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Two-step design method for highly compact three-dimensional freeform optical system for LED surface light source

Xianglong Mao, Hongtao Li, Yanjun Han, and Yi Luo

Open Access Open Access

Abstract

Designing an illumination system for a surface light source with a strict compactness requirement is quite challenging, especially for the general three-dimensional (3D) case. In accordance with the two key features of an expected illumination distribution, i.e., a well-controlled boundary and a precise illumination pattern, a two-step design method is proposed in this paper for highly compact 3D freeform illumination systems. In the first step, a target shape scaling strategy is combined with an iterative feedback modification algorithm to generate an optimized freeform optical system with a well-controlled boundary of the target distribution. In the second step, a set of selected radii of the system obtained in the first step are optimized to further improve the illuminating quality within the target region. The method is quite flexible and effective to design highly compact optical systems with almost no restriction on the shape of the desired target field. As examples, three highly compact freeform lenses with ratio of center height h of the lens and the maximum dimension D of the source ≤ 2.5:1 are designed for LED surface light sources to form a uniform illumination distribution on a rectangular, a cross-shaped and a complex cross pierced target plane respectively. High light control efficiency of η > 0.7 as well as low relative standard illumination deviation of RSD < 0.07 is obtained simultaneously for all the three design examples.

© 2014 Optical Society of America

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Figures (16)
Fig. 1
Fig. 1 Two key points for illumination design and the corresponding two-step optimization strategy.

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Fig. 2
Fig. 2 A flow diagram of the two-step optimization process. The first step (in the red box) is a combination of two algorithms: iterative feedback modification of the illumination and target shape scaling. The second step (in the blue box) is realized by optimizing a set of selected radii of the initial optimal lens model obtained in the first step.

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Fig. 3
Fig. 3 Establish the source-target mapping using an assumed point source which is at the geometric center of the surface light source with the same luminous intensity distribution as the surface source. For a point source, a point on the lens profile will generate a single point on the target plane.

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Fig. 4
Fig. 4 For a surface light source, a point on the lens profile will create a finite-size light spot on the target plane. Through the overlapping of all the spots, a target distribution is obtained.

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Fig. 5
Fig. 5 Numerical configuration of the profile by geometrical construction method.

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Fig. 6
Fig. 6 Optimize the preset shape of the target plane.

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Fig. 7
Fig. 7 Second-step optimization: optimize the polar radii of the freeform lens obtained in the first-step optimization in selected directions.

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Fig. 8
Fig. 8 Sketch of the setting for designing freeform lens for LED square surface light source to form a uniform illumination pattern within a far-field rectangular region.

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Fig. 9
Fig. 9 Simulated illumination distributions of the optical systems generated by (a) point source assumption, (b) the first-step optimization, and (c) the second-step optimization.

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Fig. 10
Fig. 10 (a) Models and (b) cross-sectional profiles of the optimal freeform lens.

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Fig. 11
Fig. 11 Sketch of the setting for designing freeform lens for discoid LED surface light source to form a uniform illumination pattern within a far-field cross-shaped region.

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Fig. 12
Fig. 12 Simulated illumination distributions of the optical systems obtained after (a) the first-step optimization, and (b) the second-step optimization.

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Fig. 13
Fig. 13 (a) Models and (b) cross-sectional profiles of the optimal freeform lens.

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Fig. 14
Fig. 14 Sketch of the setting for designing a freeform lens for discoid LED surface light source to form a uniform illumination pattern within a complex-shaped target region.

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Fig. 15
Fig. 15 Final simulation result after the two-step optimization.

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Fig. 16
Fig. 16 (a) Models and (b) cross-sectional profiles of the optimal freeform lens.

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Tables (3)

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Table 1 Parameters set for the first example

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Table 2 Lighting parameters calculated for the two-step optimization

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Table 3 Lighting parameters calculated for the two-step optimization

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Equations (25)

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∬ Ω S I(θ,φ)sinθdθdφ = ∬ Ω T E 0 (x,y)dxdy ,
(x,y)=( f 0 (θ,φ), g 0 (θ,φ)).
φ i = φ min + φ max − φ min M ⋅ i     ( i = 0 , 1 , ⋯ M ) ,
θ j = θ min + θ max − θ min N ⋅ j     ( j = 0 , 1 , ⋯ N ) ,
γ i = φ i     ( i = 0 , 1 , ⋯ M ) .
S ( ρ B , γ ) = 0 ,
∫ θ 0 θ j I ( θ , φ i ) d θ ∫ θ 0 θ N I ( θ , φ i ) d θ = ∫ ρ i , 0 ρ i , j E 0 ( ρ , γ i ) d ρ ∫ ρ i , 0 ρ B i E 0 ( ρ , γ i ) d ρ ( i = 0 , 1 , ⋯ M , j = 0 , 1 , ⋯ N ) ,
ρ i , j = F ( θ j , φ i ) .
( θ j , φ i )→( ρ i,j , γ i )⇔{ γ i = φ i ρ i,j =F( θ j , φ i )     (i=0,1,⋯M,j=0,1,⋯N).
N 0 = ( n 2 O u t 0 − n 1 I n 0 ) / | n 2 O u t 0 − n 1 I n 0 | ,
β k (ρ,γ)= { E 0 (ρ,γ)/[ λ 1 ⋅ E Sk (ρ,γ)+(1− λ 1 )⋅ E 0 (ρ,γ)] } λ 2 ,
E Mk (ρ,γ)= Π i=1 k β i (ρ,γ)⋅ E 0 (ρ,γ).
M F 1 = ω 1 ⋅RS D shape +(1− ω 1 )⋅RSD,
γ ′ i = φ min + φ max − φ min M 1 ⋅i  (i=0,1,⋯, M 1 ),
ρ ′ i,j = ρ ′ mini ( γ ′ i )+ ρ ′ maxi ( γ ′ i )− ρ ′ mini ( γ ′ i ) N 1 ⋅j  (j=0,1,⋯, N 1 ),
RS D 2 shape = ∑ i=0 M 1 ( ρ ′ Si ( γ ′ i )− ρ ′ maxi ( γ ′ i ) ρ ′ maxi ( γ ′ i ) ) 2 M 1 ,
RS D 2 = ∑ i=0 M 1 ∑ j=0 N 1 ( E S ( ρ ′ i,j , γ ′ i )− E 0 ( ρ ′ i,j , γ ′ i ) E 0 ( ρ ′ i,j , γ ′ i ) ) 2 ( M 1 +1)⋅( N 1 +1)−1 ,
S ( α 1 ρ B α 2 , γ ) = 0 ,
{ min α 1 , α 2 M F 1 ( α 1 , α 2 ) Constraint:η≥ η T ,
P ' m , l = r ′ m , l ⋅ ( cos φ ′ m sin θ ′ l , sin φ ′ m sin θ ′ l , cos θ ′ l ) .
M F 2 = υ 1 ⋅RSD+(1− υ 1 )⋅(1−η),
min r ′ m,l M F 2 ( r ′ m,l )  (m=0,1,⋯, N m ;l=0,1,⋯, N l ).
| ρ cos γ α 1 | α 3 + | ρ sin γ α 2 | α 3 = 1 ,
R S D 2 = ∑ i = 0 M 1 ∑ j = 0 N 1 ( E S ( ρ ′ i , j , γ ′ i ) E ¯ S − 1 ) 2 ( M 1 + 1 ) ⋅ ( N 1 + 1 ) − 1 ,
E ¯ S = ∑ i = 0 M 1 ∑ j = 0 N 1 E S ( ρ ′ i , j , γ ′ i ) ( M 1 + 1 ) ⋅ ( N 1 + 1 ) .
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