Illuminance and caustic surfaces in multi-interface variable-index media. 3: Source imbedded in variable-index medium, light reflected or refracted by multiple surfaces

Donald G. Burkhard

doi:10.1364/AO.19.003704

Applied Optics
Vol. 19,
Issue 21,
pp. 3704-3713
(1980)
•https://doi.org/10.1364/AO.19.003704

Illuminance and caustic surfaces in multi-interface variable-index media. 3: Source imbedded in variable-index medium, light reflected or refracted by multiple surfaces

Donald G. Burkhard

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Donald G. Burkhard, "Illuminance and caustic surfaces in multi-interface variable-index media. 3: Source imbedded in variable-index medium, light reflected or refracted by multiple surfaces," Appl. Opt. 19, 3704-3713 (1980)

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Abstract

All terms required to calculate the illuminance and caustic points along a ray path are evaluated for a source imbedded in a z-dependent variable-index medium. The ray path may undergo reflections or refractions from multiple surfaces imbedded in the medium. The procedure is general and applies to multiple surfaces and multiple media and is valid for all rays.

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A	B	C
Normal	Modified A	Option C
$σ_{1} = \frac{σ_{0}}{L (0)}$	$σ_{1} = \frac{σ_{0}}{L (0)}$	$σ_{1} = \frac{σ_{0}}{L (0)}$
$σ_{2} = \frac{σ_{1}}{L (1)}$	$σ_{2} = \frac{σ_{1}}{L (1)}$	$σ_{2} = \frac{σ_{0}}{L (0) K_{1} (1) + K_{2} (1)}$
$σ_{3} = \frac{σ_{2}}{L (2)}$	$σ_{3} = \frac{σ_{1}}{L (1) K_{1} (2) + K_{2} (2)}$	$σ_{3} = \frac{σ_{1}}{L (1) K_{1} (2) + K_{2} (2)}$
$σ_{4} = \frac{σ_{3}}{L (3)}$	$σ_{4} = \frac{σ_{3}}{L^{'} (3)}$	$σ_{4} = \frac{σ_{2}}{L (2) K_{1} (3) + K_{2} (3)}$
$σ_{5} = \frac{σ_{4}}{L (4)}$	$σ_{5} = \frac{σ_{4}}{L (4)}$	$σ_{5} = \frac{σ_{3}}{L (3) K_{1} (4) + K_{2} (4)}$
Column A	Column B	Column C
No caustic surface intersects a refracting surface.	Caustic surface formed by rays emerging from surface 2 intersects surface 3.	Alternative to column A. No apparent advantage since this procedure must be modified when the caustic intersects a real surface.

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Applied Optics