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Diffractive Optical Element for Direct-Lit Laser Backlight Unit
DOI: 10.12677/OE.2018.82010, PDF , HTML, XML, 下载: 1,243  浏览: 2,711  科研立项经费支持

Abstract: When used in a direct-lit backlight, the ellipse light spot of a laser diode has to be modulated to be rectangular. Aiming at the problem of small divergence angle and long mixing distance, a diffractive optical element for shaping laser light spot is designed by using diffractive optical element algorithm. First, the amplitude distribution of the input and output light fields and the imaging distance are determined. The diffraction formula and Gerchberg-Saxton algorithm are applied to calculate the phase distribution of the DOE in Matlab. Then the obtained phase distribution is input into the simulation software Virtual Lab for simulation. The simulation results show there exists the worse distortion on the spot and the power efficiency is not very high. The output light field distribution is modified and the DOE is then redesigned. The results show that the optimized DOE can effectively shape the elliptical light spot emitted by the LD into a rectangular spot of 14 mm × 11 mm. The energy efficiency is improved to 56.08% from the original 46.69%. The uniformity is improved to 87.16% from 80.59%. The design of the DOE in this paper can realize the shaping requirements of laser beam from circular Gauss beam to rectangular uniform spot, satisfying the requirements of a direct-lit backlight unit on luminance and uniformity.

1. 引言

2. 直下式激光背光模组结构

2.1. 现有直下式LED背光模组结构

2.2. 直下式LD背光模组结构

Figure 1. Direct-lit LED backlight unit

Figure 2. Direct-lit laser backlight unit

3. 衍射光学元件设计理论

3.1. 理论基础

$g\left({x}_{1},{y}_{1}\right)={g}_{0}\left({x}_{1},{y}_{1}\right)\ast t\left({x}_{1},{y}_{1}\right)$ (1)

$u\left({x}_{2},{y}_{2}\right)=\frac{1}{i\lambda }\int {\int }_{-\infty }^{\infty }g\left({x}_{1},{y}_{1}\right)\frac{\mathrm{exp}\left(ikr\right)}{r}K\left(\theta \right)\text{d}{x}_{1}\text{d}{y}_{1}$ (2)

$r=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}+{z}^{2}}$ (3)

$K\left(\theta \right)=\frac{r+z}{2r}$ (4)

3.2. DOE理论设计

${U}_{in}\left({x}_{1},{y}_{1}\right)=\mathrm{exp}\left[-\left({x}_{1}^{2}+{y}_{1}^{2}\right)/{\omega }^{2}\right]$ (5)

Figure 3. GS algorithm flow chart

${U}_{\text{ideal}}\left({x}_{2},{y}_{2}\right)=\left\{\begin{array}{l}1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }{x}_{2},{y}_{2}\in S\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{x}_{2},{y}_{2}\notin S\end{array}$ (6)

4. 软件仿真及优化

${R}_{0}={r}_{0}+d\ast \mathrm{tan}\theta$ (7)

${U}_{in}\left(x,y\right)=\mathrm{exp}\left[-\left(\frac{{x}_{1}^{2}}{{R}_{x}^{2}}+\frac{{y}_{1}^{2}}{{R}_{y}^{2}}\right)\right]$ (8)

$\eta =\frac{{E}_{\text{target}}}{E}$ (9)

Figure 4. Ideal light field distribution and its simulation results

Figure 5. 9 points

Table 1. Illumination value of nine points

$u={I}_{\mathrm{min}}/{I}_{\text{ave}}$ (10)

$r=z+\frac{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}{2z}+o\left(\frac{{\left({\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}\right)}^{2}}{8{z}^{3}}\right)$ (11)

$r=R+\frac{-2{x}_{1}{x}_{2}-2{y}_{1}{y}_{2}+{x}_{1}^{2}+{y}_{1}^{2}}{2R}+o\left(\frac{{\left(-2{x}_{1}{x}_{2}-2{y}_{1}{y}_{2}+{x}_{1}^{2}+{y}_{1}^{2}\right)}^{2}}{8{R}^{3}}\right)$ (12)

$\begin{array}{c}u\left({x}_{2},{y}_{2}\right)=\frac{\mathrm{exp}\left(ikR\right)}{i\lambda z}\frac{z}{R}\int {\int }_{-\infty }^{\infty }g\left({x}_{1},{y}_{1}\right)\mathrm{exp}\left(ik\frac{{x}_{1}^{2}+{y}_{1}^{2}}{R}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}×\mathrm{exp}\left[-\frac{ik}{z}\left({x}_{1}\frac{z{x}_{2}}{R}+{y}_{1}\frac{z{x}_{2}}{R}\right)\right]\text{d}{x}_{1}\text{d}{y}_{1}\end{array}$ (13)

$\left\{\begin{array}{l}{x}_{3}=\frac{z}{R}{x}_{2}\\ {y}_{3}=\frac{z}{R}{y}_{2}\\ u\left({x}_{2},{y}_{2}\right)=\frac{z}{R}u\left({x}_{3},{y}_{3}\right)\end{array}$ (14)

Figure 6. The optimized ideal light field distribution and its simulation results

Table 2. Illumination value of nine points of the optimized design

5. 结论

NOTES

*通讯作者。

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