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Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source

Wenchang Situ, Yanjun Han, Hongtao Li, and Yi Luo

Open Access Open Access

Abstract

A combined feedback design method based on variable separation mapping is proposed in this paper to design free-form optical systems for an extended LED source with complicated illumination patterns. In this method, macro energy division and micro illuminance distribution feedback modifications are carried out according to the deviation between the simulated illumination results and the target requirements. The free-form optical system is then regenerated, and the deviation could be minimized through multiple iterations. Results indicate that free-form optical system designed by this method could achieve precise energy distribution, high regional illuminance uniformity (89.7%), and high light output efficiency (94.9%) simultaneously.

©2011 Optical Society of America

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Figures (9)
Fig. 1
Fig. 1 Energy matrix, area matrix, and the corresponding (u,v) and (x,y) divisions.

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Fig. 2
Fig. 2 Different accuracy of construction: (a) high construction accuracy with small source angle division, (b) low construction accuracy with large source angle division.

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Fig. 3
Fig. 3 Mesh grid mismatch between the area matrix and the prescribed illuminance matrix.

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Fig. 4
Fig. 4 Combined feedback process: (a) frame curves established, (b) regional curves established.

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Fig. 5
Fig. 5 Design example: (a) design parameters, (b) prescribed illuminance distribution pattern.

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Fig. 6
Fig. 6 Simulated results: (a) initial result of feedback with fixed A , (b) final result of feedback with fixed A , (c) initial result of feedback with fixed E , (d) final result of feedback with fixed E , (e) initial result of combined feedback design, (f) final result of combined feedback design.

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Fig. 7
Fig. 7 Comparisons between simulated results on three parameters: (a) total energy ratio between white and blue regions, (b) average regional illuminance uniformity, (c) light output efficiency (Fresnel loss ignored).

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Fig. 8
Fig. 8 Profiles of the final optical system models designed by three feedback methods: (a) cross-sectional profiles in the y-z plane (x = 0), (b) cross-sectional profiles in the x-z plane (y = 0).

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Fig. 9
Fig. 9 3-D geometry of the final optical system model designed by the combined feedback method.

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Equations (8)

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∫ u min u k + 1 J ( u ) cos u d u ∫ u min u max J ( u ) cos u d u = ∑ i = 1 k ∑ j = 1 n E ( i , j ) ∑ i = 1 m ∑ j = 1 n E ( i , j ) ,
∫ v min v s + 1 k + 1 J ( v ) cos v d v ∫ v min v max J ( v ) cos v d v = ∑ j = 1 s E ( k , j ) ∑ j = 1 n E ( k , j ) ,
∫ x min x k + 1 J ( x ) d x ∫ x min x max J ( x ) d x = ∑ i = 1 k ∑ j = 1 n A ( i , j ) ∑ i = 1 m ∑ j = 1 n A ( i , j ) ,
∫ y min y s + 1 k + 1 J ( y ) d y ∫ y min y max J ( y ) d y = ∑ j = 1 s A ( k , j ) ∑ j = 1 n A ( k , j ) ,
E k ( i , j ) = P p r e k − 1 ( i , j ) P s i m k − 1 ( i , j ) • P p r e k − 2 ( i , j ) P s i m k − 2 ( i , j ) • ⋅ ⋅ ⋅ • P p r e 0 ( i , j ) P s i m 0 ( i , j ) • E 0 ( i , j ) , i = 1... m , j = 1... n ,
A k ( i , j ) = P s i m k − 1 ( i , j ) P p r e k − 1 ( i , j ) • P s i m k − 2 ( i , j ) P p r e k − 2 ( i , j ) • ⋅ ⋅ ⋅ • P s i m 0 ( i , j ) P p r e 0 ( i , j ) • A 0 ( i , j ) , i = 1... m , j = 1... n ,
E w k ( i , j ) = E w 0 ( i , j ) E w s i m k − 1 ( i , j ) • E w 0 ( i , j ) E w s i m k − 2 ( i , j ) • ⋅ ⋅ ⋅ • E w 0 ( i , j ) E w s i m 0 ( i , j ) • E w 0 ( i , j ) , i = 1... m w , j = 1... n w ,
A s k ( i , j ) = P s i m s k − 1 ( i , j ) P p r e s k − 1 ( i , j ) • P s i m s k − 2 ( i , j ) P p r e s k − 2 ( i , j ) • ⋅ ⋅ ⋅ • P s i m s 0 ( i , j ) P p r e s 0 ( i , j ) • A s 0 ( i , j ) , i = 1... m s , j = 1... n s , s = 1... m w × n w ,
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