Typical
drop images obtained using this technique are shown in Fig. 3.
We used fixed thresholding to convert the gray-scale raw images to
binary images, leading to the detection of the drop boundaries. Since
only the images of drops within a short distance from the focal plane
were captured, the drop images were sharp and fixed thresholding
was sufficient to accurately detect the drop boundaries. Fig. 4 shows a
representative raw image (Fig. 4a), the corresponding processed
image after fixed thresholding (Fig. 4b), and the gray level histogram
plot of the raw drop image (Fig. 4c). As can be seen in Fig. 4c, the gray
level intensity histogram plots of raw images showed a distinct peak
that corresponds to a steep gradient in gray level intensity at the drop
boundary. Such a distinct peak indicates that a fixed threshold value
can be selected for accurate processing of raw drop images to detect
drop boundaries. The suitability of the selected threshold value
(which is 235 for the gray level intensity range of 0–black to 255–
white) was verified in three ways: (i) through experiments with the
spherical ball lenses that are discussed later in this section, (ii) through
comparing the detected and visual boundaries of water drops, and (iii)
through a sensitivity analysis for the axis ratio measurements with the
selected threshold value. The experiments with the spherical lenses
showed that the measured diameter values of the lenses were almost
identical to the actual diameter values. Similarly, the experiments
with water drops showed that the detected and visual boundaries of
water drops were almost identical. These visual verifications for the
drop boundaries were conducted by superimposing the raw drop images
and the detected drop boundaries. The sensitivity analysis with different
threshold values that are ±10 gray level intensities around the
selected threshold value of 235 showed that measured axis ratio values
vary only up to 6% from those that are obtained using the selected
threshold value. Consequently, it was concluded that the selected
fixed threshold value is suitable to extract accurate drop shape information.
Note that the setup including the camera and background light
remained unaltered for the entire experiments, ensuring consistency
for the image processing purposes. The conversion to binary images
was followed by an analysis to extract the necessary drop information
on the shape characteristics and the fall velocity. Drop fall velocities
were calculated by the displacement of the drop's centroid between
two consecutive frames. For non-equilibrium shaped drops, the centroid
location obtained from the captured drop images may shift,
resulting in fall velocity calculation errors. The fall velocity of a given
drop was calculated multiple times using the sequential high-speed
images as the drop passes through the short vertical distance within
the camera view frame. The differences between the calculated fall velocities
for a given drop at consecutive instances were insignificant
(with standard deviation values less than 0.5%, 0.9%, and 3.2% of the respective
terminal velocities for 2.6 mm, 3.7 mm, and 5.1 mm drops at a
given station). This indicates that fall velocity calculation errors were
unimportant. Furthermore, the calculated fall velocity values for a
given drop at consecutive instances were averaged to minimize these
errors.