第50卷第2期Vol.50No.2
2021年2月
Feb.2021
红外与激光工程
Infrared and Laser Engineering
Optical design of freeform Fresnel TIR lens for
LED uniform illumination
Hu Tiantian1,2,Zeng Chunmei12,Rui Congshan1-2,Hong Yang12.Ma Suodong1,2
(1.School of Optoelectronic Science and Engineering,Soochow University,Suzhou215006,China;
2.Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province&Key Lab of Modem Optical
Technologies of Education Ministry of China,Soochow University,Suzhou215006,China)
Abstract:A new design of total internal reflection(TIR)lens was presented which had a freeform Fresnel surface in the central part of the front to improve the heat dissipation capability.Snell's law and the reflection law were applied to construct the freeform refractive surface and the freefonn reflective surface for the TIR lens.The freeform refractive surface was transformed into the freefonn Fresnel surface with universal design method of Fresnel lens.The simulation result for the freeform Fresnel TIR lens obtained by Monte Carlo ray tracing shows that the far field illumination uniformity of82.0%and the luminous efficiency of96.6%are achieved for the light source size of2mm><2mm,in the meanwhile the lens weight is only21.94g.The freeform Fresnel TIR lens has nearly20%reduction in lens weight and volume,only a2%reduction in luminous efficiency,and no reduction in illumination uniformity compared to the TIR lens without the Fresnel surface.The result indicates that the Fresnelization for freeform surface of TIR lens can significantly reduce the volume and weight of TIR lens and shorten the optical path length,thus effectively improve its heat dissipation efficiency and service life while maintaining a high performance.
Key words:optical design;Fresnel TIR lens;Snell's law;heat dissipation
CLC number:0439Document code:A DOI:10.3788/IRLA20200183
胡甜甜込曾春梅叫芮丛珊"，洪洋迢马锁冬2
(1.苏州大学光电科学与工程学院，江苏苏州215006；
2.江苏省先进光学制造技术重点实验室&教育部现代光学技术重点实验室，江苏苏州215006)
摘要：为了提高透镜的散热能力，设计了一种新型全内反射(TIR)透镜，该透镜的出射面中央为自由曲面菲涅耳面'采用斯涅尔定律和全反射定律分别求解TIR透镜折射部分和反射部分自由曲面的面形。同时，采用一种菲涅耳透镜的普适设计方法将折射部分自由曲面转变成菲涅耳面。通过蒙特卡洛光线追迹模拟自由曲面菲涅耳TIR透镜的照明效果，结果显示：当光源尺寸为2mmx2mm时，其远场照度均匀性为82%，光效为96.6%，透镜质量为21.94g o与未加菲涅耳面的TIR透镜相比，带自由曲面菲涅耳面的TIR透镜在光效仅下降2%，在照度均匀性未变的情况下，透镜质量减少了约20%。这说明对TIR透镜的自由曲面出射面进行菲涅耳化可明显地缩小透镜的体积和质量，缩短光线在透镜
收稿日期:2020-05-19；修订日期:2020-07-30
基金项目：江苏高校优势学科建设工程资助项目
红外与激光工程
www.irla
第2期第50卷内部的光程，因此可有效提高透镜的散热效率和使用寿命，同时保持良好的照明效果。
关键词：光学设计；菲涅耳TIR透镜；斯涅尔定律；散热
0Introduction
Light-emitting diode(LED)light source characterized by high luminous efficiency,durability and reliability is considered to be the most promising light source of the next generation111.LED is close to the theoretical"point source",so it is easy to accurately locate the light source when designing the optical system. However,due to its Lambertian distribution and large divergence angle,it is necessary to redistribute the spatial intensity distribution of a LED,which is called secondary light distribution.
At present,the main light distribution lenses on the market are peanut lens and TIR lens.However,peanut lens has a large size and the poor heat dissipation effect, which reduces its service life as well as increases the cost. Dai Yidan121added a gradient Fresnel surface on the peanut lens to reduce the thickness of the lens and improve the heat dissipation efficiency.However,the illumination uniformity is relatively low,only68%. Zhang Yuebin⑴of Yanshan University proposed heat dissipation method for LED arrays based on water cooling.This method is more effective in reducing the temperature of the LED array,but it will reduce the luminous efficiency
and shorten its service life.Sun Lixia of Zhejiang University⑷added a heat sink to the LED light source to improve the heat dissipation efficiency of the lens.However,it has the disadvantage that when the LED light source reaches its service life and need to be replaced,the LED lens is supposed to be redesigned which is very inconvenient.There is also a problem of poor heat dissipation for the TIR lens[5_81which is commonly used at present.Wan Yunjia[9]of Hubei University proposed a design method of freeform Fresnel lens and designed a thin Fresnel lens with a freeform surface which greatly improve the heat dissipation efficiency.However,the thin Fresnel lens with two transmission surfaces is too simple to achieve a good far field illumination performance.Therefore,the heat dissipation design on the TIR lens is expected to achieve the dual goals of high heat dissipation efficiency and satisfactory far field illumination performance.
The freeform surface can accurately perform the light distribution for the secondary light distribution lens. There are several methods for the design of freeform surfaces:trial and error method"®,numerical analysis method111_14],and SMS design method(Simultaneous Multiple Surface)115-171.The trial and error method require constant modification of parameters thus it is not efficient. The numerical analysis method and the SMS design method can effectively establish the iterative relationship between adjacent sampling points through the numerical relationship,and obtain
the discrete point data of the free surface.This method is not only suitable for Lambertian LEDs,but also for non・Lambertian LEDs with wide applicability1181.
椒盐噪声In order to improve the heat dissipation efficiency of TIR lens,we designed a freeform TIR lens based on field illumination with numerical analysis method,and applied a segmentation method to design a freeform Fresnel TIR lens,then analyzed and compared the far field illumination uniformity,luminous efficiency,lens volume and weight of this two kinds of freeform TIR lens.
1Design method
The flow chart for the design of the freeform TIR lens is shown in Fig」.Step1and Step2are shown in Section 1.1,mainly to divide the luminous flux of the LED light source and the area of the target plane equally, and establish the equation of unit luminous flux and unit area of the target plane.Step3and Step4shown in Section 1.2describes how the freeform TIR lens is designed.The design of the freeform Fresnel surface is accomplished by segmentation method shown in Section1.3.
Fig.l Flow chart for designing the freeform TIR lens
1.1Equalize the luminous flux and the target plane
The luminous intensity distribution of the currently used LED light source is Lambertian distribution.As shown in Fig.2,in order to achieve uniform illumination on the target plane,the illumination angle and the area of the target plane are equally divided[19].
J®+i rSj+i
I e Q=EdS(1)
0i J s,
where I e is the luminous intensity;and E is the illuminance on the target plane.
The total luminous flux(p t of the LED light source is:
ip t=2兀I d sin0d3(2) We divide the luminous fluxof the LED light source into N equal parts:
2tz[I e sin0d6=鑒=$f'I e sin0d6(3) J伏N N J o
threadx系统where0,is the cone angle of the sampling ray.
We further divide the target plane into N equal-area concentric annulus.The radius of the target plan
e is R, and the radius of each annulus on target plane is r z.The area S0of each annulus is:
So=兀忌i-兀彳=^-(/=0,1,2,3,•••N-V)(4) The solid angle of the source and the area of the target plane are equally divided based on the Eqs.(1)-(4), thus the directions of the incident ray and the emergent ray are determined.
Fig.2Equalize the luminous flux and the target plane(®:the cone angle of the sampling rays;R:the radius of the target plane;r,:the radius of each annulus on target plane)
1.2Design of freeform TIR lens
The freeform TIR lens has been designed using a numerical analysis method[19].The cross section schematic diagram of the freeform TIR lens⑹is shown in Fig.3. Surface1is a circular plane,surface2is a freeform surface to be designed,surface3is a cylindrical surface inside,surface4is a freeform TIR surface to be designed, and the surface5is an annular plane.The LED is placed at the origin of the coordinates(0,0),where there is a cylindrical cavity inside the TIR lens.
Fig.3Schematic diagram of the freeform TIR lens(1:a circular plane;
2:a freeform surface to be designed;3:a cylindrical surface inside;4:a freeform TIR surface to be designed;5:an annular plane)
Two freeform surfaces of the TIR lens is solved by the Snell's law and the reflection law,respectively.The freeform refractive surface2of the TIR lens is solved by the Snell's law:
[1+n2-2n(O-/)]'~N=O~nI(5)
The freeform reflective surface4of the TIR lens is solved by the reflection law:
y/2-2(O-I)-N=0-1(6)
A.Freefonn refractive surface design
The rays emitted from the point O(LED source) with small spread angles will be collimated by the freeform refractive surface.A series of sampled rays are taken at equal angular intervals as shown in Fig.4(a).The coordinates of the points on plane S\is e,+i(X|/+1,yi/+1)[18]:
=h(7)
Xh+1=Atan(A/+i) (8)
(a)Freeform refractive surface(b)Freeform reflective surface
Fig.4Optical geometry of freeform surface
Constructing the freeform refractive surface S2is the process of calculating the coordinates of the points E h £2,…,Ej.The main iteration between two adjacent sampling points耳(力，九)and F,+1(x2/+1,y2l+|)on S2is derived by using Snell's law as shown in Eqs.(9)-(10):
y2i-yii+l+cot(尺+|)Qi+i一k2iX2i
COt(P/+1)—k，2i
(9)
£2,1X27—yii+l+COt(P i+|)X|j+i—比2注2订
cot(P,+1)-fc2,(10) kiiX2i+y2i
where k2i is the tangent slope of the freeform surface S2at E：
________(勺厂血)___________料(血一兀口)
_Q(%4i_%2i)2+_『2/)2VX2F+
'________(>4厂九)________
沙画工具
V^2+>2；2y/(x4i-x2i)2+(y4i-y2i)2
(11)
If the initial point E,is known,the coordinates of all points on the surface S2can be calculated using the iterative Eqs.(9)-(10).
B.Freeform TIR surface design
As shown in Fig.4(b),the rays emitted from the point O(LED source)with large spread angles first travel through the vertical plane surface S3,then hit the TIR surface S4being reflected,and are finally redirected
(14)
(15)
parallel to the y-axis through the horizontal plane surface
S 5. The points on surface S3 is F,(x 3j ,y 3j ), and the points
on surface S 4 is The iteration for two adjacent sampling points
and 龙+1("+1，九+1) on the
surface S 4 is as fbllows I ，8]:
-^4,/
+力卄1 一 加3J+M3J+1 + 卩4.注4丿
(1
小
N/+1 =-------------------------------------------------------------------------------------------------
(12)卩4./ 一加3.r+l
%/+1 =
P4J (氐』+1 - x 4J +A ；
(13)
where 加3,/+1 is the slope of F /+1/+1, and p 4 [ is the slope of
the tangent at the point f t :
^4,/+1 _j3j+l
〃3j+l =---------------二----兀4j+l —兀3,/+1
_______(兀4丿一兀3»________________ J gr _ 兀3丿)2 + (j% _ 旳./)2
_______血丿-九)_______ J(g _ ^3,/)2 +_九)2
Thus, the coordinates of all points on the surface S 4
can be obtained using the iterative Eqs. (12)-(13) to construct freeform TIR surface S 4.
1.3 Freeform Fresnel surface design with the
segmentation method
After designing the freeform TIR lens, we use the segmentation method® to perform Fresnelization on the freeform surface S 2- Figure 5 shows a Fresnel surface. Assuming that the refractive index of the lens material is
uniform, the Fresnel lens maintains the curvature of the lens surface and the direction of the ray does not change while the excess material of the lens being removed.
The hal 匸diameter of the lens is defined as R, and the
surface of the lens is divided into N equal annulus, and the width of each annulus is d, then d=R/N. The half-diameter of the target plane is L which is also divided into N equal突起路标
annulus, then the width of each annulus is w=LIN. The
incident light on the 丿th Fresnel annulus of the lens is required to arrive at the yth annulus of the target plane, which does not guarantee that the illumination distribution on the target plane is uniform. Thus, each Fresnel annular
zone of the lens should continue to be subdivided. As
shown in Fig.5, the width of theyth Fresnel annular zone Fig.5 Schematic diagram of Fresnel lens (R: the half-diameter of the
lens; d: the width of each annulus; Rj ： the half inside-diameter of the jth Fresnel annulus; Rj +i : the half outer-diameter of the /th
Fresnel annulus)
between the Rj and the R j+l is:实验室制硝酸
新药管疗法A/? = Rj+\- Rj = d(0 W j W N)
(16)
When the Fresnel annular zone is divided into M
parts at equal space, the width of each part is:
Ar = d/M
(17)
The radius Rj can be expressed as:
Rj = jxd
(18)
In this way, the radius r y/ of each equidistant points on theyth annulus is:
rjj = Rj + ZAr(0 W i < M)
(19)
The 丿th annulus of the target plane can also be
equally divided in the same way, and the radius of each
equidistant points is t ”. The incident light on the r ；,- and
r ji+i regions of yth Fresnel annular zone is controlled to
arrive on the tj, and t ji+i region of the target plane S 6, where is equivalent to the discrete point coordinate E,
on the freeform surface S 2 in section 1.2, and g is
equivalent to A/, on the target plane S & The ordinate y 2i of each point E,- is simultaneously reduced by a height h, and
the abscissa x 2l - remains unchanged. This produces a
uniform illuminance distribution on the target plane.
2 Simulation and analysis
The freeform TIR lens is designed using the method described in the section 1.2, and the lighting simulation
(ray tracing) is performed. In order to improve the
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