Angular Distribution of Intensity of Light Scattered by Large Droplets of Water

R. O. Gumprecht; Neng-Lun Sung; Jin H. Chin; C. M. Sliepcevich

doi:10.1364/JOSA.42.000226

Journal of the Optical Society of America
Vol. 42,
Issue 4,
pp. 226-231
(1952)
•https://doi.org/10.1364/JOSA.42.000226

Angular Distribution of Intensity of Light Scattered by Large Droplets of Water

R. O. Gumprecht, Neng-Lun Sung, Jin H. Chin, and C. M. Sliepcevich

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R. O. Gumprecht, Neng-Lun Sung, Jin H. Chin, and C. M. Sliepcevich, "Angular Distribution of Intensity of Light Scattered by Large Droplets of Water," J. Opt. Soc. Am. 42, 226-231 (1952)

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Abstract

The angular distribution of intensity of light scattered by spherical particles whose index of refraction with respect to the surrounding medium is 1.33 has been computed for values of α (circumference of the particle divided by the wavelength of the incident beam) equal to 6.0, 8.0, 10, 15, 20, 25, 30, 35, and 40. The results are presented in tabular form and give the intensities of the two incoherent, plane-polarized components of the scattered light as well as the real and imaginary parts of the complex functions from which the intensities are computed for angles of observation in the range 0° (10°) 170° and 170° (1°) 180°. A sample light-scattering diagram for α=40 is included.

The tabulated values were calculated and checked by high speed computers; they extend considerably the range of values previously published.

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γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	3.506	3.506	−0.3130	+1.846	−0.3130	+1.846
10	2.082	3.677	−0.8009	+1.200	−0.2366	+1.903
20	3.011	3.899	−1.714	−0.2691	−0.1756	+1.967
30	5.973	3.320	−1.950	−1.474	−0.4104	+1.775
40	3.098	2.013	−0.9657	−1.472	−0.9011	+1.096
50	0.415	1.310	+0.6110	−0.2037	−1.145	−0.00340
60	4.104	1.356	+1.521	+1.338	−0.5923	−1.003
70	4.303	1.801	+1.082	+1.770	+0.6711	−1.162
80	0.218	2.884	−0.09949	+0.4564	+1.692	−0.1494
90	3.453	3.694	−0.6959	−1.723	+1.330	+1.387
100	7.692	4.136	−0.06383	−2.773	−0.5156	+1.967
110	2.184	5.543	+0.9309	−1.148	−2.321	+0.3937
120	7.044	11.76	+0.6802	+2.565	−1.954	−2.818
130	30.04	26.27	−1.356	+5.311	+1.191	−4.986
140	23.86	31.37	−3.646	+3.250	+4.953	−2.616
150	43.11	70.05	−3.734	−5.401	+5.846	+5.989
160	340.1	357.9	−0.7254	−18.43	+2.414	+18.76
170	926.1	928.2	+3.407	−30.24	−2.827	+30.33
171	981.9	983.4	+3.749	−31.11	−3.270	+31.19
172	1034.	1035.	+4.064	−31.90	−3.679	+31.96
173	1083.	1083.	+4.349	−32.61	−4.049	+32.66
174	1126.	1126.	+4.601	−33.24	−4.379	+33.27
175	1164.	1164.	+4.819	−33.77	−4.663	+33.79
176	1195.	1195.	+5.000	−34.21	−4.899	+34.23
177	1221.	1221.	+5.143	−34.56	−5.085	+34.56
178	1239.	1239.	+5.246	−34.80	−5.220	+34.81
179	1250.	1250.	+5.308	−34.95	−5.302	+34.95
180	1254.	1254.	+5.329	−35.00	−5.329	+35.00

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	3.810	3.810	+1.949	−0.09833	+1.949	−0.09833
10	0.971	6.891	−0.5527	+0.8156	+2.610	+0.2828
20	19.43	10.02	−4.135	+1.529	+2.943	+1.166
30	8.999	3.151	−2.994	−0.1828	+0.9397	+1.506
40	7.678	3.052	+1.632	.−2.240	−1.739	+0.1671
50	12.60	6.294	+3.176	−1.586	−1.593	−1.938
60	0.236	5.285	−0.3052	+0.3784	+1.107	−2.015
70	9.993	4.093	−3.145	+0.3177	+1.952	+0.5320
80	1.514	4.987	−0.9486	−0.7837	−0.8638	+2.059
90	6.134	8.239	+2.423	+0.5106	−2.862	−0.2176
100	8.220	7.366	+1.247	+2.582	+0.01850	−2.714
110	5.083	13.87	−2.247	+0.1901	+3.724	−0.04192
120	25.76	25.84	−1.277	−4.913	+1.275	+4.921
130	21.53	31.23	+3.475	−3.075	−4.988	+2.521
140	70.93	87.52	+3.573	+7.626	−4.694	−8.093
150	156.0	154.9	−3.840	+11.89	+4.726	−11.51
160	158.9	216.4	−11.11	−5.947	+13.06	+6.771
170	1536.	1589.	−12.27	−37.22	+13.20	+37.61
171	1747.	1792.	−12.15	−39.99	+12.93	+40.31
172	1955.	1994.	−12.01	−42.55	+12.65	+42.82
173	2157.	2188.	−11.87	−44.90	+12.37	+45.10
174	2345.	2369.	−11.73	−46.98	+12.11	+47.14
175	2515.	2532.	−11.60	−48.79	+11.87	+48.90
176	2662.	2673.	−11.48	−50.30	+11.66	+50.37
177	2781.	2788.	−11.39	−51.49	+11.49	+51.54
178	2869.	2872.	−11.31	−52.36	+11.36	+52.38
179	2923.	2924.	−11.27	−52.88	+11.28	+52.88
180	2941.	2941.	−11.25	−53.05	+11.25	+53.05

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	14.03	14.03	−3.620	−0.9600	−3.620	−0.9600
10	18.04	10.00	−1.802	+3.846	−0.7197	−3.080
20	36.29	12.76	−1.150	+5.913	+2.186	−2.824
30	14.92	5.063	−3.162	−2.217	−0.9416	+2.044
40	21.22	17.10	−1.544	−4.340	−3.876	+1.443
50	8.915	7.456	+1.327	+2.675	−0.2237	−2.721
60	7.289	7.027	+0.1049	+2.698	+2.647	+0.1408
70	5.018	11.52	−0.2055	−2.231	−0.8780	+3.278
80	2.568	4.969	+1.601	+0.06507	−1.603	−1.549
90	2.442	14.32	−0.5316	+1.470	+2.852	−2.487
100	13.20	12.31	−2.024	−3.017	+0.6330	+3.450
110	3.691	22.70	+1.880	+0.3945	−4.759	+0.2404
120	38.14	36.53	+1.276	+6.042	+1.156	−5.932
130	35.04	62.76	−4.105	−4.265	+6.887	+3.915
140	102.1	109.3	+0.3456	−10.10	−3.807	+9.736
150	200.4	242.5	+9.702	+10.31	−11.93	−10.01
160	279.8	236.6	+4.197	+16.19	+0.6725	−15.37
170	790.2	929.8	−13.63	−24.59	+17.43	+25.02
171	1106.	1239.	−15.27	−29.55	+18.54	+29.91
172	1459.	1579.	−16.80	−34.31	+19.52	+34.61
173	1834.	1937.	−18.19	−38.77	+20.38	+39.01
174	2213.	2296.	−19.44	−42.84	+21.10	+43.02
175	2577.	2640.	−20.51	−46.44	+21.71	+46.57
176	2908.	2950.	−21.41	−49.49	+22.20	+49.57
177	3186.	3211.	−22.12	−51.93	+22.57	+51.98
178	3397.	3409.	−22.63	−53.72	+22.83	+53.74
179	3529.	3532.	−22.94	−54.80	+22.99	+54.80
180	3574.	3574.	−23.04	−55.16	+23.04	+55.16

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	214.1	214.1	−13.80	+4.876	−13.80	+4.876
10	63.06	112.1	−0.5882	+7.919	+2.900	−10.18
20	35.47	12.37	−2.815	−5.249	−0.5255	+3.478
30	37.02	2.972	+6.002	+1.001	+0.4567	−1.662
40	6.768	17.56	+0.3672	+2.576	+4.186	+0.1873
50	8.971	11.00	−1.690	−2.473	−2.969	+1.477
60	4.620	18.34	+2.075	−0.5596	+2.414	−3.537
70	12.75	24.18	−3.570	−0.03507	−3.657	+3.287
80	12.97	22.85	+2.067	+2.948	+3.855	−2.827
90	13.28	30.82	+1.013	−3.501	−3.867	+3.983
100	7.618	47.90	−1.721	+2.157	+4.057	−5.608
110	5.774	57.91	−0.7566	−2.281	−2.981	+7.002
120	43.38	68.21	+4.819	+4.490	−0.4465	−8.247
130	139.3	109.1	−9.968	−6.322	+6.698	+8.018
140	243.5	208.1	+14.90	+4.642	−13.96	−3.625
150	131.1	203.8	−10.91	+3.468	+12.52	−6.855
160	232.1	133.0	−15.23	−0.4649	+10.68	+4.344
170	4218.	3416.	+22.39	−60.97	−9.406	+57.68
171	5920.	5038.	+22.71	−73.51	−10.42	+70.21
172	7968.	7066.	+22.35	−86.42	−11.25	+83.30
173	10310.	9454.	+21.45	−99.26	−11.93	+96.49
174	12860.	12100.	+20.17	−111.6	−12.47	+109.3
175	15480.	14860.	+18.68	−123.0	−12.90	+121.2
176	17980.	17540.	+17.17	−133.0	−13.22	+131.8
177	20190.	19920.	+15.79	−141.2	−13.46	+140.5
178	21930.	21800.	+14.70	−147.3	−13.63	+147.0
179	23040.	23000.	+14.00	−151.1	−13.72	+151.0
180	23420.	23420.	+13.75	−152.4	−13.75	+152.4

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	239.9	239.9	−5.274	+14.56	−5.274	+14.56
10	23.14	483.3	+3.897	+2.820	+10.11	−19.52
20	19.23	85.81	+4.143	−1.437	−2.250	+8.986
30	67.71	0.058	−7.704	+2.891	+0.1689	+0.1720
40	39.79	51.26	+3.938	−4.928	−2.424	−6.737
50	52.25	72.45	−4.224	+5.866	+0.09282	+8.511
60	29.00	16.56	+4.147	−3.435	+1.245	−3.874
70	3.964	5.373	−1.390	+1.426	+0.3666	−2.289
80	2.714	49.34	−1.058	−1.262	−2.807	+6.439
90	3.575	72.05	+1.192	+1.468	+4.697	−7.070
100	1.437	44.63	+0.4950	−1.092	−5.579	+3.674
110	6.469	34.81	−2.529	+0.2741	+5.285	+2.623
120	15.69	104.5	+3.856	+0.9028	−4.139	−9.347
130	24.09	212.6	−3.926	−2.945	+3.010	+14.27
140	44.60	265.5	+3.442	+5.723	−3.511	−15.91
150	111.1	267.0	−7.545	−7.362	+10.51	+12.51
160	405.3	742.9	+20.01	−2.231	−26.84	+4.771
170	832.8	1596.	+2.624	+28.74	+8.635	−39.01
171	25.42	527.5	−1.823	+4.701	+14.63	−17.70
172	624.4	510.2	−7.216	−23.92	+20.49	+9.504
173	3283.	2384.	−13.39	−55.71	+26.07	+41.29
174	8310.	6721.	−20.06	−88.92	+31.21	+75.81
175	15510.	13570.	−26.84	−121.6	+35.80	+110.8
176	24160.	22300.	−33.28	−151.8	+39.70	+143.9
177	33070.	31670.	−38.90	−177.6	+42.84	+172.7
178	40830.	40080.	−43.27	−197.4	+45.13	+195.0
179	46130.	45920.	−46.05	−209.8	+46.53	+209.2
180	48010.	48010.	−47.00	−214.0	+47.00	+214.0

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	62.92	62.92	+2.783	+7.428	+2.783	+7.428
10	98.12	3.578	−6.566	+7.417	−1.725	−0.7756
20	30.73	135.9	−2.690	+4.847	−10.47	−5.129
30	115.4	11.32	+6.063	−8.870	−1.006	+3.210
40	53.73	82.37	−3.299	+6.546	+8.663	+2.705
50	3.526	13.32	+1.779	−0.5998	+0.7709	−3.568
60	25.58	32.88	−2.867	−4.167	−4.933	+2.923
70	17.34	3.886	+2.977	+2.912	+0.5275	−1.900
80	3.527	11.73	−1.684	+0.8320	−0.4963	−3.388
90	12.79	20.10	+3.571	−0.1902	+0.04654	+4.483
100	52.22	34.81	−5.237	−4.980	+4.276	+4.065
110	44.81	60.11	+0.544	+6.672	+1.221	−7.656
120	14.67	150.8	+3.471	+1.619	−11.80	−33.95
130	250.6	287.5	+0.988	−15.80	+4.526	+16.34
140	601.5	579.6	−7.667	+23.30	+14.39	−19.30
150	409.1	682.0	+13.89	−14.70	−22.43	+13.38
160	757.7	754.3	−27.51	−0.9938	+27.18	−3.913
170	145.0	113.5	+11.67	−2.977	−8.562	+6.338
171	965.1	950.1	+20.97	−22.92	−18.40	+24.73
172	3735.	3667.	+26.84	−54.91	−25.13	+55.09
173	10440.	10170.	+28.81	−98.05	−28.04	+96.87
174	23190.	22580.	+27.02	−149.9	−27.04	+147.8
175	43120.	42190.	+22.14	−206.5	−22.65	+204.1
176	69400.	68330.	+15.29	−263.0	−15.97	+260.9
177	98760.	97850.	+7.879	−314.2	−8.442	+312.7
178	126000.	125500.	+1.311	−355.0	−1.629	+354.2
179	145400.	145200.	−3.183	−381.3	+3.092	+381.1
180	152400.	152400.	−4.778	−390.4	+4.778	+390.4

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	89.11	89.11	−9.398	+0.8872	−9.398	+0.8872
10	67.94	20.69	−1.293	−8.141	+4.513	−0.5691
20	20.79	186.8	+4.362	+1.330	+10.43	−8.830
30	146.4	53.06	+0.1308	+12.10	−0.06777	−7.284
40	46.94	34.11	+6.835	−0.4683	−4.376	−3.868
50	27.27	48.87	−4.034	−3.316	−2.684	+6.455
60	62.67	16.23	−4.133	−6.752	−0.1044	+4.027
70	0.832	18.22	−0.8126	+0.4141	−0.01310	+4.269
80	3.259	9.745	+0.8097	−1.614	+2.694	−1.578
90	35.35	20.97	−0.3858	+5.933	+3.025	−3.438
100	10.21	57.25	−1.792	+2.646	+0.2322	−7.563
110	90.32	77.90	+8.912	+3.302	−7.252	−5.032
120	45.14	174.1	+6.506	+1.674	−12.49	+4.252
130	313.2	378.3	−6.778	−16.35	+0.1964	+19.45
140	630.3	733.5	−21.25	−13.37	+25.36	+9.508
150	1003.	1080.	+16.32	+27.15	−7.675	−31.95
160	1298.	1109.	+27.14	−23.70	−20.59	+26.17
170	13580.	13290.	+18.10	+115.1	−20.86	−113.4
171	15050.	14550.	+19.44	+121.1	−17.04	−119.4
172	11100.	10600.	+18.93	+103.6	−11.66	−102.3
173	3748.	3461.	+14.64	+59.45	−3.798	−58.70
174	135.1	156.9	+5.506	−10.24	+6.971	+10.41
175	10000.	10296.	−8.308	−99.65	+20.32	+99.42
176	40240.	40660.	−25.36	−199.0	+35.16	+198.6
177	89320.	89710.	−43.20	−295.7	+49.77	+295.4
178	145500.	145700.	−58.86	−376.8	+62.16	+376.6
179	190400.	190400.	−69.59	−430.7	+70.47	+430.7
180	207600.	207600.	−73.40	−449.6	+73.40	+449.6

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	183.9	183.9	−0.3463	+13.56	−0.3463	+13.56
10	52.96	305.9	−0.2789	−7.272	+2.693	+17.28
20	103.6	285.5	−10.06	−1.542	−2.923	+16.64
30	166.9	109.3	−7.491	−10.53	+3.709	+9.774
40	223.8	130.7	−14.93	−1.015	+4.813	+10.37
50	132.3	44.78	−11.44	+1.233	+2.636	+6.151
60	10.37	63.57	−2.870	+1.461	+3.244	+7.283
70	41.73	22.58	−3.593	−5.368	−0.6480	+4.708
80	18.73	41.44	+4.157	−1.207	+0.2174	+6.434
90	9.926	58.42	−3.043	+0.8173	−3.232	+6.926
100	51.35	73.37	−0.9954	−7.096	−4.915	+7.015
110	94.80	138.8	+6.788	−6.980	−7.179	+9.340
120	147.8	291.3	+11.16	−4.819	−10.52	+13.44
130	97.57	457.3	+6.964	−7.005	−8.234	+19.74
140	263.2	745.6	−10.45	−12.41	+8.320	+26.01
150	1979.	1682.	−43.44	+9.630	+41.01	+0.3054
160	4009.	3460.	+5.863	+63.05	−14.18	−57.09
170	3279.	2318.	−56.54	−9.065	+45.11	+16.80
171	1566.	834.8	−34.67	+19.08	+25.98	−12.63
172	827.6	656.4	−8.242	+27.56	+5.888	−24.94
173	268.7	129.4	+16.35	+1.166	−10.80	−3.579
174	5823.	4248.	+32.83	−68.88	−20.36	+61.91
175	34310.	29980.	+37.10	−181.5	−20.87	+171.9
176	106100.	99320.	+28.73	−324.5	−12.87	+314.9
177	227200.	220200.	+11.20	−476.6	+0.7761	+469.3
178	374200.	369500.	−9.122	−611.7	+15.60	+607.7
179	497400.	495900.	−25.08	−704.8	+26.89	+703.7
180	545700.	545700.	−31.09	−738.0	+31.09	+738.0

γ⁰	i₁	i₂	R(i₁*)	I(i₁*)	R(i₂*)	I(i₂*)
0	517.2	517.2	+1.935	+22.66	+1.935	+22.66
10	20.12	394.1	−3.119	−3.223	−2.450	+19.70
20	146.5	23.54	+9.207	−7.855	−3.715	−3.121
30	155.4	117.3	+10.55	+6.648	−8.787	−6.330
40	117.6	110.0	+10.54	+2.538	−6.543	−8.199
50	29.41	7.264	+5.421	−0.1592	+2.417	−1.192
60	45.53	10.32	−6.746	−0.1406	+1.673	+2.743
70	1.281	16.13	+1.098	+0.2736	+4.003	−0.3196
80	47.50	15.62	+0.2914	+6.886	−0.8837	−3.852
90	33.40	43.60	−5.142	+2.638	−0.4693	−6.587
100	82.39	33.94	−7.153	−5.589	+5.813	+0.3869
110	155.5	205.4	−2.604	−12.20	+6.820	+12.61
120	270.8	365.7	+6.583	−15.08	−1.037	+19.09
130	751.7	638.1	+18.92	−19.84	−16.03	+19.52
140	1627.	1353.	+26.57	−30.35	−28.45	+23.37
150	3587.	2734.	+14.32	−58.15	−18.09	+49.06
160	6539.	5773.	−61.35	−52.68	+59.42	+47.35
170	1848.	1962.	+33.94	+26.39	−37.75	−23.17
171	10070.	8992.	+26.63	+96.76	−30.74	−89.71
172	26850.	24840.	+29.09	+161.3	−31.95	−154.3
173	36920.	35930.	+36.61	+188.6	−37.15	−185.9
174	24470.	25400.	+40.96	+151.0	−38.96	−154.6
175	2407.	2885.	+34.28	+35.10	−30.46	−44.24
176	22700.	19280.	+12.98	−150.1	−8.639	+138.6
177	139500.	132300.	−20.10	−372.9	+23.65	+362.9
178	346500.	339900.	−56.28	−585.9	+58.29	+580.1
179	553600.	551200.	−84.32	−739.2	+84.90	+737.5
180	641100.	641100.	−94.87	−795.0	+94.87	+795.0

Abstract

Cited By

Figures (1)

Tables (9)

Equations (4)

Journal of the Optical Society of America