Infrared Transmission through the Atmosphere

A. E. S. Green; M. Griggs

doi:10.1364/AO.2.000561

Applied Optics
Vol. 2,
Issue 6,
pp. 561-570
(1963)
•https://doi.org/10.1364/AO.2.000561

Infrared Transmission through the Atmosphere

A. E. S. Green and M. Griggs

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A. E. S. Green and M. Griggs, "Infrared Transmission through the Atmosphere," Appl. Opt. 2, 561-570 (1963)

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Abstract

An analytic expression for transmission in terms of optical path and pressure is combined with an analytical expression for equivalent atmospheric path length in terms of height and slant angle to yield a single expression for transmission in terms of height and slant angle. Separate equations are developed for carbon dioxide absorption, and for water vapor absorption. The latter may be used with almost any water vapor distribution in the atmosphere. A function due to Chapman is used instead of the usual secant factor for slant paths in order to extend the use of the equations to angles of incidence up to 90°. Wavelength dependent parameters are presented based upon Zachor’s analytic fits to laboratory data.

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θ	f(800, θ)
20	1.064
21	1.071
22	1.078
23	1.086
24	1.094
25	1.103
26	1.112
27	1.122
28	1.132
29	1.143
30	1.154
31	1.166
32	1.179
33	1.192
34	1.206
35	1.220
36	1.235
37	1.251
38	1.268
39	1.286
40	1.304
41	1.324
42	1.344
43	1.366
44	1.388
45	1.412
46	1.438
47	1.464
48	1.492
49	1.522
50	1.553
51	1.586
52	1.621
53	1.658
54	1.697
55	1.739
56	1.783
57	1.831
58	1.881
59	1.935
60	1.993
61	2.054
62	2.121
63	2.192
64	2.269
65	2.353
66	2.443
67	2.542
68	2.650
69	2.767
70	2.897
71	3.040
72	3.199
73	3.376
74	3.575
75	3.800
76	4.055
77	4.348
78	4.687
79	5.083
80	5.551
81	6.113
82	6.799
83	7.650
84	8.732
85	10.144
86	12.051
87	14.730
88	18.686
89	24.905
90	35.466
91	55.211
92	96.753

θ	f(800, θ)
20	1.064
21	1.071
22	1.078
23	1.086
24	1.094
25	1.103
26	1.112
27	1.122
28	1.132
29	1.143
30	1.154
31	1.166
32	1.179
33	1.192
34	1.206
35	1.220
36	1.235
37	1.251
38	1.268
39	1.286
40	1.304
41	1.324
42	1.344
43	1.366
44	1.388
45	1.412
46	1.438
47	1.464
48	1.492
49	1.522
50	1.553
51	1.586
52	1.621
53	1.658
54	1.697
55	1.739
56	1.783
57	1.831
58	1.881
59	1.935
60	1.993
61	2.054
62	2.121
63	2.192
64	2.269
65	2.353
66	2.443
67	2.542
68	2.650
69	2.767
70	2.897
71	3.040
72	3.199
73	3.376
74	3.575
75	3.800
76	4.055
77	4.348
78	4.687
79	5.083
80	5.551
81	6.113
82	6.799
83	7.650
84	8.732
85	10.144
86	12.051
87	14.730
88	18.686
89	24.905
90	35.466
91	55.211
92	96.753

	CO₂

λ	8–35 km		0–8 km		n	H₂O K

	C	h	C	h
1.03						3.7 × 10⁻³
1.04						5.8 × 10⁻³
1.05						9.0 × 10⁻³
1.06						8.4 × 10⁻³
1.07						2.5 × 10⁻²
1.08						4.6 × 10⁻²
1.09						7.7 × 10⁻²
1.10						1.2 × 10⁻¹
1.11						1.8 × 10⁻¹
1.12						2.4 × 10⁻¹
1.13						2.8 × 10⁻¹
1.14						2.6 × 10⁻¹
1.15						2.0 × 10⁻¹
1.16						1.4 × 10⁻¹
1.17						1.0 × 10⁻¹
1.18						7.6 × 10⁻²
1.19						5.4 × 10⁻²
1.20						3.6 × 10⁻²
1.21						2.2 × 10⁻²
1.22						1.0 × 10⁻²
1.23						5.6 × 10⁻²
1.24						1.1 × 10⁻²
1.25						1.9 × 10⁻²
1.26						3.4 × 10⁻²
1.27						5.7 × 10⁻²
1.28						9.5 × 10⁻²
1.29						1.5 × 10⁻¹
1.30						2.2 × 10⁻¹
1.31						3.4 × 10⁻¹
1.32						4.9 × 10⁻¹
1.33						7.0 × 10⁻¹
1.34						9.6 × 10⁻¹
1.35						1.3
1.36						1.5
1.37	3.01 × 10⁻⁵	4.3	2.07 × 10⁻⁵	6.0	0.735	1.6
1.38	4.24 × 10⁻⁴	4.3	2.91 × 10⁻⁴	6.0	0.735	1.5
1.39	1.35 × 10⁻³	4.3	9.23 × 10⁻⁴	6.0	0.735	1.4
1.40	3.05 × 10⁻³	4.3	2.10 × 10⁻³	6.0	0.735	1.2
1.41	6.93 × 10⁻³	4.3	4.75 × 10⁻³	6.0	0.735	1.0
1.42	6.17 × 10⁻²	8.0	5.03 × 10⁻²	11.1	0.399	8.5 × 10⁻¹
1.44	6.38 × 10⁻²	8.0	5.20 × 10⁻²	11.1	0.399	5.4 × 10⁻¹
1.46	7.68 × 10⁻³	4.3	5.27 × 10⁻³	6.0	0.735	3.2 × 10⁻¹
1.48	2.21 × 10⁻³	4.3	1.52 × 10⁻³	6.0	0.735	2.0 × 10⁻¹
1.50	8.16 × 10⁻⁵	4.3	5.60 × 10⁻⁵	6.0	0.735	1.2 × 10⁻¹
1.52	4.65 × 10⁻⁶	4.3	3.19 × 10⁻⁶	6.0	0.735	7.4 × 10⁻²
1.54	8.39 × 10⁻⁴	4.3	5.76 × 10⁻⁴	6.0	0.735	3.9 × 10⁻²
1.56	4.41 × 10⁻³	4.3	3.03 × 10⁻³	6.0	0.735	3.7 × 10⁻³
1.58	1.36 × 10⁻²	4.3	9.34 × 10⁻³	6.0	0.735	8.7 × 10⁻³
1.60	5.95 × 10⁻²	7.2	4.74 × 10⁻²	9.9	0.446	3.8 × 10⁻⁵
1.63	7.39 × 10⁻³	4.3	5.07 × 10⁻³	6.0	0.735	5.8 × 10⁻³
1.65	3.13 × 10⁻³	4.3	2.15 × 10⁻³	6.0	0.735	5.5 × 10⁻³
1.67	7.03 × 10⁻⁴	4.3	4.83 × 10⁻⁴	6.0	0.735	1.8 × 10⁻²
1.68	1.18 × 10⁻⁴	4.3	8.11 × 10⁻⁵	6.0	0.735	2.4 × 10⁻²
1.69						3.2 × 10⁻²
1.70						4.4 × 10⁻²
1.72						8.2 × 10⁻²
1.74						1.5 × 10⁻¹
1.76						2.9 × 10⁻¹
1.78						5.4 × 10⁻¹
1.80						9.5 × 10⁻¹
1.82						1.6
1.84						2.5
1.86						2.7
1.88						2.0
1.90	2.95 × 10⁻³	4.3	2.03 × 10⁻³	6.0	0.735	1.3
1.92	2.20 × 10⁻²	4.3	1.51 × 10⁻²	6.0	0.735	7.7 × 10⁻¹
1.94	1.09 × 10⁻¹	4.3	7.47 × 10⁻²	6.0	0.735	4.7 × 10⁻¹
1.95	2.29 × 10⁻¹	4.7	1.62 × 10⁻¹	6.5	0.676	3.7 × 10⁻¹
1.96	2.58 × 10⁻¹	4.3	1.77 × 10⁻¹	6.0	0.735	2.8 × 10⁻¹
1.97	1.63 × 10⁻¹	4.1	1.09 × 10⁻¹	5.7	0.776	2.2 × 10⁻¹
1.98	1.21 × 10⁻¹	4.3	8.33 × 10⁻²	6.0	0.735	1.7 × 10⁻¹
1.99	1.00 × 10⁻¹	3.2	6.03 × 10⁻²	4.5	0.993	1.3 × 10⁻¹
2.00	4.22 × 10⁻¹	4.5	2.92 × 10⁻¹	6.2	0.717	1.0 × 10⁻¹
2.01	8.79 × 10⁻¹	7.2	7.00 × 10⁻¹	9.9	0.446	8.0 × 10⁻²
2.02	6.15 × 10⁻¹	8.9	5.12 × 10⁻¹	12.4	0.358	6.3 × 10⁻²
2.03	3.60 × 10⁻¹	7.1	2.86 × 10⁻¹	9.9	0.447	4.9 × 10⁻²
2.04	1.66 × 10⁻¹	4.3	1.14 × 10⁻¹	6.0	0.735	3.9 × 10⁻²
2.05	2.19 × 10⁻¹	4.3	1.50 × 10⁻¹	6.0	0.735	3.1 × 10⁻²
2.06	2.97 × 10⁻¹	4.3	1.97 × 10⁻¹	6.0	0.735	2.5 × 10⁻²
2.07	2.63 × 10⁻¹	5.2	1.93 × 10⁻¹	7.3	0.610	2.1 × 10⁻²
2.08	2.25 × 10⁻¹	8.0	1.83 × 10⁻¹	11.1	0.399	1.7 × 10⁻²
2.10	3.78 × 10⁻⁴	4.3	2.60 × 10⁻⁴	6.0	0.735	1.1 × 10⁻²
2.12						7.9 × 10⁻³
2.14						5.7 × 10⁻³
2.16						4.3 × 10⁻³
2.18						5.0 × 10⁻³
2.20						6.9 × 10⁻³
2.24						1.6 × 10⁻²
2.28						3.4 × 10⁻²
2.32						7.0 × 10⁻²
2.36						1.3 × 10⁻¹
2.40						2.3 × 10⁻¹
2.44						4.1 × 10⁻¹
2.48						1.4
2.52						1.8
2.54						2.7
2.56						4.0
2.58						4.6
2.60						5.1
2.62						5.8
2.64	2.02 × 10⁻¹	7.2	1.60 × 10⁻¹	9.9	0.446	7.2
2.66	8.85 × 10⁻¹	8.5	7.31 × 10⁻¹	11.8	0.375	8.9
2.68	3.34	7.1	2.66	9.9	0.448	9.8
2.70	6.86	7.2	5.46	9.9	0.446	9.3
2.72	4.71	7.7	3.81	10.7	0.414	6.4
2.74	4.41	6.4	3.41	8.8	0.500	4.8
2.76	13.30	4.4	9.14	6.0	0.735	4.3
2.78	7.36	6.4	5.69	8.8	0.500	4.0
2.80	3.23	8.0	2.63	11.1	0.399	3.7
2.82	1.50	10.9	1.29	15.2	0.292	3.2
2.84	5.86 × 10⁻¹	14.8	5.25 × 10⁻¹	20.5	0.216	2.6
2.86	2.68 × 10⁻¹	16.9	2.44 × 10⁻¹	23.4	0.189	2.0
2.88	1.13 × 10⁻¹	10.9	9.74 × 10⁻²	15.2	0.292	1.5
2.90						1.1
2.92						7.6 × 10⁻¹
2.94						6.5 × 10⁻¹
2.96						5.9 × 10⁻¹
2.98						5.8 × 10⁻¹
3.00						5.7 × 10⁻¹
3.02						5.9 × 10⁻¹
3.04						6.3 × 10⁻¹
3.06						6.6 × 10⁻¹
3.08						6.6 × 10⁻¹
3.10						5.9 × 10⁻¹
3.12						4.4 × 10⁻¹
3.14						3.0 × 10⁻¹
3.16						2.5 × 10⁻¹
3.18						3.4 × 10⁻¹
3.20						1.9 × 10⁻¹
3.22						1.5 × 10⁻¹
3.24						1.5 × 10⁻¹
3.26						1.7 × 10⁻¹
3.28						1.9 × 10⁻¹
3.30						2.2 × 10⁻¹
3.32						2.5 × 10⁻¹
3.34						2.9 × 10⁻¹
3.36						3.4 × 10⁻¹
3.40						2.4 × 10⁻¹
3.44						1.7 × 10⁻¹
3.48						1.2 × 10⁻¹
3.52						1.2 × 10⁻¹
3.56						6.0 × 10⁻²
3.60						4.2 × 10⁻²
3.64						2.9 × 10⁻²
3.68						2.1 × 10⁻²
3.72						1.5 × 10⁻²
3.76						1.0 × 10⁻²
3.80						7.3 × 10⁻³
3.84						5.2 × 10⁻³
3.88						3.7 × 10⁻³
3.92						2.6 × 10⁻³
3.96
4.05	4.16 × 10⁻²	4.3	2.85 × 10⁻²	6.0	0.735
4.10	3.20 × 10⁻²	3.9	1.90 × 10⁻²	5.7	0.735
4.15	8.30 × 10⁻²	5.5	6.10 × 10⁻²	7.6	0.735
4.20	8.29	4.3	5.69	6.0	0.735
4.35	15.40	7.2	12.26	9.9	0.446
4.40	8.63	6.4	6.68	8.5	0.500	3.4 × 10⁻³
4.45	3.46	6.4	2.68	8.5	0.500	5.5 × 10⁻³
4.50	1.13	3.7	6.50 × 10⁻¹	5.7	0.735	8.6 × 10⁻³
4.55	4.81 × 10⁻²	4.3	3.30 × 10⁻²	6.0	0.735	1.3 × 10⁻²
4.60	2.13 × 10⁻²	4.3	1.46 × 10⁻²	6.0	0.735	1.9 × 10⁻²
4.65	1.53 × 10⁻²	4.3	1.05 × 10⁻²	6.0	0.735	2.9 × 10⁻²
4.70	4.07 × 10⁻²	4.3	2.80 × 10⁻²	6.0	0.735	4.1 × 10⁻²
4.75	1.70 × 10⁻¹	4.0	1.10 × 10⁻¹	6.2	0.735	6.0 × 10⁻²
4.80	3.90 × 10⁻¹	3.6	2.20 × 10⁻¹	5.6	0.735	8.6 × 10⁻²
4.85	5.60 × 10⁻¹	4.0	3.1 × 10⁻¹	6.5	0.735	1.2 × 10⁻¹
4.90	1.8 × 10⁻¹	5.5	1.4 × 10⁻¹	6.5	0.735	1.5 × 10⁻¹
4.95						2.0 × 10⁻¹
5.05						3.0 × 10⁻¹
5.10						3.6 × 10⁻¹
5.15						4.3 × 10⁻¹
5.20						5.1 × 10⁻¹
5.25						6.1 × 10⁻¹
5.35						8.7 × 10⁻¹
5.40						1.1
5.45						1.3
5.50						1.5
5.60						2.3
5.70						3.5
5.80						5.1
5.85						6.1
5.90						7.6
5.95						8.8
6.00						1.0 × 10
6.05						1.0 × 10
6.10						9.9
6.15						8.3
6.20						6.9
6.25						5.7
6.30						4.9
6.35						4.8
6.40						5.1
6.45						6.3
6.50						8.1
6.55						1.0 × 10
6.60						1.2 × 10
6.65						1.3 × 10
6.70						1.3 × 10
6.75						1.2 × 10
6.80						1.1 × 10
6.85						9.8
6.90						8.6
6.95						7.6
7.00						6.7
7.10						5.2
7.20						4.0
7.40						2.4
7.60						1.4
7.80						8.4 × 10⁻¹
8.00						5.1 × 10⁻¹
8.20						3.4 × 10⁻¹
8.40						2.3 × 10⁻¹
8.60						1.6 × 10⁻¹
8.80						1.2 × 10⁻¹
9.00						8.5 × 10⁻²
9.20						6.2 × 10⁻²
9.40						4.5 × 10⁻²
9.60						3.1 × 10⁻²
9.80						2.2 × 10⁻²
10.00						1.5 × 10⁻²
10.20						9.5 × 10⁻³
10.40						5.7 × 10⁻³
10.60						3.2 × 10⁻³
10.80						τ ≃ 1

Abstract

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Figures (4)

Tables (2)

Equations (31)

Applied Optics