Simple ray-tracing model for a rough surface including multiple scattering effects

Yoshifumi Sekiguchi; Hiroki Kaneko

doi:10.1364/AO.56.000035

Applied Optics
Vol. 56,
Issue 1,
pp. 35-45
(2017)
•https://doi.org/10.1364/AO.56.000035

Simple ray-tracing model for a rough surface including multiple scattering effects

Yoshifumi Sekiguchi and Hiroki Kaneko

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Yoshifumi Sekiguchi and Hiroki Kaneko, "Simple ray-tracing model for a rough surface including multiple scattering effects," Appl. Opt. 56, 35-45 (2017)

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Table of Contents Category
- Scattering
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: September 27, 2016
- Revised Manuscript: November 23, 2016
- Manuscript Accepted: November 25, 2016
- Published: December 20, 2016

Abstract

To simulate lighting systems, we developed a rough surface ray-tracing (RSRT) model on the basis of the facet model. The model needs to conserve energy to analyze how much light is lost in each component in the lighting system. Though a single scattering rough surface model with a shadowing/masking function successfully describes the scattering distribution, masking output light violates the energy conservation law because it lacks multiple scattering. We thus developed an advanced RSRT (A-RSRT) model satisfying the energy conservation law that includes a shadowing/masking effect as a consequence of multiple scattering. To determine the accuracy, we set up a real shape (RS) model that outputs rigorous simulation results, although this RS model was impractical. The comparisons between the calculated results of the A-RSRT and RS models revealed that the A-RSRT model satisfied the energy conservation law and reproduced the scattering distribution precisely.

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	Ray Condition		Subsequent Procedure
$Q_{p} \cdot ω_{m} > 0$	Transmit	$Q_{z} \geq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} < 0$	Multiple scattering
	Reflect	$Q_{z} \leq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} > 0$	Multiple scattering
$Q_{p} \cdot ω_{m} < 0$	Transmit	$Q_{z} \leq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} > 0$	Multiple scattering
	Reflect	$Q_{z} \geq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} < 0$	Multiple scattering

	Reflectance		Transmittance		Sum
Incident Angle	RS	A-RSRT	RS	A-RSRT	RS	A-RSRT
60 deg	0.44	0.44	1.11	1.13	1.55	1.57
75 deg	1.39	1.41	2.44	3.07	3.83	4.48

	Ray Condition		Subsequent Procedure
$Q_{p} \cdot ω_{m} > 0$	Transmit	$Q_{z} \geq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} < 0$	Multiple scattering
	Reflect	$Q_{z} \leq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} > 0$	Multiple scattering
$Q_{p} \cdot ω_{m} < 0$	Transmit	$Q_{z} \leq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} > 0$	Multiple scattering
	Reflect	$Q_{z} \geq 0$	Exit if $ξ_{1} \leq G_{1 c}$ and multiple scattering if $ξ_{1} > G_{1 c}$
		$Q_{z} < 0$	Multiple scattering

	Reflectance		Transmittance		Sum
Incident Angle	RS	A-RSRT	RS	A-RSRT	RS	A-RSRT
60 deg	0.44	0.44	1.11	1.13	1.55	1.57
75 deg	1.39	1.41	2.44	3.07	3.83	4.48

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Applied Optics