Ray tracing method in phase space for two-dimensional optical systems

C. Filosa; J. H. M. ten Thije Boonkkamp; W. L. IJzerman

doi:10.1364/AO.55.003599

Applied Optics
Vol. 55,
Issue 13,
pp. 3599-3606
(2016)
•https://doi.org/10.1364/AO.55.003599

Ray tracing method in phase space for two-dimensional optical systems

C. Filosa, J. H. M. ten Thije Boonkkamp, and W. L. IJzerman

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C. Filosa, J. H. M. ten Thije Boonkkamp, and W. L. IJzerman, "Ray tracing method in phase space for two-dimensional optical systems," Appl. Opt. 55, 3599-3606 (2016)

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Abstract

Ray tracing is a forward method to calculate the photometric variables at the target of a non-imaging optical system. In this paper, a new ray tracing technique is presented to improve the accuracy and to reduce the computational time of the classical ray tracing approach. The method is based on the phase space representation of the source and the target of the optical system, and it is applied to a two-dimensional TIR-collimator. The strength of the method lies in tracing fewer rays through the system. Only rays that lie in the meridional plane are considered. A procedure that disregards rays in smooth regions in phase space, where the luminance is continuous, is implemented and only the rays close to discontinuities are traced. The efficiency of the method is demonstrated by numerical simulations that compare the new method with Monte Carlo ray tracing. The results show that the phase space approach is faster and more accurate than the already existing ray tracing method; moreover the phase space method converges as one over the number of rays traced unlike Monte Carlo ray tracing in which the speed of convergence is proportional to one over the square root of the number of rays.

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Number of Rays	$ϵ_{x_{max}}$	$ϵ_{τ_{max}}$	Étendue	Error
1403	$1.0 \times 10^{- 1}$	$5.00 \times 10^{- 2}$	7.4836	$3.57 \times 10^{- 4}$
3237	$5.0 \times 10^{- 2}$	$2.50 \times 10^{- 2}$	7.6614	$2.22 \times 10^{- 4}$
7299	$2.5 \times 10^{- 2}$	$1.25 \times 10^{- 2}$	7.7787	$1.38 \times 10^{- 4}$
15919	$1.0 \times 10^{- 2}$	$5.00 \times 10^{- 3}$	7.8475	$7.31 \times 10^{- 5}$
33651	$7.0 \times 10^{- 3}$	$3.50 \times 10^{- 3}$	7.8839	$3.80 \times 10^{- 5}$
69330	$3.0 \times 10^{- 3}$	$1.50 \times 10^{- 3}$	7.9017	$2.02 \times 10^{- 5}$

Number of Rays	${Error}_{MC}$
970	$2.20 \times 10^{- 3}$
9702	$6.60 \times 10^{- 4}$
97104	$1.74 \times 10^{- 4}$
971436	$6.34 \times 10^{- 5}$
9715391	$2.06 \times 10^{- 5}$

Number of Rays	$ϵ_{x_{max}}$	$ϵ_{τ_{max}}$	Étendue	Error
1403	$1.0 \times 10^{- 1}$	$5.00 \times 10^{- 2}$	7.4836	$3.57 \times 10^{- 4}$
3237	$5.0 \times 10^{- 2}$	$2.50 \times 10^{- 2}$	7.6614	$2.22 \times 10^{- 4}$
7299	$2.5 \times 10^{- 2}$	$1.25 \times 10^{- 2}$	7.7787	$1.38 \times 10^{- 4}$
15919	$1.0 \times 10^{- 2}$	$5.00 \times 10^{- 3}$	7.8475	$7.31 \times 10^{- 5}$
33651	$7.0 \times 10^{- 3}$	$3.50 \times 10^{- 3}$	7.8839	$3.80 \times 10^{- 5}$
69330	$3.0 \times 10^{- 3}$	$1.50 \times 10^{- 3}$	7.9017	$2.02 \times 10^{- 5}$

Number of Rays	${Error}_{MC}$
970	$2.20 \times 10^{- 3}$
9702	$6.60 \times 10^{- 4}$
97104	$1.74 \times 10^{- 4}$
971436	$6.34 \times 10^{- 5}$
9715391	$2.06 \times 10^{- 5}$

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Applied Optics