Optics Express
Vol. 20,
Issue S6,
pp. A843-A855
(2012)
•https://doi.org/10.1364/OE.20.00A843

Designing LED array for uniform illumination distribution by simulated annealing algorithm

Zhouping Su, Donglin Xue, and Zhicheng Ji

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Zhouping Su, Donglin Xue, and Zhicheng Ji, "Designing LED array for uniform illumination distribution by simulated annealing algorithm," Opt. Express 20, A843-A855 (2012)

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Abstract

We propose a numerical optimization method designing LED array for achieving a good uniform illumination distribution on target plane. Simulated annealing algorithm is employed to optimize LED array arrangement. Using the method, we optimized three LED arrays with various luminous intensity profiles. In order to exhibit the design freedom of the method, we use some LEDs with different intensity value in the first and third array, respectively. By optimizing, the three arrays all produced highly uniform illumination distribution with the uniformity of 0.12, 0.23 and 0.13, respectively. It indicates our method can design various luminous intensity distribution LED arrays and design array consisting of LEDs with different intensity value. In addition, the method is simple and can optimize the LED array automatically by computer program. To the best of our knowledge, it is first time to use numerical optimization method to design the optimal LED array arrangement for uniform irradiance.

©2012 Optical Society of America

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Figures (15)

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Fig. 1

Fig. 1 (a) Diagram of LED illumination. (b) Target plane with M × N grids.

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Fig. 2

Fig. 2 The flowing chart of optimization.

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Fig. 3

Fig. 3 The luminous intensity distribution of different types of LEDs.

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Fig. 4

Fig. 4 The optimized arrangement of the first LED array.

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Fig. 5

Fig. 5 The irradiance map (left) and profile (right) of the first LED array after optimization.

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Fig. 6

Fig. 6 The luminous intensity distribution of LED without free-form lens.

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Fig. 7

Fig. 7 The luminous intensity distribution of LED with free-form lens.

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Fig. 8

Fig. 8 The original and fitted intensity distribution curve of LED in the circular array.

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Fig. 9

Fig. 9 Schematic of circular array with n LEDs.

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Fig. 10

Fig. 10 The irradiance map (left) and profile (right) of the optimized circular array.

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Fig. 11

Fig. 11 The intensity distribution of LED with a special lens.

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Fig. 12

Fig. 12 2-D and 3-D layout of the special lens.

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Fig. 13

Fig. 13 The luminous intensity distribution curve of different types of LED in the third array.

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Fig. 14

Fig. 14 The optimized arrangement of the third LED array.

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Fig. 15

Fig. 15 The irradiance map (left) and profile (right) of the third optimized LED array .

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Tables (2)

Table 1 Initial Condition for Optimizing the First LED Array

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Table 2 Initial Condition for Optimizing Circular LED Array

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Equations (11)

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I (θ) = I_{0} \cos^{m} θ

m = \frac{- l n 2}{\ln (\cos θ_{1/2})}

E (x_{p}, y_{q}, z) = \frac{z^{m + 1} I_{0}}{{[{(x_{p} - X)}^{2} + {(y_{q} - Y)}^{2} + z^{2}]}^{\frac{m + 3}{2}}}

E (x_{p}, y_{q}, z) = \sum_{i = 1}^{n} \frac{z^{m + 1} I_{0}}{{[{(x_{p} - X_{i})}^{2} + {(y_{q} - Y_{i})}^{2} + z^{2}]}^{\frac{m + 3}{2}}} \cdot

f (X_{1}, Y_{1}, ..., X_{i}, Y_{i}, ..., X_{n}, Y_{n}) = \frac{σ}{\bar{E}} \cdot

\bar{E} = \frac{1}{M \times N} \sum_{q = 1}^{N} \sum_{p = 1}^{M} E (x_{p}, y_{q}, z)

σ = \sqrt{\frac{{\sum_{p = 1}^{N} \sum_{q = 1}^{M} (E (x_{p}, y_{q}, z) - \bar{E})}^{2}}{M \times N}} \cdot

N C C = \frac{\sum_{v} [I {(θ_{v})}_{F} - {\bar{I}}_{F}] [I {(θ_{v})}_{O} - {\bar{I}}_{O}]}{\sqrt{\sum_{v} {[I {(θ_{v})}_{F} - {\bar{I}}_{F}]}^{2} \sum_{v} {[I {(θ_{v})}_{O} - {\bar{I}}_{O}]}^{2}}}

E (x_{p}, y_{q}, z) = \sum_{i = 1}^{n} \frac{z^{m + 1} I_{0}}{{[{(x_{p} - X_{1} \cos (\frac{(i - 1) .2 π}{n}))}^{2} + {(y_{q} - X_{1} \cos (\frac{(i - 1) .2 π}{n}))}^{2} + z^{2}]}^{\frac{m + 3}{2}}}

I (θ) = a_{8} \cos^{8} θ + a_{7} \cos^{7} θ + \cdot \cdot \cdot + a_{1} \cos θ + a_{0}

E (x_{p}, y_{q}, z) = \sum_{i = 1}^{n} (\sum_{k = 0}^{9} \frac{z^{k + 1} a_{k}}{{[{(x_{p} - X_{i})}^{2} + {(y_{q} - Y_{i})}^{2} + z^{2}]}^{\frac{k + 3}{2}}}) \cdot

Table 1

Initial Condition for Optimizing the First LED Array

Target plane size	Distance between LED and Target plane		The initial Temperature		Stop criteria
Target plane size	Distance between LED and Target plane		The initial Temperature		OFV COFV
40x40		50	5000	≤0.1 ≤10⁻¹⁰

Table 2

Initial Condition for Optimizing Circular LED Array

Target plane size	Distance between LED and Target plane	The initial Temperature		Stop criteria
Target plane size	Distance between LED and Target plane	The initial Temperature		OFV COFV
40x40	100	5000	≤0.1 ≤10⁻¹⁰

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