1. science
2. physics

Optical backscattering from near-spherical water, ice,
and mixed phase drops
Kenneth Sassen
An experimental assessment of the scattering behavior of freely falling artificial raindrops and mechanically
suspended drops in the ice and mixed phase has been undertaken with a device which simultaneously measures the parallel and cross polarized components of backscattered linearly polarized laser light (6328 A).
Among the findings are that linear depolarization ratios () are generally <0.01 for raindrops up to nearly
6-mm diam, near 0.5 for regularly shaped frozen drops, and between 0.35 and 1.0 for more irregular ice parti-
cles. Anomalous scattering behavior has been observed during the liquid to solid drop phase transition (6
> 1.0) and in the relatively great amounts of parallel polarized energy returned from raindrops >-4 mm.
Backscattered signal variations produced during drop melting reveal that 6 values tend to remain near the
initial ice value until most of the ice has changed phase. The details of the variations aid in the determination of the dominant scattering mechanisms responsible for the backscatter from large, near-spherical particles. The results are shown to have some bearing on measurements
by lidar.
1.
Introduction
Investigations of the backscattering behavior of
water drops larger than the wavelength have been performed primarily to elucidate the causes of certain atmospheric optical phenomena, such as the rainbow and
the glory. Recent theoretical studies have utilized both
detailed Mie calculations and approximate geometrical
optics theory, assuming homogeneous spherical scatterers. While the scattering mechanisms responsible
for the rainbow can be satisfactorily explained on the
basis of the traditional ray tracing methods of geometrical optics, the mechanisms involved in producing true
backscattering from spheres, as in the case of the glory,
are not adequately described by this approximate
analysis.
For water spheres and light in the visible region, the
results of the ray tracing method indicate that the
backscattered energy consists almost entirely of rays
reflected normally from the front and rear faces of the
drop along the axis of symmetry (i.e., the axial rays),
while multiple reflected off-axis rays contribute negligibly. Of the paraxial return, about four times more
energy results from the internally reflected ray bundle
than is reflected from the front surface. As the amplitudes of two axial components add coherently, the total
far-field intensity can vary from about one to nine times
of atmospheric hydrometeors obtained
the intensity of the front surface reflection alone due to
phase interference. Since it followsthat the total axial
intensity varies strongly with minute variations in
droplet diameter, this interference method should be
amenable to determining precise rates of change in the
diameter of growing or evaporating drops. This principle has been used by Ro et al. 1 in experiments which
measured the period of the intensity cycles in light
backscattered from a narrow laser beam directed toward
the exact center of evaporating drops. In agreement
with theory, the axial beam was observed to oscillate
sinusoidally with the predicted period in the size parameter (the ratio of droplet circumference to incident
wavelength) inversely proportional to the refractive
index. However, this treatment alone cannot account
for the glory, and what was neglected in the calculations
was first pointed out by van de Hulst.2
The reason for the failure of the geometrical optics
method to describe completely true backscattering lies
in its inability to treat circumferentially backscattered
energy, that is, the surface wave. This phenomenon
results when energy incident at the interface between
two dielectrics at or greater than the critical angle of
total reflection (from the more dense medium) becomes
trapped at the interface. For water spheres which are
uniformly irradiated, the axial backscatter component
is small in comparison to the contribution from surface
The author is with University of Utah, MeteorologyDepartment,
Salt Lake City, Utah 84112.This work was performed at University
of Wyoming, Department of Atmospheric Science, Laramie, Wyoming
82071.
Received 23 July 1976.
1332
APPLIED OPTICS/ Vol. 16, No. 5 / May 1977
waves, as light striking at every point on the edge of the
drop will result in the formation of a surface wave provided that spherical symmetry is strictly maintained.
Propagating along the interface of a spherical drop,
surface wave energy is continuously being lost tangen-
tially to the surface into the less dense medium and also
at the critical refractive angle into the drop. The latter
process results in internal reflection and refraction
which create optical shortcuts through the drop (the
so-called jump rays) and, when coupled with segments
or cycles of surface waves, permit a number of ray paths
of high enough energy to cause considerable interference
with the reradiating surface wave. The resulting
backscattered intensity variations in the circumferential
component during drop evaporation have been measured and found to agree qualitatively with the complex,
but apparently periodic, set of humps and spikes predicted by the Mie theory and also with a simple scaler
model incorporating surface waves and the geometrical
shortcuts.3
Thus, the dual backscatter mechanisms of spherical
particles have been demonstrated experimentally by
probing suspended drops with a narrow laser beam and
corroborated by theoretical simulations of both an approximate and exact nature. The results of Mie calculations given in the form of the intensity growth
curves of the series-expansion solution by Byrant and
4
are particularly illustrative of this dual nature.
Cox
Via the localization principle, the order of the expansion
term can be related to the position of a ray from the
origin in order to assess the various contributions of the
scattering mechanisms. At a scattering angle of 1800,
the backscattered intensity was shown to arise from
large jumps near the origin and just before the series
converges, the axial and circumferential components,
respectively.
The consideration of polarization has been omitted
in the above discussion, since for homogeneous spherical
particles the backscattered energy retains the incident
state of polarization. Such is not likely to be the case
for inhomogeneous or aspherical scatterers, even for
raindrops of a few millimeters diameter which display
only slight perturbations from spherical symmetry.
For
such near-spherical particles, the axial and circumferential rays will likely contribute predominantly to the
backscatter, but the effect of off-axis internal scatterings may no longer be negligible. Those latter ray paths
which involve a transformation of the scattering plane
will yield depolarized energy.
Similarly, optically in-
homogeneous particles (e.g., severely melted ice particles) would likely produce depolarization. Unfortunately, Mie scattering calculations have yet to be performed for near-spherical particles much larger than the
were suspended within the scattering volume at room
temperature and observed during the change of phase.
In addition, the deformation and breakup of falling
drops induced by grazing interactions with an obstacle,
and the freezing of suspended drops, were also briefly
examined.
The main objective has been to ascertain the amounts
of depolarization produced in the backscatter by these
particles. The experimental apparatus simultaneously
measures the amounts of backscattered energyreturned
in the planes of polarization orthogonal and parallel to
the E vector of the laser source. Hence, linear depolarization ratios (6, the ratio of these values) could be
used to describe the change in the state of polarization
of the scattered energy. In all cases, the particles were
interrogated singly with the apparatus oriented in the
horizontal direction. Samples of collected rainwater,
kept frozen until use, were used exclusively for the
particles.
In the final section, the experimental results are examined to assess the dominant scattering mechanisms
believed to be responsible for the backscattering from
near-spherical particles. These inferences are based
on the known spherical particle scattering analogies
discussed above. Then, the applicability of the depolarization measurements to the interrogation of atmospheric hydrometeors of similar character is discussed.
The laboratory measurements are shown to be a valuable aid to the evaluation of data remotely sensed with
polarization diversity lidar systems.
II.
A.
Experimental Arrangement
Apparatus
A schematic portrayal of the cw laser backscatter
system is given in Fig. 1. The basic components of the
system, the optical source and detector, are rigidly
mounted in an enclosure at right angles to one another.
The vertically polarized laser beam is directed down the
optical axis of the receiver through the use of a small 450
mirror mounted directly before the receiver lens. The
He-Ne laser (Hughs model 3076H/R) emits -3 mW of
energy at 6328 A with a beam divergence of <0.75 mrad
(full angle). The output is linearly polarized to better
than one part in a thousand and displays a beam amplitude ripple of <0.1%rms. After collimation the expanded laser beam is reduced to a diameter of 6 mm to
improve the uniformity of the energy distribution across
wavelength, as even a slight distortion in sphericity
would introduce formable complexities into the calculations.
This experimental study is concerned with the optical
backscattering behavior of near-spherical water drops
in the liquid and solid phase and during the water-ice
phase transition. In contrast to the earlier laser studies,
the particles have been uniformly irradiated in a collimated laser beam 6 mm in diameter through two experimental techniques. Water drops of diameters between 2.5 mm and 5.8 mm were sampled near terminal
velocity by allowing the particles to fall through the
the beam.
scattering volume of the apparatus, while drops (of from
1.6-mm to 3.3-mm diam) frozen on a thin wire support
showing the design for controlling the scattering volume. The light
RECEIVER
DUA
PHOTOTUBES
45
° MIRROR
GLAN-AIROR
PRISM
COLIMATOR
AND
LASER
l_ LASERl
LIGHT
TRAP
SCATTERING
VOLUME
l
25cm
Fig. 1.
A schematic top view of the cw laser backscatter apparatus,
trap is normally located 1.65 m from the receiver lens.
May 1977 / Vol. 16, No. 5 / APPLIED OPTICS
1333
The receiver utilizes a 25-cm focal length lens,
6328-A-centered spike interference filter (16 A
halfwidth), and a 2.5-mm diam diaphragm to collect
only that energy scattered at angles >Ž1780 with respect to the direction of incidence from the scattering
volume. The simultaneous measurement of the returned parallel and orthogonal polarized components
is achieved through the use of a Glan-air polarizing
prism and two appropriately positioned photomultiplier
tubes (EMI 9558). A more detailed description of the
receiver design is given elsewhere. 5
On the basis of a computerized simultation of the
paths of all rays processed by the optics in the receiver,
an area along the optical axis was chosen for the sampling of the particles centered at a distance of 73 cm
from the receiver lens. In this region, the receiver views
uniformly all energy returned within a 3.0-mm radius
of the optical axis, displaying a sharp cutoff outside this
area. These properties combined with the occulting of
the laser beam make this an ideal region for the sampling of single particles.
As shown in the figure, a series
of tubular enclosures are used to shield the rest of the
laser beam from scatterers. The spacing between the
tubes, which are internally threaded and treated with
an optically flat paint, controls the length of the scattering volume. The far tube is terminated with a light
trap.
B.
Experimental Technique
Two separate methods were employed to permit the
examination of the particles. Since in the first case it
was desired to assess the scattering behavior of large
water drops which departed from sphericity due to
aerodynamic drag forces, these particles were interro-
gated after a free fall distance of nearly 8 m. Laws 6 has
shown that drops up to 6-mm diam had attained 95%
of their terminal velocities after falling this distance, so
that the induced shape distortions can be considered
typical of freely falling raindrops in still air. Although
the path of the drops was confined within a pipe for
shielding from air motions, the drops nonetheless displayed considerable variability in their final position
with respect to the 3.5-cm3 scattering volume. Hence,
a -8-mm
wide slit of metal foil was positioned just
below the scattering volume so that the data from most
partially irradiated particles could be rejected by noting
the characteristic noise from their impaction on the
foil.
Monodisperse streams of drops were generated at the
tip of a capillary tube by allowing the gravitational
separation of drops from a water jet supplied by a con-
stant head reservoir. To produce streams of particles
of various diameters, a number of different orifices were
fitted to the syringe containing the rainwater samples.
Drop diameters were found by measuring a number of
splash sizes formed on filter paper treated with a dye,
in the usual manner. Using this technique, successive
drop diameters appeared to vary by as much as a few
tenths of millimeters, but the frequent presence of radiating splash products would presumably set a limit
to the measurements' accuracy of about this order.
In order to observe frozen particles before and during
1334
APPLIED OPTICS/ Vol. 16, No. 5 / May 1977
melting, drops frozen on a support in an adjacent freezer
(at -- 15 0 C) would be transferred to a previously
aligned mounting fixture at the center of the scattering
volume on an open laboratory bench. A loop of 0.1-mm
diam wire coiled about a 0.35-mm needle form was used
for the suspension of the drops. Although this method
of support undoubtably introduced unnatural shape
distortions in large drops, the freezing process often
caused more significant distortions, and depolarization
values for the completely melted particles were usually
comparable to those observed for the freely falling
particles. In general, the drops frozen in this manner
appeared to be almost entirely opaque, displayed some
vertical elongation in shape from gravity-induced distortions of the original water drops, and frequently
developed irregularities such as protuberances or needlelike spicules during freezing.
The positioning of the frozen drops was adjusted so
that the wire loop lay just within the top edge of the
laser beam. The transfer from the freezer could be
accomplished in a period of a few seconds, and the initial
laser returns were taken to be representative of pure ice
particles. Immediately after emplacement, a photomicrographic record of the frozen particle's size and
shape was taken.
Stereomicroscopic observations were
conducted during melting in order to relate the extent
of the phase change to its scattering behavior. These
observations were performed at an angle of
160°, or
as close to the backscatter direction as possible, and
typically showed the presence of bright spots at the
particle's center or edge localities indicative of the axial
and circumferential returns. At the termination of each
experiment, the melted drops were photographed and
removed from the support in order to obtain an estimate
of the background signal contributed by the drop support.
A small number of observations of the liquid to solid
phase transition were also performed by suspending a
supercooled drop in a similar manner within a dry ice
cooled diffusion chamber. Entrance and exit ports for
the laser beam were provided at positions corresponding
to roughly the -5°C isotherm of the devices stable
temperature gradient and also at a level well above the
0C level to observe their subsequent melting after relocation. The suspended drops were nucleated by
bringing a dry ice granule on a probe into the vicinity
of the drop. Microscopic observations revealed that
typically an ice shell would initially form followed by
freezing progressing inward from the shell and aided by
the growth of internal ice branches. Drop opacity increased gradually, but would often display an instantaneous increase when freezing was far advanced, presumably from internal fracturing. Ice spicules were
occasionally noted to extend slowly from a fracture in
the ice shell.
A glass hypodermic syringe was normally used as a
water reservoir in these experiments to avoid the contamination of the rainwater samples with the lubricant
found in disposable plastic syringes.
The use of plastic
(tygon) tubing was also minimized in the drop generating device to avoid the possible alteration of the surface tension properties of the rainwater, although many
6f the capillary tubes were comprised of short lengths
of this material, and the rainwater samples were collected and stored in plastic bags.
C.
Data Recording and Analysis
Drop phase transitions have been continuously
monitored by recording the output of the photomultiplier tubes without preamplification on strip chart recorders.
These data were analyzed for
values by
measuring the paired signal deflections at points with
circles) sampled with the apparatus extending out of a
laboratory window. In these cases,the modal diameters
obtained with the dyed filter technique were used. For
comparative purposes, a graph of the variation of calculated raindrop terminal velocities for an atmospheric
pressure of 800 mb (approximate surface pressure at
Laramie, Wyoming) with drop diameter 7 is inserted in
the figure.
An examination of the frequency distributions of E 1
and values for each drop group shows that the dis-
a millimeter rule. The figures of the phase change vs
time, shown in the following section, were made by
persion of depolarization ratios remained approximately
tracing the signal records on a single graph and conse-
cases, but while this was also true for E 11values for drop
quently preserve the original recorder sensitivities.
In
obtaining the 6 values, inaccuracies result primarily
from uncertainties associated with the determination
of the background signal level contributed by the drop
support. Assuming that the presence of the particle
during experimentation and its removal from the support did not affect the magnitude of this value, the
background values were subtracted from the parallel
polarized signal levels (since background measurements
in the cross-polarized channel were negligible) during
the data analysis. Additional inaccuracies may also
have resulted from random data reading errors and the
possibility of a small phototube calibration and optical
alignment error. Total maximum probable uncertainties have been estimated to be '-10%
of the 6
values for the data from suspended particles, with an
additional 0.025 inaccuracy in the absolute 6 values
for single data points.
To record the dual-channel signal pulses generated
by the passage of the falling drops through the laser
beam, the data were read off photographs of the CRT
display of a dual-trace storage oscilloscope with a more
than adequate frequency response rate. The signals
from the photodetectors were preamplified prior to
normally distributed about the arithmetic mean in most
diameters <-4 mm, the distributions for larger drops
became increasingly broad and skewed toward higher
E 11 values. This is seen as encouraging with respect to
the experimental technique in that drops which were
only slightly irradiated were apparently properly
identified (as evidenced by the lack of skewness toward
lower values), while, on the other hand, the Ell distributions for the larger drops might have been influenced
by the increasing degrees if oscillatory motions experienced by these large particles. 8 A few typical standard
deviations of the drop group 6 and EI values are shown
as bars in Fig. 2.
With regard to the variation of average backscattered
energy with drop diameter shown in Fig. 2, both the
natural and artificial raindrops of sizes up to -4-mm
diam yielded an E1 increase proportional to the square
of the drop radius as expected.
Cross-polarized signals
for those particles were below the detection threshold,
but could not have produced 6 values >-0.05% for the
most part. When drops of diameters >-4 mm were
interrogated, however, measurable depolarization ratios
were obtained which tended to increase from values of
about 0.08-0.5%with increasing diameter. Moreover,
display, so that 6 = 0.05% could be detected for drops
>3 mm in diameter. Since negligible background sig-
nals were produced during these experiments and a
large number of data points were averaged so that the
random data reading error could be ignored, uncertainties in the absolute value of depolarization ratios
were estimated to be -- 0.01. However, particle signal
returns often exceeded those values for which the cali-
UNEARDEPOLARIZATION
RATIO (%)
01
1.0
IIll
I
I I
I IIIll
I
6 6.0
bration had been performed (up to signal levels of -0.7
: 20
V), so that the phototube response rates could only be
0
assumed to remain linear throughout this region of large
signal returns.
E
-
4.0
fa
d
o 1.0
a 0.8
z
5 06
Data from artificial raindrops are given in Fig. 2,
which shows the amount of returned parallel-polarized
energy (Ell, in volts) and linear depolarization ratio (6,
in percent) obtained from series of drops of the indicated diameter. Each data point represents the numerical average of values from individual drops produced under a given set of conditions which varied in
number from about 50 to 200 drops. Also included are
a few E11 values obtained from natural raindrops (solid
I
6 8 10
4
VT (m secI
0I
Drops in Free Fall
I
*
2
CO
111. Experimental Results
A.
E,,- r I3/_
I
0.1
E,1
,,I I 1
I
I
I,
1.0
(volts)
Fig. 2. A compilation of linear depolarization ratios (, in percent)
and returned parallel polarized energy values (E t, open circles) ob-
tained from monodispersed streams of artificial raindrops near terminal velocity (see insert). Data from natural raindrops also shown
as solid circles. The detection threshold of 3 values is 0.05% for drops
>3 mm in diameter. Anomalous parallel-polarized scattering behavior of drops >4 mm in diameter is indicated, despite the generation
of only minute amounts of depolarized energy. Horizontal bars give
typical standard deviations in the Ell and a value samples.
May 1977 / Vol. 16, No. 5 / APPLIED OPTICS
1335
the increasing depolarization ratios were accompanied
by a trend of strongly increasing E1l values which were
no longer proportional to the particle cross-sectional
area. Although the data display considerable variability, the Ell variation with particle size can be approximated by a dependence on drop radius of roughly
to the thirteenth power. As shown by the insert in the
figure, terminal velocities increase only slightly in this
size range, indicating that increasing degrees of drop
deformations are being incurred which nearly compensate for the effect of increasing particle masses. It
is clear that for raindrops of >-4-mm diam, scattering
mechanisms are acting which are very dissimilar from
those of more spherical drops, and yet these mechanisms do not involve the production of more than
minute amounts of depolarization. This behavior is not
found, on the other hand, when often destructive drop
oscillations are induced in falling drops by grazing in-
cidence with an obstruction.
Although it was not possible to observe the drop
shape variations accompanying raindrop coalescence
or breakup under more realistic conditions, particle
oscillations often resulting in drop breakup were produced by the method mentioned above. Figure 3 shows
tracings of the oscilloscope records of a number of drops
which had both interacted and failed to come in contact
with the obstacle. The data are presented with the
cross-polarized signal (EI) increasing downward from
the top trace, while the parallel component (Ell) increases in the usual sense but at 0.1 times the El
channel sensitivity. Examples of drops (of 3.2-mm
diam) which fell through the scattering volume unaffected by the obstruction can be seen as the rather
symmetrical Ell signal pulses at the right side of the
figure and display little variability. These particles
failed to produce any measurable depolarization. In
contrast, the pulses from the drops with the induced
I
E1 ,
I
I
~I
I
I
I
I
I
I
particles usually varied considerably during the passage
of a single drop through the laser beam, but often averaged to a value of -0.3, and occasionally up to -0.5.
It is interesting to note, though, that corresponding E1l
values were slightly to considerably less than those
values for unaffected, similarly sized drops, indicating
that in this case the distortions yielding the high depolarizations did not generate the strong parallel-returned energy increases evident from the increasing
asphericity with drop size described above.
Before describing the data from drops in the ice
phase, a brief discussion of the variability of the data
portrayed in Fig. 2 may be in order. First, it is not unlikely that the processes controlling the backscattering
behavior of near-spherical
|
1
|
<--j ~1
1
AI ;I
2 ALs
Fig. 3. Oscilloscope display tracings of dual-channel pulses from
3.2-mm diam drops near terminal velocity. Nondepolarizing interactions of two freely falling drops can be seen at the right side of the
trace, while significant amounts of depolarized energy are generated
as a result of severe drop distortions caused by grazing incidence of
the remaining drops with an obstruction positioned above the edge
of the scattering volume. E channel shown at ten times the sensitivity of the E11 channel.
APPLIED OPTICS/ Vol. 16, No. 5 / May 1977
drops in free fall act in a
nonuniform fashion with increasing drop size, so that
small changes in drop deformation may lead to more
significant variations in scattering behavior depending
on exact scatterer geometry. The data also suggest that
different rainwater samples used over single data collection intervals produced a more uniform increase in
values with increasing particle diameter than what is
indicated in the figure. Hence, characteristics of the
rainwater samples such as surface tension and suspended or dissolved particulate matter may also have
had an effect. And finally, with regard to the generation of the unexpectedly great EjI values for drops >-4
mm, it should be mentioned that in consideration of the
possible approach of response saturation of the photodetectors, and the higher probability of incomplete
particle irradiation for drops of nearly the beam diameter, it is possible that the parallel energy values given
in the figure were underestimated.
B.
Frozen Drops
As described earlier, the initial scattering properties
of frozen rainwater drops immediately after emplacement in the laser beam were taken to be representative
of pure ice phase particles. Since a number of forms
were assumed by the drops during freezing, the experimental results will be given with regard to the three
chief structures of the frozen drops. Hence, symbols
are presented in the following figures which represent
frozen drops with a regular circular or elliptical appearance (circles),with an irregular, asymmetrical shape
(semicircles), and with large spicules (short lines). As
a further aid to the data interpretation, axial ratios (the
vertical to horizontal dimensions) measured from
photomicrographs
I
J
1336
oscillations display considerable irregularities and significant amounts of depolarization. values for such
are considered as a variable as well
as particle diameters. In general, axial ratios increased
with diameter, on the average from about 1.0 to 1.2 over
the size interval of 2-3-mm diam, respectively.
Figure 4 compiles the results of this phase of study.
Depicted are the variations of 6 (top) and E11 (bottom)
values with ice particle diameter and axial ratio. Differences in the scattering behavior of the ice particles
can be seen as a function of particle shape.
The in-
crease in E1l values with increasing diameter and axial
ratio tends to be less strong with the irregular particles
than those frozen more regularly, while those few drops
displaying needlelike extensions appear to display little
dependence on either parameter. In other words, the
regular particles tended to backscatter relatively more
energy for frozen drops of a given diameter or axial ratio.
The over-all increase in Ell values with increasing di-
ameter is considerably stronger than what would be
expected from the cross-sectional area increase, but it
should be remembered that axial ratios also similarly
increase and that relative contributions from each factor
cannot be judged independently from the data.
Linear depolarization ratios analogously display some
stratification with particle diameter and axial ratio.
For the regular ice particles, 6 are all between 0.45 and
0.60, whereas 6 for the more severely distorted drops
range from 0.35 to nearly 1.0. Average depolarization
values for the former type are 0.52, and 0.59 for all the
particles. Although 6 values are not clearly related to
particle diameter, the data do suggest that depolariza-
Ld
tion ratios diverge increasingly from a value of -0.5 with
axial ratios increasing and decreasing from unity, particularly for the irregular drops. This again may be
.,Ell
partly an effect of correspondingly increasing diameters,
but since irregular particle 6 values have shown a preference for being inversely related to E11 values, the following generalization can be made. Assuming that the
balance of spherical particle scattering mechanisms and
"I ,
I
depolarization from internal optical inhomogeneities
drops, the more variable depolarization ratios for the
irregular drops reflect the added or detracted contributions from spherical particle scattering mechanisms
(as determined by exact drop geometry) in conjunction
with the more uniform amounts of depolarized energy
generated through internal scattering.
10r-
ICE PARTICLES
)
T
o
09 I
REGULAR
) IRREGULAR
/ SPICULE
)
)
)
08
o
C.7
&
0.6
A.
0.5
<
0.4
J
0.2
)s 3 / //)
0000
0
0
Q/
I
T
I
.
)3
0
0
o
1.5
2.0
3.0
(min)
Fig. 5. Typical parallel and orthogonal polarized (dashed) traces
vs time of the phase changes of suspended drops. E traces shown
at two times the sensitivity of the E 11traces: (a) Record of the melting
behavior of a 2.4-mm average diameter drop (top). Note the maintenance of high 6 values throughout much of the phase change and
the presence of the E signal spike and the E11 single jump at -2.5 min
associated with the initial internal axial contribution to the backscattered energy. (b) Record of the freezing behavior of a 2.1-mm
average diam supercooled drop (bottom). Note anomalous a value
of -1.3 at 2 min with cessation of protuberance growth.
0
0
3
0
3
p 3//
25
3.0
AVERAGE DIAMETER mm)
09
- 1.0
(b) (with an axial ratio of 1.05) did develop a relatively
3,
1.1
small protuberance during freezing. The ice particle
1.2
1.3
AXIAL RATIO
Fig. 4. Values of (top) and Ell (bottom) from a number of suspended frozen drops as functions of ice particle average diameter and
axial ratio. Data stratified into three ice particle shape types (see
key). Note that the near-spherical regularly frozen drops produce
a
values of -0.5.
As examples of the variations in the parallel and orthogonal polarization channels incurred during the
phase transition, representative records of drop melting
appearance, although the 2.1-mm average diam drop in
)8) ) /
3.5
Drops Undergoing the Phase Change
and freezing are provided in Figs. 5(a) and 5(b), respectively. The particles whose records are illustrated
in this figure were when frozen rather symmetrical in
. O
0)
60
TIME
C.
) )
*
0.1
I
I
2.0
E
/
00
)/3
0.2
I
1.0
_9/
Po
)
I
I
0
0
CI
0.3
--------------
0.5 value for the regular
the average 6
determines
in record (a) was 2.4 mm in diameter, with axial ratios
of 1.02 in both phases. A sequence of four photomi-
crographs encompassing the phase transition of a
2.7-mm diam ice particle is shown in Fig. 6. It is in-
teresting to note that, as was usually the case, the
presence of bright spots on areas of the drops surface or
edge could be used to locate visually regions of strong
energy return.
May 1977 / Vol. 16, No. 5 / APPLIED OPTICS
1337
a
b
decreases, and a jump in the Ell signal occurs almost
instantaneously. As a result, 6 values drop to <0.2 and
then decline as both polarization signals decay correspondingly until a value of 0.005 is reached, in this case
at -3 min. Signal levels and 6 values generated by the
pure water drop remain fairly constant afterward.
This record illustrates several important features of
the scattering behavior of mixed phase particles which
will now be examined more closely. First, that despite
the growing relative amount of water, the 6 values for
the most part typically maintain a value not too different from the initial pure ice value. During this interval, the return signals decay appreciably, initially
more rapidly so during about the first minute of melting.
Then, after most of the phase change has been completed, a E signal spike occurs which is followed by a
rapid Ell signal increase. With the aid of the microscopic observations of the particles, it has been verified
that these features are associated with the initial contribution of backscattered energy from the internal axial
d
C
Fig. 6. Four photomicrographs of the appearance of a melting
2.7-mm average diam ice particle illuminated in the laser beam, taken
at a scattering angle of-160°.
Bright areas on the particle indicate
region of intense backscatter. Times (t) below refer to time from
implacement in scattering volume: (a) frozen particle, t = 10 sec,
= 0.52; (b) significantly melted particle t = 135 sec, 1 = 0.45; (c)
particle at EI value jump, t = 200 sec, 6 = 0.18 (note area of diffuse
ice return from just above drop center); (d) water particle, t = 255 sec,
= 0.01.
ray bundle. The often abrupt removal of residual ice
from the drops central area suddenly discloses the far
internal face of the drop to the incident radiation and
conveniently provides a means of assessing the relative
importance of this mechanism with respect to the contributions from additional energy sources. Knowing
that for spherical particles the added contribution from
the internal axial component should increase the
backscattered intensity of the total axial component
from one to nine times that of the front external component alone (or -5 times on the average) as a result of
phase interference, the average ratio of Ell signals in the
experimental records at the jump peak to immediately
preceding the signal jump should give an indication of
the importance of this mechanism. Figure 7 shows the
results of such an analysis where the E11 ratios for each
record are depicted as a function of the melted drop
In general, the records from drops undergoing the
solid to liquid phase transition were considerably less
complex for the regular drops in comparison to those
displaying irregularities.
10
9
This may have been primarily
a result of the fact that the ice content of the latter type
would frequently be observed to move to more stable
positionsduring melting, thereby altering the scattering
properties of the particle. But when the drops remained fairly stable during melting, records of the type
displayed in Fig. 5(a) were obtained in the majority of
cases. In the figure, the E 1 signal trace is shown at
twice the sensitivity of the E signal, so that signals of
8
6
aE
5
4
o
_
_
3
2
equal vertical deflection represent a value of 6 = 0.5.
The abscissa gives the time in minutes from the emplacement of the frozen drop in the laser beam. It can
be seen that depolarization ratios remain between 0.55
and 0.60 for nearly 2 min and then begin to decrease
somewhat before a spike in the E
trace occurs at -2.5
min. During this time, the ice particle was being enclosed in a water shell of increasing thickness until at
-2.5 min the residual ice had receded to a position just
occupyingthe drop center. Within a short time interval
following this condition, the E signal spike rapidly
1338
APPLIED OPTICS/ Vol. 16, No. 5 / May 1977
F
7
-A
0
I
I
I
1.5
2.0
2.5
DROP
Fig. 7.
AVERAGE
DIAMETER
3.0
I
3.5
(mm)
Ratio of parallel polarized signals at the EI signal jump to
just preceding the jump plotted against averagewater drop diameter.
Cross-hatched area indicates the region of ratios to be expected for
spherical particles from the contribution of the rear face axial component to the total axial return if no other scattering mechanisms were
to contribute to the backscattered energy. Axial returns are shown
to contribute substantially to the backscattered energy from nearspherical particles.
diameter. With an average ratio of 2.6, or about one-
6 values for such enclosed particles were typically fairly
half of the value to be expected on the average if no
close to 0.5, but subsequent values fluctuated consid-
other scattering mechanisms were acting, it is apparent
that the combined contributions from multiple internal
erably during freezing. As in the example, however, 6
values were often close to 0.5 during most of the freezing
scatterings and surface waves are of roughly the same
process. An additional interesting feature of these
importance as the total axial component. The effect
records is the presence for a short duration of 6 > 1.0
values in about half of the cases, usually following -1
min after nucleation when the particle was quite opaque
and apparently mostly frozen. In Fig. 5(b), a maximum
6 value of 1.3 is found for a brief interval at 2.0 min. At
of the remaining ice content of the drop could serve only
to increase the Ell signal ratio slightly over the short
time interval spanned by choosing signal values im-
mediately proceeding and coincident with the signal
jump. And in support of the view that the gradual
signal decays in both channels following the jump is due
this stage it was noted that the extrusion of liquid from
within the particle to form an irregularity on the par-
to the completion of the phase change, the amount of
signal decrease in excess of the return from the pure
ticles surface ceased. Similarly, the cessation of growth
of a long needlelike spicule was approximately accom-
water phase particle corresponds to a 6 value of roughly
0.5, as would be expected to be contributed from an
value of 2.2 in one case. The surprising presence of such
opaque ice mass. Although it is possible that surface
wave contributions may have been artificially reduced
by the presence of the drop support, the proportion of
drop circumference actually occupied by the support
was relatively small. A more basic question which will
be addressed in another section, though, is in the over-
all effect of the drop support on particle shape and in
the applicability of these measurements to those of
natural hydrometeors.
As for the corresponding E 1 spike increase, this
feature has no analog in spherical, homogeneous particle
scattering behavior and so must be considered to have
resulted from the presence of ice at the drop center.
Thus, it can be assumed that this behavior was caused
by the creation of internally reflected and refracted ray
paths through the ice mass at this position which favored the transformation of the vibration plane (with
panied by the generation of the highly anomalous 6
high depolarization ratios, unique in the author's experience with measurements of the backscattering behavior of numerous hydrometeor types, is at present
unaccountable for on the basis of known scattering
mechanisms. It is hoped that the specific conditions
under which these anomalous values occurred may
provide some insight into the likely responsible mechanisms.
IV.
Summary and Conclusions
The experimental results discussed in this report are
believed to have value in describing the general scattering behavior of near-spherical particles and also in
aiding in the interpretation of field data sensed from
natural hydrometeors with the optical backscatter depolarization technique. However, a limitation in the
applicability of these data must be acknowledged in that
respect to the incident energy). An examination of all
all measurements had to be performed in the back-
the data records also reveals that some particles
<-2-mm diam failed to display this feature, while the
relative strength of the signal spike tended to increase
scatter with the vertically polarized laser beam oriented
with increasing particle diameter, as did consequently
disturbances resulting from the balance of surface
tension and aerodynamic drag forces with the directional gravitational field, the particles tend to orient in
space, so that the scattering behavior of the particles
the magnitude of the depolarization ratio. For maximum values (drops >3 mm), 6 approached values of 1.0,
while the ratios of E signals at the spike peak to that
immediately preceding on one occasion was nearly 6.
The increase in these values may have been induced by
the increasing extent of the central ice mass with increasing particle size.
in the horizontal direction. Since liquid hydrometeors
of the size range encountered in this study display shape
would likely depend on the angle of incidence of the
radiation to some degree. Nonetheless, in view of the
total lack of theoretical predictions of the scattering
properties of such aspherical particles (much larger than
any peculiar scattering behavior not displayed by
melting drops. The drop freezing record in Fig. 5(b)
the wavelength), these measurements clearly can provide useful insights into the dominant scattering
mechanisms acting in large, near-spherical particles.
To summarize, it is apparent that the character of the
backscatter from particles distorted either by aerodynamic drag forces or mechanical suspension is vastly
different for drops in the liquid and solid phase.
Whereas liquid drops depolarize the incident energy to
<-1%, frozen drops are capable of strongly altering the
polarization properties of the returned energy. Since
the shapes of suspended particles before and after the
phase transition were often similar and since ice particles with considerable liquid coverings still produced
shows a particle which produced 6 of -0.01 and 0.65 in
the liquid and ice phase, respectively. Upon nucleation,
large 6 values, the generation of the depolarized energy
must result by virtue of the optical inhomogeneity of the
In other respects, it is also noteworthy that the pure
ice particles were more efficient backscatterers than the
resultant liquid drops, nearly two times so on the average. Individual ice particles yielded Ell signal values
which varied from 0.9 to 7.0 times the values for the
completely melted drops. This difference in backscattering efficiency could not likely be explained in
terms of the small decrease in diameter produced during
the phase change.
Finally, the behavior of drops undergoing the liquid
to solid phase change will be considered with regard to
the signals in both channels rise instantaneously with
the formation of an ice shell around the drop. Initial
ice bodies. The nonuniformities in the internal structure of the ice particles, as evidenced by their opaqueMay 1977 / Vol. 16, No. 5 / APPLIED OPTICS
1339
ness, provide opportunities for ray paths involving the
multiple internal scattering of the incident light. That
this behavior is efficient in producing backscatter is
shown by the maintenance of high 6 values during most
of the phase change. During much of this period, the
scattering mechanisms responsible for much of the returns from the completely melted particle (i.e.,surface
waves, the frontal axial reflection, and likely some in-
ternally reflected ray paths), with the exception of the
internal axial component, are contributing to the return
energy and are yet incapable of lowering 6 values to any
great extent. A particularly strong and perhaps different depolarizing process for melting drops is indicated in most records just as the receding ice body occupies a position at the center of the particle. (The ice
mass typically rose to near the top of the drop due to
entrapped air bubbles.) As represented by the El
signal spike, this mechanism is a counterpart of the
emergence of the Ell signal internal axial component,
but probably involves ray paths which are refracted
through the ice mass and which utilize the drops far
internal face to aid in returning the energy in the
backward direction.
The scattering behavior of pure liquid drops can be
examined with the aid of the experiments involving both
the freely falling and suspended particles. From the
latter measurements, it was inferred (for drops with the
geometry induced by the suspension technique) that the
combined external and internal face axial components
comprised perhaps a half of the total returned energy.
For truly spherical scatterers, the contribution of surface waves to the return would dominate, indicating that
even slight distortions in sphericity are more destructive
to the circumferential than the axial component. Depending on drop shape, the latter contribution may be
significantly enhanced from the decrease in drop surface
curvature from particle elongation. That both mechanisms contribute to the return is apparent from the
photomicrographs of the particles such as shown in Fig.
6, which were taken at a scattering angle as close to the
backward direction as possible (1600). It is interesting to note that on regularly frozen drops, the presence of bright areas at the particle's edges and center
demonstrates that the corresponding scattering
mechanisms were acting with the ice particles. After
melting, it was often noted that surface wave generating
areas would become localized at areas along the drop
edge that varied according to exact drop shape. The
strongest areas of return, however, were always at the
center and edge of the drop at a point through the horizontal plane of the drop's center.
An analysis of the data from freely falling drops where
the influences caused by the artificial drop suspension
were absent reveals that both experimental methods
yielded comparable data. Contrasting the Ell and 6
values obtained in each case, the suspended drops
produced on the average only slightly greater values,
although Ell values were sometimes considerably
greater. Hence, it is thought that the results discussed
above are generally representative of those from more
naturally shaped raindrops.
The striking behavior of the artificial raindrops >-4
1340
APPLIED OPTICS/ Vol. 16, No. 5 / May 1977
mm in diameter implies that for these highly distorted
particles the scattering mechanisms are vastly different
from those producing the observed radius-squared Ell
signal dependence for smaller drops. In reality, though,
measurable raindrop deviations from sphericity commence at diameters of about 0.3 mm,9 with the drops
thereafter increasing in degree of oblateness with size.
Jones,8 observing natural raindrops in free fall, found
large drops to resemble oblate spheroids which oscillated about an average axial ratio to an extent dependent on equivalent spherical diameter. Mean axial
ratios of only -0.98
have been found for a 1-mm
(equivalent spherical) diameter drop, with values then
decreasing more strongly with increasing size until a
-0.75 ratio was produced by drops of 4 mm (see Ref. 10).
However, a discontinuity in the rate of change of axial
ratios (with diameter) in the vicinity of the 4-mm diam
drop value is lacking, so that the severe alteration in
scattering behavior displayed by drops >-4 mm is
likely due to an exaggeration of the deformation form.
The precise geometry of such large drops can be approximated by a cap cyclide with a concavity on the
bottom surface which increases in extent as drop size
increases. The variation in experimental results shown
in Fig. 2 may be related to the development of this
structural feature with the creation of internally reflected ray paths, but more conclusive evidence would
require the modeling of raindrop backscattering behavior. Such simulations seem permissible by means
of the approximate geometrical optics approach in view
of the successful treatment of surface waves by approximate theory3 and the availability of models describing numerically the shapes of large raindrops.1 0 "'1
This endeavor would be particularly useful in assessing
any scattering dependence on the angle of incidence of
the radiation.
Despite the generation of the unexpectedly great
amounts of backscattered energy from the large drops,
it is important to note that only relatively minute
amounts of energy were returned depolarized from these
interactions. And yet, often significant depolarization
accompanied the drop deformations caused by artificially induced oscillations and breakup. Thus, it appears that the effects of aerodynamic drag forces on
drop shape are peculiar in that the resultant geometry
tends to minimize the creation of ray paths capable of
producing the depolarization of the incident light, at
least as far as horizontal incidence is concerned.
The inferences concerning near-spherical particle
scattering behavior summarized above have their main
applicability in the field of remote sensing with lidar and
in the in situ hydrometeor discrimination with cwlaser
systems. Both techniques can employ polarization
sensitive receivers and in such form have received in-
creasing attention in recent years to define the potential
of the optical backscatter depolarization technique.
These experimental results, although limited to horizontal incidence, have value in aiding in the delineation
of this potential.
Studies performed in recent years of both a theoretical and experimental nature have demonstrated that
crystalline ice particles could be distinguished from
spherical cloud droplets, but uncertainties about the
depolarizing characteristics of distorted raindrops and
near-spherical ice particles (e.g.,ice pellets, hailstones)
left doubt about the ambiguity of the technique, at least
in principle.1 2 The polarization measurements reported here substantiate this basic utility with regard
to these hydrometeor forms. It is surprising, however,
that linear depolarization ratios of about 0.5 have been
recovered from the regularly frozen ice particles and
liquid drops with an ice shell, since this same value is
frequently encountered in studies of hexagonal ice
particles with lidar and laboratory ice crystal clouds and
natural snowflakes with cw laser systems. 1 3 Further-
more, the generally higher amounts of depolarization
produced by the irregular frozen drops appear to imitate
more closely the 6 values of 0.65 to 0.70 observed for the
opaque and irregular natural graupel particles.1 4 The
6 value variations observed during the phase transition
are also valuable in identifying the presence of melting
hydrometeors through the characteristic trends obtained from the artificial particles and natural snowflakes and graupel. Depolarization ratios and relative
E 11values have been taken from these data and used in
a model of the optical scattering properties of particles
in the atmospheric melting region in an apparently
successful comparison to actual lidar data (paper in
preparation).
The data from the freely falling artificial raindrops
also have additional significance to lidar remote sensing:
first, that raindrops with diameters >-4 mm can be
expected to return relatively great amounts of energy;
second, that atmospheric regions containing accumulations of large raindrops involved in coalescence or
breakup can possibly be recognizable from the increased
6 values generated by this activity. The latter processes, however, apparently do not involve the genera-
tion of increased Ell values. It is also significant that
6 > 1.0 during the freezing of drops have been found on
several occasions. Although the occasional presence
of similar anomalous values in lidar measurements has
usually been attributed to anisotropic scattering
properties of some ice crystal clouds, 1 3 it is now clear
that the scattering from single particles can lead to such
a drastic alteration of the polarization character of
backscattered light.
In view of the lack of theoretical support to aid in the
interpretation of data remotely sensed via the optical
backscatter depolarization technique, the characterization of the scattering behavior of various forms of
atmospheric hydrometeors through experimental
means is helping to demonstrate that the technique
offers considerable promise to the evaluation of cloud
and precipitation composition.
References
1. P. S. Ro, T. S. Fahlen, and H. C. Bryant, Appl. Opt. 7, 883
(1968).
2. H. C. van de Hulst, Light Scattering from Small Particles (Wiley,
New York, 1957).
3. T. S. Fahlen and H. C. Bryant, J. Opt. Soc. Am. 58, 304 (1968).
4. H. C. Bryant and A. J. Cox, J. Opt. Soc. Am. 56, 1529 (1966).
5. K. Sassen, J. Appl. Meteorol. 13, 923 (1974).
6. J. 0. Laws, Trans. Am. Geophys. Union 22, 709 (1941).
7. R. Gunn and G. D. Kinzer, J. Meteorol. 6, 243 (1949).
8. D. M. A. Jones, J. Meteorol. 16, 504 (1959).
9. H. R. Pruppacher and K. Beard, Q. J. R. Meteorol. Soc. 96, 247
(1970).
10. A. W. Green, J. Appl. Meteorol. 14, 1578 (1975).
11. H. R. Pruppacher and R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
12. Lidar polarization measurements appear in some cases to be also
influenced by the design of the lidar system through the viewing
of photon multiple scattering (see Ref. 13).
13. K. Sassen, J. Appl. Meteorol. 15, 292 (1976).
14. K. Sassen, Nature 255, 316 (1975).
Some of the participants in the Garmisch-Partenkirchen Symposium on Radiation in the Atmosphere with Special Emphasis on Structure and
Radiation Properties of Aerosols and Clouds Including Remote Sensing and Satellite Measurements: R. A. McClatchey (AFGL), V. E. Derr
(NOAA-ERL), John Garing (AFGL), V. E. Zuev (U.S.S.R. Institute of Atmospheric Optics), and Sharon McClatchey. The meeting was held
last August, and V. E. Derr was a section chairperson. Photo: F. S. Harris, Jr., (NASA-Langley).
May 1977 / Vol. 16, No. 5 / APPLIED OPTICS
1341