Reliability of the polar nephelometer for the measurement of visibility in fog

G. Tonna; K. S. Shifrin

doi:10.1364/AO.31.002932

Applied Optics
Vol. 31,
Issue 15,
pp. 2932-2941
(1992)
•https://doi.org/10.1364/AO.31.002932

Reliability of the polar nephelometer for the measurement of visibility in fog

G. Tonna and K. S. Shifrin

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G. Tonna and K. S. Shifrin, "Reliability of the polar nephelometer for the measurement of visibility in fog," Appl. Opt. 31, 2932-2941 (1992)

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Abstract

The relation between the extinction coefficient of light at λ = 0.55 μm and the scattered intensity was studied as a function of the scattering angle and the wavelength, in connection with its use in the measurement of visibility with the polar nephelometer. Computations used 239 spectra of natural fogs; they considered 181 scattering angles, 22 wavelengths from 0.25 to 5 μm, three cases of polarization, and four classes of visibility. Results show that for each wavelength within the interval λ = 0.25–1.06 μm and for each polarization and visibility class, there exists a corresponding well-defined angular interval in which the above relation is linear and quite reliable. The center and the width of the angular intervals, as well as the relative standard deviation concerning the relation at hand, depend strictly on the wavelength and the class of visibility considered; they range between 26 and 56 deg, 6 and 23 deg, and 0.5 and 3.5%, respectively, so that by a proper choice of wavelength and related angular interval, visibility can be determined within 0.5%.

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	V = 0–100 m		V = 100–200 m		V = 200–∞		V = 0–∞

Quantity	Mean	Disp.	Mean	Disp.	Mean	Disp.	Mean	Disp.
$\bar{r}$ (μm)	6.22	36	6.46	33	8.2	37	7.06	38
σ (μm)	2.62	36	2.92	38	3.6	41	3.09	41
N (cm⁻³)	926	256	174	359	45	428	301	421
W (g m⁻³)	0.24	36	0.13	29	0.06	52	0.13	67

λ(μm)	(∊₀)_min	(∊₁)_min	(∊₂)_min
0.25	0.82	0.68	0.94
0.3	0.58	0.51	0.65
0.3472	0.80	0.85	0.74
0.40	0.56	0.64	0.57
0.45	0.75	0.61	0.92
0.4880	0.86	0.63	1.15
0.55	1.31	0.93	1.74
0.6	1.82	1.53	2.15
0.6328	2.38	2.26	2.55
0.6943	2.29	2.16	2.47
0.75	1.87	1.79	2.00
0.8	1.69	1.79	1.72
0.85	1.60	1.82	1.55
0.9	1.85	2.20	1.64
1.06	2.75	3.54	2.19
1.2	3.04	4.01	2.53
1.4	4.11	5.40	3.39
1.6	4.04	4.55	3.98
2	8.55	8.02	9.22
2.4	12.60	11.60	13.60
3.5	22.80	20.20	25.40
5	19.90	18.60	21.30

λ(μm)	θ₁	θ₂	$\bar{∊_{0}}$	$\bar{α_{0}}$	θ₁	θ₂	$\bar{∊_{1}}$	$\bar{α_{1}}$	θ₁	θ₂	$\bar{∊_{2}}$	$\bar{α_{2}}$
0.25	52	59	0.95	3.17	50	59	0.81	3.37	53	59	1.12	2.91
0.3	46	53	0.86	2.09	43	53	0.99	2.13	47	53	0.85	1.95
0.3472	41	49	0.60	1.54	41	49	0.58	1.69	42	49	0.59	1.45
0.4	36	46	0.63	1.17	36	46	0.81	1.27	36	46	0.62	1.09
0.45	20	35	0.98	0.50	18	36	1.36	0.51	21	35	0.79	0.49
0.4880	27	37	0.68	0.64	25	37	0.90	0.64	29	37	0.84	0.65
0.55	34	43	1.19	0.98	33	43	1.06	1.02	35	43	1.60	0.95
0.6	38	47	1.62	1.29	36	47	1.46	1.32	38	48	2.06	1.24
0.6328	32	49	2.17	1.17	30	49	1.85	1.20	40	49	2.25	1.36
0.6943	33	51	2.32	1.30	32	51	2.08	1.38	35	51	2.52	1.27
0.75	36	44	1.76	1.07	34	44	1.63	1.08	37	45	2.01	1.07
0.8	37	47	1.75	1.24	36	46	1.64	1.25	39	48	1.80	1.27
0.85	40	49	1.60	1.46	40	48	1.52	1.53	40	51	1.73	1.45
0.9	40	52	1.93	1.65	40	50	1.91	1.66	40	53	1.91	1.57
1.06	41	57	2.82	2.05	44	57	3.45	2.47	40	55	2.35	1.69

λ(μm)	θ₁	θ₂	$\bar{∊_{0}}$	$\bar{α_{0}}$	θ₁	θ₂	$\bar{∊_{1}}$	$\bar{α_{1}}$	θ₁	θ₂	$\bar{∊_{2}}$	$\bar{α_{2}}$
0.25	41	56	1.08	1.98	40	56	0.98	2.16	43	56	1.18	1.88
0.3	41	50	0.69	1.58	40	50	0.57	1.70	43	50	0.81	1.53
0.3472	30	50	1.30	1.17	30	50	1.35	1.27	32	50	1.25	1.14
0.4	31	44	0.72	0.94	30	43	0.77	0.94	32	44	0.72	0.91
0.45	31	40	0.89	0.80	30	40	0.81	0.83	32	40	1.06	0.78
0.4880	33	42	1.24	1.03	32	42	1.05	0.95	34	42	1.46	0.89
0.55	38	47	1.76	1.29	37	47	1.52	1.36	39	47	2.07	1.24
0.6	42	50	2.22	1.65	42	51	2.05	1.89	42	50	2.51	1.51
0.6328	43	52	2.78	1.83	43	52	2.68	2.03	43	52	2.93	1.68
0.6943	30	39	3.05	0.75	30	38	3.16	0.76	30	42	3.04	0.72
0.75	31	43	2.61	0.89	31	41	2.79	0.88	31	45	2.54	0.91
0.8	34	45	2.13	1.05	35	44	2.47	1.12	34	47	2.02	1.06
0.85	35	47	1.90	1.17	35	46	2.40	1.21	35	49	1.73	1.18
0.9	35	49	1.88	1.27	35	47	2.39	1.26	35	50	1.68	1.22
1.06	36	51	2.33	1.40	36	47	2.57	1.28	36	52	2.32	1.35

λ(μm)	θ₁	θ₂	$\bar{∊_{0}}$	$\bar{α_{0}}$	θ₁	θ₂	$\bar{∊_{1}}$	$\bar{α_{1}}$	θ₁	θ₂	$\bar{∊_{2}}$	$\bar{α_{2}}$
0.25	46	57	0.75	2.39	43	57	0.85	2.47	48	57	0.74	2.27
0.3	41	53	0.63	1.79	40	52	0.61	1.85	43	53	0.62	1.72
0.3472	39	49	0.51	1.44	38	48	0.52	1.47	39	50	0.65	1.38
0.4	28	46	0.73	0.94	27	46	0.69	0.98	29	46	0.83	0.90
0.45	17	35	0.73	0.46	17	35	0.71	0.47	17	36	0.86	0.46
0.4880	19	38	1.08	0.54	18	38	0.94	0.55	19	38	1.29	0.52
0.55	34	43	1.58	0.98	33	43	1.37	1.02	36	43	1.78	0.98
0.6	26	48	2.23	0.97	25	48	2.05	1.01	28	48	2.40	0.95
0.6328	29	49	2.38	1.09	27	49	2.26	1.12	30	49	2.54	1.04
0.6943	32	43	2.29	0.92	31	42	2.11	0.92	34	44	2.40	0.95
0.75	34	45	2.15	1.06	33	44	2.01	1.05	35	46	2.29	1.06
0.8	36	47	2.14	1.21	35	45	2.06	1.17	37	48	2.17	1.21
0.85	38	48	2.16	1.33	38	47	2.21	1.39	38	49	2.16	1.28
0.9	37	50	2.64	1.40	38	48	2.70	1.44	37	51	2.52	1.35
1.06	34	46	2.94	1.09	33	44	3.37	1.04	35	47	2.51	1.09

λ(μm)	θ₁	θ₂	$\bar{∊_{0}}$	$\bar{α_{0}}$	θ₁	θ₂	$\bar{∊_{1}}$	$\bar{α_{1}}$	θ₁	θ₂	$\bar{∊_{2}}$	$\bar{α_{2}}$
0.25	50	57	1.06	2.72	49	57	1.01	2.99	51	57	1.21	2.51
0.3	42	53	0.98	1.85	41	53	0.92	2.00	44	53	1.01	1.78
0.3472	40	49	0.96	1.49	40	49	1.06	1.64	40	49	0.96	1.37
0.4	29	46	0.84	0.96	28	45	0.92	0.96	29	46	0.87	0.90
0.45	28	37	1.17	0.66	28	37	1.18	0.69	28	38	1.28	0.65
0.4880	31	39	1.25	0.77	31	39	1.14	0.82	31	39	1.46	0.73
0.55	37	44	1.64	1.12	36	44	1.45	1.16	38	44	1.91	1.07
0.6	40	48	2.18	1.43	40	48	2.01	1.56	40	48	2.41	1.32
0.6328	41	50	2.67	1.58	41	50	2.62	1.74	41	50	2.78	1.46
0.6943	32	40	2.62	0.82	31	39	2.55	0.81	33	41	2.72	0.82
0.75	34	43	2.27	0.97	34	42	2.20	1.00	35	45	2.37	1.01
0.8	36	46	2.12	1.16	36	45	2.18	1.20	37	48	2.14	1.20
0.85	38	48	2.05	1.33	38	47	2.24	1.38	38	49	1.98	1.27
0.9	39	49	2.20	1.42	39	49	2.57	1.54	39	50	2.01	1.37
1.06	39	48	2.92	1.35	37	52	3.96	1.62	38	49	2.50	1.26

Abstract

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Applied Optics