Calculating the model of a nondiagonal rotation invariant angle for a complicated scatterer

Xiaojun Zhou; Guohua Gu; Kan Ren; Dongming Lu; Minjie Wan; Qian Chen

doi:10.1364/AO.58.007733

Applied Optics
Vol. 58,
Issue 28,
pp. 7733-7740
(2019)
•https://doi.org/10.1364/AO.58.007733

Calculating the model of a nondiagonal rotation invariant angle for a complicated scatterer

Xiaojun Zhou, Guohua Gu, Kan Ren, Dongming Lu, Minjie Wan, and Qian Chen

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Xiaojun Zhou, Guohua Gu, Kan Ren, Dongming Lu, Minjie Wan, and Qian Chen, "Calculating the model of a nondiagonal rotation invariant angle for a complicated scatterer," Appl. Opt. 58, 7733-7740 (2019)

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Abstract

In the research on scattering polarimetry, a scattering mechanism is described by an internal degree of freedom called rotation invariant parameter $α$ . Traditionally, $α$ is calculated by the diagonal scattering matrix of the single scatterer. However, when the research object is a scatterer with complicated surface and microstructure, the traditional calculation of parameter $α$ is biased, since the corresponding scattering matrix is a nondiagonal matrix. To address this problem, this paper proposes a scientific model based on Cameron decomposition to raise the accuracy of parameter $α$ in the complicated scatterer. The rotation invariant parameter with higher accuracy is renamed as a nondiagonal rotation invariant angle. In the verified experiments, the experimental values of each nondiagonal rotation invariant angle are compared with the referenced values calculated by optical constant and incident angle. The results demonstrate that fewer residuals are achieved than by the traditional method. Based on the presented calculating model, the scattering mechanism difference interval between two different materials is proposed as a judging area to distinguish the differences between scattering mechanisms in application.

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	Copper			Graphite			Polypropylene
Incident Angle (°)	$α_{non-diag}$	$α_{0}$	$α_{r}$	$α_{non-diag}$	$α_{0}$	$α_{r}$	$α_{non-diag}$	$α_{0}$	$α_{r}$
30	89.5441	89.5437	89.3090	89.1005	89.1004	88.5269	87.6339	87.8554	86.3479
37.5	88.7811	88.7804	88.2318	87.3508	87.3506	86.2065	82.3904	83.0064	80.5025
45	87.2745	87.2710	86.0921	83.8406	83.8406	81.6795	73.5365	73.5004	69.7306
52.5	82.0560	82.0473	82.1214	76.5232	76.5231	73.7760	56.5873	56.7449	53.8269
60	74.2963	74.3819	75.0122	63.4389	63.4388	61.3565	35.8926	35.7255	35.5660
67.5	60.7509	60.7139	62.5947	43.6823	43.6782	44.1305	21.3079	20.9495	19.3946
75	33.7768	33.7357	42.1379	21.4916	21.4909	24.1357	6.8490	6.4582	8.1106

	Side A of Leaf			Side B of Leaf			Camouflage Coating
Incident Angle (deg)	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$
30	0.0559	1.4065	0.0030	0.1575	0.4499	$6.7 E - 04$	0.0147	0.8108	0.0041
37.5	0.1723	1.3087	0.0016	0.3417	0.3674	$2.4 E - 04$	0.0979	0.9392	0.0026
45	0.3775	1.1969	$1.9 E - 05$	0.5275	0.2522	$4.4 E - 04$	0.2171	0.8259	0.0037
52.5	0.7192	0.952	$7.6 E - 05$	0.7866	0.1964	$3.9 E - 04$	0.5194	0.5902	$- 8 E - 05$
60	1.1745	0.6956	−0.0003	0.9461	0.2027	$1.1 E - 03$	0.9981	0.3500	$5.5 E - 04$
67.5	1.4786	0.3694	$2.4 E - 04$	1.1472	0.1163	$- 2 E - 04$	1.3584	0.2182	$- 3 E - 04$
75	1.6562	0.0982	−0.0002	1.5785	0.0422	$- 2 E - 05$	1.4438	0.1593	$5.5 E - 04$

	Copper			Graphite			Polypropylene
Incident Angle (°)	$α_{non-diag}$	$α_{0}$	$α_{r}$	$α_{non-diag}$	$α_{0}$	$α_{r}$	$α_{non-diag}$	$α_{0}$	$α_{r}$
30	89.5441	89.5437	89.3090	89.1005	89.1004	88.5269	87.6339	87.8554	86.3479
37.5	88.7811	88.7804	88.2318	87.3508	87.3506	86.2065	82.3904	83.0064	80.5025
45	87.2745	87.2710	86.0921	83.8406	83.8406	81.6795	73.5365	73.5004	69.7306
52.5	82.0560	82.0473	82.1214	76.5232	76.5231	73.7760	56.5873	56.7449	53.8269
60	74.2963	74.3819	75.0122	63.4389	63.4388	61.3565	35.8926	35.7255	35.5660
67.5	60.7509	60.7139	62.5947	43.6823	43.6782	44.1305	21.3079	20.9495	19.3946
75	33.7768	33.7357	42.1379	21.4916	21.4909	24.1357	6.8490	6.4582	8.1106

	Side A of Leaf			Side B of Leaf			Camouflage Coating
Incident Angle (deg)	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$	$2 A_{0}$	$B_{0} + B$	$B_{0} - B$
30	0.0559	1.4065	0.0030	0.1575	0.4499	$6.7 E - 04$	0.0147	0.8108	0.0041
37.5	0.1723	1.3087	0.0016	0.3417	0.3674	$2.4 E - 04$	0.0979	0.9392	0.0026
45	0.3775	1.1969	$1.9 E - 05$	0.5275	0.2522	$4.4 E - 04$	0.2171	0.8259	0.0037
52.5	0.7192	0.952	$7.6 E - 05$	0.7866	0.1964	$3.9 E - 04$	0.5194	0.5902	$- 8 E - 05$
60	1.1745	0.6956	−0.0003	0.9461	0.2027	$1.1 E - 03$	0.9981	0.3500	$5.5 E - 04$
67.5	1.4786	0.3694	$2.4 E - 04$	1.1472	0.1163	$- 2 E - 04$	1.3584	0.2182	$- 3 E - 04$
75	1.6562	0.0982	−0.0002	1.5785	0.0422	$- 2 E - 05$	1.4438	0.1593	$5.5 E - 04$

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Applied Optics