John C. Johnson and James R. Terrell, "Transmission Cross Sections for Water Spheres Illuminated by Infrared Radiation*," J. Opt. Soc. Am. 45, 451-454 (1955)
The Mie theory is used in the computation of several transmission cross sections for absorbing spheres. For each sphere a complex index of refraction is selected such that the cross section corresponds to that of a water sphere illuminated by infrared radiation of mean wavelength less than 14 microns. The real part of the index is a value between 1.14≤m≤1.42 and the imaginary part, the absorption index, lies between 0≤mk≤0.40.
Also included is a study of the change in the transmission cross section as the absorption index is varied. For these computations, the real index of refraction is kept constant at m=1.29.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
A table of transmission cross sections of spheres as a function of α and k for a real index of refraction, m=1.29. If r is the radius of the sphere and λ is the free space wavelength of the incident plane parallel radiation, then α=2πr/λ. The complex index of refraction m* is related to the real index of refraction m and the absorption index mk through m*=m(1−ik). Throughout this table m=1.29. The transmission cross section σT is the tabular value and σT=σT(1.29, 1.29k, α).
k
α
0
0.05
0.10
0.25
0.50
0.90
1.00
0
0
0
0
0
0
0
0
0.05
0.00
0.0750
0.10
0.0750
0.150
0.268
0.15
0.118
0.20
0.152
0.25
0.172
0.702
0.50
0.395
0.811
1.58
1.00
0.0723
0.261
0.438
0.879
1.61
2.57
2.78
2.00
0.535
0.864
1.13
1.69
2.27
2.95
3.00
2.43
4.00
2.30
2.28
2.26
2.30
2.45
2.77
6.00
3.67
3.07
2.54
2.47
2.63
6.60
3.85
3.19
2.70
2.53
2.40
7.00
3.91
3.06
2.68
2.35
7.17
3.83
7.35
3.84
8.00
3.70
8.20
2.33
9.00
3.30
9.50
3.08
2.67
2.31
10.00
2.97
12.00
1.92
2.25
2.27
12.40
1.75
2.27
12.50
2.27
2.27
12.60
2.26
12.80
1.90
2.29
13.00
1.71
2.25
2.26
13.10
1.86
13.50
1.87
2.24
16.00
2.38
2.31
2.25
17.00
2.40
2.23
18.00
2.78
2.32
2.22
18.60
2.84
19.30
2.63
25.00
2.18
k
α
1.10
1.732
2.00
2.25
4.00
100
∞
0
0
0
0
0
0
0
0
0.50
1.67
1.44
1.22
0.523
0.218
0.217
1.00
2.98
3.74
3.85
3.87
3.31
2.07
2.04
2.00
3.37
3.40
3.38
3.01
2.23
2.21
4.00
3.02
2.18
6.00
2.83
8.20
2.07
12.00
2.05
25.00
2.03
Table II
A step function approximation to the complex dispersion curve for water. The complex index of refraction is m* and Δλ is the wavelength interval in which m* is the approximation value.
The transmission coefficient for m*=1.33 can be found in a paper by H. G. Houghton and W. R. Chalker, J. Opt. Soc. Am. 39, 955–957 (1949). For m*=1.33, the transmission and scattering cross sections are identical.
Table III
Transmission cross sections for spheres having a complex index of refraction, m*=m (1−ik), where r is the radius of the sphere and λ is the wavelength of the illuminating plane parallel radiation, α=2πr/λ.
m=1.14
m=1.17
m=1.22
m=1.28
m=1.28
m=1.33
m=1.33
m=1.33
m=1.42
α
k=0.10
k=0.18
k=0.05
k=0.04
k=0.23
k=0.01
k=0.03
k=0.30
k=0.01
1.00
0.32
0.58
0.21
0.21
0.83
0.13
0.20
1.10
0.19
1.75
0.59
0.99
0.50
0.59
1.43
0.55
0.67
1.78
0.88
2.50
0.87
1.34
0.88
1.12
1.86
1.27
1.37
2.15
1.91
3.25
1.11
1.60
1.27
1.67
2.12
2.05
2.08
2.33
2.90
4.00
1.34
1.80
1.65
2.18
2.27
2.77
2.69
2.40
3.61
4.75
1.53
1.94
2.00
2.60
2.34
3.33
3.13
2.42
3.91
5.50
1.69
2.04
2.29
2.91
2.37
3.66
3.38
2.41
3.82
6.25
1.83
2.11
2.52
3.08
2.37
3.72
3.41
2.39
3.44
7.00
1.94
2.15
2.69
3.15
2.36
3.57
3.29
2.37
2.92
7.75
2.03
2.18
2.79
3.11
2.34
3.28
3.06
2.36
2.43
8.50
2.10
2.20
2.84
3.01
2.33
2.92
2.80
2.34
2.09
9.25
2.15
2.21
2.84
2.85
2.31
2.56
2.54
2.33
1.98
10.00
2.19
2.21
2.80
2.68
2.30
2.26
2.34
2.31
2.07
10.75
2.22
2.21
2.73
2.51
2.29
2.06
2.21
2.30
2.28
11.50
2.24
2.21
2.65
2.38
2.28
1.97
2.16
2.29
2.50
12.25
2.24
2.21
2.57
2.28
2.27
1.98
2.16
2.28
2.65
13.00
2.25
2.20
2.48
2.22
2.26
2.07
2.21
2.27
2.69
13.75
2.25
2.20
2.41
2.20
2.25
2.22
2.29
2.27
2.60
14.50
2.24
2.19
2.34
2.21
2.25
2.39
2.36
2.26
2.43
15.25
2.24
2.19
2.29
2.23
2.24
2.53
2.42
2.25
2.24
16.00
2.23
2.19
2.26
2.27
2.23
2.63
2.45
2.25
2.11
16.75
2.22
2.18
2.23
2.30
2.23
2.64
2.44
2.24
2.07
17.50
2.21
2.18
2.22
2.32
2.22
2.57
2.40
2.23
2.11
Tables (3)
Table I
A table of transmission cross sections of spheres as a function of α and k for a real index of refraction, m=1.29. If r is the radius of the sphere and λ is the free space wavelength of the incident plane parallel radiation, then α=2πr/λ. The complex index of refraction m* is related to the real index of refraction m and the absorption index mk through m*=m(1−ik). Throughout this table m=1.29. The transmission cross section σT is the tabular value and σT=σT(1.29, 1.29k, α).
k
α
0
0.05
0.10
0.25
0.50
0.90
1.00
0
0
0
0
0
0
0
0
0.05
0.00
0.0750
0.10
0.0750
0.150
0.268
0.15
0.118
0.20
0.152
0.25
0.172
0.702
0.50
0.395
0.811
1.58
1.00
0.0723
0.261
0.438
0.879
1.61
2.57
2.78
2.00
0.535
0.864
1.13
1.69
2.27
2.95
3.00
2.43
4.00
2.30
2.28
2.26
2.30
2.45
2.77
6.00
3.67
3.07
2.54
2.47
2.63
6.60
3.85
3.19
2.70
2.53
2.40
7.00
3.91
3.06
2.68
2.35
7.17
3.83
7.35
3.84
8.00
3.70
8.20
2.33
9.00
3.30
9.50
3.08
2.67
2.31
10.00
2.97
12.00
1.92
2.25
2.27
12.40
1.75
2.27
12.50
2.27
2.27
12.60
2.26
12.80
1.90
2.29
13.00
1.71
2.25
2.26
13.10
1.86
13.50
1.87
2.24
16.00
2.38
2.31
2.25
17.00
2.40
2.23
18.00
2.78
2.32
2.22
18.60
2.84
19.30
2.63
25.00
2.18
k
α
1.10
1.732
2.00
2.25
4.00
100
∞
0
0
0
0
0
0
0
0
0.50
1.67
1.44
1.22
0.523
0.218
0.217
1.00
2.98
3.74
3.85
3.87
3.31
2.07
2.04
2.00
3.37
3.40
3.38
3.01
2.23
2.21
4.00
3.02
2.18
6.00
2.83
8.20
2.07
12.00
2.05
25.00
2.03
Table II
A step function approximation to the complex dispersion curve for water. The complex index of refraction is m* and Δλ is the wavelength interval in which m* is the approximation value.
The transmission coefficient for m*=1.33 can be found in a paper by H. G. Houghton and W. R. Chalker, J. Opt. Soc. Am. 39, 955–957 (1949). For m*=1.33, the transmission and scattering cross sections are identical.
Table III
Transmission cross sections for spheres having a complex index of refraction, m*=m (1−ik), where r is the radius of the sphere and λ is the wavelength of the illuminating plane parallel radiation, α=2πr/λ.
Add to BibSonomy