Scattering from infinitely sloped surfaces by use of the Kirchhoff approximation

Neil C. Bruce

doi:10.1364/AO.42.002398

Applied Optics
Vol. 42,
Issue 13,
pp. 2398-2406
(2003)
•https://doi.org/10.1364/AO.42.002398

Scattering from infinitely sloped surfaces by use of the Kirchhoff approximation

Neil C. Bruce

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Neil C. Bruce, "Scattering from infinitely sloped surfaces by use of the Kirchhoff approximation," Appl. Opt. 42, 2398-2406 (2003)

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Abstract

A simple reformulation of the double-scatter Kirchhoff approximation is presented to extend the use of this calculation method to infinitely sloped surfaces. Examples are presented for square grooves and lines on perfectly conducting surfaces. The results presented show the accuracy of the method and the errors produced by not including higher-order scattering in the calculations.

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Groove Depth	Incident Angle (deg)	Kirchhoff Results			Integral Equation Results
Groove Depth	Incident Angle (deg)	Single Scatter	Double Scatter	Total Scatter	Integral Equation Results
0.5λ	0	1.017		1.017	0.999
	10	0.987	0.008	1.014	0.998
	20	0.976	0.016	1.009	1.004
	30	0.928	0.026	0.975	0.998
	40	0.911	0.045	0.989	1.001
	50	0.914	0.079	1.042	0.987
	60	0.675	0.170	0.988	0.976
1.0λ	0	1.018		1.018	1.002
	10	0.990	0.015	1.021	0.998
	20	0.898	0.030	0.952	1.001
	30	0.860	0.082	0.992	0.990
	40	0.759	0.123	0.953	0.969
	50	0.721	0.293	1.111	0.991
	60	0.690	0.272	0.999	0.989
1.75λ	0	0.935	0.020	1.050	1.005
	10	0.910	0.027	0.990	0.987
	20	0.905	0.076	1.038	0.985
	30	0.796	0.177	0.992	0.980
	40	0.574	0.335	0.973	0.972
	50	0.657	0.347	1.071	0.991
	60	0.638	0.134	0.787	1.040

Incident Angle (deg)	Kirchhoff Results			Integral Equation Results
Incident Angle (deg)	Single Scatter	Double Scatter	Total Scatter	Integral Equation Results
0	1.011		1.011	1.007
10	0.987	0.007	1.003	1.006
20	0.955	0.020	0.982	1.001
30	0.924	0.046	0.990	0.987
40	0.917	0.081	1.017	0.981
50	0.875	0.121	1.011	0.997
60	0.789	0.174	1.001	1.006

Grooves	Incident Angle (deg)	Kirchhoff Results			Integral Equation Results
Grooves	Incident Angle (deg)	Single Scatter	Double Scatter	Total Scatter	Integral Equation Results
2	20	0.952	0.015	0.987	1.003
	40	0.887	0.049	0.994	0.988
4	20	0.920	0.024	1.006	0.998
	40	0.736	0.146	0.968	0.980

Groove Depth	Incident Angle (deg)	Kirchhoff Results			Integral Equation Results
Groove Depth	Incident Angle (deg)	Single Scatter	Double Scatter	Total Scatter	Integral Equation Results
0.5λ	0	1.017		1.017	0.999
	10	0.987	0.008	1.014	0.998
	20	0.976	0.016	1.009	1.004
	30	0.928	0.026	0.975	0.998
	40	0.911	0.045	0.989	1.001
	50	0.914	0.079	1.042	0.987
	60	0.675	0.170	0.988	0.976
1.0λ	0	1.018		1.018	1.002
	10	0.990	0.015	1.021	0.998
	20	0.898	0.030	0.952	1.001
	30	0.860	0.082	0.992	0.990
	40	0.759	0.123	0.953	0.969
	50	0.721	0.293	1.111	0.991
	60	0.690	0.272	0.999	0.989
1.75λ	0	0.935	0.020	1.050	1.005
	10	0.910	0.027	0.990	0.987
	20	0.905	0.076	1.038	0.985
	30	0.796	0.177	0.992	0.980
	40	0.574	0.335	0.973	0.972
	50	0.657	0.347	1.071	0.991
	60	0.638	0.134	0.787	1.040

Incident Angle (deg)	Kirchhoff Results			Integral Equation Results
Incident Angle (deg)	Single Scatter	Double Scatter	Total Scatter	Integral Equation Results
0	1.011		1.011	1.007
10	0.987	0.007	1.003	1.006
20	0.955	0.020	0.982	1.001
30	0.924	0.046	0.990	0.987
40	0.917	0.081	1.017	0.981
50	0.875	0.121	1.011	0.997
60	0.789	0.174	1.001	1.006

Abstract

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Figures (11)

Tables (3)

Equations (18)

Applied Optics