New Backscattering Computation and Tables for Dielectric and Metal Spheres

Simpson B. Adler; Robert S. Johnson

doi:10.1364/AO.1.000655

Applied Optics
Vol. 1,
Issue 5,
pp. 655-660
(1962)
•https://doi.org/10.1364/AO.1.000655

New Backscattering Computation and Tables for Dielectric and Metal Spheres

Simpson B. Adler and Robert S. Johnson

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Simpson B. Adler and Robert S. Johnson, "New Backscattering Computation and Tables for Dielectric and Metal Spheres," Appl. Opt. 1, 655-660 (1962)

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Abstract

This paper presents the results of new computations of radar cross sections for dielectric and metal spheres. Tables resulting from digital computer solutions of the classical Mie scattering coefficients are given in increments of 0.01 circumference to wavelength ratio. The phase of the backscattered wave is also given. Recursion relations are used to transform the scattering coefficients for machine computation. The precision of the new computation is discussed.

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Equations (15)

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ρ	σ/πr²	ψ (deg)
0.4000	0.2229	−1.4489
0.5000	0.5296	−3.0260
0.6000	1.0451	−5.5349
0.7000	1.7707	−9.0909
0.8000	2.5960	−13.5323
0.9000	3.2939	−18.3288
1.0000	3.6376	−22.7189
1.1000	3.5477	−26.0263
1.2000	3.1046	−27.8520
1.3000	2.4543	−27.9681
1.4000	1.7377	−25.9683
1.5000	1.0756	−20.6233
1.6000	0.5727	−8.4286
1.7000	0.3115	18.0585
1.8000	0.3290	54.8465
1.9000	0.5936	78.1788
2.0000	1.0081	89.0380
2.1000	1.4445	94.5851
2.2000	1.7862	98.0825
2.3000	1.9569	100.9409
2.4000	1.9286	103.9221
2.5000	1.7200	107.6555
2.6000	1.3895	112.9593
2.7000	1.0227	121.1512
2.8000	0.7126	134.2634
2.9000	0.5336	154.0184
3.0000	0.5208	177.6036
3.1000	0.6627	197.7373
3.2000	0.9093	211.6438
3.3000	1.1892	221.0060
3.4000	1.4284	227.8129
3.5000	1.5676	233.4059
3.6000	1.5751	238.7127
3.7000	1.4543	244.5255
3.8000	1.2419	251.6997
3.9000	0.9974	261.2719
4.0000	0.7853	274.3550
4.1000	0.6580	291.3352
4.2000	0.6422	310.3806
4.3000	0.7351	327.9355
4.4000	0.9063	341.9116
4.5000	1.1074	352.5338
4.6000	1.2844	0.8825
4.7000	1.3914	8.0038
4.8000	1.4031	14.7594
4.9000	1.3204	21.9066
5.0000	1.1688	30.1965
5.1000	0.9909	40.4132
5.2000	0.8336	53.2326
5.3000	0.7361	68.6973
5.4000	0.7207	85.5386
5.5000	0.7877	101.5538
5.6000	0.9160	115.2063
5.7000	1.0691	126.3344
5.8000	1.2057	135.5616
5.9000	1.2903	143.6793
6.0000	1.3026	151.4219
6.1000	1.2424	159.4603
6.2000	1.1279	168.4415
6.3000	0.9909	178.9876
6.4000	0.8677	191.5557
6.5000	0.7896	206.0796
6.6000	0.7753	221.6136
6.7000	0.8260	236.6284
6.8000	0.9258	249.9611
6.9000	1.0465	261.3434
7.0000	1.1557	271.1429
7.1000	1.2250	279.9554
7.2000	1.2377	288.3976
7.3000	1.1923	297.0587
7.4000	1.1025	306.5023
7.5000	0.9931	317.2377
7.6000	0.8933	329.5951
7.7000	0.8287	343.4708
7.8000	0.8151	358.1353
7.9000	0.8541	12.4605
8.0000	0.9337	25.5378
8.1000	1.0314	37.0690
8.2000	1.1212	47.2664
8.3000	1.1798	56.5839
8.4000	1.1926	65.5434
8.5000	1.1576	74.6631
8.6000	1.0854	84.4362
8.7000	0.9960	95.2879
8.8000	0.9133	107.4663
8.9000	0.8585	120.8659
9.0000	0.8452	134.9145
9.1000	0.8754	148.7460
9.2000	0.9399	161.6234
9.3000	1.0208	173.2474
9.4000	1.0962	183.7337
9.5000	1.1466	193.4349
9.6000	1.1595	202.7932
9.7000	1.1324	212.2646
9.8000	1.0735	222.2812
9.9000	0.9992	233.2037
10.0000	0.9292	245.2319

ρ	σ/πr²	ψ (deg)
0.2000	0.0005	−2.1358
0.3000	0.0023	−2.3572
0.4000	0.0071	−2.7872
0.5000	0.0167	−3.5050
0.6000	0.0326	−4.5978
0.7000	0.0559	−6.1601
0.8000	0.0863	−8.2921
0.9000	0.1216	−11.0980
1.0000	0.1570	−14.6875
1.1000	0.1856	−19.1866
1.2000	0.1996	24.7691
1.3000	0.1923	−31.7329
1.4000	0.1619	−40.6793
1.5000	0.1140	−53.0116
1.6000	0.0629	−72.6551
1.7000	0.0296	68.4667	−180
1.8000	0.0349	9.0318	↓
1.9000	0.0874	−27.9194
2.0000	0.1751	−48.6276
2.1000	0.2711	−63.4930
2.2000	0.3479	−76.0250
2.3000	0.3864	−87.9883
2.4000	0.3764	79.1593	−360
2.5000	0.3181	63.7943	↓
2.6000	0.2286	43.5670
2.7000	0.1451	14.3999
2.8000	0.1102	−26.8545
2.9000	0.1448	−68.0675
3.0000	0.2391	83.2484	−540
3.1000	0.3661	63.4339	↓
3.2000	0.4935	47.4691
3.3000	0.5849	32.3670
3.4000	0.6022	16.3050
3.5000	0.5259	−1.9088
3.6000	0.3855	−23.4329
3.7000	0.2513	−50.4406
3.8000	0.1827	−85.1872
3.9000	0.2025	57.8681	−720
4.0000	0.3087	28.4344	↓
4.1000	0.4834	6.0734
4.2000	0.6791	−13.3276
4.3000	0.8079	−32.1432
4.4000	0.7931	−50.9463
4.5000	0.6502	−69.7785
4.6000	0.4680	−89.6747
4.7000	0.3240	66.5718	−900
4.8000	0.2592	35.9153	↓
4.9000	0.2988	1.0089
5.0000	0.4562	−30.7682

ρ	σ/πr²
0.2000	0.0008
0.3000	0.0040
0.4000	0.0122
0.5000	0.0287
0.6000	0.0566
0.7000	0.0979
0.8000	0.1520
0.9000	0.2143
1.0000	0.2741
1.1000	0.3158
1.2000	0.3220
1.3000	0.2812
1.4000	0.1974
1.5000	0.0994
1.6000	0.0413
1.7000	0.0759
1.8000	0.1986
1.9000	0.3444
2.0000	0.4568
2.1000	0.5181
2.2000	0.5197
2.3000	0.4461
2.4000	0.3080
2.5000	0.1951
2.6000	0.2143
2.7000	0.3617
2.8000	0.5650
2.9000	0.7783
3.0000	0.9862
3.1000	1.1381
3.2000	1.0962
3.3000	0.8312
3.4000	0.5843
3.5000	0.5381
3.6000	0.7017
3.7000	1.0625
3.8000	1.6547
3.9000	2.3912
4.0000	2.7083
4.1000	2.2910
4.2000	1.6517
4.3000	1.2125
4.4000	1.1044
4.5000	1.4243
4.6000	2.3759
4.7000	3.7111
4.8000	4.2674
4.9000	3.8841
5.0000	3.1578

ρ	σ/πr²
0.2000	0.0016
0.3000	0.0078
0.4000	0.0242
0.5000	0.0577
0.6000	0.1151
0.7000	0.2007
0.8000	0.3113
0.9000	0.4289
1.0000	0.5145
1.1000	0.5106
1.2000	0.3668
1.3000	0.1187
1.4000	0.0294
1.5000	0.3319
1.6000	0.6325
1.7000	0.6947
1.8000	0.6587
1.9000	0.6668
2.0000	0.7867
2.1000	1.0682
2.2000	1.5839
2.3000	2.1516
2.4000	2.5493
2.5000	2.8235
2.6000	3.6047
2.7000	5.5696
2.8000	5.1723
2.9000	3.8064
3.0000	3.3068
3.1000	3.3088
3.2000	3.6863
3.3000	6.7074
3.4000	9.4308
3.5000	8.0491
3.6000	6.4456
3.7000	4.2459
3.8000	2.5464
3.9000	3.0459
4.0000	5.6918
4.1000	5.9825
4.2000	7.0778
4.3000	7.0125
4.4000	3.7286
4.5000	2.2518
4.6000	2.4128
4.7000	1.7282
4.8000	2.1928
4.9000	4.2308
5.0000	3.7463

ρ	σ/πr²
0.2000	0.0016
0.3000	0.0081
0.4000	0.0252
0.5000	0.0600
0.6000	0.1196
0.7000	0.2082
0.8000	0.3219
0.9000	0.4404
1.0000	0.5206
1.1000	0.5002
1.2000	0.3302
1.3000	0.0740
1.4000	0.0445
1.5000	0.3793
1.6000	0.6292
1.7000	0.6547
1.8000	0.6085
1.9000	0.6100
2.0000	0.7015
2.1000	0.9918
2.2000	1.5579
2.3000	2.1205
2.4000	2.4809
2.5000	2.7956
2.6000	3.7635
2.7000	4.8423
2.8000	3.8236
2.9000	2.9077
3.0000	2.6968
3.1000	2.8424
3.2000	3.6760
3.3000	6.5351
3.4000	6.9608
3.5000	5.8743
3.6000	4.2642
3.7000	2.4639
3.8000	1.7040
3.9000	2.8279
4.0000	3.7600
4.1000	4.4146
4.2000	5.1272
4.3000	3.7554
4.4000	1.8409
4.5000	1.3705
4.6000	0.8708
4.7000	0.8635
4.8000	1.5951
4.9000	2.3705
5.0000	1.6867

ρ	σ/πr²
0.1000	0.0004
0.2000	0.0050
0.3000	0.0251
0.4000	0.2062
0.5000	0.5131
0.6000	0.8415
0.7000	1.3832
0.8000	2.1040
0.9000	2.5087
1.0000	2.5236
1.1000	2.3419
1.2000	1.9657
1.3000	1.4520
1.4000	0.9331
1.5000	0.5089
1.6000	0.2370
1.7000	0.1584
1.8000	0.2756
1.9000	0.5296
2.0000	0.8302
2.1000	1.0918
2.2000	1.2496
2.3000	1.2719
2.4000	1.1619
2.5000	0.9542
2.6000	0.7081
2.7000	0.4891
2.8000	0.3487
2.9000	0.3186
3.0000	0.3980
3.1000	0.5488
3.2000	0.7262
3.3000	0.8909
3.4000	0.9897
3.5000	0.9887
3.6000	0.9142
3.7000	0.7932
3.8000	0.6289
3.9000	0.4815
4.0000	0.4160
4.1000	0.4071
4.2000	0.4430
4.3000	0.5655
4.4000	0.7076

Abstract

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Figures (6)

Tables (6)

Equations (15)

Applied Optics