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Design of high-efficient freeform LED lens for illumination of elongated rectangular regions

Mikhail A. Moiseev, Leonid L. Doskolovich, and Nikolay L. Kazanskiy

Open Access Open Access

Abstract

We propose a method for the design of an optical element generating the required irradiance distribution in a rectangular area with a large aspect ratio. Application fields include streetlights, the illumination of halls or corridors, and so forth. The design assumes that the optical element has a complex form and contains two refractive surfaces. The first one converts a spherical beam from the light source to a cylindrical beam. The second one transforms an incident cylindrical beam and generates the required irradiance distribution in the target plane. Two optical elements producing a uniform irradiance distribution from a Cree® XLamp® source in rectangular regions of 17 m × 4 m and 17 m × 2 m are designed. The light efficiency of the designed optical element is larger than 83%, whereas the irradiance nonuniformity is less than 9%.

©2011 Optical Society of America

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Figures (8)
Fig. 1
Fig. 1 Design of the optical element.

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Fig. 2
Fig. 2 Collimating profile.

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Fig. 3
Fig. 3 Optical element producing the uniform irradiance distribution in a 17 × 4 m rectangle area (overall dimensions are given in millimeters).

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Fig. 4
Fig. 4 Irradiance distribution in the target plane produced by the optical element in Fig. 3. (a) The grayscale distribution. (b) The irradiance profiles–solid line: v = 0 ; dashed line, u = 0 .

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Fig. 5
Fig. 5 Optical element with a single refractive surface producing the uniform irradiance distribution in a 17 × 4 m rectangle area (overall dimensions are given in millimeters).

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Fig. 6
Fig. 6 Irradiance distribution in the target plane produced by the optical element in Fig. 5. (a) The grayscale distribution. (b) The irradiance profiles–solid line, v = 0 ; dashed line, u = 0 .

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Fig. 7
Fig. 7 Optical element producing the uniform irradiance distribution in a shifted 17 × 2 m rectangle area (overall dimensions are given in millimeters).

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Fig. 8
Fig. 8 Irradiance distribution in the target plane produced by the optical element in Fig. 7. (a) The grayscale distribution. (b) The irradiance profiles–solid line. v = 0 ; dashed line, u = 0 .

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Equations (12)

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r ( φ , y ; p ) = ( r ( φ , y ; p ) sin φ ;   y ;   r ( φ , y ; p ) cos φ )
f ( p ) = ‖ E ( u , v ; p ) − E 0 ( u , v ) ‖ → min ,
T ( φ , y ; p ) E ′ ( φ , y ) R d φ d y = E ( u ( φ , y ; p ) ) d u d v , E ( u ( φ , y ; p ) ) = T ( φ , y ; p ) E ′ ( φ , y ) R | J ( u ( φ , y ; p ) ) | ,
a 0 ( φ ) = { sin φ , 0 , cos φ } ,
a 1 ( φ , y ; p ) = n 1 n 2 a 0 ( φ ) + ( 1 − [ n 1 n 2 a 0 , n ] 2 − n 1 n 2 ( a 0 , n ) ) n ( φ , y ; p ) .
u ( φ , y ; p ) = r ( φ , y ; p ) sin φ + a 1 x ( φ , y ; p ) l ( φ , y ; p ) , v ( φ , y ; p ) = y + a 1 y ( φ , y ; p ) l ( φ , y ; p ) ,
f ( x , y ) | J ( u ( x , y ) ) | | x = x ˜ y = y ˜ = ∫ − ∞ + ∞ ∫ − ∞ + ∞ f ( x , y ) δ ( u ˜ − u ( x , y ) , v ˜ − v ( x , y ) ) d x d y ,
E ( u , v ; p ) = R ∫ − y max y max ∫ − π / 2 π / 2 T ( φ , y ; p ) E ′ ( φ , y ) δ ( u − u ( φ , y ; p ) ) d φ d y .
δ σ ( u , v ) = 1 2 π σ 2 exp ( − u 2 + v 2 2 σ 2 ) .
E ( u , v ; p ) = ∫ − y max y max ∫ − π / 2 π / 2 R T ( φ , y ; p ) E ′ ( φ , y ) δ σ ( u − u ( φ , y ; p ) ) d φ d y .
∂ f ∂ p i = 1 f ( p ) ∬ u , v ( E ( u , v ; p ) − E 0 ( u , v ) ) ∂ E ( u , v ; p ) ∂ p i d u d v ,
∂ E ( u , v ; p ) ∂ p i = ∫ − y max y max ∫ − π / 2 π / 2 R E ′ ( φ , y ) ∂ ∂ p i ( T ( φ , y ; p ) δ σ ( u − u ( φ , y ; p ) ) ) d φ d y .
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