration selected. The optimum optical configuration can be very difficult to choose 

without apriori knowledge of the diameter range to be measured. Therefore, a straightforward 

experimental method to determine the optical configuration that provides the least bias for an 

unknown droplet diameter range is presented. 

 

†

 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 diagnostic technique capable of nonintrusive diameter measurement of both drops and particles in multi-phase flows. In general 

Phase Doppler Anemometry does not require calibration since the measurements are based off of 

light scattering theories. As a result, PDA diameter measurements were reported as absolute 

measurements and were not reported with any error. However, the recent demand for error 

analysis reporting for all measurements has sparked an interest into several effects that could 

cause a bias in the diameter measurements recorded using PDA. 

The most researched phenomenon that can cause a bias in diameter measurements is known as 

the trajectory ambiguity effect (TAE), or measurement volume effect (MVE). Many 

researchers have attempted remedies for TAE or even used TAE to their advantage.1-3 This 

paper will not further address TAE since absolute measurements were are not required. Naqwi4

provides a more relevant study investigating different receiving aperture shapes and sizes. 

However, this study does not include the combination of the optical lens selection with the 

receiving aperture. Another study5

 presented a three step procedure for determining the 

important parameters of a PDA system but was never tested experimentally and requires apriori 

knowledge of the diameter range to be measured. Therefore the need exists for a relatively easy 

to use method in which a proper selection of PDA optical lens / receiving aperture configuration 

can be chosen for an unknown drop diameter range. 

This paper is a continuation of an ongoing effort focused on the effect on PDA measurements 

due to varying optical parameters. A previous work by Davis and Disimile6 presented the first 

published results of this ongoing work. The current paper clears up the confusion of the 

difference in the mean velocities measured at the two off centerline positions presented in the 

previous paper6 and presents a more complete analysis by investigating the Sauter mean diameter 

and the diameter concentration differences between each configuration. In addition, this paper 

better describes how the noted differences between optical configurations can effect a 

suppressant spray nozzle characterization. 

EXPERIMENTAL SETUP 

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

velocity and drop diameter distribution downstream of a two phase air/water spray nozzle. 

Preliminary measurements were acquired at three separate spatial locations across the center of 

the spray for each optical configuration examined. At each location 20,000 samples were 

acquired and velocity and diameter statistics computed. Two separate lens configurations were 

used. The first lens configuration consisted of 1000mm lenses on both the transmitting and 

receiving optics. The second configuration consisted of a 402.5mm lens installed on the U, and V 

component transmitting probe and a 310mm lens installed on the receiving optic/W component 

transmitter. Velocity and drop size measurements were taken at each position, each using three 

different apertures or masks (namely Mask A, B, and C) for each lens configuration. All three 

masks are shown in Figure 1. 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. 
3

Figure 1: Aperture Masks 

Data was collected at three radial positions across the center of the jet. The zero position 

represents the center position of the jet while the other two positions were located ±25.4 mm 

(1.0”) off the centerline. All measurements were located at 27.9 cm (11”) downstream of the 

nozzle exit. Each aperture mask was used with each lens configuration to take measurements at 

all three positions in the jet. This resulted in six lens/mask configurations measuring at three 

locations combining for a test matrix of 18 total test points. The actual test matrix used can be 

seen in the previous work of Davis and Disimile.7

Table 1 shows how changing the aperture masks and/or lens configuration affects the maximum 

diameter size that the PDA system could measure. These maximums were generated using the 

software provided by the PDA system manufacturer. The column to the far right indicates the 

percent change from the previous configuration (directly above it). From this table it can be seen 

that the receiving optic’s aperture mask, as well as the focal length of the lenses will change the 

diameter range that the system can effectively measure. 

Table 1: Maximum Configuration Diameter 

Transmitting 

Lens 

Receiving 

Lens 

Mask Max Diam. 

(μm) 

Max Diam % 

Change 

310 mm 402.5 mm A 193 0 

310 mm 402.5 mm B 313 62 

310 mm 402.5 mm C 751 140 

1000 mm 1000 mm A 827 10 

1000 mm 1000 mm B 1340 62 

1000 mm 1000 mm C 3213 140 

RESULTS 

The experimental results are displayed here in the form of tables and charts. For all of the data 

presented, it was thought that the zero position represents the center of the spray. The other two 

positions are ± 25.4 mm relative to this position and extend radially outward along the centerline 

of the jet. It will be shown later that what was thought to be the zero position for this experiment 

was not actually in the center of the jet. The term ‘Long Lenses’ refers to the measurements 

using the 1000mm lenses, and the term ‘Short Lenses’ refers to the cases when the 310mm and 

402.5mm lenses were used. 

Velocity Measurement Effects

Since the measured drop velocity is only a function of the Doppler frequency and fringe spacing, 

the lens/mask configuration should not pose a direct effect on the velocities measured. However, 

Mask A Mask B Mask C
4

since each data sample was validated on the signal for all three velocity components and the 

diameter, an improper lens/mask configuration could have a slight indirect effect on the 

measured velocities. This is due to the concentration difference and a bias toward larger or 

smaller drops (smaller drops tend to move faster than larger ones). Figure 2 presents the mean 

streamwise velocities for each configuration for each of the three positions within the jet. At the 

-25.4 mm and 0.0 mm positions the velocity data is grouped within ± 7%, while the velocity data 

at the +25.4 mm position has a much larger spread. 

Streamwise Velocities vs. Radial Position

0

5

10

15

20

25

30

-30 -20 -10 0 10 20 30

Z Position (mm)

U Velocity (m/s)

Short Lenses Mask A

Short Lenses Mask B

Short Lenses Mask C

Long Lenses Mask A

Long Lenses Mask B

Long Lenses Mask C

Figure 2: Mean Streamwise Velocities for Each Configuration 

It should also be noted that the velocities measured at the +25.4 mm position are much higher 

than those measured at the -25.4 mm position. Assuming that these two positions are the same 

distance from the jet’s centerline, the velocities measured should be relatively equal. Two main 

factors are most likely the cause of the discrepancy between the +25.4 mm and -25.4 mm 

positions and the scatter in the data at +25.4 mm. The first cause is signal attenuation due to the 

dense spray pattern. At the +25.4 mm position the transmitted and received signal must pass 

completely through the center of the jet thus attenuating the received signal. The second cause 

can be contributed to a mis-positioning of the measurement volume. The zero position which 

was initially thought to be on the jet’s centerline, was determined to be off center, thus the 

velocities at the radial positions would not match. The second cause will be investigated later 

when a complete nozzle characterization has been completed. 

Diameter Measurement Effects

PDA systems measure drop diameter by actually measuring the Doppler signal reflected, or 

refracted from the drop using two or more separate photo detectors. The diameter measurement 

is then formulated using the phase shift between the measured Doppler signals as well as 

knowing the distance and angle between the photo detectors. Unlike velocity measurements, the 

lens/mask configuration changes parameters in the diameter size relations such that the diameter 

dynamic range of the PDA system is increased or decreased. In turn, the diameter measurements 

rely heavily on the user’s choice of the lens/mask configuration. 

An important indicator that aids the PDA system user to verify if the physical parameters of the 

system meet the range of measurements actually collected is the histogram. The histogram 
5

shows the frequency distribution of the collected drop population. However, the user should not 

rely on this tool alone. 

If a relatively large amount of data was collected at the maximum diameter set by the physical 

constraints of the system, then the physical properties of the system (lens/mask configuration) 

were not optimally configured. Figure 3 shows an example of a histogram in which the 

lens/mask configuration was improper. The vertical red line in Figure 3 (and Figs. 4 and 5) 

represents the arithmetic mean diameter. The measurement shown in Figure 2 was taken in the -

25.4 position in the jet with the short lenses/Mask A configuration. Referring back to Table 2 

the maximum diameter that can be measured for this configuration is 193 μm. The extreme of 

the abscissa of Figure 3 is set to this maximum diameter. In determining if the diameter 

histogram is acceptable, one should observe the number of samples collected at the maximum 

cut-off diameter. It can be easily determined that the configuration used for Figure 3 was not 

optimal since a large amount of data was measured at the maximum cut-off diameter. This 

suggests that the drop diameter range is beyond the dynamic range of this configuration. 

0

100

200

300

400

500

600

700

800

0.0 50.0 100.0 150.0

Counts

PD A D [μm]

Figure 3: Diameter Histogram, Short Lenses/Mask A, -25.4mm Pos. 

Figure 4 shows the histogram of the measured diameters acquired at the +25.4 mm position of 

the jet, when an optimized optical configuration (i.e., long lenses/mask A) was used. Again the 

extreme of the abscissa in Figure 4 is set to this maximum diameter for the given configuration 

found in Table 2. It can be seen that the frequency of measurements tapers off toward the 

maximum diameter and not a single measurement was acquired at this maximum. This could 

possibly indicate a proper lens/mask configuration. 

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 .0 2 0 0 .0 4 0 0 .0 6 0 0 .0 8 0 0 .0

Co u n ts

P D A D [μm ]

Figure 4: Diameter Histogram, Long Lenses/Mask A, -25.4mm Pos. 
6

However, it cannot be readily determined that a low drop count recorded at the maximum cut-off 

diameter indicates an optimum configuration. The reasoning for this can be seen in Figure 5 

where the extreme of the abscissa was not set to the maximum cut-off diameter but rather the 

maximum diameter that was actually encountered during experimentation. Figure 5 clearly 

indicates that no diameters were measured past approximately 830 μm. However, for the given 

configuration (long lenses/Mask C) the maximum diameter that could have been measured was 

3213 μm. Therefore solely using this reasoning of no data cut-off due to configuration 

limitations, the lens/mask configuration can be determined to be appropriate. It will be later 

shown that the configuration used to obtain Figure 5 was not the proper configuration for the 

given measurement condition, and the diameter measurements were biased toward the larger 

diameters. Therefore, a more reliable method to help select the proper lens/mask configuration is 

needed for each application. 

0

200

400

600

800

1000

1200

1400

1600

0.0 200.0 4 00.0 600.0 800.0

Counts

PD A D [μm]

Figure 5: Diameter Histogram, Long Lenses/Mask C, -25.4mm Pos. 

Measured Sauter mean diameters for all six lens/mask configurations at all three positions in the 

spray are shown in Figure 6. From an examination of position 0.0 mm it can be noted that the 

long lenses with both aperture Masks A and B are both measuring Sauter diameters relatively 

close to one another (279 microns ± 3%). Through examination of the Sauter mean diameters 

measured with the long lenses and aperture Masks A and B at the edges of the spray the 

following measurements are observed. At the lower edge of the spray (-25.4 mm) Sauter mean 

drop diameters were determined to be 330 microns ± 1%. Likewise at the positive edge the 

diameter was 295.5 microns ± 6%. 
7

Sauter Mean Diam. vs Radial Position

50

100

150

200

250

300

350

400

450

-30 -20 -10 0 10 20 30

Z Position (mm)

Sauter Mean Diameter (μm)

Short Lenses Mask A

Short Lenses Mask B

Short Lenses Mask C

1000mm Mask A

1000mm Mask B

1000mm Mask C

Figure 6: Sauter Mean Diameters for Each Configuration 

As expected larger drops reside at the edges of the spray and have a corresponding lower 

velocity, while drops toward the center of the spray are smaller in size and have a higher 

velocity. At all three positions the Sauter mean diameter increases as the diameter dynamic 

range of the system is increased. The Sauter mean diameters measured with the remaining four 

optical configurations were not as closely matched as the long lenses / Masks A and B. The 

overall spread from the short lens/Mask A to the long lens/Mask C configurations was 66% or on 

the order of approximately 250 microns. This gives further insight into which optical 

configuration is optimal for the given measurement condition. 

A similar plot displaying the diameter concentration or number density (in #/cm3

) is shown in 

Figure 7. Here the short lens/Mask C and the long lens/Masks A and B configurations were all 

measuring relatively close to the same diameter concentrations, while the remaining optical 

configurations showed much different values. In general, the diameter concentration decreases 

with increasing diameter dynamic range of the system. At all three positions it can also be noted 

that for any given set of lenses Mask C recorded much lower diameter concentrations than with 

Masks A or B. This is intuitive since examination of Figure 1 shows that Mask C blocks 

considerably more light than Masks A or B. Also it can be seen that at the +25.4 mm position 

the diameter concentration is lower than expected by comparison to the other two positions. This 

is again thought to be due to signal attenuation caused by the dense spray pattern. 
8

Diameter Concentration vs. Radial Position

0

100

200

300

400

500

600

700

-30 -20 -10 0 10 20 30

Z Position (mm)

Concentration (#/cm 3 )

Short Lenses Mask A

Short Lenses Mask B

Short Lenses Mask C

1000mm Mask A

1000mm Mask B

1000mm Mask C

Figure 7: Diameter Concentrations for Each Configuration 

Lens/Mask Configuration Selection

Figure 8 presents a final method of highlighting the best lens/mask configuration for the current 

PDA application. This method takes into account the bias that the configurations have on 

measuring either larger or smaller drops, and the arithmetic mean diameter increase. The 

configuration bias is determined by inspecting the diameter histograms and determining the 

number of diameters measured below and above 100 μm. This 100 μm limit was chosen in order 

to best determine the loss of sensitivity for smaller drops. Since the velocity remained relatively 

unaffected by the lens/mask configuration the velocity is neglected in this method. 

Figure 8 displays the percentage change for the mean diameter, number of samples lost below 

100 μm, and the number of samples gained above 100 μm between mask/lens configurations, for 

two separate positions in the jet. The mask/lens configurations were put into order by the 

maximum diameter of the dynamic range for each configuration (Table 2), least to greatest. 

Thus, for this case: 1- Mask A, Short Lenses; 2-Mask B, Short Lenses; 3-Mask C, Short Lenses; 

4-Mask A, Long Lenses; 5-Mask B, Long Lenses; and 6-Mask C, Long Lenses. The chart 

abscissa (x-axis) describes between which two configurations the percentages were acquired. 

The first x position (x = 1 index) indicates the change from configuration 1 (described above) to 

configuration 2. The second x position indicates the change from configuration 2 to 

configuration 3 and so on. 
9

Lens/Mask Configuration Selection Chart

-60%

-40%

-20%

0%

20%

40%

60%

0123456

Configuration Index

Percent Difference 

Mean Diam Increase Pos 1

Sample <100μm Loss Pos 1

Sample >100μm Inc Pos 1

Mean Diam Increase Pos 2

Sample<100μm Loss Pos 2

Sample >100μm Inc Pos 2

 A (S) - B (S) B (S) - C (S) C (S) - A (L) A (L) - B (L) B (L) - C (L)

Figure 8: Configuration Selection Chart 

From Figure 8 it can be observed that the least percentage change in all three plotted values for 

both positions is at the x = 3 index, corresponding to the change between Mask C/short lenses, 

and Mask A/long lenses. Therefore, Mask A with the long lenses was selected for the test 

conditions examined. The reason for selecting the long lens/Mask A configuration was chosen 

over the short lens/Mask C configuration was two fold. First, the difference between the 

measurements produced by the short lens/Mask B and the short lens/Mask C configurations (x = 

2 index) were much larger than the difference between the long lens/Mask A and long lens/Mask 

B configurations (x = 4 index). The second reason is not shown in Figure 8 but involves 

examining the data rate of the incoming measurements. The data rate of the measurements can 

be of high importance especially when monitoring transient events. The long lens/Mask A 

provided a faster data rate than the short lens / Mask C configuration which further supports our 

selection of an optimal optical configuration. 

Suppressant Nozzle Characterization

After the optimal optical configuration was chosen using the method described above, a full 

spray characterization was completed for the two-phase (air/water) nozzle. The suppressant 

spray nozzle used in the present study was a dual-fluid, solid cone nozzle patented by the Navy 

as a Liquid Atomizing Nozzle, under the patent number of 5,520,331. Based on preliminary 

PDA measurements it was decided to reverse the gas liquid entrance locations as opposed to the 

specifications listed in the patent. The full characterization includes measuring drop diameter 

and three dimensional velocities at several downstream distances. The downstream distances 

measured included 8”, 10”, 12”, and 14”. 
10

Figure 9 shows the measured spray pattern in the u-v plane and the corresponding arithmetic 

mean diameters at each location. This plot provides a representation of not only the velocity and 

diameter profile across the jet but also how the jet develops downstream. The arrows represent 

the u-v velocity vectors at the given location while the circles are representative of the droplet 

diameters. 

Figure 9: Nozzle Characterization 

The higher the velocity the longer the arrow or velocity vector, in turn, large circles represent 

large diameters. It can be seen that at any downstream location the droplet velocity is highest in 

center position of the jet where the droplet diameter reaches a minimum. From the center 

outward, the droplet velocity follows a Gaussian distribution decreasing outward. It follows that 

when a decrease in the droplet velocity is evident the droplet had a larger diameter. This type of 

characterization can be of great importance in droplet transport models and shows how useful the 

PDA technique can be in spray research. 

Figure 10 shows the streamwise velocity profile 11” downstream of the nozzle exit. This data 

was measured with the optimum optical configuration selected above (long lenses/mask A). The 

measurements taken for the examination of the optical configuration shown in Figure 2 were 

overlaid on this nozzle profile to confirm the location of these measurements. In doing this it 

was observed that the three points measured above, matched the profile within 7% if the position 

of the three points was corrected by –9.5 mm. The data was also compared in the same manner 

for the arithmetic and Sauter mean diameters and diameter concentration with all comparisons 

suggesting that all three positions were -9.5 mm off the location they were originally we thought 

to be. Therefore, it can be confirmed that the measurements presented for the investigation into 

the optical configuration were actually –9.5 mm off their stated values. This explains why the 
11

velocity and diameter data at the +25.4 mm position did not match that measured at the –25.4 

mm position. So it can now be said that the data that what was thought to be the +25.4 mm 

position was higher in velocity due to a mis-positioning of the measurement volume in the jet. 

Now only the spread in the velocity between configurations at this position (shown in Figure 2) 

is accredited to the signal attenuation of the dense spray pattern. 

Overlay of Lens/Mask Comparison Data onto Nozzle Characterization

Under Same Measurement Conditions

0

5

10

15

20

25

30

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80

Z Position (mm)

U Mean Velocity (m/s)

Nozzle Profile

Lens Comp Data

The Z-Pos of this data set (all 3 points) was corrected 

by 9.53 mm off-center.

Figure 10: Lens/Mask Comp. Data Overlay 

ERROR ANALYSIS 

Several parameters can cause error in both the measurement of drop velocity and size using a 

PDA system. The biggest source of error using laser scattering measurement techniques comes 

from the Gaussian intensity distribution of laser light beams. These Gaussian effects, sometimes 

referred to as measurement volume effects can cause a considerable bias in the diameter 

measurements for any drop over 1/3 the size of the measurement volume.7

 Therefore one might 

ask if the difference reported in the diameter measurements is due to the Gaussian effect. The 

biggest concern would then be directed at the how the size of the measurement volume changed 

for each lens/mask configuration. The Gaussian effects can only be ignored in this paper if the 

measurement volume size remained relatively constant over the range of lens/mask 

configurations and only comparisons between diameter measurements are reported rather than 

absolute drop diameters. 

Since the mask is attached to the receiving optics only, the measurement volume size does not 

depend on the aperture mask used. Therefore during the present experiments the measurement 

volume size only changed between lens configurations. For all configurations using the smaller 

lenses the measurement volume’s size was reported to be 150 microns in diameter. This changed 

to 260 microns for configurations using the long lenses. In turn, the Gaussian effects could be 
12

biasing any drop over 50 microns with the smaller lenses and 86 microns for the longer lenses. 

Despite this difference, the fact that the diameter measurements between the short lenses with 

Mask C and the long lenses with Mask A were in close agreement gave us confidence that the 

Gaussian effects can be ignored if the diameter measurements are taken as relative measurements 

and not absolute. 

The repeatability checks indicated a maximum error of ± 2% for all quantities measured. The 

repeatability measurement shows that nozzle fluctuations, user error setting experimental 

parameters, among other equipment and user errors are all relatively low. 

Another error causing concern is the laser power output and the photo detector amplification 

settings. To evaluate the impact of laser power a large range of laser powers were used during 

the drop velocity and size measurements. It was shown that the velocity measurements can 

differ up to 5% and the arithmetic mean diameter by up to 12% if a less than optimal laser power 

was used. However, these percentages were taken from the extremes of the laser power range 

and in actuality as long as a laser power was chosen to be within 50 mW of the power required 

for accurate measurement this percentage decreases to less than 2%. Since the diameter 

measurements leveled off to a nominal value as the high voltage was increased, it is believed that 

this power level was indeed appropriate. This was also confirmed by monitoring the received 

Doppler signals using an oscilloscope. 

In addition to the possible errors described above, a nominal error of 4% for diameter 

measurements and 2% for velocity measurements was suggested by the PDA system 

manufacturer. This is the error associated with the measurement system itself and should not be 

taken as the sole source of error. 

As it can be seen further study is needed to enable the reporting of absolute diameter 

measurements. Although to date some research has been conducted to explain Gaussian effects, 

experimental investigations quantifying these effects using standard PDA systems has yet to be 

reported. 

SUMMARY 

Phase Doppler Anemometry can appear to provide very good diameter data during a first 

inspection. However, upon further investigation it has been shown that the acquired data may 

have a considerable bias based on the specific geometric configuration. From the present tests it 

was determined that the Sauter mean drop diameters could be as much as 66% higher than that 

actually produced by the spray jet. This is of high importance for the input of diameter 

measurements into droplet transport models which heavily depend on accurate diameter 

measurements. This paper shows that the researcher could be easily mislead into using an 

improper optical configuration for PDA measurements thus unknowingly biasing all diameter 

results. The bias in this data would then be passed on to the model in which it is used thus 

creating unknown inaccuracies in the model. Therefore, a relatively simple method is presented 

to help determine the optical lens/receiving aperture mask configuration giving the least bias 

when the diameter range of the drops to be measured is unknown. 
13

ACKNOWLEDGEMENTS 

The authors would like to thank Mr. Nathaniel McElroy with General Dynamics for technical 

support on this project. 

REFERENCES 

1. 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. 

2. 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. 

3. 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. 

4. Naqwi, A. A., “Optimization of the Shape of Receiving Aperture in a Phase Doppler 

System,” 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, 1997. 

5. 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. 

6. 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. 

7. Dantec Dynamics, “Laser Doppler Anemometry: Introduction to Principles and 

Applications,” Dantec Dynamics, Publication 9040U5717, Dantec Dynamics A/S, Denmark.