Acta Polytechnica


https://doi.org/10.14311/AP.2025.65.0177
Acta Polytechnica 65(2):177–187, 2025 © 2025 The Author(s). Licensed under a CC-BY 4.0 licence

Published by the Czech Technical University in Prague

PHOTOGRAMMETRIC IMAGE PROCESSING AND COMPARISON
OF EXPERIMENTAL RESULT WITH LASER DIFFRACTION AND

THE PDA METHOD

Adam Huněk∗, Ondřej Bartoš

Czech Technical University in Prague, Faculty of mechanical engineering, Department of Energy engineering,
Technická 4, 166 07 Prague, Czech Republic

∗ corresponding author: adam.hunek@fs.cvut.cz

Abstract. Optical methods have been established as a standard tool for aerosol size measurement.
The aim of this paper is to compare the results of two commercial optical instruments based on Phase
Doppler Anemometry (PDA) and Laser Diffraction (LD) with an in-house optical photogrammetric
measurement method. For the purpose of this comparison, a new in-house image processing procedure
was developed with the use of a MATLAB script. The accuracy of the method was tested on several
calibration particle samples as well as on PDA and LD commercial instruments. The analysis of the
measurements with calibration standard particles was done using the Bias-Variance decomposition
method. All three methods were tested on the polydisperse sand particle sample. The results are
applicable to determine the benefits and drawbacks of these methods in their application to the broader
field of aerosol technology.

Keywords: Light scattering, phase Doppler anemometry, photogrammetry, image analysis, Otsu
method, automatic thresholding.

1. Introduction
For the evaluation of the size distribution of polydis-
perse particle systems, certain optical methods have
been established as standard diagnostic tools. In many
cases of measuring the droplet size, these methods
remain the only feasible means [1]. The motivation
for this study arose from the analysis of liquid sprays
and the study of liquid film breakup in steam tur-
bines at transonic flow. In this scenario, droplets form
on the trailing edge and are further accelerated to
the bulk velocity of the steam flow. The accelerated
droplets subsequently hit the rotating blades, caus-
ing erosion. The entire process contains the liquid
film breakup, formation of droplets, and final flow
in the carrier gas; these phenomena can be observed
using various optical methods. Photogrammetry (also
known as the shadowgraph imaging technique) plays
an important role in observing the liquid film breakup
and droplet acceleration. Alongside photogrammetry,
Phase Doppler Anemometry (PDA) and light diffrac-
tion methods are used to measure the final aerosol
(wet steam) flow. Moreover, PDA can also be used to
measure the velocity at specific positions [2]. Because
photogrammetry is applied at the beginning of the
droplet formation process (focused on the blade’s trail-
ing edge), and the other two optical methods are used
when the droplet formation process is complete, it is
useful to identify the overlap between these methods.
The goal of this paper is to compare all three methods
as applied to monodisperse particles of 10, 15, 20,
30, 40, and 80 µm. A new in-house image processing
procedure was developed for droplet size evaluation

using a photogrammetric method based on the image
obtained with a rapid exposure time. The MATLAB
development environment was used. For practical ap-
plications, a test measurement was performed with
a two-phase water nozzle. This nozzle is used in the
experiment, where the nozzle generates water droplets,
which subsequently saturate the neighbouring air. To
set the required condition of the mixture, an exact
understanding of the distribution of water droplets
from the nozzle is necessary [3]. These results may
then be generalised for similar situations, ultimately
determining the measurement limitations of all the
methods used. For this paper, the experiment was
conducted in ambient air and open environment.

A similar method for aerosol size evaluation using
image analysis was developed by Kashdan et al. [4].
This method is based on the evaluation of the diameter
of the object by segmenting it with a specified thresh-
old. The experimental setup consisted of a 12-bit
CCD camera (PCO Sensicam) with a microscopic
optical lens, providing a resolution of 0.7 µm/pixel.
Illumination was provided by an infrared diode laser
beam, which was diverged at a maximal angle with
two prisms, and subsequently diffused with an opal
glass lens to ensure even illumination of the photo.
This paper focusses primarily on calibrating the depth
of field with a Patterson globe and then determining
the acceptable depth of field, derived from the linear
calibration of the uncertain “halo area”. The sensi-
tivity of threshold determination decreases with the
diameter of the object. Moreover, as the sensitivity
decreases, it is necessary to ensure a sufficient differ-
ence between the background and object intensities.

177

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Adam Huněk, Ondřej Bartoš Acta Polytechnica

Subsequently, a measurement was performed on a noz-
zle, and the comparison with a PDA measurement
showed good agreement.

Among the published papers, comparisons of im-
age analysis with other optical methods are very
rare. Sijs et al. [5] compared laser diffraction, phase
Doppler anemometry, and image analysis for several
nozzles with an expected droplet diameter range of
150 µm to more than 550 µm. They found that larger
droplets cause greater deviations in the evaluation of
these methods. However, all methods are reliable for
droplets up to approximately 400 µm. The main dis-
advantages of each method were identified. While the
laser diffraction method is straightforward, it can inac-
curately evaluate the increased distribution of smaller
droplets as a result of their lower velocity, which leads
to an increase in their concentration within the mea-
surement volume. This effect has to be taken into
account and the measurement has to be performed
in a sufficiently large volume to avoid small particles
accumulating in the measuring laser beam. Phase
Doppler anemometry evaluation can be affected by
air bubbles present in the droplets, which can then
be falsely evaluated as smaller droplets. Herbst [6]
compared the three optical methods for agricultural
sprays, with droplet diameters ranging from approx-
imately 100 to 500 µm, and found variations in the
results of the individual methods that increased with
larger droplet sizes. De Cock et al. [7] developed
a high-speed imaging method and compared it with
phase Doppler anemometry in ISO reference nozzles
with droplet diameters ranging from 40 to 1 300 µm.
The results, again, demonstrated comparable conclu-
sions for smaller droplets, along with variations for
larger ones. The imaging method tended to measure
a similar Dv50, a larger Dv90, and a smaller Dv10
compared to the PDA. Kashdan et al. [8] developed
a digital image analysis technique and compared it
to PDA on a pressure-swirl atomiser for fuel droplets
with diameters of 5 to 30 µm, finding slight differences
in D10 (5 %) and D30 (3 %). The digital image analy-
sis technique was able to detect large, non-spherical
droplets that the PDA device could not detect. Kash-
dan et al. [9] then used the digital image analysis tech-
nique in a high-speed two-phase flow, using a pulsed
laser for particle illumination with diameters ranging
from 10 to 30 µm and velocities of up to 50 m s−1, and
compared it with PDA measurements. Both meth-
ods were highly compatible for objects larger than
25 µm. In recent years, comparisons of PDA and high-
speed camera measurements of droplets from a water
nozzle have been published, showing good agreement
between the two methods [2].

Most of these published papers focus on distri-
butions with droplets greater than 100 µm or those
larger than 400 µm, which are often used in agricul-
ture. The aim of this paper is to use samples with
known monodisperse size distributions to calibrate
the developed photogrammetric method and compare

Figure 1. The detected object with the intensity
values of the pixels at its axis.

it to those of PDA (Dantec Dynamics) and Spraytec
(Malvern Panalytical Ltd.). Subsequently, all of these
methods are compared using non-monodisperse distri-
butions for samples with particles ranging from 10 to
150 µm and a two-phase nozzle. This article is the
culmination of a long-term research at the Depart-
ment of Energy Engineering at CTU Prague on the
identification of polydisperse systems. Partial results
were recently published, for example, by Hunek [10].
The presented article also provides a complete set of
experimental data and their processing.

2. The principle of image analysis
methods for aerosol size
measurement

Most image analysis methods for aerosol size measure-
ment rely on capturing images with a short exposure
time and a quick flash, typically in the order of mi-
croseconds, from a diode or laser, to capture rapidly
moving objects. In the resulting greyscale image, the
intensity distribution function theoretically has two
peaks, representing pixels that clearly belong to the
background and the object groups. However, there
are many “uncertain” pixels that cannot be clearly
determined. The main challenge of image analysis
methods is to automatically determine whether these
pixels are part of the object or background groups.
An example of a detected aerosol is shown in Fig-
ure 1. The blue line represents the pixel intensity
values along the horizontal axis of the aerosol. There
is a well visible transition area between the object and
the background (the “halo area”) reported by Kash-
dan et al. [4], as well as light reflection at the centre
of the aerosol. One possible method to segment these
pixels is thresholding such as OTSU segmentation.
To eliminate this uncertainty and achieve a reliable
measurement method, a calibration is necessary.

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2.1. OTSU segmentation
The photogrammetric method proposed in this paper
is based on the OTSU segmentation of the object
from the background, as proposed by Otsu [11]. This
method can determine the threshold automatically
and has the advantage of being fast and straightfor-
ward. The OTSU method uses a greyscale image
histogram and attempts to find the borderline be-
tween the background and object pixels. The max-
imum value of between-class variance is used to get
the optimal threshold k∗ as described by the following
equation:

σ2
B (k∗) = max

1≤k<L
σ2

B(k) = max
1≤k<L

[µT ω (k) − µ(k)]2

ω(k) [1 − ω(k)] , (1)

where
[1, . . . , k, . . . , L] are the pixel levels,

ω(k) =
∑k

i=1 pi is the zeroth-order cumulative mo-
ment of the histogram up to k pixel level,

µ(k) =
∑k

i=1 ipi is the first-order cumulative moment
of the histogram up to k pixel level,

µT =
∑L

i=1 ipi is the overall mean,
pi is the value of probability distribution at ith pixel

level [11].
Goh et al. [12] performed an analysis of the OTSU

segmentation accuracy in the dependence of the ob-
ject area to the segmentation area ratio, background
intensity to the object intensity ratio, level of noise
and position of the object. It was determined that
the ideal object area to segmentation area ratio and
ideal background intensity to object intensity ratio
(for a dark object and light background) to avoid over-
segmentation or under-segmentation is 72 % and 35 %,
respectively. These ideal conditions apply to all levels
of noise. As expected, the quality of segmentation is
independent to the position of the segmented object.

3. Optical methods
This chapter is devoted to a brief description of the
two commercial optical devices, the PDA Dantec Dy-
namics and the Spraytec Malvern Panalytical. Subse-
quently, the developed photogrammetric method with
the in-house MATLAB script is described.

3.1. The Phase-Doppler anemometer
The first optical device for the aerosol size measure-
ment is the Phase-Doppler anemometer manufactured
by Dantec Dynamics (Figure 2). The measurement
setup consists of a laser with an adjustable power of
up to 500 mW (continuous laser) and front lenses with
a 350 mm focus length placed on the receiver. The
detector is set in a forward refraction mode at an
angle of 30° for all measurement cases. When mea-
suring the duke standards, this configuration has the
confidence of linearity of the PDA around 95.39 %.
Although the optimal angle of the receiving optics for

Figure 2. The Phase Doppler anemometer.

Figure 3. The Spraytec Malvern device.

the case of water droplets in the air is approximately
68°, the confidence of linearity for the angle of 30°
is 97.04 %, which is approximately 1 % less than the
optimal angle. Depending on the expected aerosol
size, the mask type A or B is used on the receiver. The
light signal collected by the detection optics passes to
a photomultiplier, activated by a voltage of 1 000 V.
Compared to the laser diffraction method, the mea-
surement volume is much lower, and the position of
the device is controlled by a traversing system. The
data are processed by flow control software, which
is able to evaluate the diameter and velocity of each
particle individually.

3.2. Laser diffraction
The laser diffraction method is based on the Mie the-
ory of angular light energy distribution of a scattered
laser light at small angles. In this case, the commer-
cial instrument, Spraytec Malvern, is used (Figure 3).
It consists of a laser module with λ = 635 nm laser
light and a receiver module with a 300 mm lens. The
data from the receiver are continuously processed by
a software that evaluates the particle size distribution.
It can detect particles with diameters ranging from
0.1 µm to 1 mm.

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Adam Huněk, Ondřej Bartoš Acta Polytechnica

Figure 4. The typical Photogrammetry configuration.

Figure 5. 1951 USAF resolution test chart.

3.3. The photogrammetric method
(shadowgraph)

Similarly to the other image analysis methods for the
evaluating droplet size, the photogrammetric method
is based on taking pictures with a short exposure
time and a quick flash from a diode in the order of
microseconds to capture fast-moving objects. For
this purpose, the XIMEA MC050CG-SY with Sony
IMX250LQR-C digital sensor with 2 464×2 056 active
pixels (3.4 µm pixel-pitch), and a telecentric lens was
used. Sometimes the term “shadowgraph” is used.
As shown in Figure 4, the flash is placed behind the
spray cone so that the objects are represented by their
shadow. For the calibration of the pixel-to-object size
ratio, the 1951 USAF resolution test chart (Figure 5)
was used. To evaluate object diameters from the
images obtained, a new in-house MATLAB script
was developed, the flowchart is shown on Figure 8.
The aim of this method is to evaluate sharp objects,
while eliminating those out of focus, which would
not be evaluated accurately (Figures 6 and 7). The
usage of a telecentric lens has the advantage of being
independent of the detected object size to the distance
of the object from the lens. However, this type of
lens has a very narrow depth of field, which results
in a blunter object concentration and many out-of-
focus objects. This disadvantage can be eliminated by
different approaches. First, the ratio between the out-
of-focus distance and the gradient can be found [3]
or, as was done for this paper, one can take more
subsequent photos and only the focused objects are
processed.

Figure 6. An example of a pre-processed image.

Figure 7. An example of a segmented image.

The OTSU threshold method was applied, as it
possesses the advantage of quick evaluation and is
able to automatically determine the threshold. First,
the image is pre-processed to appropriately adjust it
for the segmentation and to reduce the noise. Sub-
sequently, the OTSU segmentation method is used
throughout the picture to detect all objects. Then,
the defocused objects are eliminated using the gra-
dient method. This part of the script is applied for
object detection and approximate object size evalu-
ation in order to obtain an initial iteration of the
ideal object-to-background ratio, which determines
the required segmentation area for each detected ob-
ject. The second part of the script is a loop with the
possibility of additional iterations of the segmentation
area. The purpose is to accurately segment each de-
tected object individually according to the iterated
segmentation area and to subsequently acquire the
correct size distribution.

There are several adjustable parameters which af-
fect the quality of the segmentation, and therefore
the accuracy of this method. The source of this un-
certainty (other than resolution) are the “uncertain
pixels” between the clear object and the background
pixels. The segmentation area adjusts the ratio of

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Figure 8. The photogrammetry image processing path.

the clear object and background pixels. In the script,
it is adjusted with the parameter Segmentation win-
dow (dimensionless), which can be computed with the
following Equation (2), where Sobject represents the
area of the detected object and Ssegmentation represents
the area, around the object, where segmentation is
performed, usually square or rectangle in shape.

Segmentation window = Sobject

Ssegmentation
. (2)

The background intensity (contrast) changes the
distance between the two peaks in the histogram of
the picture. The gradient method eliminates objects
according to the adjustable gradient boundary. Lower
values of the gradient boundary could lead to an in-
correct segmentation of out-of-focus objects, while
higher values could lead to the non-inclusion of ac-
ceptable objects. The Gradient boundary is adjusted
with the Gradient function as shown in Equation (3),
where IB represents a bright pixel with the 95th per-
centile of pixel intensity value, while ID represents
the 200th darkest pixel.

Gradient boundary = Gradient function (IB − ID) . (3)

Another adjustable parameter is the number of
additional iterations of the ideal segmentation area.
A lower number of additional iterations can lead to
inaccuracy due to a differing segmentation area.

4. Calibrating the
photogrammetric method

For the calibration of the photogrammetric method,
six samples with latex particles of known monodis-
perse distributions of 10, 15, 20, 30, 40 and 80 mi-
crometres were used. These particles were placed in
a cuvette filled with water and equipped with a stirrer
as shown in Figure 9. Information on all samples is
shown in Table 1.

Figure 9. Photogrammetry measurement of a sample
in cuvette.

Sample 1 2 3 4 5 6
D10 [µm] 10.1 14.97 20 30.07 39.6 81.4
s [µm] 0.9 0.13 0.2 0.3 3.6 1.5

Table 1. Information regarding all tested samples.

The photogrammetric measurement was performed
by obtaining several pictures. In this case, the 8-bit
monochromatic resolution was used. For each sam-
ple, three different intensity levels of the background
pixels were taken. This corresponded to background
intensity modes of 180, 150, and 110 on a scale from
0 to 255, where 255 represents the lightest intensity
and 0 represents the darkest intensity. Here, the back-
ground intensity mode of 180 approximately corre-
sponds to the ideal ratio of the object intensity to the
background intensity as proposed by Goh et al. [12].

The evaluation of the in-house image processing
method was done for several script configurations
with variables of the segmentation window (Equa-
tion (2)) and the gradient function (Equation (3)).
The number of additional iterations was set to 8, to
minimise the iteration inaccuracy. The goal of the

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Adam Huněk, Ondřej Bartoš Acta Polytechnica

calibration process was to find an ideal configuration
of the evaluation of different particle sizes and differ-
ent properties of the images. The individual output
distributions were modified by the Grubbs test, which
detected and erased outliers caused by impurities in
the cuvette. Subsequently, the arithmetic mean and
standard deviation were determined.

The measurement error was estimated using the
theory of bias-variance decomposition [13]. This ap-
proach was chosen because the measurement error,
determined in this way, includes all uncertainties in
the measurement chain, the accuracy of the method,
measurement facility, and systematic error of an ex-
perimenter. The authors performed all measurements
with the utmost care to reduce these uncertainties.
Firstly, the Bias (systematic error) of the measure-
ment was computed by Equation (4), where D10m is
the arithmetic mean of the measurement and D10s is
the arithmetic mean of the sample.

Bias = D10m − D10s. (4)

The random error is defined by Equation (5), where
sm is the standard deviation of the measurement and
s2

m is the variance of the measurement. According
to the law of total variance [14], the variance of the
measurement contains the variance of the sample,
the variance of the photogrammetric method, and
noise. This means that the reference value of the error
computation is the arithmetic mean of the sample.

Random error = s2
m. (5)

The Absolute error (AE) is then defined as the
combination of the systematic and random errors, by
the following:.

AE =
√

Bias2 + Random error. (6)

Finally, the Relative error (RE) is computed using
Equation (7), where D10 is the mean of the sample:

RE = AE
D10s

. (7)

Figure 10 shows the evaluation of sample 5 (D10 =
39.6 µm), where the dependence of the relative er-
ror on the Segmentation window and the Gradient
function is shown. In this case, the mode of the back-
ground pixel intensities was estimated to be 183. The
figure shows a strong dependence of the Segmenta-
tion window on the Relative error (RE) with clear
minimal values in each Gradient function level. RE
also depends on the gradient function until approx-
imately Gradient function = 0.6. This is the value
where the out of focus objects are eliminated, and
rising the value would lead to rejecting the objects
that are focused. Setting the Gradient function to
0.6, the ideal value of the Segmentation window was
estimated to be 0.64, slightly deviating from the value
of 0.72 reported in [12]. Similarly, Figure 11 shows

Figure 10. The calibration of the photogrammetry
method – sample 5 (D10 = 39.6 µm), where the de-
pendence of the relative error on the Segmentation
window and the Gradient function is shown. In this
case, the mode of the background pixel intensities was
estimated to be 183.

Figure 11. The calibration of the photogrammetry
method – sample 3 (D10 = 20 µm), where the mode
of background pixel intensities is 184.

the evaluation of sample 3 (D10 = 20 µm), where
the mode of background pixel intensities is 184. The
evaluation shows a similar trend, however, the ideal
segmentation window for Gradient function = 0.6 is
0.68, which is closer to the value of 0.72 reported by
Goh et al. [12].

Subsequently, the gradient function was set to 0.6
and the rest of the calibration was carried out. Ta-
ble 2 shows the optimal segmentation window for the
individual samples and background intensities along
with the relative error (RE) and other evaluations.
The results show dependence on the mode of the back-
ground intensity, as lower values (darker images) lead
to under-segmentation. For darker images, the ideal
segmentation window must be set higher. The results
also show a strong dependence of the object size on
the ideal segmentation window, as the evaluation of
smaller objects requires the segmentation window to

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vol. 65 no. 2/2025 Photogrammetric image processing and comparison of . . .

Sample Background Segmentation RE [%]intensity window
1 191 0.88 6.42
1 151 0.88 6.83
1 110 0.88 7.82
2 197 0.78 2.51
2 156 0.78 3.00
2 118 0.80 2.63
3 184 0.68 2.30
3 155 0.74 2.08
3 107 0.76 1.48
4 211 0.62 1.59
4 161 0.62 1.56
4 115 0.70 1.73
5 183 0.64 6.59
5 145 0.66 7.29
5 101 0.72 2.94
6 199 0.48 4.21
6 154 0.56 4.47
6 94 0.54 3.93

Table 2. The evaluation of the photogrammetry
calibration.

be higher and, conversely, the evaluation of larger par-
ticles requires the segmentation window to be lower.

The charts in Figures 10 and 11, together with Ta-
ble 2, show that the evaluation of the droplet size is
dependent on the image properties. The optimal value
of gradient function, segmentation window, and back-
ground intensity level are possible to find. This has
to be taken into account for proper data processing.

5. The result of comparing the
optical methods using
monodisperse particle samples

A new set of photogrammetric measurements of the
samples was carried out. The goal was to capture
images with the optimal background intensities. The
evaluation script was supplemented by the ideal values
of the segmentation window for individual object sizes,
and the gradient function was set to 0.6. In addition to
the photogrammetric method, these samples were also
evaluated by the Spraytec Malvern device based on
laser diffraction and the Phase-Doppler anemometer
by Dantec Dynamics (PDA). The goal was to verify
the photogrammetric method and to compare these
methods. Spraytec measurement was done continu-
ously for 1 minute for each sample, and the PDA was
set to a limit of 1 000 detected particles. The advan-
tage of the Spraytec measurement was the possibility
of calibration of the transmitted light previously to the
addition of the samples, while the photogrammetry
and PDA evaluation is affected by impurities in the
cuvette. As the monodisperse samples are measured
in the cuvette, the window correction in the PDA eval-
uation was used. Subsequently, the evaluation settings
were carried out so that only high-quality signals were
evaluated. For this purpose, a high signal-to-noise

ratio of 5 dB and high 1st to 2nd peak ratio of 8:1 were
set. Additionally, the phase validation ratio was set
to 5 %. The centre and span of velocity were set to
minimal values because of the slowly moving particles
in the cuvette. The power of the laser was set to
31 mW, the sensitivity of the photomultipliers was set
to 1 000 V, and the gain to 20 dB.

In the case of Photogrammetric and PDA evalua-
tion, the Grubbs test was used to eliminate outliers
caused by the impurities in the cuvette as described
in the chapter of the photogrammetric calibration. To
compare the evaluation of all samples with each of the
individual methods, the volumetric size distribution
and dimensionless diameter Df was used. The dimen-
sionless diameter Df is defined by Equation (8), where
d is the diameter corresponding to the Vof specific
value of the function in the volumetric size distribu-
tion and D10s is the arithmetic mean diameter of the
corresponding sample.

Df = d

D10s
. (8)

By comparing the results with the theoretical distri-
butions of the samples, the absolute and relative errors
were estimated (Equations (6) and (7)). The resulting
volumetric size distributions are shown in Figure 12.
This figure mainly serves for verification of how much
the mode and each evaluated distribution coincide
with the theoretical arithmetic mean diameter D10.
All methods show very good accuracy for most sam-
ples. However, each method has certain disadvantages.
The photogrammetry method has a mostly identical
modification to the theoretical value, but is the most
affected by the impurities in the cuvette. However,
this disadvantage was eliminated by the Grubbs test.
The Spraytec measurement is calibrated prior to the
dosing of the standard duke samples dosing and is
affected the least. The Spraytec measurement in Sam-
ple 6 has a correct mode; however, the distribution
is wider. The PDA measurement seems to be less
accurate for Samples 1 and 5, but the information
on the velocity distribution of particles is available as
well. All methods evaluated slightly smaller droplets
during the measurements of Sample 4.

Table 3 shows the evaluation of all samples with
the individual methods, where D10 is the arithmetic
mean, s is the standard deviation, D32 is the Sauter
mean diameter, AE is the absolute error, RE is the rel-
ative error, and N is the number of evaluated particles.
The absolute error of the photogrammetry evaluation
ranges from around 0.7 µm to 3.9 µm. This corre-
sponds to the descending relative error from 8.13 %
of Sample 2 to 3.64 % of Sample 6. Comparing these
values to the evaluation of the other methods verify
that the photogrammetric method is able to evalu-
ate the monodisperse distributions comparably to the
other two methods. The relative error of the Spraytec
measurement ranges from 10.37 % to 5.78 % and the
relative error of the PDA measurement ranges from

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Adam Huněk, Ondřej Bartoš Acta Polytechnica

Figure 12. The volumetric size distributions of each sample.

17.04 % to 3.20 %. These results show that when the
photogrammetry detects a particle (assuming thin
spray), it is able to evaluate the size very accurately.
The main obstacle for an accurate photogrammetric
evaluation is the background intensity values and ob-
ject sharpness, which are related to the exposure time
and flash. In the case of dense spray measurement
and the measurement of fast-moving objects with the
exposure time set in order of µs, the resulting picture
has a darker background. The results shown in Table 2
show very good agreement when measuring the same
samples with a different exposure time and subse-
quently evaluating them with different Segmentation
window values.

Comparing the evaluated photogrammetry measure-
ment (Table 3) with the calibration shown in Table 2,
the relative error is slightly higher. This might be
caused by a slightly different reference sample or differ-
ent settings for image acquisition. Although the goal
was to acquire images with the mode of background
pixel intensities around the value 180, it is tricky to
adjust the settings. However, the relative error is
still mostly less than 7 %, which is acceptable. The

sample 5 has a wider standard deviation so even the
results are affected by this fact and the deviation of
the results is bigger than for other samples for all three
methods. In all cases, the measurement was done with
the same sample for all three methods to measure with
the same cuvette and same concentration.

The aim of this measurement is not to denigrate
any of the methods used, but to show their behaviour
under the same conditions. For example, the PDA
seems to be less accurate, but the mean diameters
(D10, D32) are in good agreement with the original
samples, only the final distribution is wider. This
knowledge can be generalised, because all methods
are very precise to determine the mean diameters
(D10, D32), but the description of the distribution is
usually wider. The explanation can come from the
data processing of the raw optical signal. In this paper,
we mention that the reason for the wider distribution
for the photogrammetric method may be coagulated
particles. Despite the effort to avoid the junction of
two or more particles, some “doublets” can appear.
The two tested commercial facilities are using the data
processing without providing the necessary details.

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Sample 1 2 3 4 5 6

Duke standards D10 [µm] 10.1 14.97 20 30.07 39.6 81.4
s [µm] 0.9 0.13 0.2 0.3 3.6 1.5

Photogrammetry

D10 [µm] 10.13 14.15 19.19 29.17 38.30 79.64
s [µm] 0.66 0.42 0.30 0.41 2.67 1.71

D32 [µm] 10.22 14.18 19.20 29.18 38.68 79.71
AE [µm] 0.70 0.94 0.96 1.09 3.22 3.91
RE [%] 6.94 6.25 4.79 3.64 8.13 4.80
N [#] 571 568 487 327 455 102

Laser diffraction

D10 [µm] 9.87 14.62 19.86 29.46 39.08 79.34
s [µm] 0.88 1.47 1.15 2.74 2.95 8.18

D32 [µm] 10.03 17.40 20.72 31.62 39.53 81.23
AE [µm] 0.91 1.51 1.16 2.81 3.00 8.44
RE [%] 9.03 10.09 5.78 9.35 7.58 10.37

PDA

D10 [µm] 9.35 14.00 19.25 29.58 39.55 80.74
s [µm] 1.33 1.18 1.34 1.90 5.40 2.30

D32 [µm] 9.72 14.19 19.43 29.83 40.99 80.87
AE [µm] 1.72 1.98 1.71 2.29 6.14 2.60
RE [%] 17.04 13.21 8.56 7.62 15.51 3.20
N [#] 1 000 1 000 1 000 1 000 1 000 1 000

Table 3. The measurement evaluation.

Sample Dv10 [µm] Dv50 [µm] Dv90 [µm]
7 36.56 60.59 88.36

Table 4. Information on Sample 7 as defined by its
manufacturer.

6. The example of polydisperse
distribution measurement

This chapter introduces an example of the measure-
ment with all three methods. The measured sam-
ple contains sand particles ranging from 15 to 150
micrometres in length with the distribution shown
Table 4. This sample was mixed in the water in the
cuvette. The results are shown in Table 5 and Fig-
ure 13. To prevent sedimentation of the particles in
the corners of the cuvette, it was mixed with a mag-
netic mixer. The phase Doppler anemometry is the
most accurate according to Dv10 and photogramme-
try, and Spraytec is the most accurate according to
Dv50. The Dv90 percentile is distorted by the im-
purities in the cuvette and by the clustering of the
particles.

The analysis of the results has to include all the as-
pects of practical measurement. During the measure-
ment, the homogeneity of the sample in the cuvette
must be ensured by sample mixing, which helps to
avoid the sedimentation of bigger particles. The un-
wanted presence of foreign particles would also affect
the result. The optical measurement is also sensi-
tive to sphericity of the particle, refraction index of
particles, dispersant, and other parts of the optical
measurement chain. The resulting difference between

the declared diameter Dv50 of the polydisperse sam-
ple and the measured value is, for all measurements,
lesser than 5 %. This photogrammetry measurement
was performed according to the data processing men-
tioned above, as well as the PDA and light scattering
measurement. The Sauer mean diameter is listed in
Tab. 5 to compare the results with the same parame-
ter as in previous cases. Unfortunately, the original
polydisperse sample does not have D32 defined by the
manufacturer and an assumption of normal distribu-
tion does not fit well.

7. Conclusion
The in-house photogrammetric method was tuned and
compared with two optical methods, laser diffraction
(Spraytec Malvern) and phase Doppler anemometry
(PDA Dantec Dynamics), for aerosol size measurement.
Six Duke samples with known, mostly monodisperse
size distributions were dosed into a cuvette filled with
filtered and demineralised water, and then evaluated
by the three optical methods. The photogrammetric
method was assessed for different background inten-
sity levels to measure accurately for the non-optimal
measurements of the wider range of real applications.
The results showed that the accuracy of the devel-
oped photogrammetric method was comparable with
other two optical methods. The results indicate that
the measurements of the particles are in very good
agreement for all three methods; the uncertainty of
the measurements was determined. As an example
of the practical measurement, all methods were com-
pared using polydisperse distributions in a sample
with known volumetric percentile diameters.

185



Adam Huněk, Ondřej Bartoš Acta Polytechnica

Sample Dv10 [µm] Dv50 [µm] Dv90 [µm] D32 [µm]
Photogrammetry 40.36 61.93 84.95 61.79
LD – Spraytec 40.05 61.15 89.08 60.98
PDA 37.26 57.44 86.35 56.77

Table 5. Information on Sample 7 as defined by its manufacturer.

Figure 13. The volumetric size distributions of Sample 7.

Maximum effort was devoted to acquiring a clean
sample, the photogrammetric and PDA evaluation
samples may have been affected by impurities in the
cuvette, while the Spraytec measurement was cali-
brated before the dosing of the samples. The effect
of particle binding was suppressed by using a small
amount of surfactant, but some clusters or impurities
can appear. Generally, it can be supposed that the
measurement with the monodispersed and polydis-
perse particles is sufficiently precise for all methods
in the tested range of particles.

The purpose of this paper is not to make a competi-
tion between the optical methods, as all the methods
tested are great and well established, and each of them
has its advantages. However, there is an overlap be-
tween them. There are known examples in which two
methods were used for the same measurement, but
with slightly different results. This has led to unfair
accusations against one of the methods. The purpose
of this paper is to introduce the alternative approach
for processing photogrammetric images and also to
show their results obtained for the measurement, as
similar as possible. The resulting accuracy, in the
ideal case, shows that any of the methods has a sig-
nificant advantage over the calibration measurement
that was performed in this work.

All three methods are reliable and accurate, al-
though it is necessary to understand the advantages
and disadvantages of their data processing chains. De-
spite the simplicity of the advantage of the Spraytec
device, it can be sensitive to parasitic light. The PDA
device is a highly robust point measurement; however,
it might be difficult to correctly setup. The developed
photogrammetric method proved to be sufficiently ac-
curate compared to the other two methods. The main
limitations of this method include the pixel-to-object

ratio, exposure time, flash duration, quality of the
image, and the sphericity of the object. In addition,
the method might not detect low numbers of density
large particles that do, however, prove significant in re-
gard to volumetric size distribution. Eliminating these
disadvantages under certain conditions can result in
a very reliable method for aerosol size measurement.
The use of standard particles yields a valuable data
set that is valuable to other users of each method.

List of symbols
D10 Mean diameter [µm]
D32 Sauter mean diameter [µm]
Dv10 Volumetric 10 percentile diameter [µm]
Dv50 Volumetric 50 percentile diameter [µm]
Dv90 Volumetric 90 percentile diameter [µm]
d Diameter corresponding to the value of distribution

[mm]
Df Volumetric size distribution dimensionless diameter

[-]
s Standard deviation
V Volumetric or mass fraction (normalize)

[Fraction/∆ ln Df ]

Acknowledgements
We gratefully acknowledge the support of the Grant
Agency of the Czech Republic Grant No. 22-28869S.

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	Acta Polytechnica 65(2):177–187, 2025
	1 Introduction
	2 The principle of image analysis methods for aerosol size measurement
	2.1 OTSU segmentation

	3 Optical methods
	3.1 The Phase-Doppler anemometer
	3.2 Laser diffraction
	3.3 The photogrammetric method (shadowgraph)

	4 Calibrating the photogrammetric method
	5 The result of comparing the optical methods using monodisperse particle samples
	6 The example of polydisperse distribution measurement
	7 Conclusion
	List of symbols
	Acknowledgements
	References