Howard K. Roscoe, Tom A. Lachlan-Cope, and John Roscoe, "Feasibility of an airborne TV camera as a size spectrometer for cloud droplets in daylight," Appl. Opt. 38, 441-450 (1999)
Photographs of clouds taken with a camera with a large aperture
ratio must have a short depth of focus to resolve small
droplets. Hence the sampling volume is small, which limits the
number of droplets and gives rise to a large statistical error on the
number counted. However, useful signals can be obtained with a
small aperture ratio, which allows for a sample volume large enough for
counting cloud droplets at aircraft speeds with useful spatial
resolution. The signal is sufficient to discriminate against noise
from a sunlit cloud as background, provided the bandwidth of the light
source and camera are restricted, and against readout noise. Hence,
in principle, an instrument to sample the size distribution of cloud
droplets from aircraft in daylight can be constructed from a simple TV
camera and an array of laser diodes, without any components or screens
external to the aircraft window.
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Comparison of Our Calculated Intensities of the Internally
Reflected Ray from a Large Spherical Water Droplet to Those
Calculated by van de Hulst
(1981)a
The values are in units of 1/4π
sr-1, so that they are the power relative to that which
would be reflected from a perfectly reflecting sphere of the same size.
TW means this work.
Table 2
Comparison of Our Calculations of the Intensities of the
Reflected Rays from a Large Glass Sphere to our
Measurementsa
The two 20° measurements were made on
different days. The calculated values are in units of 1/4π
sr-1, so that they are the intensity relative to that
which would be reflected from a perfectly reflecting sphere of the same
size. The measured values are relative to the intensity
simultaneously measured from a polished steel sphere, multiplied by the
square of the ratio of their diameters. I1 is the externally
reflected and I2 the internally reflected intensity. I2c
is the center, and I2e the edge ray.
C is calculated.
M is measured.
Table 3
Calculated Intensity Reflected from a Large Water
Droplet: Ratios of the Minimum Intensity Due to Interference to the
Intensity without Interferencea
Backscatter Angle (deg)
Polarization 1
Polarization 2
Sum of Both Polarizations
10
0.185
0.202
0.194
15
0.155
0.203
0.181
20
0.018
0.026
0.022
30
0.004
0.062
0.038
Interference occurs between the three
rays: externally reflected, center internally reflected, edge
internally reflected.
Table 4
Variables and Equations Used in the Calculation of
Instrument Feasibility
[R
1/(4π)+ R
2
c * (1 - R
2
c)
2
* §c + R
2
e * (1 - R
2
e)
2
* §e] * i
L
Light scattered from droplet
d
2
* s * A
2
* M
2
* P * π
2
* W * r * f/(16 * spd)
I
Solar irradiance at λ
Linear dependence on λ
b
Bandwidth of filter
Independent
S
Solar power
(I * b)/E
R
Sunlight from background
(S * A
2
* p
2
* 0.3)/(16
f)
rn
Readout noise
Independent
Table 5
Values of the Variables for a Typical Calculation for an
Airborne Instrument
Symbol
Value
Units
Value in SI Units
SI Unit
r
5
µm
5.00 × 10-6
m
spd
100
Knots
5.14 × 10
m s-1
t
1
s
1.00 × 100
s
f
50
Exposures s-1
5.00 × 10
Exposures s-1
N
50
Exposures
5.00 × 10
Exposures
∊
0.1
1.00 × 10-1
n
10
cm-3
1.00 × 107
m-3
V
0.2
cm3
2.00 × 10-7
m3
p
12
µm
1.20 × 10-5
m
p
2
144
µm2
1.44 × 10-10
m2
Æ
4.424 × 105
4.42 × 105
M
2.4
2.40
l
0.067495
mm
6.75 × 10-5
m
A
0.1778
rad
1.78 × 10-1
rad
u
500
mm
5.00 × 10-1
m
o
213.4
mm
2.13 × 10-1
m
v
1200
mm
1.20
m
e
0.318
3.18 × 10-1
O
6
W
6.00
W
λ
795
nm
7.95 × 10-7
m
ν
3.822 × 1014
Hz
3.82 × 1014
Hz
E
2.500 × 10-19
J
2.50 × 10-19
J
P
7.534 × 109
Photons/exposure µm-2
7.53 × 1021
Photons/exposure m-2
d
5
µm
5.00 × 10-6
m
β
16
deg
2.79 × 10-1
rad
ñ
1.3291
1.33
ï1
8.0
deg
1.40 × 10-1
rad
ı̂1
6.011
deg
1.05 × 10-1
rad
R
1
0.01997
2.00 × 10-2
ï2
c
16.128
deg
2.81 × 10-1
rad
ı̂2
c
12.064
deg
2.11 × 10-1
rad
R
2
c
0.020036
2.00 × 10-2
§c
0.3222
sr-1
3.22 × 10-1
sr-1
ï2
e
89.614
deg
1.56
rad
ı̂2
e
48.797
deg
8.52 × 10-1
rad
R
2
e
0.9584
9.58 × 10-1
§e
0.003948
sr-1
3.95 × 10-3
sr-1
i
0.17
1.70 × 10-1
s
0.001325
sr-1
1.33 × 10-3
sr-1
L
104624
Photons/exposure/droplet
1.05 × 105
Photons/exposure/droplet
I
1.149
W m-2 nm-1
1.15 × 109
W m-3
b
6
nm
6.00 × 10-9
m
S
2.758 × 1015
Photons cm-2 s-1
2.76 × 1019
Photons m-2 s -1
R
187633
Photons/exposure/pixel
1.88 × 105
Photons/exposure/pixel
rn
100
Electrons/exposure/pixel
1.00 × 102
Electrons/exposure/pixel
Signal = e * L
3.33 × 104
Electrons/exposure/droplet
Sunlight noise =
3.39 × 103
Electrons/exposure/line
Readout noise = rn * W-1
2.77 × 103
Electrons/exposure/line
Tables (5)
Table 1
Comparison of Our Calculated Intensities of the Internally
Reflected Ray from a Large Spherical Water Droplet to Those
Calculated by van de Hulst
(1981)a
The values are in units of 1/4π
sr-1, so that they are the power relative to that which
would be reflected from a perfectly reflecting sphere of the same size.
TW means this work.
Table 2
Comparison of Our Calculations of the Intensities of the
Reflected Rays from a Large Glass Sphere to our
Measurementsa
The two 20° measurements were made on
different days. The calculated values are in units of 1/4π
sr-1, so that they are the intensity relative to that
which would be reflected from a perfectly reflecting sphere of the same
size. The measured values are relative to the intensity
simultaneously measured from a polished steel sphere, multiplied by the
square of the ratio of their diameters. I1 is the externally
reflected and I2 the internally reflected intensity. I2c
is the center, and I2e the edge ray.
C is calculated.
M is measured.
Table 3
Calculated Intensity Reflected from a Large Water
Droplet: Ratios of the Minimum Intensity Due to Interference to the
Intensity without Interferencea
Backscatter Angle (deg)
Polarization 1
Polarization 2
Sum of Both Polarizations
10
0.185
0.202
0.194
15
0.155
0.203
0.181
20
0.018
0.026
0.022
30
0.004
0.062
0.038
Interference occurs between the three
rays: externally reflected, center internally reflected, edge
internally reflected.
Table 4
Variables and Equations Used in the Calculation of
Instrument Feasibility