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Design of efficient LED optics with two free-form surfaces

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Abstract

Most LED illumination applications require generation of complex light patterns for which the secondary optics with two free-form surfaces needs to be used. We present a novel optimization method for computing such type of optical elements. An analytical solution for the generation of the initial surfaces is proposed. To accelerate the optimization process, a specific surface representation is used, that eliminates the need to run a time-expensive raytracing procedure. As an example, an optical element generating uniformly illuminated rectangular area with size of 60° by 40° is computed. Lighting efficacy for the extended Lambertian source 1x1 mm is 88.5% and nonuniformity is less than 8.5%.

© 2014 Optical Society of America

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Figures (12)

Fig. 1
Fig. 1 Arrangement of light source, optical element and exit plane.
Fig. 2
Fig. 2 (a) and (b) profiles of axisymmetrical surfaces generating uniformly illuminated circular areas with diameters of 1200 mm and 750 mm, respectively; (c) combined profiles; (d) fitted spline surface.
Fig. 3
Fig. 3 Illuminance distribution generated by the optical element in Fig. 2(d) for point light source: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).
Fig. 4
Fig. 4 Optimized optical element.
Fig. 5
Fig. 5 Illuminance distribution generated by the optical element in Fig. 4 for a point light source: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).
Fig. 6
Fig. 6 Illuminance distribution generated by the optical element in Fig. 4 for an extended light source 1x1 mm: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).
Fig. 7
Fig. 7 Optical element with a single working free-form surface.
Fig. 8
Fig. 8 Illuminance distribution generated by the optical element in Fig. 7 for an extended light source 1x1 mm: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).
Fig. 9
Fig. 9 Dependences of the lighting efficacy on the source’s size for the designs with two free-form surfaces (square markers) and single free-form surface (triangular markers).
Fig. 10
Fig. 10 Optical element with two free-form surfaces generating uniformly illuminated hexagon spot.
Fig. 11
Fig. 11 Illuminance distribution generated by the optical element in Fig. 10 for a point light source: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).
Fig. 12
Fig. 12 Illuminance distribution generated by the optical element in Fig. 10 for an extended light source 1x1 mm: (a) grayscale distribution; (b) profiles of illuminance distribution (solid line – v = 0, dashed line – u = 0).

Equations (6)

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M( φ,ψ )=R( φ,ψ )+l( φ,ψ ) a 1 (φ,ψ).
ε( c )= E( u,v;c ) E 0 ( u,v ) = 1 S S ( E 0 ( u,v )E( u,v;c ) ) 2 dudv min c ,
E( u,v;c )= φ,ψ I( φ,ψ )sin( ψ ) δ σ ( u u ˜ ( φ,ψ;c ),v v ˜ ( φ,ψ;c ) )dφdψ,
a 1 =n a 0 +( 1[ n a 0 , n 1 ] 2 n( a 0 , n 1 ) ) n 1 ,
a 2 =n a 1 +( 1[ n a 1 , n 2 ] 2 n( a 1 , n 2 ) ) n 2
u ˜ ( φ,ψ;c )=R( φ,ψ; c R ) a 0x +l( φ,ψ; c l ) a 1x +d( φ,ψ;c ) a 2x , v ˜ ( φ,ψ;c )=R( φ,ψ; c R ) a 0y +l( φ,ψ; c l ) a 1y +d( φ,ψ;c ) a 2y , d( φ,ψ;c )= ( fR( φ,ψ; c R ) a 0z l( φ,ψ; c l ) a 1z ) / a 2z ,
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