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Designing optical free-form surfaces for extended sources

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Abstract

LED lighting has been a strongly growing field for the last decade. The outstanding features of LED, like compactness and low operating temperature take the control of light distributions to a new level. Key for this is the development of sophisticated optical elements that distribute the light as intended. The optics design method known as tailoring relies on the point source assumption. This assumption holds as long as the optical element is large compared to the LED chip. With chip sizes of 1 mm2 this is of no concern if each chip is endowed with its own optic. To increase the power of a luminaire, LED chips are arranged to form light engines that reach several cm in diameter. In order to save costs and space it is often desirable to use a single optical element for the light engine. At the same time the scale of the optics must not be increased in order to trivially keep the point source assumption valid. For such design tasks point source algorithms are of limited usefulness. New methods that take into account the extent of the light source have to be developed. We present two such extended source methods. The first method iteratively adapts the target light distribution that is fed into a points source method while the second method employs a full phase space description of the optical system.

© 2014 Optical Society of America

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Figures (5)

Fig. 1
Fig. 1 The rays emitted by a point source travel through the optical system to the target plane. The optical system is designed so that ray paths don’t cross.
Fig. 2
Fig. 2 Target irradiance distribution adaptation using the solution of a Monge-Ampère equation. The desired target distribution a) is fed into a point source method. The distribution b) is computed with the lens of step a) using a point source. Distribution c) shows the case with extended source. Now a mapping is computed via a solution of a Monge-Ampère equation using the method outlined in [14] to transform the distribution c) into distribution b). This mapping is then applied to the original distribution a) which results in distribution d). Distribution d) is now fed into the point source method which results in the distribution e) for the extended source case.
Fig. 3
Fig. 3 Example setup of a source, a spherical lens and a target plane. Rays are traced from the target plane back to the source plane. Rays that hit the source contribute to the integral Eq. (12). The squares on the left and right show the points in phase space of those rays that hit the source. The phase space on the source is densely occupied whereas on the target side only a small part of phase space is occupied. In order to avoid unnecessary computations the target side phase space has to be restricted to the relevant parts. This is achieved by first tracing forward from the source to the target. The curve designated by ”integration” is the result of integral Eq. (12). The dots represent results obtained by using a Monte-Carlo ray tracer.
Fig. 4
Fig. 4 The source has an extend of 6 mm, the lens is 14 mm wide, the target has a width of 50 mm and the distance from source to target is 25 mm. The output angle of the source is restricted to 46.5°.
Fig. 5
Fig. 5 Target irradiance distribution generated by the setup Fig. 4 computed using FRED (www.photonengr.com). The prescribed target distribution was uniform within ±25mm.

Tables (3)

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Table 1 Optical surface parametrizations.

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Table 2 Table of symbols used in this article.

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Table 3 Principal point source algorithms.

Equations (13)

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n s L s ( u s , s s ) d Ω s cos ( θ s ) d A s = n t L t ( u t , s t ) d Ω t cos ( θ t ) d A t
n s d Ω s cos ( θ s ) d A s n t d Ω t cos ( θ t ) d A t = 1
L s ( u s , s s ) = L t ( u t , s t )
I s ( s x , s y ) d s x d s y = E t ( u x , u y ) d u x d u y
u x = u x ( s x , s x )
u y = u x ( s x , s y )
I s ( s x , s y ) d s x d s y = E t ( u x ( s x , s y ) , u y ( s x , s y ) ) det ( J ) d s x d s y
det ( J ) = ( u x s x u y s y u x s y u y s x )
( u x , u y ) = ϕ
I s ( s x , s y ) = E t ( ϕ , ϕ ) ( 2 ϕ s x 2 2 ϕ s y 2 ( 2 ϕ s x s y ) 2 )
Ω t L t ( u t , s t ) cos ( θ t ) d Ω t = Ω t L s ( u s , s s ) cos ( θ t ) d Ω t
E t ( u t ) = Ω t L s ( u s , s s ) cos ( θ t ) d Ω t
E t ( u t ) 1 2 i [ L s , i ( u s , s s ) cos θ t , i + L s , i + 1 ( u s , s s ) cos θ t , i + 1 ] Δ Ω t , i , i + 1
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