Wavelength Dependence of the Polarization of the Sunlit Sky*

Thomas Gehrels

doi:10.1364/JOSA.52.001164

Journal of the Optical Society of America
Vol. 52,
Issue 10,
pp. 1164-1173
(1962)
•https://doi.org/10.1364/JOSA.52.001164

Wavelength Dependence of the Polarization of the Sunlit Sky

Thomas Gehrels

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Thomas Gehrels, "Wavelength Dependence of the Polarization of the Sunlit Sky*," J. Opt. Soc. Am. 52, 1164-1173 (1962)

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Abstract

The blue sky was observed near 90° from the sun, in the vertical plane through the direction of the sun, with the sun above and just below the horizon. The observations were made with six filters ranging from 3250 to 9400 Å. For a normal clear sky at the McDonald Observatory with the sun $11_{.}^{°} 5$ above the horizon, 75% polarization was found at 5500 Å. The agreement of the Rayleigh–Chandrasekhar theory with the observations is good. The difference of the above 75% with 100% polarization appears to be due to multiple scattering (6%), molecular anisotropy (6%), and reflection by the ground (5%), while a residual 8% is presumably due to aerosols. At the McDonald Observatory, the polarization of the daytime sky has a maximum near 5500 Å, with a decrease toward longer as well as toward shorter wavelengths. The decline in the ultraviolet is caused by multiple scattering, while in the infrared it is mostly due to ground reflection, which is especially strong when green plants are present.

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Date UT	Tel. ^a	R.A. (1960)	Dec. (1960)	Phase	Sky conditions
1959
May 2	36″	20^h35^m5	+30°40′	$97_{.}^{°} 6$	Clear.
Aug. 10	82″	3 18.0	30 40	97.8	Clear.
Nov. 2	GL	18 22.2	56 00	94.1	Clear.
Dec. 24	36″	14 50.0	56 00	90.1	Varying, thin clouds in the field and over the sun. Rather cloudy during first observation at 1/λ = 1.89.
Dec. 26A	36″	11 26.0	47 00	64.5	Dust and slight haze, transparency not good; but fairly uniform.
Dec. 26B	36″	13 42.0	30 40	94.7
Dec. 26C	36″	15 37.0	12 00	127.1
1960
Jan. 1	36″	13 00.0	30 40	81.7	Thin clouds about, and some dust. Clouds in the field during the observation at 1/λ = 2.82.
Jan. 6A	36″	14 00.0	30 40	89.4	Perfectly clear.
Jan. 6B	36″	15 30.0	20 00	112.1
Jan. 6C	36″	12 30.0	41 00	68.9
Apr. 6	82″	19 06.4	30 00	94.2	Clear, but sky not hard blue.
Apr. 9	82″	19 10.0	30 00	93.2	Hazy; clouds about. Clouds in the field only for the first observation at 1/λ = 1.46.
Aug. 31	82″	4 38.9	+30 40	94.3	Clouds at start, for the first observation at 1/λ = 2.29; clear otherwise.

UT Date	1/λ	Sun’s elev.	P	θ _r
			%	°
1959 May 2	1.06	$5_{.}^{°} 2$	40.3	179.2
	1.06	6.6	40.1	179.0
	1.89	3.7	72.3	178.4
	1.89	8.8	68.2	178.4
	2.82	2.2	63.9	178.4
	2.82	10.3	63.1	178.5
Aug. 10	1.06	7.7	64.9	178.4
	1.06	9.4	63.8	178.4
	1.46	24.7	69.5	179.6
	1.46	26.5	69.3	179.5
	1.89	5.2	71.3	179.8
	1.89	11.2	68.4	179.7
	2.29	23.0	64.4	179.2
	2.29	28.2	64.1	179.4
	2.82	2.7	60.9	179.2
	2.82	12.8	59.4	179.4
	3.08	21.7	53.2	179.3
	3.08	29.9	52.8	179.2
Nov. 2	1.06	34.8	42.8	0.5
	1.06	35.7	42.7	0.4
	1.46	35.8	63.8	179.0
	1.46	35.0	62.7	179.3
	1.89	35.2	71.0	179.7
	2.29	35.6	68.9	179.7
	2.82	35.4	61.6	178.5
	3.08	35.4	55.9	179.1
Dec. 24	1.06	32.1	29.1:	178.9
	1.46	35.3	50.4	0.4
	1.89	31.6	52.1	179.5
	1.89	33.3	66.5	179.8
	2.29	35.7	66.5	0.4
	2.82	32.7	56.8	179.8
	3.08	35.8	56.3	0.5
Dec. 26A	1.06	25.1	36.6	178.8
	1.46	7.8	56.7	179.2
	1.46	19.8	52.8	⋯
	1.89	27.0	51.2	0.5
	2.29	8.9	51.8	179.4
	2.29	19.5	49.8	⋯
	2.82	27.6	42.8	2.3
	3.08	9.7	40.4	179.0
	3.08	19.3	39.8	⋯
Dec. 26B	1.06	29.0	36.1:	178.8
	1.46	11.3	71.8	179.3
	1.89	29.7	71.0	0.1
	2.29	12.3	75.9	179.7
	2.82	30.2	67.0	0.4
	3.08	+12.9	61.9	179.2
			%	°
1959 Dec. 26C	1.06	$23_{.}^{°} 8$	22.2	⋯
	1.06	+31.4	16.0	177.8
	1.46	+17.8	30.1	177.9
	1.89	+24.0	35.2	⋯
	1.89	+31.9	34.4	178.6
	2.29	+16.9	34.6	179.1
	2.82	+24.2	34.1	⋯
	2.82	+32.5	36.1	177.8
	3.08	+15.9	29.1	178.1
1960 Jan. 1	1.06	+ 5.4	52.3	178.9
	1.89	−8.1	56.6	179.1
	1.89	+ 6.3	75.9	0.0
	2.82	+ 7.6	62.8	179.7
Jan. 6A	1.06	+ 9.6	72.1	178.8
	1.26	+11.1	76.5	⋯
	1.89	−6.4	71.1:	0.2
	1.89	+10.6	79.6	⋯
	2.82	+10.8	68.7	⋯
Jan. 6B	1.06	+ 2.8	47.4	178.2
	1.06	+14.8	42.4	⋯
	1.26	+ 4.2	52.0	⋯
	1.26	+13.9	50.1	⋯
	1.89	+ 3.7	59.0	⋯
	1.89	+14.3	58.8	⋯
	2.82	+ 4.0	51.9	⋯
	2.82	+14.1	53.7	⋯
Jan. 6C	1.06	+ 6.4	64.0	179.1
	1.06	+12.9	58.7	⋯
	1.26	+ 7.8	64.2	⋯
	1.26	+12.2	62.1	⋯
	1.89	+ 7.2	62.1	⋯
	1.89	+12.5	61.1	⋯
	2.82	+ 7.6	50.9	⋯
	2.82	+12.3	50.3	⋯
Apr. 6	1.06	+22.2	50.4	179.7
	1.89	+19.3	66.8	179.4
	2.82	+20.8	61.1	179.4
Apr. 9	1.06	+44.1	45.4	178.2
	1.46	+51.7	49.0:	179.1
	1.46	+55.6	53.9	179.6
	1.89	+45.1	58.0	178.4
	1.92	+54.6	58.0	178.8
	2.29	+52.6	57.1	178.9
	2.82	+45.9	53.3	178.5
	3.08	+53.7	50.5	178.8
Aug. 31	1.06	+ 4.1	61.2	178.7

Sun’s elev.	1/λ	P	Sun’s elev.	1/λ	P	Sun’s elev.	1/λ	P
January 1, 1960; observations at $θ = 16_{.}^{°} 3$
		%			%			%
$- 7_{.}^{°} 7$	1.89	47.3:	$- 4_{.}^{°} 9$	1.89	64.2	$+ 1_{.}^{°} 2$	1.89	67.3
−7.3	1.06	38.3	−4.7	1.06	64.2	+1.7	2.82	57.0
−7.0	1.89	51.4:	−4.2	1.06	69.2	+2.0	1.26	58.0
−6.7	2.82	44.1:	−4.0	1.89	66.6	+2.2	1.26	55.9
−5.9	1.26	56.9:	−3.9	2.82	58.8	+2.6	2.82	57.0
−5.7	1.26	57.0	−3.0	1.26	68.8:	+3.0	1.89	66.3
−5.1	2.82	54.5	+1.0	1.06	62.2:	+3.3	1.06	44.0
January 6A, 1960; observations at $θ = 177_{.}^{°} 1$
		%			%			%
$- 5_{.}^{°} 9$	1.89	73.9	$- 3_{.}^{°} 5$	1.06	84.3	$- 0_{.}^{°} 7$	1.89	81.6
−5.7	1.06	75.9:	−3.0	1.89	80.0	−0.3	2.82	68.9
−5.2	1.89	76.3:	−2.7	2.82	70.2	0.0	1.26	82.4
−5.0	2.82	66.5	−2.5	1.26	84.1	+0.5	1.26	81.6
−4.8	1.26	82.3	−2.0	1.26	84.0	+0.7	2.82	68.8
−4.2	1.26	83.2	−1.8	2.82	69.8	+1.0	1.89	81.2
−4.0	2.82	69.1	−1.7	1.89	81.0	+1.1	1.06	77.7
−3.8	1.89	79.2	−1.3	1.06	84.5
−3.6	1.06	84.5	−0.8	1.06	85.3
August 31, 1960; observations at $θ = 176_{.}^{°} 3$
		%			%			%
$- 4_{.}^{°} 6$	1.06	83.0	$- 1_{.}^{°} 5$	1.06	78.0	$+ 1_{.}^{°} 5$	1.26	73.9
−4.2	1.89	77.4	−1.3	1.06	76.5	+1.8	1.06	67.0
−4.0	2.82	63.2	−1.0	1.26	78.8	+2.0	1.06	66.3
−3.8	1.26	80.9	−0.7	1.89	79.1	+2.4	1.26	73.2
−3.2	1.06	81.8	−0.4	1.06	72.3	+2.6	1.89	77.6
−2.6	2.82	67.0	0.0	2.82	66.1	+3.0	2.82	65.6
−2.2	1.89	79.0	+0.5	2.82	65.9	+3.5	1.06	63.0
−2.0	1.26	81.2	+1.1	1.89	78.5	+4.6	1.06	62.2

					Sun’s elevation
Object	Date UT	B−R	G−I	U−G	for B, R	for U, G, I
Daytime sky	Dec. 24	$- 1_{.}^{m} 09$	$- 1_{.}^{m} 75$	$- 1_{.}^{m} 60$	$35_{.}^{°} 0$	$33_{.}^{°} 9$
	Dec. 26A	−1.29	−1.84	−1.52	10.5	28.1
	Dec. 26B	−1.31	−1.73	−1.70	13.8	30.6
	Dec. 26C	−1.14	−1.55	−1.61	18.6	33.0
	Jan. 1	⋯	−1.52	−0.68	⋯	4.5
	Jan. 6B	⋯	−1.48	−0.78	⋯	5.2
	Jan. 6C	⋯	−2.15	−1.17	⋯	9.0
	Apr. 9	⋯	−1.67	−1.91	⋯	42.3
α Vir; B1 V	⋯	−1.12	−1.38	−2.06	⋯	⋯
β Lib; B8 V	⋯	−1.00	−1.02	−1.24	⋯	⋯
α Lyr; A0 V	⋯	⋯	−0.98	−0.84	⋯	⋯
τ CrB; K0 III	⋯	+0.37	+0.35	+1.15	⋯	⋯
α Ser; K2 III	⋯	+0.52	+0.47	+1.68	⋯	⋯
γ Dra; K5 III	⋯	⋯	+1.12	+2.56	⋯	⋯

Date UT	Phase	Sun’s elev.		Interpolated polarization at 1/λ						Est. Pol. ^a at $90_{.}^{°} 0$	Line	Normalized polarization at 1/λ
Date UT	Phase	Sun’s elev.		1.06	1.46	1.89	2.29	2.82	3.08	Est. Pol. ^a at $90_{.}^{°} 0$	Line	1.06	1.46	2.29	2.82	3.08

1959				%	%	%	%	%	%	%		%	%	%	%	%
May 2	$97_{.}^{°} 6$		$6_{.}^{°} 5$	40.1	⋯	70.0	⋯	63.5	⋯	72.6	1	35.0	⋯	⋯	55.4	⋯
Aug. 10	97.8		+ 15.0	61.2:	71.6:	67.3	65.0	59.2	54.0	69.4	2	55.6:	65.0:	59.0	53.7	49.0
Nov. 2	94.1		+35.8	42.7	63.6	71.0	68.9	61.5	55.9	71.7	3	36.7	54.7	59.3	52.9	48.1
Dec. 24	90.1		+34.0	29.1:	50.4:	65.5:	66.5:	56.8:	56.3:	65.5:	4	27.1:	47.0:	62.0:	53.0:	52.5:
Dec. 26A	64.5		+18.0	38.8	53.0	53.4	49.9	42.9	39.9	⋯	5	44.4	60.6	57.1	49.1	45.7
Dec. 26B	94.7		+18.0	44.1:	69.5	72.5	74.9	66.5	61.2	73.3	6	37.2:	58.6	63.1	56.0	51.6
Dec. 26C	127.1		+18.0	28.2:	30.0	36.8	34.6	32.1	29.5	⋯	7	46.8:	49.8	57.4	53.3	49.0
			−5.8	53.0	(56.7)	59.9	⋯	50.8	⋯	74.7	8	54.1	(57.8)	⋯	51.8	⋯
1960			−4.0	71.0	(65.5)	66.8	⋯	58.6	⋯	83.2	9	64.9	(59.9)	⋯	53.6	⋯
Jan. 1	81.7		+ 1.0	62.2:	(63.0:)	67.4	⋯	57.1	⋯	83.9	10	56.4:	(57.1:)	⋯	51.8	⋯
			+ 2.6	49.6	(53.9)	66.5	⋯	57.0	⋯	82.8	11	45.6	(49.5)	⋯	52.4	⋯
			+ 6.3	52.0	⋯	75.9	⋯	62.9	⋯	78.6	12	41.9	⋯	⋯	50.6	⋯
			−4.0	83.0	(83.5)	78.9	⋯	69.1	⋯	79.3	13	64.3	(64.7)	⋯	53.5	⋯
Jan. 6A	89.4		−1.3	85.3	(83.6)	81.3	⋯	69.4	⋯	81.7	14	64.1	(62.8)	⋯	52.2	⋯
			+ 1.0	78.4	(80.9)	81.4	⋯	68.7	⋯	81.8	15	58.8	(60.7)	⋯	51.6	⋯
			+ 10.6	71.8	(76.6)	79.6	⋯	68.7	⋯	79.8	16	55.1	(58.8)	⋯	52.7	⋯
Jan. 6B	112.1		+ 4.0	46.8	(52.0)	59.0	⋯	51.9	⋯	⋯	17	48.5	(53.9)	⋯	53.7	⋯
			+14.0	42.6	(50.1)	58.8	⋯	53.7	⋯	⋯	18	44.3	(52.1)	⋯	55.8	⋯
Jan. 6C	68.9		+ 7.5	63.0	(64.4)	62.0	⋯	50.9	⋯	⋯	19	62.1	(63.5)	⋯	50.2	⋯
			+12.4	59.0	(62.0)	61.1	⋯	50.3	⋯	⋯	20	59.0	(62.0)	⋯	50.3	⋯
Apr. 6	94.2		+20.8	50.7	⋯	66.5	⋯	61.1	⋯	67.1	21	46.6	⋯	⋯	56.1	⋯
Apr. 9	93.2		+49.9	45.4:	53.9	58.0	57.1	53.3	50.5	58.4	22	47.8:	56.8	60.2	56.1	53.2
			−4.0	82.8	(80.5)	77.5	⋯	63.2	⋯	78.5	23	65.3	(63.5)	⋯	49.8	⋯
Aug. 31	94.3		−1.3	76.9	(79.5)	79.1	⋯	67.6:	⋯	80.2	24	59.4	(61.4)	⋯	52.2:	⋯
			+ 1.0	68.5	(74.4)	78.6	⋯	66.0	⋯	79.6	25	53.2	(57.8)	⋯	51.3	⋯
			+ 2.6	65.2	(73.2)	77.6	⋯	65.6	⋯	78.5	26	51.3	(57.6)	⋯	51.7	⋯

Conditions	Lines used (of Table V)	Average polarization at 1/λ
Conditions	Lines used (of Table V)	1.06	1.26	1.46	2.29	2.82	3.08

		%	%	%	%	%	%
Sun below horizon	9,13,23	64.8	62.7	⋯	⋯	52.3	⋯
Sun above horizon	11,16,26	50.7	55.3	⋯	⋯	52.3	⋯
Clear sky	1,2,3,16,26	45.8:	58.2:	58.1:	59.2:	53.3	48.6:
Sky not perfectly clear	4,6,11,12,21,22	42.3	⋯	55.6	61.7	54.1	52.4
Infrared polarization high	2,8,9,10,13,14,15,16,19,20,23,24,25,26	59.0	60.7	⋯	⋯	51.9	⋯
Infrared polarization low	1,3,4,5,6,7,11,12,17,18,21,22	42.2	51.8	55.3	59.7	53.7	49.8

Site	1/λ	Obs. P	Opt. Depth	Anisotr. factor	Computed at R			For this site
Site	1/λ	Obs. P	Opt. Depth	Anisotr. factor	0%	25%	80%	R	Comp. P	O−C

		%			%	%	%	%	%	%
McDonald ^a Observatory 6800-ft alt	1.11	55.0	0.01	0.940	93.9	82.9	65.4	51	73.8	−18.8
	1.31	63.5	0.02	0.941	93.0	82.1	65.1	32	79.9	−16.4
	1.66	74.8	0.05	0.942	90.2	80.3	64.2	14	84.4	−9.6
	1.96	74.9	0.10	0.942	87.3	78.1	62.5	11	83.0	−8.1
	2.17	74.0	0.15	0.943	84.6	75.8	60.6	7	81.9	−7.9
	2.46	70.9	0.25	0.943	79.7	71.7	57.0	5	78.3	−7.4
	2.92	63.3	0.50	0.944	69.5	62.3	48.0	4	68.4	−5.1

Cactus Peak ^a (Sekera 1956) 5400-ft alt	1.62	73.4	0.05	0.942	90.2	80.3	64.2	28	79.5	−6.1
	1.92	74.6	0.10	0.942	87.3	78.1	62.5	20	79.8	−5.2
	2.13	74.9	0.15	0.943	84.6	75.8	60.6	16	78.5	−3.6
	2.40	73.0	0.25	0.943	79.7	71.7	57.0	12	75.6	−2.6
	2.86	64.0	0.50	0.944	69.5	62.3	48.0	11	66.5	−2.5

Goethe Link ^b Observatory 900-ft alt	1.04	42.1	0.01	0.940	92.1	66.5	41.2	41	57.9	−15.8
	1.24	52.4	0.02	0.941	91.0	65.8	41.0	36	58.9	−6.5
	1.56	67.1	0.05	0.941	88.5	64.9	40.4	8	78.2	−11.1
	1.84	71.1	0.10	0.942	85.3	63.7	39.7	10	74.7	−3.6
	2.04	70.4	0.15	0.943	82.2	62.0	39.0	5	77.4	−7.0
	2.30	68.9	0.25	0.943	76.8	59.4	36.9	4	73.4	−4.5
	2.75	62.9	0.50	0.944	66.4	52.8	33.0	3	64.7	−1.8
	3.27	50.6	1.00	0.946	50.6	41.1	25.3	3:	49.4	+ 1.2

Abstract

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Figures (5)

Tables (7)

Equations (3)

Journal of the Optical Society of America