# An Optical Approach for the Determination of Droplet Volumes in Nanodispensing

Authors: Kerstin Thurow; Thomas Krüger; Norbert Stoll
Journal: Journal of Automated Methods and Management in Chemistry
 (2009)

---

## Abstract

This paper looks at the use of drop-on-demand technology in automated life science laboratories. One significant feature of the droplets generated is the enormously high uniformity under constant conditions. However, there is also a relatively strong dependency on environmental conditions. Many different kinds of liquids are used in laboratory applications, some with unknown properties in advance. In light of this and the special way in which the droplets are created, there is one major question which needs answering in relation to the use of this technology in the area of laboratory automation: What is the volume of the drops generated? This paper will present a solution which can be applied in practice. Besides the technical implementation demonstrated, further alternatives will also be presented. Ultimately, dosing systems with greater autonomy should result from the optimizations demonstrated in this paper.


---

## Body

## 1. Introduction

Inkjet  dispensing technologies have
an increasing number of applications in chemical and biotechnological
applications with a major focus on drug discovery [1–5]. With the
ability to generate any number of drops with nanodspensing devices, larger
quantities can be generated very precisely. However, drop volume is not a
constant as it depends on the properties of the liquid and the dosing
parameters. In the case of this technology and design, an individual drop has a
volume of between 50–500 pl. There are procedures for
measuring individual drops and methods for measuring dosed quantities in
nanoliters. However, these methods may be based on very complex measurement
technology and/or not allow for real-time measurement of the volume.Thus, the goal of this paper is to
find a procedure for the real-time measurement of the volume of a drop. Finding
a balance between the effort and benefit involved in integrating this into the
existing equipment is to the fore in this, along with practical use in laboratory
automation.Due to the properties of liquids,
such as density, viscosity, and surface tension, different levels of activation
energy must be applied to eject the drops. At the same time, the duration of
the pressure pulse has an important role to play. Liquids will only be pushed
out of the nozzle if the values are aligned. However, this is not all that is
involved in the calibration process. The drops being formed must meet certain
standards in order to ensure high-quality dosing.


## 2. Classical Procedures for
Volume Measurements

Liquid dispensers based on
piezoelectric technology can currently dispense the smallest volumes. The
amount to be dispensed is quantizised in the specific generation of individual
drops with almost identical properties. However, such high reproducibility is
only possible under constant conditions. The drop volume depends on the dosing
parameters, the liquid, and the nozzle used. Therefore, the size of the drops
generated is unknown for each new configuration. However, dosing of large
volumes relies on a defined number of drops with a known volume being
dispensed. Thus, the dosing quantity is the product of the drop volume and
number of drops. Even given larger numbers of drops, measuring the volume is
technically challenging due to the small quantities, in the nanoliter and
microliter ranges.


### 2.1. Analytical Measurement Procedures

There are several methods applicable
for the determination of the volume of a droplet. Usually they are offline
methods which require the dosing of a defined number of drops prior to the analysis.
Conclusions on the volume of an individual drop are arrived at by using the
knowledge of the number of drops, specific additional information depending on
the procedure, and a likewise procedure-specific measured physical property.Volume determination using weight is
the procedure that requires the least effort. The volume can be calculated
using the density of the liquid. A high-precision weighing scale is required
for this method. Disadvantages of this method include the fact that the density
of the substance must be known, and that there is a risk of evaporation. In
respect of increasing the level of automation, the technical realization is in
the realm of the possible. However, due to the limitations, it does not really
represent a viable alternative but could be used as a reference procedure for
the visual procedure presented in this paper [6].Another method for the determination
of the volume is the use of chromatographic procedures. In this procedure, a
substance with a specified volume is used as a reference, and a defined number
of drops are added to it. This mixture of substances can be analyzed using
liquid or gas chromatography. The volume is calculated using the measured
concentration and the known quantity of the reference substance used. The
reference substance must also be dosed with great precision. Furthermore, the
analysis is based on very complex measurement technology [7, 8].Fluorescence measurement is also
based on a concentration measurement. A substance with known fluorescence
properties is added to the wells of a microtiter plate in a test series with an
increasing number of drops. The known ratio of the measured radiation of the
respective fluorescent substance is used to determine the volume. Besides the
limitations mentioned, complex measurement technology is also needed for this
[9].


### 2.2. Real-Time Measurement Procedures from Particle Measurement Technology

Procedures based on optical
instruments for the very precise measurement of generated drops already exist
in the area of particle measurement technology. The measurement technology
facilitates real-time recording; but very complex hardware is required.The spatial filter technology
method, now established in particle and flow measurement technology, involves
the use of cameras with CMOS sensors which, unlike CCD sensors, allow for
individual areas, rows, and even pixels to be read out. The underlying
operational principle is that of lattice diffraction. The lattice is replaced
by a line scan or matrix camera. The lattice constant is then derived from the
size and distance of the individual pixels. If an object moves along a row, a
characteristic signal emerges after the summation due to the alternating
weighting (positive, negative) of the individual pixel signal. The signal is
evaluated on the basis of a frequency analysis. When knowledge of the
properties of the optical system, pixels, readout characteristics, and
evaluation electronics are combined, the speed of the particle can be
calculated [10]. The particle size can be determined if the speed is known. As
the readout cycle has to be significantly faster than the movement of the
measurement object, sampling rates in the MHz range are required. These can be
achieved using CMOS sensors and DSPs for signal processing [11, 12].The laser measurement technology is
a high-resolution procedure from particle measurement technology based on the
illumination of a drop with a laser. On penetrating the liquid, refraction
occurs in accordance with the properties of the liquid. These refractions are
captured by a camera. Small light spots can be seen in the focused image. By
using a defocused camera, there is an overlapping of this spots. The characteristic
of the overlap of the two points results from the refraction index of the
liquid. By counting the fringes in the defocused picture, the drop diameter can
be determined.The level of precision in
determining the drop diameter is up to 1μm. However, the drops have to have
a spherical shape. The procedure is only suitable for measuring size. There are
other procedures which rely on this measurement principle. They are based on
more extensive technology but also deliver more precise and enhanced results.
Another advantage of this procedure is that it can be applied without there
being any link to the control of the dosing head. This means that no
information is required about the dosing or stroboscope parameters. By dosing
using this device, volume can be measured. However, no information regarding
other criteria in the dosing procedure can be obtained by using this procedure.The procedures based on particle
measurement technology are suitable for both very precise real-time measurement
of the drop volume and also automated implementation. However, very complex
measurement technology is needed for them, and the expense required to
integrate them into commercial equipment may not be justifiable in certain circumstances.


## 2.1. Analytical Measurement Procedures

There are several methods applicable
for the determination of the volume of a droplet. Usually they are offline
methods which require the dosing of a defined number of drops prior to the analysis.
Conclusions on the volume of an individual drop are arrived at by using the
knowledge of the number of drops, specific additional information depending on
the procedure, and a likewise procedure-specific measured physical property.Volume determination using weight is
the procedure that requires the least effort. The volume can be calculated
using the density of the liquid. A high-precision weighing scale is required
for this method. Disadvantages of this method include the fact that the density
of the substance must be known, and that there is a risk of evaporation. In
respect of increasing the level of automation, the technical realization is in
the realm of the possible. However, due to the limitations, it does not really
represent a viable alternative but could be used as a reference procedure for
the visual procedure presented in this paper [6].Another method for the determination
of the volume is the use of chromatographic procedures. In this procedure, a
substance with a specified volume is used as a reference, and a defined number
of drops are added to it. This mixture of substances can be analyzed using
liquid or gas chromatography. The volume is calculated using the measured
concentration and the known quantity of the reference substance used. The
reference substance must also be dosed with great precision. Furthermore, the
analysis is based on very complex measurement technology [7, 8].Fluorescence measurement is also
based on a concentration measurement. A substance with known fluorescence
properties is added to the wells of a microtiter plate in a test series with an
increasing number of drops. The known ratio of the measured radiation of the
respective fluorescent substance is used to determine the volume. Besides the
limitations mentioned, complex measurement technology is also needed for this
[9].


## 2.2. Real-Time Measurement Procedures from Particle Measurement Technology

Procedures based on optical
instruments for the very precise measurement of generated drops already exist
in the area of particle measurement technology. The measurement technology
facilitates real-time recording; but very complex hardware is required.The spatial filter technology
method, now established in particle and flow measurement technology, involves
the use of cameras with CMOS sensors which, unlike CCD sensors, allow for
individual areas, rows, and even pixels to be read out. The underlying
operational principle is that of lattice diffraction. The lattice is replaced
by a line scan or matrix camera. The lattice constant is then derived from the
size and distance of the individual pixels. If an object moves along a row, a
characteristic signal emerges after the summation due to the alternating
weighting (positive, negative) of the individual pixel signal. The signal is
evaluated on the basis of a frequency analysis. When knowledge of the
properties of the optical system, pixels, readout characteristics, and
evaluation electronics are combined, the speed of the particle can be
calculated [10]. The particle size can be determined if the speed is known. As
the readout cycle has to be significantly faster than the movement of the
measurement object, sampling rates in the MHz range are required. These can be
achieved using CMOS sensors and DSPs for signal processing [11, 12].The laser measurement technology is
a high-resolution procedure from particle measurement technology based on the
illumination of a drop with a laser. On penetrating the liquid, refraction
occurs in accordance with the properties of the liquid. These refractions are
captured by a camera. Small light spots can be seen in the focused image. By
using a defocused camera, there is an overlapping of this spots. The characteristic
of the overlap of the two points results from the refraction index of the
liquid. By counting the fringes in the defocused picture, the drop diameter can
be determined.The level of precision in
determining the drop diameter is up to 1μm. However, the drops have to have
a spherical shape. The procedure is only suitable for measuring size. There are
other procedures which rely on this measurement principle. They are based on
more extensive technology but also deliver more precise and enhanced results.
Another advantage of this procedure is that it can be applied without there
being any link to the control of the dosing head. This means that no
information is required about the dosing or stroboscope parameters. By dosing
using this device, volume can be measured. However, no information regarding
other criteria in the dosing procedure can be obtained by using this procedure.The procedures based on particle
measurement technology are suitable for both very precise real-time measurement
of the drop volume and also automated implementation. However, very complex
measurement technology is needed for them, and the expense required to
integrate them into commercial equipment may not be justifiable in certain circumstances.


## 3. Analysis of the Dispensing
of a Drop

Capturing the dosing procedure was
the basis for all further steps. This aim can be achieved using various
technologies. These range from different models of simple light barriers and
cameras to laser-guided measuring procedures. With regard to all measurement
methods, practical applicability was of particular interest and led to a
compromise between the resolution of the procedure and the integration
complexity. Furthermore, the procedure had to be digitalized for automated
evaluation.The drops generated had an average
volume of approximately 250 pl (∅ 78 μm) and flew with a velocity of about
2 m/s.


### 3.1. Using Measurement Technology to Capture the Drop Flight

Visualization is usually implemented
in most appliances with the aid of a stroboscope camera system. This is already
of great benefit in the manual evaluation of drop formation. The camera image
can be imported into the dosing software using a frame grabber or USB camera,
for example. Some of the dosing robot’s control applications already applied
simple image processing algorithms to monitor drop formation.


#### 3.1.1. Visualization Using a Stroboscope and Camera

The nanodoser used in the tests
here, S-5 from Scion, has a stroboscope camera system and thus the technical requirements
for monitoring drop formation. The existing hardware is made up of a camera
with an enlarging lens and an LED stroboscope. The stroboscope was needed as
the drops move too quickly to  get  an individual image of them with a
conventional camera. The synchronous triggering of the stroboscope with the
activation from the piezoelectric crystal provided an image of overlapping
drops in continuous operation. In addition to this, it was possible to change
the delay between the rising flanks of the piezoelectric signal and the
activation of the stroboscope. By doing so, the drops could be visualized at
any point in time after being dispensed [13–15]. (See Figure 1.)Figure 1
Overview of the nozzle’s visualisation and control system.In  order to get an idea of the temporal progress of the drop ejection, the
stroboscope flash delay was continuously increased from zero upwards. By doing
so, still images of the continuous process could be generated at different
points in time.


#### 3.1.2. Optical Component Parameters

The lens with aperture, intermediate
rings, and camera sensor are the most important parts of the system. It was
possible to calculate selected statistical values on the basis of this setup [16, 17].β Reproduction Scale
This depends
in particular  on the lens and its focal length and position in the optical
system;
(1)β=lf,where l: extension length and f: focal length.
For the lens used,
(2)β=lf=llens+ltubeflens=35mm+30mm12mm=6512=5.42¯¯.Pixel↔micrometer Conversion Factor
The
reproduction-scale data from the individual CCD sensor and the resolution of
the camera can be used to determine this factor.  (See Table1.)
Thus, 768 pixels are the maximum vertical
image size possible ofBvertical=6451μm. The object size can be calculated
using the reproduction  scale and the β=B/G formula:
(3)G=Bβ=Bhorizontalβ=6451μm5.42=1191μm¯¯. For the individual pixels, this
resulted in
(4)GPa=1191μm768pixels=1.55μm/pixels¯¯. Analogous to this, the width of the
image was vertically calculated using
(5)G=Bβ=Bverticalβ=4841μm5.42=894μm¯¯. The CCD sensor consisted of 576 rows.
Thus, for the conversion in the vertical direction, we get
(6)GPa=894μm576pixels=1.55μm/pixels¯¯.Table 1
Technical data from the
camera’s CCD sensor.
Number of pixelsPixel sizeSensor size(Pa)(Pg)(Pa∗Pg)Horizontal7688.4μm6451μmVertical4949.8μm4841μmDepth of Field of the System
This
parameter describes the space between two planes which are vertical to the
optical axis. Focusing is optimal in the region between the planes. The
distance between these planes depends on the optical components mentioned and
the f-number. The f-number is defined and standardized in accordance with DIN
4522 and describes the ratio between the focal length and the diameter of the
lens’ entrance pupil:
(7)κ=fD,where f: focal length
and D: diameter of the entrance pupil.
Further requirements, also
calculable from the system data, are the dispersion circle diameter and the
hyperfocal distance. The dispersion  circle diameter is determined using a
generally accepted approximation formula:(8)Z=d1730from[112],where d: diagonal of the camera’s CCD sensor.
For the apparatus used here, we get(9)Z=d1730=Bhorizontal2+Bvertical21730=(6451μm)2+(4841μm)21730=4.7μm.With a dispersion circle diameter Z, we can calculate the hyperfocal distance dh:(10)dh=f2Z⋅κ,where f: focal length of the lens.
The near and far points, the limits of the depth of field, were
calculated usingdn=g⋅dh/(dh+(g−f)) for the near point, df=g⋅dh/(dh−(g−f)) for the far point.
The difference between the far
and near points is the region of optimal focus. The values calculated for
selected f-numbers for the lens used are shown in Table2. The favoured
aperture setting for the measurements is κ=4.
Information on the depth of field
increases in significance when combined with the determination of the focusing.
With these two statistical values, the three-dimensional trajectory of the drop
can be determined.Table 2
Depths of field for particularf-numbers.
κ=2κ=4κ=8Near point17.555μm17.549μm17.536μmFar point17.568μm17.574μm17.587μmDepth of field12μm25μm51μm


### 3.2. Algorithm for Extracting the Image Data

With the aid of image processing
algorithms, the drop data can be extracted from the image generated by the
visualisation system described. In order to be in a position to capture the
drops even given insufficient focusing or unfavourable lighting conditions, the
algorithms must be designed to be robust. This procedure is described in the
following sections. Optimal focusing on the drop is a precondition to actually
determining the drop parameters [18].Four steps are necessary for
extracting the image data.


#### 3.2.1. Isolation of the Region of Interest

This step establishes which region
of the image should be inspected for a drop. This is statically determined. It
is possible to do this as the positioning of the nozzle in front of the camera
is defined and carried out in advance. Another reason for the limitation is
that the drop is usually dispensed vertically. Reducing the image region to be analyzed
also reduces the computational effort required. For these reasons, the region
of interest was limited to the middle third of the lower half of the image.


#### 3.2.2. Creation of the Binary Image

A binary image is the basis for
further algorithms for determining the properties of the drop. The black and
white images in
this case consist
of pixel values of 0 for black and 255 for white. A threshold is needed for the
division. It is calculated dynamically from the mean value of the grey-scale
values in the image. The fact that the drops displayed are always darker than
the background is used for this. The actual threshold is calculated by
multiplying the mean value by the correction factor 0.9 for a robust
measurement. (See Figure2.)Figure 2
Generation of the binary image from the region of
interest.Following the conversion, the image
consists of a white background (TRUE or 255) and the drop (FALSE or 0).
However, this setup is disadvantageous for further calculations as the drop is
the object of interest. Therefore, a negative is generated after the
conversion.


#### 3.2.3. Preparation of the Drop Contour

Morphological Opening
Due to the type of visualization and
associated blurred edge, the binary image was morphologically opened with a
circle. By doing so, the edges of the remaining contour were smoothed, and
individual interfering pixels which had remained were eliminated [19, 20].Deleting Objects at the Edge
This step
is necessary to remove unwanted contours at the edge of the image, a result of
unfavourable light conditions, and to avoid measurement errors caused by drops
that have only been partially mapped. The first point is secondary in
importance given good lighting conditions. However, the second aspect is
significant once the drop image is located at the edge of the image during the
measurement. If the drop is measured despite touching the edge, this will lead
to considerable measurement errors if only a fraction of the true size of the
image is within the region captured.Filtering out Unwanted Contours
Individual
contours and those remaining from the preceding steps which do not represent
drops must be filtered out. These contours can be caused by luminance noise,
dust on the lens, and the like. The principle approach in this is the
systematic eradication of all remaining contours. The area of the contour is
the criterion for elimination. Connected areas bigger than 300 pixels should be
kept. The threshold for an area is a matter of experience. This procedure
removes almost all interfering contours but still permits satellite drop
detection.Filling of Holes
Usually, light focused in the centre of the drop is brighter than at the edge.
Therefore, the drop contour has a hole in the middle following inversion.
Filling is necessary for further calculations and was carried out using an
algorithm in the image processing library. This was systematically applied to
the remaining contours in the image. The result of this operation was the basis
for all further procedures used to gain information on the drop.


#### 3.2.4. Projecting the Drop Detection into the Camera Image

The drop detected was superimposed
onto the original image in order to get an impression of the actual capturing
of the drop image. In addition to this, the edge line of the drop contour from
the final binary image was laid in a visibly light tone over the captured
frame.This
illustration of the results of the image processing is particularly important
in development. The developer or user can monitor the extent to which the drop
detection corresponds with the reality. Although this is a subjective finding,
individual parameters, such as the conversion threshold, can be aligned in the
binary image.


### 3.3. Volume Calculation from the Drop Image

There are several ways in which a
three-dimensional body can be calculated from a two-dimensional drop contour.
The radius or the 3 axes of the contour can be used as a basis if a spherical
shape or ellipsoid is assumed. Another method, and the one used here, is the
procedure shown in Figure3. However, both calculations rely on the assumption
that the drop is rotation-symmetric in the direction of flight.Figure 3
Principle
by which the drop volume was calculated.The volume of a slice is(11)Vn=πrn2⋅d,where d: unit thickness
of 1 pixel
and r: radius of
the slice/width of the strip.The volume of the rotational body of half of the drop is(12)Vdrop=∑n=1LVn=∑n=1Lπrn2⋅d,where d; unit thickness
of 1 pixel,
L: length of
the drop, and
r: radius of
the slice/width of the strip.The contour is cut into strips in
order to calculate the volume of the rotational body of the respective half.
These strips run vertically to the axis of symmetry and are each one pixel in
thickness. Slices of equal thickness are then calculated from these strips.
This process is carried out for each strip of the respective half in sequence.
Following this, the volumes of the individual slices are added together. The
result of this sum corresponds to the volume of the drop. This process is
carried out in the same way for the other half of the drop. The mean value from
both volumes is taken to be the final volume.Another approximation can be made by
calculating a sphere or ellipsoid. If we assume a sphere, the width of the
contour is equal to the diameter. Likewise, the width and height of the drop
contour provide two of the three axes required. The third axis is the width,
assuming rotational symmetry. However, the disadvantage of these methods, as
opposed to the division into slices, is that there is always imprecision in
respect of the shape deviation. This phenomenon also exists with the strip
method but does not play as comparatively great of a role.The contours, their centroids, and
the data of the “bounding rectangle” are needed to calculate the volume. With
the aid of the “bounding rectangle,” the limits of the contour and the
calculation can be determined. The centroid is used to establish the vertical
axis of symmetry.The volume calculated was in units
of voxels (pixel3). For further use, this was converted into picoliters
with the aid of the optical system calculations, with one voxel corresponding
to a cube with an edge length of 1.55 μm.


### 3.4. Influences on the Determination of the Droplet Volume

Different conditions have an impact
on the determination of the precise droplet volume.


#### 3.4.1. Influence of Different Drop Shapes

There
is a certain tolerance with respect to different drop shapes when calculating
drop volumes according to the integration procedure. However, there can be
large fluctuations in the volumes calculated if there are extreme contortions
in the drop shape. It may not be appropriate to assume rotationally symmetric
drops in some cases. The drop shape can fluctuate strongly at the beginning of
the flight phase in particular due to the forces which arise during release,
and symmetry is not given at that time.One way of circumventing this
interference effect is to only capture the drop after it has gone a certain
distance. The drop shape becomes increasingly stable and strives for a
perfectly spherical shape. The disadvantage of this is that the drop has to
travel a distance of approximately 2 mm. The recording of the drop at another
position or at another time requires additional effort as the dosing head has
to be put up high, and the delay in the LED stroboscope has to be adjusted.A second method involves averaging
the volume values measured across the drop's entire flight phase. When applying
this method, the nozzle position in front of the camera does not need to be
changed. This procedure was used for the volume measurements carried out here.
A third alternative, carrying out the volume measurement at a defined point, is
possible with the help of evaluation of the circularity of the drop. For
example, this could be the stroboscope delay/flight position at which the drop
has the greatest circularity in the trackable trajectory. Both the strip method
and the calculation of the spherical volume can be used in this.


#### 3.4.2. Enlarged Appearance of the Drops

Using a frequency of 500 Hz and a
stroboscope light duration of 5 microseconds, a volume 1.17 times greater
than the weighing was arrived at with the measurements from the procedure based
on image processing. This behavior is a consequence of the visualization principle.
The camera used did not have a fast shutter or triggering. Therefore, the
duration of the stroboscope flash was crucial for the size of the appearance of
the drops.


#### 3.4.3. Frequency Dependency of the Correction Factor

When the measurements were carried
out at different frequencies, the systematic error increased as can be seen in Figure4.Figure 4
Frequency
dependence of the dispensed volume.The frame rate of the camera used, a
Sony XC-ES 50, is 30 images per second. The camera was not triggered via the
stroboscope signal. The shortest possible shutter speed was 100 microseconds,
far longer than the light duration of the LED stroboscope. The number of drops
overlapping in the picture depends on the dosing frequency [21].As the number of overlapping drops
in an image increases, the effect described below has a greater influence. The
distance between the drops in the droplet jet generated can vary periodically.
As the frequency increases, the drops appear much larger than they would
otherwise. However, this phenomenon does not always appear and is not
predictable. It was not possible to detect it with the methods shown here. (See Table3.)Table 3
Number of
overlapping drops in the image depending on the drop rate.
Drop rate (Hz)400500600800100015002000300040005000Overlapping drops13162026335066100133166The measurements taken show that
the systematic error increases sharply in frequencies above 800 Hz because of
this effect. Conditional on the fact that the fluctuation in the drop distance
cannot be detected with the procedures used here, it was not advisable to
measure the volume with the procedures shown at higher frequencies.


#### 3.4.4. Uncertainty in Edge Detection

Besides the uncertainties in the
recording technology, the image processing procedure can also influence the
measurement error. The edge detection has a crucial weighting. The slices of
which the drop volume is comprised were calculated on the basis of this edge
data. Using the example of the calculation of a sphere, Table4 illustrates the
degree to which the incorrect detection of the radius can affect the entire
volume.Table 4
Estimate of the difference in volume if the edge is
incorrectly detected.
Drop volumeDiameter (rounded)Difference in volume witha−1
diameterDifference in volume witha+1
diameter100 pl37 pixels7.9%8.3%150 pl43 pixels6.8%7.1%200 pl47 pixels6.2%6.5%250 pl50 pixels5.9%6.1%300 pl54 pixels5.5%5.7%350 pl56 pixels5.3%5.5%400 pl59 pixels5.0%5.2%450 pl61 pixels4.8%5.0%500 pl64 pixels4.6%4.8%Table 5
Composition of the parameters of the stroboscope camera system for the standardized
measurement.
CameraCamera frame rate30 images/s (full frame)Minimal shutter speed100μs (not used)Triggering and synchronizationnoneControl pulse of the piezoelectric
elementDosing frequency500 HzStroboscopeStroboscope frequency500 HzLight duration of the LED stroboscope5μsLensConversion factor pixel:μm1:1.55


#### 3.4.5. Illumination from the LED Stroboscope

The environmental light is another
influencing factor. It is hard to take all fluctuations into account. In order
to counter the effects of external light influences, a box is recommended. The
entire unit was covered by a nonlight transparent box for the tests carried out
here.The light needed was generated by
the visualization system itself. The light duration and frequency of the LED
stroboscope were thus primarily responsible for the brightness of the image.As the
brightness and thereby changed contrast ratios in the image influence the drop
detection procedure, it is recommended that measurements should be taken with the
most constant illumination possible. The ratio of the grey-scale values in the
background to those of the drop is reduced at both high and also low
intensities of the light source. The detection procedure fails in these limit
ranges despite a certain robustness in the edge detection. However, the
brightness must be standardized to ensure measurements with the lowest
influence of error possible. Therefore, it is recommended that constant
aperture, camera settings, and constant stroboscope parameters to be used when
taking the measurements.


## 3.1. Using Measurement Technology to Capture the Drop Flight

Visualization is usually implemented
in most appliances with the aid of a stroboscope camera system. This is already
of great benefit in the manual evaluation of drop formation. The camera image
can be imported into the dosing software using a frame grabber or USB camera,
for example. Some of the dosing robot’s control applications already applied
simple image processing algorithms to monitor drop formation.


### 3.1.1. Visualization Using a Stroboscope and Camera

The nanodoser used in the tests
here, S-5 from Scion, has a stroboscope camera system and thus the technical requirements
for monitoring drop formation. The existing hardware is made up of a camera
with an enlarging lens and an LED stroboscope. The stroboscope was needed as
the drops move too quickly to  get  an individual image of them with a
conventional camera. The synchronous triggering of the stroboscope with the
activation from the piezoelectric crystal provided an image of overlapping
drops in continuous operation. In addition to this, it was possible to change
the delay between the rising flanks of the piezoelectric signal and the
activation of the stroboscope. By doing so, the drops could be visualized at
any point in time after being dispensed [13–15]. (See Figure 1.)Figure 1
Overview of the nozzle’s visualisation and control system.In  order to get an idea of the temporal progress of the drop ejection, the
stroboscope flash delay was continuously increased from zero upwards. By doing
so, still images of the continuous process could be generated at different
points in time.


### 3.1.2. Optical Component Parameters

The lens with aperture, intermediate
rings, and camera sensor are the most important parts of the system. It was
possible to calculate selected statistical values on the basis of this setup [16, 17].β Reproduction Scale
This depends
in particular  on the lens and its focal length and position in the optical
system;
(1)β=lf,where l: extension length and f: focal length.
For the lens used,
(2)β=lf=llens+ltubeflens=35mm+30mm12mm=6512=5.42¯¯.Pixel↔micrometer Conversion Factor
The
reproduction-scale data from the individual CCD sensor and the resolution of
the camera can be used to determine this factor.  (See Table1.)
Thus, 768 pixels are the maximum vertical
image size possible ofBvertical=6451μm. The object size can be calculated
using the reproduction  scale and the β=B/G formula:
(3)G=Bβ=Bhorizontalβ=6451μm5.42=1191μm¯¯. For the individual pixels, this
resulted in
(4)GPa=1191μm768pixels=1.55μm/pixels¯¯. Analogous to this, the width of the
image was vertically calculated using
(5)G=Bβ=Bverticalβ=4841μm5.42=894μm¯¯. The CCD sensor consisted of 576 rows.
Thus, for the conversion in the vertical direction, we get
(6)GPa=894μm576pixels=1.55μm/pixels¯¯.Table 1
Technical data from the
camera’s CCD sensor.
Number of pixelsPixel sizeSensor size(Pa)(Pg)(Pa∗Pg)Horizontal7688.4μm6451μmVertical4949.8μm4841μmDepth of Field of the System
This
parameter describes the space between two planes which are vertical to the
optical axis. Focusing is optimal in the region between the planes. The
distance between these planes depends on the optical components mentioned and
the f-number. The f-number is defined and standardized in accordance with DIN
4522 and describes the ratio between the focal length and the diameter of the
lens’ entrance pupil:
(7)κ=fD,where f: focal length
and D: diameter of the entrance pupil.
Further requirements, also
calculable from the system data, are the dispersion circle diameter and the
hyperfocal distance. The dispersion  circle diameter is determined using a
generally accepted approximation formula:(8)Z=d1730from[112],where d: diagonal of the camera’s CCD sensor.
For the apparatus used here, we get(9)Z=d1730=Bhorizontal2+Bvertical21730=(6451μm)2+(4841μm)21730=4.7μm.With a dispersion circle diameter Z, we can calculate the hyperfocal distance dh:(10)dh=f2Z⋅κ,where f: focal length of the lens.
The near and far points, the limits of the depth of field, were
calculated usingdn=g⋅dh/(dh+(g−f)) for the near point, df=g⋅dh/(dh−(g−f)) for the far point.
The difference between the far
and near points is the region of optimal focus. The values calculated for
selected f-numbers for the lens used are shown in Table2. The favoured
aperture setting for the measurements is κ=4.
Information on the depth of field
increases in significance when combined with the determination of the focusing.
With these two statistical values, the three-dimensional trajectory of the drop
can be determined.Table 2
Depths of field for particularf-numbers.
κ=2κ=4κ=8Near point17.555μm17.549μm17.536μmFar point17.568μm17.574μm17.587μmDepth of field12μm25μm51μm


## 3.1.1. Visualization Using a Stroboscope and Camera

The nanodoser used in the tests
here, S-5 from Scion, has a stroboscope camera system and thus the technical requirements
for monitoring drop formation. The existing hardware is made up of a camera
with an enlarging lens and an LED stroboscope. The stroboscope was needed as
the drops move too quickly to  get  an individual image of them with a
conventional camera. The synchronous triggering of the stroboscope with the
activation from the piezoelectric crystal provided an image of overlapping
drops in continuous operation. In addition to this, it was possible to change
the delay between the rising flanks of the piezoelectric signal and the
activation of the stroboscope. By doing so, the drops could be visualized at
any point in time after being dispensed [13–15]. (See Figure 1.)Figure 1
Overview of the nozzle’s visualisation and control system.In  order to get an idea of the temporal progress of the drop ejection, the
stroboscope flash delay was continuously increased from zero upwards. By doing
so, still images of the continuous process could be generated at different
points in time.


## 3.1.2. Optical Component Parameters

The lens with aperture, intermediate
rings, and camera sensor are the most important parts of the system. It was
possible to calculate selected statistical values on the basis of this setup [16, 17].β Reproduction Scale
This depends
in particular  on the lens and its focal length and position in the optical
system;
(1)β=lf,where l: extension length and f: focal length.
For the lens used,
(2)β=lf=llens+ltubeflens=35mm+30mm12mm=6512=5.42¯¯.Pixel↔micrometer Conversion Factor
The
reproduction-scale data from the individual CCD sensor and the resolution of
the camera can be used to determine this factor.  (See Table1.)
Thus, 768 pixels are the maximum vertical
image size possible ofBvertical=6451μm. The object size can be calculated
using the reproduction  scale and the β=B/G formula:
(3)G=Bβ=Bhorizontalβ=6451μm5.42=1191μm¯¯. For the individual pixels, this
resulted in
(4)GPa=1191μm768pixels=1.55μm/pixels¯¯. Analogous to this, the width of the
image was vertically calculated using
(5)G=Bβ=Bverticalβ=4841μm5.42=894μm¯¯. The CCD sensor consisted of 576 rows.
Thus, for the conversion in the vertical direction, we get
(6)GPa=894μm576pixels=1.55μm/pixels¯¯.Table 1
Technical data from the
camera’s CCD sensor.
Number of pixelsPixel sizeSensor size(Pa)(Pg)(Pa∗Pg)Horizontal7688.4μm6451μmVertical4949.8μm4841μmDepth of Field of the System
This
parameter describes the space between two planes which are vertical to the
optical axis. Focusing is optimal in the region between the planes. The
distance between these planes depends on the optical components mentioned and
the f-number. The f-number is defined and standardized in accordance with DIN
4522 and describes the ratio between the focal length and the diameter of the
lens’ entrance pupil:
(7)κ=fD,where f: focal length
and D: diameter of the entrance pupil.
Further requirements, also
calculable from the system data, are the dispersion circle diameter and the
hyperfocal distance. The dispersion  circle diameter is determined using a
generally accepted approximation formula:(8)Z=d1730from[112],where d: diagonal of the camera’s CCD sensor.
For the apparatus used here, we get(9)Z=d1730=Bhorizontal2+Bvertical21730=(6451μm)2+(4841μm)21730=4.7μm.With a dispersion circle diameter Z, we can calculate the hyperfocal distance dh:(10)dh=f2Z⋅κ,where f: focal length of the lens.
The near and far points, the limits of the depth of field, were
calculated usingdn=g⋅dh/(dh+(g−f)) for the near point, df=g⋅dh/(dh−(g−f)) for the far point.
The difference between the far
and near points is the region of optimal focus. The values calculated for
selected f-numbers for the lens used are shown in Table2. The favoured
aperture setting for the measurements is κ=4.
Information on the depth of field
increases in significance when combined with the determination of the focusing.
With these two statistical values, the three-dimensional trajectory of the drop
can be determined.Table 2
Depths of field for particularf-numbers.
κ=2κ=4κ=8Near point17.555μm17.549μm17.536μmFar point17.568μm17.574μm17.587μmDepth of field12μm25μm51μm


## 3.2. Algorithm for Extracting the Image Data

With the aid of image processing
algorithms, the drop data can be extracted from the image generated by the
visualisation system described. In order to be in a position to capture the
drops even given insufficient focusing or unfavourable lighting conditions, the
algorithms must be designed to be robust. This procedure is described in the
following sections. Optimal focusing on the drop is a precondition to actually
determining the drop parameters [18].Four steps are necessary for
extracting the image data.


### 3.2.1. Isolation of the Region of Interest

This step establishes which region
of the image should be inspected for a drop. This is statically determined. It
is possible to do this as the positioning of the nozzle in front of the camera
is defined and carried out in advance. Another reason for the limitation is
that the drop is usually dispensed vertically. Reducing the image region to be analyzed
also reduces the computational effort required. For these reasons, the region
of interest was limited to the middle third of the lower half of the image.


### 3.2.2. Creation of the Binary Image

A binary image is the basis for
further algorithms for determining the properties of the drop. The black and
white images in
this case consist
of pixel values of 0 for black and 255 for white. A threshold is needed for the
division. It is calculated dynamically from the mean value of the grey-scale
values in the image. The fact that the drops displayed are always darker than
the background is used for this. The actual threshold is calculated by
multiplying the mean value by the correction factor 0.9 for a robust
measurement. (See Figure2.)Figure 2
Generation of the binary image from the region of
interest.Following the conversion, the image
consists of a white background (TRUE or 255) and the drop (FALSE or 0).
However, this setup is disadvantageous for further calculations as the drop is
the object of interest. Therefore, a negative is generated after the
conversion.


### 3.2.3. Preparation of the Drop Contour

Morphological Opening
Due to the type of visualization and
associated blurred edge, the binary image was morphologically opened with a
circle. By doing so, the edges of the remaining contour were smoothed, and
individual interfering pixels which had remained were eliminated [19, 20].Deleting Objects at the Edge
This step
is necessary to remove unwanted contours at the edge of the image, a result of
unfavourable light conditions, and to avoid measurement errors caused by drops
that have only been partially mapped. The first point is secondary in
importance given good lighting conditions. However, the second aspect is
significant once the drop image is located at the edge of the image during the
measurement. If the drop is measured despite touching the edge, this will lead
to considerable measurement errors if only a fraction of the true size of the
image is within the region captured.Filtering out Unwanted Contours
Individual
contours and those remaining from the preceding steps which do not represent
drops must be filtered out. These contours can be caused by luminance noise,
dust on the lens, and the like. The principle approach in this is the
systematic eradication of all remaining contours. The area of the contour is
the criterion for elimination. Connected areas bigger than 300 pixels should be
kept. The threshold for an area is a matter of experience. This procedure
removes almost all interfering contours but still permits satellite drop
detection.Filling of Holes
Usually, light focused in the centre of the drop is brighter than at the edge.
Therefore, the drop contour has a hole in the middle following inversion.
Filling is necessary for further calculations and was carried out using an
algorithm in the image processing library. This was systematically applied to
the remaining contours in the image. The result of this operation was the basis
for all further procedures used to gain information on the drop.


### 3.2.4. Projecting the Drop Detection into the Camera Image

The drop detected was superimposed
onto the original image in order to get an impression of the actual capturing
of the drop image. In addition to this, the edge line of the drop contour from
the final binary image was laid in a visibly light tone over the captured
frame.This
illustration of the results of the image processing is particularly important
in development. The developer or user can monitor the extent to which the drop
detection corresponds with the reality. Although this is a subjective finding,
individual parameters, such as the conversion threshold, can be aligned in the
binary image.


## 3.2.1. Isolation of the Region of Interest

This step establishes which region
of the image should be inspected for a drop. This is statically determined. It
is possible to do this as the positioning of the nozzle in front of the camera
is defined and carried out in advance. Another reason for the limitation is
that the drop is usually dispensed vertically. Reducing the image region to be analyzed
also reduces the computational effort required. For these reasons, the region
of interest was limited to the middle third of the lower half of the image.


## 3.2.2. Creation of the Binary Image

A binary image is the basis for
further algorithms for determining the properties of the drop. The black and
white images in
this case consist
of pixel values of 0 for black and 255 for white. A threshold is needed for the
division. It is calculated dynamically from the mean value of the grey-scale
values in the image. The fact that the drops displayed are always darker than
the background is used for this. The actual threshold is calculated by
multiplying the mean value by the correction factor 0.9 for a robust
measurement. (See Figure2.)Figure 2
Generation of the binary image from the region of
interest.Following the conversion, the image
consists of a white background (TRUE or 255) and the drop (FALSE or 0).
However, this setup is disadvantageous for further calculations as the drop is
the object of interest. Therefore, a negative is generated after the
conversion.


## 3.2.3. Preparation of the Drop Contour

Morphological Opening
Due to the type of visualization and
associated blurred edge, the binary image was morphologically opened with a
circle. By doing so, the edges of the remaining contour were smoothed, and
individual interfering pixels which had remained were eliminated [19, 20].Deleting Objects at the Edge
This step
is necessary to remove unwanted contours at the edge of the image, a result of
unfavourable light conditions, and to avoid measurement errors caused by drops
that have only been partially mapped. The first point is secondary in
importance given good lighting conditions. However, the second aspect is
significant once the drop image is located at the edge of the image during the
measurement. If the drop is measured despite touching the edge, this will lead
to considerable measurement errors if only a fraction of the true size of the
image is within the region captured.Filtering out Unwanted Contours
Individual
contours and those remaining from the preceding steps which do not represent
drops must be filtered out. These contours can be caused by luminance noise,
dust on the lens, and the like. The principle approach in this is the
systematic eradication of all remaining contours. The area of the contour is
the criterion for elimination. Connected areas bigger than 300 pixels should be
kept. The threshold for an area is a matter of experience. This procedure
removes almost all interfering contours but still permits satellite drop
detection.Filling of Holes
Usually, light focused in the centre of the drop is brighter than at the edge.
Therefore, the drop contour has a hole in the middle following inversion.
Filling is necessary for further calculations and was carried out using an
algorithm in the image processing library. This was systematically applied to
the remaining contours in the image. The result of this operation was the basis
for all further procedures used to gain information on the drop.


## 3.2.4. Projecting the Drop Detection into the Camera Image

The drop detected was superimposed
onto the original image in order to get an impression of the actual capturing
of the drop image. In addition to this, the edge line of the drop contour from
the final binary image was laid in a visibly light tone over the captured
frame.This
illustration of the results of the image processing is particularly important
in development. The developer or user can monitor the extent to which the drop
detection corresponds with the reality. Although this is a subjective finding,
individual parameters, such as the conversion threshold, can be aligned in the
binary image.


## 3.3. Volume Calculation from the Drop Image

There are several ways in which a
three-dimensional body can be calculated from a two-dimensional drop contour.
The radius or the 3 axes of the contour can be used as a basis if a spherical
shape or ellipsoid is assumed. Another method, and the one used here, is the
procedure shown in Figure3. However, both calculations rely on the assumption
that the drop is rotation-symmetric in the direction of flight.Figure 3
Principle
by which the drop volume was calculated.The volume of a slice is(11)Vn=πrn2⋅d,where d: unit thickness
of 1 pixel
and r: radius of
the slice/width of the strip.The volume of the rotational body of half of the drop is(12)Vdrop=∑n=1LVn=∑n=1Lπrn2⋅d,where d; unit thickness
of 1 pixel,
L: length of
the drop, and
r: radius of
the slice/width of the strip.The contour is cut into strips in
order to calculate the volume of the rotational body of the respective half.
These strips run vertically to the axis of symmetry and are each one pixel in
thickness. Slices of equal thickness are then calculated from these strips.
This process is carried out for each strip of the respective half in sequence.
Following this, the volumes of the individual slices are added together. The
result of this sum corresponds to the volume of the drop. This process is
carried out in the same way for the other half of the drop. The mean value from
both volumes is taken to be the final volume.Another approximation can be made by
calculating a sphere or ellipsoid. If we assume a sphere, the width of the
contour is equal to the diameter. Likewise, the width and height of the drop
contour provide two of the three axes required. The third axis is the width,
assuming rotational symmetry. However, the disadvantage of these methods, as
opposed to the division into slices, is that there is always imprecision in
respect of the shape deviation. This phenomenon also exists with the strip
method but does not play as comparatively great of a role.The contours, their centroids, and
the data of the “bounding rectangle” are needed to calculate the volume. With
the aid of the “bounding rectangle,” the limits of the contour and the
calculation can be determined. The centroid is used to establish the vertical
axis of symmetry.The volume calculated was in units
of voxels (pixel3). For further use, this was converted into picoliters
with the aid of the optical system calculations, with one voxel corresponding
to a cube with an edge length of 1.55 μm.


## 3.4. Influences on the Determination of the Droplet Volume

Different conditions have an impact
on the determination of the precise droplet volume.


### 3.4.1. Influence of Different Drop Shapes

There
is a certain tolerance with respect to different drop shapes when calculating
drop volumes according to the integration procedure. However, there can be
large fluctuations in the volumes calculated if there are extreme contortions
in the drop shape. It may not be appropriate to assume rotationally symmetric
drops in some cases. The drop shape can fluctuate strongly at the beginning of
the flight phase in particular due to the forces which arise during release,
and symmetry is not given at that time.One way of circumventing this
interference effect is to only capture the drop after it has gone a certain
distance. The drop shape becomes increasingly stable and strives for a
perfectly spherical shape. The disadvantage of this is that the drop has to
travel a distance of approximately 2 mm. The recording of the drop at another
position or at another time requires additional effort as the dosing head has
to be put up high, and the delay in the LED stroboscope has to be adjusted.A second method involves averaging
the volume values measured across the drop's entire flight phase. When applying
this method, the nozzle position in front of the camera does not need to be
changed. This procedure was used for the volume measurements carried out here.
A third alternative, carrying out the volume measurement at a defined point, is
possible with the help of evaluation of the circularity of the drop. For
example, this could be the stroboscope delay/flight position at which the drop
has the greatest circularity in the trackable trajectory. Both the strip method
and the calculation of the spherical volume can be used in this.


### 3.4.2. Enlarged Appearance of the Drops

Using a frequency of 500 Hz and a
stroboscope light duration of 5 microseconds, a volume 1.17 times greater
than the weighing was arrived at with the measurements from the procedure based
on image processing. This behavior is a consequence of the visualization principle.
The camera used did not have a fast shutter or triggering. Therefore, the
duration of the stroboscope flash was crucial for the size of the appearance of
the drops.


### 3.4.3. Frequency Dependency of the Correction Factor

When the measurements were carried
out at different frequencies, the systematic error increased as can be seen in Figure4.Figure 4
Frequency
dependence of the dispensed volume.The frame rate of the camera used, a
Sony XC-ES 50, is 30 images per second. The camera was not triggered via the
stroboscope signal. The shortest possible shutter speed was 100 microseconds,
far longer than the light duration of the LED stroboscope. The number of drops
overlapping in the picture depends on the dosing frequency [21].As the number of overlapping drops
in an image increases, the effect described below has a greater influence. The
distance between the drops in the droplet jet generated can vary periodically.
As the frequency increases, the drops appear much larger than they would
otherwise. However, this phenomenon does not always appear and is not
predictable. It was not possible to detect it with the methods shown here. (See Table3.)Table 3
Number of
overlapping drops in the image depending on the drop rate.
Drop rate (Hz)400500600800100015002000300040005000Overlapping drops13162026335066100133166The measurements taken show that
the systematic error increases sharply in frequencies above 800 Hz because of
this effect. Conditional on the fact that the fluctuation in the drop distance
cannot be detected with the procedures used here, it was not advisable to
measure the volume with the procedures shown at higher frequencies.


### 3.4.4. Uncertainty in Edge Detection

Besides the uncertainties in the
recording technology, the image processing procedure can also influence the
measurement error. The edge detection has a crucial weighting. The slices of
which the drop volume is comprised were calculated on the basis of this edge
data. Using the example of the calculation of a sphere, Table4 illustrates the
degree to which the incorrect detection of the radius can affect the entire
volume.Table 4
Estimate of the difference in volume if the edge is
incorrectly detected.
Drop volumeDiameter (rounded)Difference in volume witha−1
diameterDifference in volume witha+1
diameter100 pl37 pixels7.9%8.3%150 pl43 pixels6.8%7.1%200 pl47 pixels6.2%6.5%250 pl50 pixels5.9%6.1%300 pl54 pixels5.5%5.7%350 pl56 pixels5.3%5.5%400 pl59 pixels5.0%5.2%450 pl61 pixels4.8%5.0%500 pl64 pixels4.6%4.8%Table 5
Composition of the parameters of the stroboscope camera system for the standardized
measurement.
CameraCamera frame rate30 images/s (full frame)Minimal shutter speed100μs (not used)Triggering and synchronizationnoneControl pulse of the piezoelectric
elementDosing frequency500 HzStroboscopeStroboscope frequency500 HzLight duration of the LED stroboscope5μsLensConversion factor pixel:μm1:1.55


### 3.4.5. Illumination from the LED Stroboscope

The environmental light is another
influencing factor. It is hard to take all fluctuations into account. In order
to counter the effects of external light influences, a box is recommended. The
entire unit was covered by a nonlight transparent box for the tests carried out
here.The light needed was generated by
the visualization system itself. The light duration and frequency of the LED
stroboscope were thus primarily responsible for the brightness of the image.As the
brightness and thereby changed contrast ratios in the image influence the drop
detection procedure, it is recommended that measurements should be taken with the
most constant illumination possible. The ratio of the grey-scale values in the
background to those of the drop is reduced at both high and also low
intensities of the light source. The detection procedure fails in these limit
ranges despite a certain robustness in the edge detection. However, the
brightness must be standardized to ensure measurements with the lowest
influence of error possible. Therefore, it is recommended that constant
aperture, camera settings, and constant stroboscope parameters to be used when
taking the measurements.


## 3.4.1. Influence of Different Drop Shapes

There
is a certain tolerance with respect to different drop shapes when calculating
drop volumes according to the integration procedure. However, there can be
large fluctuations in the volumes calculated if there are extreme contortions
in the drop shape. It may not be appropriate to assume rotationally symmetric
drops in some cases. The drop shape can fluctuate strongly at the beginning of
the flight phase in particular due to the forces which arise during release,
and symmetry is not given at that time.One way of circumventing this
interference effect is to only capture the drop after it has gone a certain
distance. The drop shape becomes increasingly stable and strives for a
perfectly spherical shape. The disadvantage of this is that the drop has to
travel a distance of approximately 2 mm. The recording of the drop at another
position or at another time requires additional effort as the dosing head has
to be put up high, and the delay in the LED stroboscope has to be adjusted.A second method involves averaging
the volume values measured across the drop's entire flight phase. When applying
this method, the nozzle position in front of the camera does not need to be
changed. This procedure was used for the volume measurements carried out here.
A third alternative, carrying out the volume measurement at a defined point, is
possible with the help of evaluation of the circularity of the drop. For
example, this could be the stroboscope delay/flight position at which the drop
has the greatest circularity in the trackable trajectory. Both the strip method
and the calculation of the spherical volume can be used in this.


## 3.4.2. Enlarged Appearance of the Drops

Using a frequency of 500 Hz and a
stroboscope light duration of 5 microseconds, a volume 1.17 times greater
than the weighing was arrived at with the measurements from the procedure based
on image processing. This behavior is a consequence of the visualization principle.
The camera used did not have a fast shutter or triggering. Therefore, the
duration of the stroboscope flash was crucial for the size of the appearance of
the drops.


## 3.4.3. Frequency Dependency of the Correction Factor

When the measurements were carried
out at different frequencies, the systematic error increased as can be seen in Figure4.Figure 4
Frequency
dependence of the dispensed volume.The frame rate of the camera used, a
Sony XC-ES 50, is 30 images per second. The camera was not triggered via the
stroboscope signal. The shortest possible shutter speed was 100 microseconds,
far longer than the light duration of the LED stroboscope. The number of drops
overlapping in the picture depends on the dosing frequency [21].As the number of overlapping drops
in an image increases, the effect described below has a greater influence. The
distance between the drops in the droplet jet generated can vary periodically.
As the frequency increases, the drops appear much larger than they would
otherwise. However, this phenomenon does not always appear and is not
predictable. It was not possible to detect it with the methods shown here. (See Table3.)Table 3
Number of
overlapping drops in the image depending on the drop rate.
Drop rate (Hz)400500600800100015002000300040005000Overlapping drops13162026335066100133166The measurements taken show that
the systematic error increases sharply in frequencies above 800 Hz because of
this effect. Conditional on the fact that the fluctuation in the drop distance
cannot be detected with the procedures used here, it was not advisable to
measure the volume with the procedures shown at higher frequencies.


## 3.4.4. Uncertainty in Edge Detection

Besides the uncertainties in the
recording technology, the image processing procedure can also influence the
measurement error. The edge detection has a crucial weighting. The slices of
which the drop volume is comprised were calculated on the basis of this edge
data. Using the example of the calculation of a sphere, Table4 illustrates the
degree to which the incorrect detection of the radius can affect the entire
volume.Table 4
Estimate of the difference in volume if the edge is
incorrectly detected.
Drop volumeDiameter (rounded)Difference in volume witha−1
diameterDifference in volume witha+1
diameter100 pl37 pixels7.9%8.3%150 pl43 pixels6.8%7.1%200 pl47 pixels6.2%6.5%250 pl50 pixels5.9%6.1%300 pl54 pixels5.5%5.7%350 pl56 pixels5.3%5.5%400 pl59 pixels5.0%5.2%450 pl61 pixels4.8%5.0%500 pl64 pixels4.6%4.8%Table 5
Composition of the parameters of the stroboscope camera system for the standardized
measurement.
CameraCamera frame rate30 images/s (full frame)Minimal shutter speed100μs (not used)Triggering and synchronizationnoneControl pulse of the piezoelectric
elementDosing frequency500 HzStroboscopeStroboscope frequency500 HzLight duration of the LED stroboscope5μsLensConversion factor pixel:μm1:1.55


## 3.4.5. Illumination from the LED Stroboscope

The environmental light is another
influencing factor. It is hard to take all fluctuations into account. In order
to counter the effects of external light influences, a box is recommended. The
entire unit was covered by a nonlight transparent box for the tests carried out
here.The light needed was generated by
the visualization system itself. The light duration and frequency of the LED
stroboscope were thus primarily responsible for the brightness of the image.As the
brightness and thereby changed contrast ratios in the image influence the drop
detection procedure, it is recommended that measurements should be taken with the
most constant illumination possible. The ratio of the grey-scale values in the
background to those of the drop is reduced at both high and also low
intensities of the light source. The detection procedure fails in these limit
ranges despite a certain robustness in the edge detection. However, the
brightness must be standardized to ensure measurements with the lowest
influence of error possible. Therefore, it is recommended that constant
aperture, camera settings, and constant stroboscope parameters to be used when
taking the measurements.


## 4. Verification Measurements

In order to check the findings and
ensure their general validity, a number of test series were performed. Due to
the dependency of the systematic error on the dosing frequency, stroboscope
frequency, and light duration,
these values were not varied. However, this did not limit the regular operation.Gravimetric recording was used as a
reference for the measurement of the volume with the method presented. In order
to cover a number of examples in relation to the range of applications, dosing
was implemented using the following substances.


### 4.1. Gravimetric Measurement As a Reference

The uniformity of the drops in the jet
is always given when using aligned dosing parameters. This statement can be
made because of the method of drop generation and the measurement findings of
the processed camera image. In order to minimize the error caused by
evaporation, dosing was carried out into an Eppendorf tube already filled with
the respective solution. A dosing height above the target in the range of 0.5 mm–1.5 mm was chosen so that evaporation
during the drop flight could be practically ruled out.Through electronic control, it was
possible to ensure that the desired number of pulses was generated. Due to the
knowledge acquired at that stage, the assumption could be made when using the
aligned parameters that a drop release would take place with each pulse.
However, we did not individually prove each one. Due to these facts, it was
ensured in principle that the quantity of liquid given would be quantitatively
comprised of the product of the drop volume and number of drops.The test series which followed consisted of 15 individual
measurements in each case, using the same nozzle with the same dosing
parameters, with Table7 showing the gravimetrically determined volumes of
water given different amounts of drops. In order to determine the systematic
error, the volumes measured from the optical and gravimetric methods were proportionalized.It should
be noted that the range limits of the scale were reached with masses smaller
than 0.5 mg. This factor was taken into consideration in subsequent
measurements and, where needed, the number of drops and thus the resulting mass
were increased.


### 4.2. Results of the Different Solvents

Test series with the liquids
listed in Table6, and different nozzles were carried out in the subsequent
testing. The nozzles used had diameters of 50 μm and 70 μm. In order
to make direct comparisons between nozzles  of the same diameter, two nozzles
with a diameter of 50 μm were selected.Table 6
Overview of the liquids used for testing and their
properties.
MediumDensityViscosityWater1 g/cm31 mPa sDMSO1.10 g/cm31.99 mPa sNMP1.03 g/cm31.65 mPa sAcetonitrile0.63 g/cm30.57 mPa sDichloromethane1.33 g/cm30.58 mPa sMethanol0.76 g/cm30.56 mPa sTable 7
Gravimetric measurement of different quantities of drops
under constant conditions.
Number of drops5000750010 00012 50015 000Number of measurements1515151515Mean value [mg orμL]0.72 mg1.12 mg1.48 mg1.85 mg2.24 mgStd. deviation0.03720.03730.03120.03980.0319% Std. deviation5.2%3.3%2.1%2.2%1.4%Visual volume200 pl200 pl200 pl200 pl200 plVisual/gravimetric ratio1.401.331.351.351.34Both optical and gravimetric
measurements were carried out on the water, NMP and DMSO. In the case of the
optical measurement, the mean value across the last 32 frames or the associated
volume was used in each case. In the weighing, each of these results was made
up of 15 individual measurements. In order to ensure additional certainty in
the measurement, gravimetric determination was undertaken with different drop
numbers, depending on the nozzle and liquid. The number of drops for the first
measurement was set at 10 000. The number of drops for the second measurement
was aligned with the drop volume determined from the first. If there was a risk
of the range limits of the weighing scale being reached in the case of low
mass, the drop number was increased to 15 000. If this was not the case, 5000
drops were dosed, thereby accelerating the measurement process and countering
evaporation.The dosing parameters were aligned
such that stable drop formation could take place as per the specified quality
criteria. 500 Hz was always used as the dosing frequency. Figure5 shows the
results of the optical measurements for the different solvents.Figure 5
Results of optical measurements for different solvents.In the case of the drop volume being
measured with the optical method or based on the image processing, different
properties of the liquids did not influence the measurement results.


### 4.3. Statistics

Evaluation of the Optical Process
In order
to keep the impact of the measurement error low, a mean value was derived for
the volume from the last 32 images. The Lilliefor test, a modification of the
Kolmogorov-Smirnov test in cases of low numbers of measurement points, was used
to test for normal distribution. The null hypothesis was maintained in
accordance with this test for a level of significance of 5%. The mean value and
standard deviation were then determined. In the case of stable drop formation,
the standard deviation was always between 0.6% and 1.5% of the drop volume
[22].Ratio of the Different Volumes Determined
The mean value of the ratio of the two volumes measured in different
ways could be determined from the comparative measurements undertaken. Firstly,
from the weighing  procedure with the aid of the density, and secondly, from the
optical process presented. The optical process had a systematic error,
explained in Sections3 to 3.4.5.
The weighing scale was used in this case as a reference in order to determine
the deviation. The 23 test series in total, carried out under constant lighting
conditions and with constant camera settings, showed a mean value of 1.35 with
a standard deviation of 0.04 (2.93%).The deviations in the
correction factor of 1.35 in this case and 1.17 from the measurements in
Section1
can be explained by the fact that a new box was constructed between the
measurements. The camera settings then had to be adjusted accordingly.Nevertheless,
these values are only valid for a dosing and stroboscope frequency of 500 Hz
and a stroboscope lighting duration of 5 microseconds. For higher dosing
frequencies, it is expected and has already been experimentally confirmed in
Section3.4.3 that both the ratio of the
optically measured and real volume and its distribution increase. This effect
is based on the principle of the visualization of the drops.


### 4.4. Conclusion on the Overall Measurement Uncertainty

The measurement uncertainty of the
stroboscope, the overlapping of several drops on an image, and the movement of
the drops effected a measurement uncertainty of approximately 10%. In addition
to this, there was uncertainty in relation to the edge detection. This was
related to the threshold determination and also to the resolution of the
camera’s CCD sensors (8-bit). The linear law of the propagation of uncertainty
could not be applied as the measurements, and further processing of the
measured values was not independent of one another.In summary, a systematic error arose
due to the recording technology and was primarily determined by the parameters:
light duration of the LED stroboscope, frequency of the drops, frequency of the
stroboscope, and camera frame rate.In order to keep the error as
constant as possible, the measurements here were all carried out with the same
dosing frequency (500 Hz). In the present system, the stroboscope frequency
corresponded to the drop rate as these systems were linked. Likewise, the
lighting duration of the LED stroboscope (5 microseconds) was not varied. In
order to avoid further influences from environmental light, a box was
constructed. The liquid used did not play any role in this. The entire
measurement uncertainty of the actual configuration, adhering to the conditions
named and set for the measurements, was therefore estimated at approximately
10%–15%.


### 5. Summary and Outlook

The methods presented were largely
based on the development of specific algorithms which used the existing
hardware and extended its functional scope. This process can be taken into
consideration in both the design of the dosing robots and integrated into the
existing systems. Largely, these improvements covered the automation of measuring
the drop volume.Thanks to the modular structure of
these algorithms, they can be integrated into different dosing systems of
similar design and function with just a few specific adjustments. In specific
cases, in which there is a need to enhance the values achieved, the suggested
alternatives could be applied. There is particular potential in the area of
volume measurement with regard to established processes from particle
measurement technology.Future work will include the
following topics.(i)
Measuring the
drop volume: use of high-speed cameras.(ii)
Evaluation of
drop formation: use of high-speed cameras.(iii)
Determining the
offset: integration of an additional camera for detecting the three-dimensional
trajectory.(iv)
Automatic
finding of the dosing parameters.
Software was developed as the basis
for the implementation and testing of all processes drawn up. The basic
components were used for communication and to control each component in the
dosing system. It was possible to integrate the individual algorithms into the
program sequence and assign parameters to them via a graphical user interface.
In order to be able to port these algorithms into the actual doser software
subsequently, the respective algorithms were designed as linked modules.During the programming, the
libraries of the respective manufacturers were used for the hardware access.
There was a DLL for the frame grabber and ActiveX control for the components of
the dosing system. The operations and subfunctions of the image processing
algorithms originated from the OpenCV library. The graphical user interface was
based on the Windows API. The program linking these components together was
written in Ada 2005. Further measured values of all of the processes
investigated could be displayed using this software [23].


## 4.1. Gravimetric Measurement As a Reference

The uniformity of the drops in the jet
is always given when using aligned dosing parameters. This statement can be
made because of the method of drop generation and the measurement findings of
the processed camera image. In order to minimize the error caused by
evaporation, dosing was carried out into an Eppendorf tube already filled with
the respective solution. A dosing height above the target in the range of 0.5 mm–1.5 mm was chosen so that evaporation
during the drop flight could be practically ruled out.Through electronic control, it was
possible to ensure that the desired number of pulses was generated. Due to the
knowledge acquired at that stage, the assumption could be made when using the
aligned parameters that a drop release would take place with each pulse.
However, we did not individually prove each one. Due to these facts, it was
ensured in principle that the quantity of liquid given would be quantitatively
comprised of the product of the drop volume and number of drops.The test series which followed consisted of 15 individual
measurements in each case, using the same nozzle with the same dosing
parameters, with Table7 showing the gravimetrically determined volumes of
water given different amounts of drops. In order to determine the systematic
error, the volumes measured from the optical and gravimetric methods were proportionalized.It should
be noted that the range limits of the scale were reached with masses smaller
than 0.5 mg. This factor was taken into consideration in subsequent
measurements and, where needed, the number of drops and thus the resulting mass
were increased.


## 4.2. Results of the Different Solvents

Test series with the liquids
listed in Table6, and different nozzles were carried out in the subsequent
testing. The nozzles used had diameters of 50 μm and 70 μm. In order
to make direct comparisons between nozzles  of the same diameter, two nozzles
with a diameter of 50 μm were selected.Table 6
Overview of the liquids used for testing and their
properties.
MediumDensityViscosityWater1 g/cm31 mPa sDMSO1.10 g/cm31.99 mPa sNMP1.03 g/cm31.65 mPa sAcetonitrile0.63 g/cm30.57 mPa sDichloromethane1.33 g/cm30.58 mPa sMethanol0.76 g/cm30.56 mPa sTable 7
Gravimetric measurement of different quantities of drops
under constant conditions.
Number of drops5000750010 00012 50015 000Number of measurements1515151515Mean value [mg orμL]0.72 mg1.12 mg1.48 mg1.85 mg2.24 mgStd. deviation0.03720.03730.03120.03980.0319% Std. deviation5.2%3.3%2.1%2.2%1.4%Visual volume200 pl200 pl200 pl200 pl200 plVisual/gravimetric ratio1.401.331.351.351.34Both optical and gravimetric
measurements were carried out on the water, NMP and DMSO. In the case of the
optical measurement, the mean value across the last 32 frames or the associated
volume was used in each case. In the weighing, each of these results was made
up of 15 individual measurements. In order to ensure additional certainty in
the measurement, gravimetric determination was undertaken with different drop
numbers, depending on the nozzle and liquid. The number of drops for the first
measurement was set at 10 000. The number of drops for the second measurement
was aligned with the drop volume determined from the first. If there was a risk
of the range limits of the weighing scale being reached in the case of low
mass, the drop number was increased to 15 000. If this was not the case, 5000
drops were dosed, thereby accelerating the measurement process and countering
evaporation.The dosing parameters were aligned
such that stable drop formation could take place as per the specified quality
criteria. 500 Hz was always used as the dosing frequency. Figure5 shows the
results of the optical measurements for the different solvents.Figure 5
Results of optical measurements for different solvents.In the case of the drop volume being
measured with the optical method or based on the image processing, different
properties of the liquids did not influence the measurement results.


## 4.3. Statistics

Evaluation of the Optical Process
In order
to keep the impact of the measurement error low, a mean value was derived for
the volume from the last 32 images. The Lilliefor test, a modification of the
Kolmogorov-Smirnov test in cases of low numbers of measurement points, was used
to test for normal distribution. The null hypothesis was maintained in
accordance with this test for a level of significance of 5%. The mean value and
standard deviation were then determined. In the case of stable drop formation,
the standard deviation was always between 0.6% and 1.5% of the drop volume
[22].Ratio of the Different Volumes Determined
The mean value of the ratio of the two volumes measured in different
ways could be determined from the comparative measurements undertaken. Firstly,
from the weighing  procedure with the aid of the density, and secondly, from the
optical process presented. The optical process had a systematic error,
explained in Sections3 to 3.4.5.
The weighing scale was used in this case as a reference in order to determine
the deviation. The 23 test series in total, carried out under constant lighting
conditions and with constant camera settings, showed a mean value of 1.35 with
a standard deviation of 0.04 (2.93%).The deviations in the
correction factor of 1.35 in this case and 1.17 from the measurements in
Section1
can be explained by the fact that a new box was constructed between the
measurements. The camera settings then had to be adjusted accordingly.Nevertheless,
these values are only valid for a dosing and stroboscope frequency of 500 Hz
and a stroboscope lighting duration of 5 microseconds. For higher dosing
frequencies, it is expected and has already been experimentally confirmed in
Section3.4.3 that both the ratio of the
optically measured and real volume and its distribution increase. This effect
is based on the principle of the visualization of the drops.


## 4.4. Conclusion on the Overall Measurement Uncertainty

The measurement uncertainty of the
stroboscope, the overlapping of several drops on an image, and the movement of
the drops effected a measurement uncertainty of approximately 10%. In addition
to this, there was uncertainty in relation to the edge detection. This was
related to the threshold determination and also to the resolution of the
camera’s CCD sensors (8-bit). The linear law of the propagation of uncertainty
could not be applied as the measurements, and further processing of the
measured values was not independent of one another.In summary, a systematic error arose
due to the recording technology and was primarily determined by the parameters:
light duration of the LED stroboscope, frequency of the drops, frequency of the
stroboscope, and camera frame rate.In order to keep the error as
constant as possible, the measurements here were all carried out with the same
dosing frequency (500 Hz). In the present system, the stroboscope frequency
corresponded to the drop rate as these systems were linked. Likewise, the
lighting duration of the LED stroboscope (5 microseconds) was not varied. In
order to avoid further influences from environmental light, a box was
constructed. The liquid used did not play any role in this. The entire
measurement uncertainty of the actual configuration, adhering to the conditions
named and set for the measurements, was therefore estimated at approximately
10%–15%.


## 5. Summary and Outlook

The methods presented were largely
based on the development of specific algorithms which used the existing
hardware and extended its functional scope. This process can be taken into
consideration in both the design of the dosing robots and integrated into the
existing systems. Largely, these improvements covered the automation of measuring
the drop volume.Thanks to the modular structure of
these algorithms, they can be integrated into different dosing systems of
similar design and function with just a few specific adjustments. In specific
cases, in which there is a need to enhance the values achieved, the suggested
alternatives could be applied. There is particular potential in the area of
volume measurement with regard to established processes from particle
measurement technology.Future work will include the
following topics.(i)
Measuring the
drop volume: use of high-speed cameras.(ii)
Evaluation of
drop formation: use of high-speed cameras.(iii)
Determining the
offset: integration of an additional camera for detecting the three-dimensional
trajectory.(iv)
Automatic
finding of the dosing parameters.
Software was developed as the basis
for the implementation and testing of all processes drawn up. The basic
components were used for communication and to control each component in the
dosing system. It was possible to integrate the individual algorithms into the
program sequence and assign parameters to them via a graphical user interface.
In order to be able to port these algorithms into the actual doser software
subsequently, the respective algorithms were designed as linked modules.During the programming, the
libraries of the respective manufacturers were used for the hardware access.
There was a DLL for the frame grabber and ActiveX control for the components of
the dosing system. The operations and subfunctions of the image processing
algorithms originated from the OpenCV library. The graphical user interface was
based on the Windows API. The program linking these components together was
written in Ada 2005. Further measured values of all of the processes
investigated could be displayed using this software [23].



---

*Source: 198732-2009-05-04.xml*