• Laser & Optoelectronics Progress
  • Vol. 59, Issue 17, 1722005 (2022)
Liangzhi Liu1, Liang Guo1、*, Zhitao Chen2, Zhiqing Zhang2、**, Qingmao Zhang1, and Yiqin Xu2
Author Affiliations
  • 1Guangdong Key Laboratory of Micro-Nano Photonic Functional Materials and Devices, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006, Guangdong , China
  • 2Institute of Semiconductors, Guangdong Academy of Sciences, Guangzhou 510651, Guangdong , China
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    DOI: 10.3788/LOP202259.1722005 Cite this Article Set citation alerts
    Liangzhi Liu, Liang Guo, Zhitao Chen, Zhiqing Zhang, Qingmao Zhang, Yiqin Xu. Design of Collimating Lens with Freeform Surfaces Based on Negative Focal Length Transmission Structure[J]. Laser & Optoelectronics Progress, 2022, 59(17): 1722005 Copy Citation Text show less

    Abstract

    To effectively improve the space usage of optical systems for the light-emitting diode (LED), a freeform surface optical lens with a negative focal length transmission structure was designed. The optical lens was divided into two parts, including the transmission collimating module and reflection collimating module. The collimating lens was designed using geometrical optics, Snell’s law, and the law of energy conservation. The two-dimensional curve data of the freeform surface for the collimating module was obtained through iterative calculations with Matlab software, which was then imported into Solidwork software and rotated 360° around the central axis to obtain the three-dimensional solid model. Finally, the model was introduced into the optical simulation software, Lighttools, for light tracing and optimized according to the spot situated on the receiving surface. The optimized collimating lens was simulated with an optical energy utilization rate of 88.45% and a beam angle of ±2.23°. The results show that using a negative focal length transmission structure design can effectively reduce the volume of the collimating lens by 63.13% and improve the ability to control LED beams compared with the conventional single transmission freeform surface collimating lens.
    I0N1|N1|×NA=IN2|N2|×NA
    IN2|N2|×NB=I0N3|N3|×NB
    I0N3|N3|×NC=IN4|N4|×NC
    IN2|N2|-N1|N1|=I2+1-2IN2|N2|N1|N1|1/2NA
    N3|N3|-IN2|N2|=I2+1-2IN3|N3|N2|N2|1/2NB
    IN4|N4|-N3|N3|=I2+1-2IN4|N4|N3|N3|1/2NC
    NA=Ixb-xaxb-xa2+(yb-ya)2-xaxa2+ya2R1,Iyb-yaxb-xa2+(yb-ya)2-yaxa2+ya2R1
    NB=Xb,Yb
    Xb=xc-xbxc-xb2+(yc-yb)2-Ixb-xaxb-xa2+(yb-ya)2R2
    Yb=yc-ybxc-xb2+(yc-yb)2-Iyb-yaxb-xa2+(yb-ya)2R2
    NC=-xc-xbxc-xb2+(yc-yb)2R3,I-yc-ybxc-xb2+(yc-yb)2R3
    R1=I2+1-2IN2|N2|N1|N1|1/2
    R2=I2+1-2IN3|N3|N2|N2|1/2
    R3=I2+1-2IN4|N4|N3|N3|1/2
    kA=xaxa2+ya2-Ixb-xaxb-xa2+(yb-ya)2Iyb-yaxb-xa2+(yb-ya)2-yaxa2+ya2
    kB=Ixb-xaxb-xa2+(yb-ya)2-xc-xbxc-xb2+(yc-yb)2yc-ybxc-xb2+(yc-yb)2-Iyb-yaxb-xa2+(yb-ya)2
    kC=xc-xbxc-xb2+(yc-yb)2I-yc-ybxc-xb2+(yc-yb)2
    y-yai=kai(x-xai)
    y-ybi=kbi(x-xbi)
    y-yci=kci(x-xci)
    xa(i+1)=yai-kaixai1tan(θi+1+θ1)-kai
    ya(i+1)=xa(i+1)tan(θi+1+θ1)
    yfi-yhxfi-xh=ybi-yhxbi-xh
    xb(i+1)=ybi-yh-kbixbi+xhyf(i+1)-yhxf(i+1)-xhyf(i+1)-yhxf(i+1)-xh-kbi
    yb(i+1)=kbi(xb(i+1)-xbi)+ybi
    0θi02πi0cosθsinθdθdφ0θi+102πi0cosθsinθdθdφ=πFi+12πFi2
    xf(i+1)=(cosθi+12-cosθi+22)π2πE0+xfi2
    yf(i+1)=yfi
    n2O-n1I=Nn12+n22-2n1n2OI1/2
    xc(i+1)=yci-kcixci1tanθi-kci
    yc(i+1)=xc(i+1)tanθi
    I0N5|N5|×ND=IN6|N6|×ND
    IN6|N6|×NE=IN7|N7|×NE
    IN6|N6|-N5|N5|=I2+1-2IN6|N6|N5|N5|1/2ND
    IN7|N7|-IN6|N6|=2I2-2I2N7|N7|N6|N6|1/2NE
    ND=Ixe-xdxe-xd2+(ye-yd)2-xexe2+yd2R4,Iye-ydxe-xd2+(ye-yd)2-yexe2+yd2R4
    NE=-Ixe-xdxe-xd2+(ye-yd)2R5,I-Iye-ydxe-xd2+(ye-yd)2R5
    R4=I2+1-2IN6|N6|N5|N5|1/2
    R5=2I2-2I2N7|N7|N6|N6|1/2
    kD=-Ixe-xdxe-xd2+(ye-yd)2+xexe2+yd2Iye-ydxe-xd2+(ye-yd)2-yexe2+yd2
    kE=Ixe-xdxe-xd2+(ye-yd)2R5I-Iye-ydxe-xd2+(ye-yd)2
    ρ=π2-arctan(kE)
    xd(i+1)=ydi-kdixditanγi+1-kdi
    yd(i+1)=tanγi+1xd(i+1)
    xe(i+1)=xei1-cos2γi+11-cos2γi
    ye(i+1)=kei(xe(i+1)-xei)+yei
    Ω=arctan (sin αcos α-0.67)
    θmax=arctan(xs1ys1)
    αmax=arctan(xs1ys1-yh)
    Liangzhi Liu, Liang Guo, Zhitao Chen, Zhiqing Zhang, Qingmao Zhang, Yiqin Xu. Design of Collimating Lens with Freeform Surfaces Based on Negative Focal Length Transmission Structure[J]. Laser & Optoelectronics Progress, 2022, 59(17): 1722005
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