The Brightness and Polarization of the Daylight Sky at Altitudes of 18,000 to 38,000 Feet above Sea Level

D. M. Packer; C. Lock

doi:10.1364/JOSA.41.000473

Journal of the Optical Society of America
Vol. 41,
Issue 7,
pp. 473-478
(1951)
•https://doi.org/10.1364/JOSA.41.000473

The Brightness and Polarization of the Daylight Sky at Altitudes of 18,000 to 38,000 Feet above Sea Level

D. M. Packer and C. Lock

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D. M. Packer and C. Lock, "The Brightness and Polarization of the Daylight Sky at Altitudes of 18,000 to 38,000 Feet above Sea Level," J. Opt. Soc. Am. 41, 473-478 (1951)

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Abstract

The brightness and polarization of the daylight sky over Arizona and Southern California were measured from B-29 aircraft while flying at altitudes of 18,000, 27,500, 34,000, and 38,000 feet above sea level. Comparison of the results with the Tousey and Hulburt theory of sky brightness showed that the theory agreed fairly well with the experimental data for all altitudes of observation, for all points in the sky more than 30° from the horizon, and for scattering angles greater than about 40° from the sun, when an atmospheric attenuation coefficient of 0.017/km was assumed. The values of sky brightness observed at scattering angles within 30° of the sun indicated that large scattering particles were present in the atmosphere overhead at all altitudes of observation including 38,000 feet.

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Zenith sky, P=90°
	18,000 feet		27,500 feet		34,000 feet		38,000 feet
H	B	γ	B	γ	B	γ	B	γ
30	60	0.40	41	0.43	35	0.35	26	0.35
40	70	0.56	54	0.57	43	0.52	34	0.53
50	86	0.70	68	0.70	52	0.71	41	0.71
60	114	0.83	83	0.81	59	0.85	48	0.86
70	168	0.93	101	0.91	68	0.92	63	0.95
80	250	0.98	123	0.98	80	0.98	82	0.98

	H	P=75°		P=60°		P=45°		P=30°		P=15°		P=0°		H	P=75°		P=60°		P=45°		P=30°		P=15°		P=0°
	H	B	γ	B	γ	B	γ	B	γ	B	γ	B	γ	H	B	γ	B	γ	B	γ	B	γ	B	γ	B	γ
		18,000 feet													34,000 feet
Z=0°	30	82	0.64	139	0.78	*	0.94	*	1.00	*	*	*	*	30	47	0.64	69	0.78	130	0.94	*	*	*	*	*	*
	40	101	0.77	171	0.89	*	0.98	*	0.96	450	0.85	1155	0.77	40	55	0.75	89	0.89	*	*	*	*	*	*	*	*
	50	140	0.88	*	*	*	0.98	305	0.89	393	0.73	1045	0.66	50	65	0.86	110	0.97	*	*	164	0.89	203	0.73	1230	0.50
	60	200	0.95	*	*	*	0.94	247	0.79	341	0.58	950	0.52	60	86	0.94	*	*	130	0.94	135	0.79	192	0.58	1020	0.38
	70	*	*	*	*	174	0.84	192	0.66	293	0.48	880	0.38	70	*	*	110	0.97	99	0.84	117	0.66	172	0.48	890	0.28
	80	*	*	172	0.89	149	0.73	159	0.54	265	0.37	835	0.26	80	*	*	89	0.89	74	0.73	82	0.54	143	0.37	835	0.21
Z=45°	30	65	0.56	82	0.62	143	0.67	199	0.65	349	0.58	1020	0.63	30	44	0.57	52	0.62	70	0.67	111	0.65	194	0.58	1170	0.47
	40	82	0.70	100	0.73	151	0.76	206	0.66	334	0.54	980	0.56	40	50	0.69	62	0.73	78	0.76	114	0.66	190	0.54	1070	0.41
	50	100	0.82	128	0.78	157	0.80	197	0.65	313	0.50	930	0.49	50	58	0.80	75	0.78	84	0.80	110	0.65	183	0.50	970	0.35
	60	134	0.91	160	0.88	157	0.78	181	0.63	292	0.44	885	0.39	60	69	0.88	85	0.88	84	0.78	101	0.63	170	0.44	890	0.29
	70	190	0.96	168	0.89	151	0.75	165	0.57	273	0.37	850	0.30	70	89	0.95	88	0.89	77	0.75	87	0.57	151	0.37	850	0.23
	80	232	0.97	156	0.86	143	0.68	154	0.50	258	0.30	830	0.24	80	*	*	81	.86	69	0.68	76	0.50	137	0.30	830	0.19
Z=90°	30	60	0.33	64	0.32	75	0.24	112	0.19	175	0.15	820	0.22	30	35	0.33	36	0.32	43	0.24	55	0.19	108	0.15	820	0.18
	40	73	0.47	75	0.43	82	0.33	123	0.24	191	0.17	820	0.22	40	41	0.47	41	0.43	47	0.33	61	0.24	116	0.17	820	0.18
	50	87	0.62	88	0.53	92	0.42	133	0.28	211	0.20	820	0.22	50	48	0.63	47	0.53	52	0.42	65	0.28	121	0.20	820	0.18
	60	106	0.76	110	0.63	115	0.49	141	0.33	233	0.22	820	0.22	60	54	0.76	52	0.63	56	0.49	67	0.33	124	0.22	820	0.18
	70	141	0.88	130	0.72	137	0.55	145	0.36	261	0.23	820	0.22	70	61	0.86	60	0.72	59	0.55	68	0.36	127	0.23	820	0.18
	80	179	0.93	145	0.76	150	0.59	149	0.38	286	0.23	820	0.22	80	70	0.92	67	0.76	62	0.59	74	0.38	130	0.23	820	0.18
Z=135°	30	*	*	*	*	76	0.14	118	0.20	230	0.32	880	0.63	30	*	*	36	0.15	38	0.14	56	0.20	120	0.32	1000	0.48
	40	60	0.39	64	0.22	77	0.16	120	0.17	235	0.25	860	0.57	40	38	0.45	39	0.22	42	0.16	58	0.17	120	0.25	950	0.43
	50	72	0.54	74	0.32	79	0.22	119	0.16	236	0.21	858	0.49	50	43	0.57	41	0.33	46	0.22	60	0.16	118	0.21	910	0.38
	60	87	0.68	88	0.45	92	0.29	122	0.18	238	0.17	850	0.42	60	49	0.68	44	0.45	48	0.29	61	0.18	116	0.17	880	0.31
	70	109	0.80	106	0.55	113	0.38	135	0.23	239	0.18	830	0.30	70	57	0.78	49	0.55	52	0.38	63	0.23	114	0.18	840	0.25
	80	149	0.90	123	0.67	125	0.48	138	0.30	242	0.20	825	0.27	80	67	0.87	57	0.67	60	0.48	68	0.30	114	0.20	830	0.20
Z=180°	30	*	*	*	*	*	*	*	*	*	*	*	*	30	*	*	*	*	*	*	*	*	*	*	*	*
	40	*	*	60	0.18	75	0.15	*	*	295	0.45	*	*	40	35	0.38	37	0.18	43	0.15	62	0.25	132	0.45	1150	0.64
	50	68	0.49	67	0.27	77	0.17	122	0.18	271	0.31	880	0.66	50	41	0.51	40	0.27	44	0.17	62	0.18	130	0.31	1030	0.51
	60	82	0.64	79	0.37	80	0.23	119	0.16	250	0.22	862	0.53	60	47	0.63	42	0.37	46	0.23	62	0.16	120	0.22	930	0.40
	70	101	0.77	98	0.52	103	0.35	125	0.19	239	0.16	848	0.40	70	55	0.75	47	0.52	47	0.35	62	0.19	109	0.16	870	0.30
	80	140	0.88	118	0.66	122	0.45	135	0.27	240	0.16	830	0.30	80	64	0.86	54	0.66	54	0.45	64	0.27	113	0.16	840	0.22
	27,500 feet													38,000 feet
Z=0°	30	69	0.62	95	0.78	175	0.94	*	*	*	*	*	*	30	39	0.62	64	0.78	100	0.94	*	*	*	*	*	*
	40	83	0.74	121	0.89	*	*	*	*	*	*	*	*	40	48	0.76	85	0.89	*	*	*	*	*	*	*	*
	50	92	0.85	*	*	*	*	200	0.89	*	*	1470	0.75	50	60	0.86	*	*	*	*	*	*	*	*	*	*
	60	108	0.94	*	*	175	0.94	171	0.79	267	0.58	1220	0.55	60	75	0.94	*	*	100	0.94	109	0.79	179	0.58	980	0.42
	70	*	*	*	*	131	0.84	141	0.66	224	0.46	1045	0.36	70	*	*	*	*	86	0.84	99	0.66	161	0.48	940	0.30
	80	*	*	121	0.89	103	0.73	115	0.54	196	0.37	950	0.24	80	*	*	85	0.89	73	0.73	79	0.54	142	0.37	910	0.22
Z=45°	30	62	0.55	79	0.62	99	0.67	144	0.65	275	0.58	*	*	30	35	0.54	48	0.62	69	0.67	100	0.65	182	0.58	*	*
	40	75	0.67	88	0.73	109	0.76	149	0.66	264	0.54	1285	0.61	40	43	0.69	58	0.73	75	0.76	102	0.66	177	0.54	990	0.47
	50	86	0.78	103	0.78	114	0.80	144	0.65	243	0.50	1150	0.49	50	52	0.80	70	0.78	79	0.80	100	0.65	170	0.50	970	0.38
	60	95	0.87	115	0.88	115	0.78	134	0.63	222	0.44	1060	0.38	60	63	0.89	81	0.88	79	0.78	94	0.63	160	0.44	940	0.31
	70	112	0.94	119	0.89	107	0.75	121	0.57	204	0.37	980	0.27	70	77	0.95	83	0.89	75	0.75	85	0.57	149	0.37	920	0.25
	80	126	0.96	110	0.86	97	0.68	109	0.50	191	0.30	930	0.23	80	84	0.97	76	0.86	68	0.68	73	0.50	135	0.30	910	0.22
Z=90°	30	46	0.40	50	0.32	59	0.24	84	0.19	170	0.15	905	0.24	30	29	0.38	33	0.32	39	0.24	57	0.19	103	0.15	890	0.19
	40	53	0.54	59	0.43	65	0.33	92	0.24	173	0.17	905	0.24	40	35	0.53	37	0.43	43	0.33	58	0.24	108	0.17	890	0.19
	50	64	0.65	70	0.53	71	0.42	95	0.28	175	0.20	905	0.24	50	41	0.66	43	0.53	48	0.42	59	0.28	112	0.20	890	0.19
	60	76	0.76	79	0.63	77	0.49	96	0.33	177	0.22	905	0.24	60	50	0.78	48	0.63	53	0.49	60	0.33	115	0.22	890	0.19
	70	85	0.85	86	0.72	80	0.55	97	0.36	179	0.23	905	0.24	70	59	0.86	52	0.72	56	0.55	62	0.36	116	0.23	890	0.19
	80	94	0.91	92	0.76	83	0.59	99	0.38	179	0.23	905	0.24	80	69	0.92	55	0.76	59	0.59	63	0.38	118	0.23	890	0.19
Z=135°	30	*	*	*	*	*	*	77	0.20	167	0.32	1045	0.66	30	25	0.25	26	0.15	33	0.14	47	0.20	117	0.32	*	*
	40	49	0.40	48	0.22	56	0.16	80	0.17	165	0.25	1010	0.58	40	29	0.38	29	0.22	34	0.16	49	0.17	116	0.25	875	0.56
	50	60	0.53	57	0.33	62	0.22	83	0.16	161	0.21	970	0.50	50	35	0.52	33	0.33	36	0.22	51	0.16	115	0.21	880	0.43
	60	74	0.66	67	0.45	68	0.29	84	0.18	157	0.17	940	0.41	60	41	0.67	38	0.45	40	0.29	54	0.18	110	0.17	880	0.34
	70	84	0.77	76	0.55	74	0.38	89	0.23	156	0.18	920	0.29	70	51	0.79	45	0.55	45	0.38	57	0.23	105	0.18	880	0.26
	80	94	0.86	84	0.67	79	0.48	94	0.30	160	0.20	910	0.27	80	63	0.88	53	0.67	52	0.48	59	0.30	109	0.20	890	0.22
Z=180°	30	*	*	*	*	*	*	*	*	*	*	1250	1.00	30	25	0.20	24	0.14	32	0.20	56	0.35	145	0.57	*	*
	40	45	0.35	43	0.18	52	0.15	*	*	197	0.45	1155	0.85	40	27	0.33	27	0.18	33	0.15	54	0.25	140	0.45	*	*
	50	56	0.49	51	0.27	56	0.17	81	0.18	182	0.31	1060	0.70	50	33	0.47	30	0.27	34	0.17	53	0.18	132	0.31	880	0.73
	60	69	0.62	61	0.37	64	0.23	84	0.16	172	0.22	990	0.54	60	39	0.62	35	0.37	37	0.23	53	0.16	121	0.22	880	0.49
	70	82	0.74	72	0.52	70	0.35	88	0.19	167	0.16	940	0.40	70	48	0.76	42	0.52	42	0.35	56	0.19	108	0.16	880	0.33
	80	92	0.85	81	0.66	77	0.46	93	0.27	167	0.16	915	0.29	80	60	0.86	50	0.66	50	0.45	59	0.27	107	0.16	880	0.23

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Journal of the Optical Society of America