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A two-step design method for high compact rotationally symmetric optical system for LED surface light source

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

Open Access Open Access

Abstract

A two-step optimization method is proposed to design a compact single-surface far-field illumination system, satisfying the requirements of illuminance uniformity and light control efficiency with h/D less than 3:1. In the first step, the conventional tailored edge-ray design (TED) method is employed to generate prescribed illumination distribution for the rotationally symmetric optical system, and an optimization process is added to reach a balance between illuminance uniformity and light control efficiency. Based on the improved TED method, we can construct an initial optical system more accurate than that obtained by point source assumption. In the second step, an iterative feedback modification process is employed to optimize the initial optical system, so that the degradation of performance due to insufficient control of skew rays is mitigated. Because the initial optical system constructed in the first step is accurate enough, the second-step feedback modification can converge to a satisfactory result within several iterations. As an example, a free-form rotationally symmetric lens with the height of h = 25 mm is designed for a discoidal LED source with the diameter of D = 10 mm. Both high illuminance uniformity of 0.75 and high light control efficiency of 0.86 are obtained simultaneously. The method can be further used to achieve more complex non-uniform illumination distributions. The design of an optical system with h/D = 2.5:1 and a circular linear illumination distribution is demonstrated.

© 2014 Optical Society of America

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Figures (14)
Fig. 1
Fig. 1 (a) Point light source and (b) surface light source.

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Fig. 2
Fig. 2 Lens with a center height of h = 25 mm constructed based on point source approximation to generate a uniform illuminance distribution and simulation results with (a) a point source with a diameter of D = 10−5 mm, (b) and a surface source with a diameter of D = 10 mm.

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Fig. 3
Fig. 3 Each point on a single optical surface can only precisely control one ray emitted from the LED surface light source.

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Fig. 4
Fig. 4 A flow diagram of the design process.

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Fig. 5
Fig. 5 (a) Luminous intensity and illuminance; (b) Luminous intensity and projection length of the source through the lens; (c) Meridian rays (in green) and skew rays (in red).

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Fig. 6
Fig. 6 Four types of lens design solutions: (a) and (b) are diverging solutions, (c) and (d) are converging solutions, wherein θM is the maximal emergence angle, F and F’ are two edges of the source, and the part of the lens marked with a dashed circle is where the total internal reflection inevitably happens.

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Fig. 7
Fig. 7 Geometric configuration of the profile of the lens, wherein O’ is an arbitrary point between O and F’ while Bi is an arbitrary point on the calculated profile, the output ray of the ray O’Bi will form an angle θi’ that is larger than θi with the y-axis according to the Snell’s law.

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Fig. 8
Fig. 8 The emergence angle θi’ of the ray FBi will be larger than the prescribed maximal emergence angle θmax which will cause a light spillage.

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Fig. 9
Fig. 9 Parameters of the target plane, the lens and the LED source.

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Fig. 10
Fig. 10 Light spillage is related to the preset curve: the optimized (black line) and the conventional (red line); The blue line represents the output ray angle that is corresponding to the target edge, and the light whose output ray angle is above the blue line is leaked outside of the target field.

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Fig. 11
Fig. 11 Simulation results: (a) initial result based on point source assumption without feedback; (b) final result based on point source assumption with feedback; (c) initial result based on improved TED method without feedback; (d) final result based on improved TED method with feedback.

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Fig. 12
Fig. 12 (a) Front view and dimensioning, and (b) full view of the optical system.

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Fig. 13
Fig. 13 Comparison of simulation results of the optical systems designed by the proposed method with different dimension ratios h/D on three parameters: illuminance uniformity, light control efficiency and merit function.

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Fig. 14
Fig. 14 (a) Lens model to generate a linear illumination distribution and (b) the simulated illuminance distribution.

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Equations (19)

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E 2 D ( x ) = cos 2 θ H I 2 D ( θ ) ,
I 2 D ( θ ) = L 2 D ⋅ W ( θ ) ,
W ( θ ) = W 0 ⋅ cos − 2 θ ,
y=a x 2 +bx+c.
{ Optimization variables: x B 0 , y B 0 Merit function:MF( x B 0 , y B 0 ) Constraints:η≥ η T , U E ≥ U ET ,
MF=σ⋅η+(1−σ)⋅ U E ,
β j (x)= { E 0 (x)/[ α 1 ⋅ E Sj (x)+(1− α 1 )⋅ E 0 (x)] } α 2 ,
E MJ (x)= Π j=1 J β j (x)⋅ E 0 (x).
MF=0.5⋅η+0.5⋅ U E .
β j (x)=2⋅ E 0 (x)/[ E Sj (x)+ E 0 (x)].
E 2 D ( x ) = E 0 ( 1 − 2 3 ⋅ x R ) = E 0 ( 1 − 2 3 ⋅ H ⋅ tan θ R ) .
W ( θ ) = W 0 2 ( 1 − 2 3 ⋅ H ⋅ tan θ R ) cos − 2 θ .
R S D = 1 N -1 ∑ i = 1 N ( E S ( x i ) − E ( x i ) E ( x i ) ) 2 ,
I 2D (θ)= dΦ dθ ,
E 2D (x)= dΦ dx ,
dθ= dx⋅ cos 2 θ H .
E 2D (x)= cos 2 θ H I 2D (θ).
L 2D = d 2 Φ dx⋅cosθ⋅dθ .
I 2D (θ)= L 2D ⋅cosθ⋅ ∫ dx = L 2D ⋅W(θ).
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