CN100495113C

CN100495113C - Design method and lens of a kind of three-dimensional optical lens

Info

Publication number: CN100495113C
Application number: CNB2006101134634A
Authority: CN
Inventors: 罗毅; 钱可元; 王霖; 韩彦军
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2006-09-29
Filing date: 2006-09-29
Publication date: 2009-06-03
Anticipated expiration: 2026-09-29
Also published as: CN1928624A

Abstract

A design method of a three-dimensional optical lens and the lens relate to the technical field of optical design of three-dimensional given illuminance distribution in non-imaging optics. It is characterized in that the method is based on the law of energy conservation. In the computer, the energy of the light source and the energy of the illuminance plane are divided into several small areas with correspondingly equal energies, and then on an illuminance plane whose outgoing light is correspondingly equal to its energy Select any point between the points as an initial point of the lens surface to be solved, combine the energy division results of the light source and the illuminance plane, and use the iterative solution method to solve the coordinates and normal vectors of all discrete points on the lens surface, so as to determine a lens surface. Compared with the existing lighting technology, the present invention has the characteristics of high efficiency, energy saving, flexible and convenient use, and has broad application prospects in various lighting occasions, such as road lighting, landscape lighting and display backlight lighting.

Description

Design method and lens of a kind of three-dimensional optical lens

技术领域 technical field

一种三维光学透镜的设计方法及透镜涉及非成像光学中三维给定照度分布光学设计技术领域。A design method of a three-dimensional optical lens and the lens relate to the technical field of optical design of three-dimensional given illuminance distribution in non-imaging optics.

技术背景：technical background:

传统的成像光学设计的透镜通常具有旋转对称性，用来将物平面的点经过透镜后成像到像平面上面。传统光学的透镜设计更加注重的是在成像过程中图象信息的保存，并光线能量传输效率则放在次要的位置，因此设计出来的透镜通常传输效率比较低。The lens of the traditional imaging optical design usually has rotational symmetry, which is used to image the point of the object plane on the image plane after passing through the lens. The lens design of traditional optics pays more attention to the preservation of image information during the imaging process, and the light energy transmission efficiency is placed in a secondary position, so the designed lens usually has a relatively low transmission efficiency.

非成像光学是上世纪70年代以来在国外逐渐发展起来的，专门研究光线的能量传输问题的一门新的光学分支。非成像光学最先主要研究太阳能的收集利用问题，也就是光线耦合问题，如何将一个大入射孔径的入射光线收集，完全传输一个小的输出孔径，从而提高能量密度方便利用在研究过程中逐渐产生了一套用于控制光线能量传输的理论如“边缘光线理论”(Ries，H and Rabl，A“Edge-ray principle of nonimaging optics，”J.Opt.Soc.Am.43 712-715)，“剪裁理论”(H.Ries，J.A.Muschaweck，“Tailoring freeform optical lenses for illuminations，”Novel Optical Systems Designand Optimization IV，Proc.SPIE，vol 4442，pp.43-50，(2001))(Andreas Timinger a，Julius Muschaweck a，HaraldRiesa，“Designing Tailored Free-Form Surfaces for General Illumination，”，Proc.SPIE，vol 5186，pp.128-132，(2003))和“对称性分析理论”(Ries，H Shatz，N，Bortz，J and Spirkl，W“Performance limitations ofrotationally symmetric nonimaging devices”J.O pt.Soc.AmA vol 14，10，2855-2862，1997)。非成像光学发展的另一个方向是设计一个照明系统，能够使用一个给定的光源在一个目标屏幕上面形成给定的照度分布，也就是给定照度分布问题。Non-imaging optics is a new branch of optics that has been gradually developed abroad since the 1970s, specializing in the study of energy transmission of light. Non-imaging optics first mainly studied the collection and utilization of solar energy, that is, the problem of light coupling. How to collect the incident light of a large incident aperture and completely transmit a small output aperture, so as to improve the energy density and facilitate the utilization gradually emerged during the research process. A set of theories used to control the energy transmission of light rays such as "edge-ray theory" (Ries, H and Rabl, A "Edge-ray principle of nonimaging optics," J.Opt.Soc.Am.43 712-715), "cutting Theory" (H. Ries, J.A. Muschaweck, "Tailoring freeform optical lenses for illuminations," Novel Optical Systems Design and Optimization IV, Proc. SPIE, vol 4442, pp.43-50, (2001)) (Andreas Timinger a, Julius Muschaweck a, Harald Riesa, "Designing Tailored Free-Form Surfaces for General Illumination," Proc. SPIE, vol 5186, pp.128-132, (2003)) and "Symmetry Analysis Theory" (Ries, H Shatz, N, Bortz , J and Spirkl, W "Performance limitations of rotationally symmetric nonimaging devices" J.O pt.Soc.AmA vol 14, 10, 2855-2862, 1997). Another direction of the development of non-imaging optics is to design an illumination system that can use a given light source to form a given illuminance distribution on a target screen, that is, a given illuminance distribution problem.

不同维度的空间中非成像光学面临的问题具有不同的难度。二维空间的非成像光学主要研究具有一定对称性的，如旋转对称和平移对称的光学系统。虽然对称性对非成像光学问题进行了一定的简化，方便了求解，但是对称性本身就会制约传输效率的进一步提高，因此为了根本解决能量传输效率问题，目前非成像光学主要面临的困难是如何将求解空间拓展到三维领域，设计不具有对称性的光学系统。对此国外提出了很多先进的理论和算法：The problems faced by non-imaging optics in different dimensional spaces have different difficulties. Non-imaging optics in two-dimensional space mainly studies optical systems with certain symmetry, such as rotational symmetry and translation symmetry. Although symmetry simplifies the problem of non-imaging optics to a certain extent and facilitates the solution, symmetry itself will restrict the further improvement of transmission efficiency. Therefore, in order to fundamentally solve the problem of energy transmission efficiency, what is the main difficulty faced by non-imaging optics at present? Extend the solution space to the three-dimensional field, and design optical systems without symmetry. In this regard, many advanced theories and algorithms have been proposed abroad:

在光线耦合问题方面，目前能够从理论上设计出三维空间光学系统的方法有波印廷括矢(J.C.Minano“design of three-dimensional nonimaging concentrator with inhomogeneous media”J.opt.Soc.AmA(3)pp.1345-1353，1986)、流线法(R.Winston，W.T.Welford“Geometrical vector flux and some newnonimaging concentrators”，J.opt.Soc.Am 69(4)，pp.532-536，1979)和洛伦兹几何方法(Gutiérrez，M.，Minano，J.C.，Vega，C.and Benítez，P.“Application of Lorentz Geometry to Nonimaging optics：New 3D idealconcentrators”，J.opt.Soc.Am 13，pp.532-540，1996)，这些方法从理论上证明了自由三维光学系统可以实现理论传输效率，然而由于设计的方法非常复杂，并且需要渐变折射率的介质材料，不能用来设计实用的光学系统。SMS同时多表面设计方法是最新提出的用来设计实用光学系统的方法(P.Benítez，J.C.Mi

iano，et al，“Simultaneous multiple surface optical design method in three dimensions”，Opt.Eng，43(7)1489-1502，(2004))，由于设计中采用了非成像光学特有的设计理论--“边缘光线”理论，实现了具有均匀介质材料的三维表面光学系统，然而SMS设计方法要想推广到给定照度分布问题，仍然要求将给定照度分布先转化成为光学波面然后采用用光线耦合的方法设计，因此必须求解几个二阶非线性蒙特安培方程；In terms of light coupling problems, currently there is a method that can theoretically design a three-dimensional optical system. .1345-1353, 1986), streamline method (R.Winston, WT Welford "Geometrical vector flux and some new nonimaging concentrators", J.opt.Soc.Am 69(4), pp.532-536, 1979) and Loren Lorentz geometry method (Gutiérrez, M., Minano, JC, Vega, C. and Benítez, P. "Application of Lorentz Geometry to Nonimaging optics: New 3D ideal concentrators", J.opt.Soc.Am 13, pp.532-540 , 1996), these methods have theoretically proved that the free three-dimensional optical system can achieve theoretical transmission efficiency, but because the design method is very complicated and requires a graded refractive index dielectric material, it cannot be used to design a practical optical system. The SMS simultaneous multi-surface design method is a newly proposed method for designing practical optical systems (P.Benítez, JCMi

Iano, et al, "Simultaneous multiple surface optical design method in three dimensions", Opt.Eng, 43(7)1489-1502, (2004)), due to the use of non-imaging optics-specific design theory in the design -- "edge However, if the SMS design method is to be extended to a given illuminance distribution problem, it is still required to convert the given illuminance distribution into an optical wavefront and then use the method of light coupling to design , so several second-order nonlinear Monte-Ampere equations must be solved;

在给定照度问题方面，目前主要有二个研究方向：利用变分积分优化方法、几何近似方法求解非线性二阶蒙特安培方程的方法(L.Caffarelli and V.Oliker，“Weak solutions of one inverseproblem in geometric optics”Preprint，1994.)(S.Kochengin and V.Oliker，“Determination of reflector surfacesfrom near-field scattering data II.Numerical solution，”Numerishe Mathematik 79(4)，pp.553-568，1998.)(LCaffarelli，S.Kochengin，and V.Oliker，“On thenurnerical solution of the problem of reflector design with givenfar-field scattering data，”Contemporary Mathematics 226，pp.13-32，1999.)和自由三维表面的剪裁方法(如前)。采用几何近似和变分积分这种方法主要用在求解只有一个反射表面的给定照度分布问题。利用几何近似的方法可以将求解一个反光面的问题转化成为求解一系列的反光面的问题，然后对这一系列反光面求极限的方法最终求出一个收敛的反光面，然而并不能保证反光面的光滑程度，称为弱近似解；采用变分积分的方法可以将求解反光面的问题转化成变分求极值的问题，因此便于采用优化的方法求解，以上两种方法理论上都存在收敛的解，但是由于求解过程复杂，随着求解精度的增加，计算量飞速增加，算法效率低下；自由三维表面剪裁的方法在原理上构建折射表面的数学模型，目标是能够采用折射表面实现给定照度分布，最终的数学模型仍然归结为求解几个非线性二阶蒙特安培方程，并且因为在求解过程中采用曲面高斯曲率连续的方法保证曲面的局域光滑性，可以在小角度范围内得到比较理想的照度分布，随着角度的增大，并不能保证折射表面的存在。Regarding the problem of given illuminance, there are currently two main research directions: the method of solving the nonlinear second-order Monte-Ampere equation by using the variational integral optimization method and the geometric approximation method (L.Caffarelli and V.Oliker, "Weak solutions of one inverse problem in geometric optics" Preprint, 1994.) (S.Kochengin and V.Oliker, "Determination of reflector surfaces from near-field scattering data II. Numerical solution," Numerishe Mathematik 79(4), pp.553-568, 1998.) (LCaffarelli, S. Kochengin, and V. Oliker, "On thenurnerical solution of the problem of reflector design with givenfar-field scattering data," Contemporary Mathematics 226, pp.13-32, 1999.) and clipping methods for free three-dimensional surfaces (as before). Using geometric approximation and variational integration, this method is mainly used to solve the problem of a given illuminance distribution with only one reflective surface. Using the method of geometric approximation, the problem of solving a reflective surface can be transformed into a problem of solving a series of reflective surfaces, and then the method of finding the limit of this series of reflective surfaces can finally find a convergent reflective surface, but the reflective surface cannot be guaranteed The degree of smoothness is called the weak approximate solution; the problem of solving the reflective surface can be transformed into the problem of finding the extreme value of the variation by using the method of variational integration, so it is convenient to use the optimization method to solve it, and the above two methods have convergence in theory However, due to the complexity of the solution process, as the solution accuracy increases, the amount of calculation increases rapidly, and the algorithm efficiency is low; the method of free three-dimensional surface clipping builds a mathematical model of the refraction surface in principle, and the goal is to use the refraction surface to achieve a given Illumination distribution, the final mathematical model still boils down to solving several nonlinear second-order Monte Ampere equations, and because the method of continuous Gaussian curvature of the surface is used to ensure the local smoothness of the surface during the solution process, it can be compared in a small angle range Ideal illuminance distribution, as the angle increases, does not guarantee the existence of refractive surfaces.

发明内容 Contents of the invention

本发明解决了在实际照明领域需要根据具体的照度分布，设计光学系统的问题，提出了一种三维光学透镜的设计方法以及根据该方法设计的透镜。The invention solves the problem that the optical system needs to be designed according to the specific illuminance distribution in the actual lighting field, and proposes a design method of a three-dimensional optical lens and a lens designed according to the method.

本发明提出的方法的特征在于，该方法是根据能量守恒定律，在计算机中，将光源的能量与照度平面的能量划分为能量对应相等的若干小区域，然后在一条出射光线与与之能量对应相等的照度平面上的点之间任选一点作为待求解的透镜表面的一个初始点，结合光源和照度平面的能量划分结果，利用叠代求解的方法求解出透镜表面所有离散点的坐标和法向矢量，从而确定了一个透镜表面。该方法含有在计算机中运行的以下步骤：The method proposed by the present invention is characterized in that, according to the law of energy conservation, in the computer, the energy of the light source and the energy of the illuminance plane are divided into a number of small areas corresponding to the same energy, and then an outgoing ray corresponds to the energy corresponding to it. Choose a point between the points on the equal illuminance plane as an initial point of the lens surface to be solved, combine the energy division results of the light source and the illuminance plane, use the iterative solution method to solve the coordinate sum method of all discrete points on the lens surface vector, thus defining a lens surface. The method consists of the following steps run on a computer:

1)初始化：1) Initialization:

为光源的出光方向建立一个坐标系(u，v)，为照度平面上的点建立一个坐标系(x，y)；Establish a coordinate system (u, v) for the light output direction of the light source, and establish a coordinate system (x, y) for points on the illumination plane;

给定光源出光方向上的一条初始光线(u₀，v₀)，给定照度平面上的一个初始点(x₀，y₀)；Given an initial ray (u ₀ , v ₀ ) in the light emitting direction of the light source, and an initial point (x ₀ , y ₀ ) on the illuminance plane;

给定纵向能量对应关系中离散点的个数n+1，横行能量对应关系中离散点的个数m+1，其中n和m为自然数；Given the number n+1 of discrete points in the longitudinal energy correspondence, the number m+1 of discrete points in the horizontal energy correspondence, where n and m are natural numbers;

给定光源光线之间的步长Δu₀……Δu_n、Δv_o……Δv_m；The step size Δu ₀ ... Δu _n , Δv _o ... Δv _m between the rays of a given light source;

给定透镜材料的折射率n₁和空气的折射率n₂；given the refractive index n ₁ of the lens material and the refractive index n ₂ of air;

2)对光源和照度平面进行能量的对应划分：2) Carry out corresponding division of energy for light source and illumination plane:

2.1)建立以光源的出光方向和照度平面上的点的一条纵向对应关系：2.1) Establish a vertical correspondence between the light output direction of the light source and the points on the illuminance plane:

2.1.1)计算光源光线(u₀，v₀)，在Δu₀范围内具有的能量大小：2.1.1) Calculate the energy of the light source light (u ₀ , v ₀ ) within the range of Δu ₀ :

$E ({Δu}_{0}) |_{u = u_{0}} = {&Integral;}_{u = u_{0}} I (u, v) | J (u, v) | dv \cdot {Δu}_{0},$ 其中

(u，v)为光源在(u，v)方向上的光

E. ({Δ u}_{0}) |_{u = u_{0}} = {&Integral;}_{u = u_{0}} I (u, v) | J (u, v) | dv &Center Dot; {Δu}_{0},

in

(u, v) is the light of the light source in the (u, v) direction

强大小，u，v)|为采用(u，v)坐标系需要将du·dv换算为单位面积的雅可比行列式；2.1.2)计算照度平面上的点(x₀，y₀)对应的步长Δx₀：big and small, u, v) | In order to adopt the (u, v) coordinate system, it is necessary to convert du dv into the Jacobian determinant of unit area; 2.1.2) Calculate the step size corresponding to the point (x ₀ , y ₀ ) on the illuminance plane Δx ₀ :

${Δx}_{0} = E ({Δu}_{0}) |_{u = u_{0}} / {&Integral;}_{x = x_{0}} L (x, y) | J (x, y) | dy,$ 其中L(x，y)表示在照度平面上(x，y)点处的照度值，

(x，y)|为采用(x，y)坐标系需要将dx·dy换算为单位面积的雅可比行列式；

{Δx}_{0} = E. ({Δu}_{0}) |_{u = u_{0}} / {&Integral;}_{x = x_{0}} L (x, the y) | J (x, the y) | dy,

Where L(x, y) represents the illuminance value at point (x, y) on the illuminance plane,

(x, y) | In order to use the (x, y) coordinate system, it is necessary to convert dx·dy to the Jacobian determinant of the unit area;

2.1.3)令u₁＝u₀+Δu₀，x₁＝x₀+Δx₀，从而获得点光源发出的一条光线与照度平面上的一个点的能量对应关系：(u₁，v₀)对应于(x₁，y₀)；2.1.3) Let u ₁ =u ₀ +Δu ₀ , x ₁ =x ₀ +Δx ₀ , so as to obtain the energy correspondence between a ray emitted by a point light source and a point on the illumination plane: (u ₁ , v ₀ ) corresponds to (x ₁ , y ₀ );

2.1.3)利用步骤2.1.1)中的公式计算光线(u₁，v₀)在Δu₁范围内具有的能量大小：2.1.3) Use the formula in step 2.1.1) to calculate the energy of the light (u ₁ , v ₀ ) within the range of Δu ₁ :

$E E. (({Δu Δ u}_{11})) {| |}_{u u = = {u u}_{11}} = = {&Integral; &Integral;}_{u u = = {u u}_{11}} I I ((u u,, v v)) | | J J ((u u,, v v)) | | dv dv \cdot \cdot {Δu Δu}_{11};;$

2.1.4)利用步骤2.1.2)中的公式计算照度平面上的点(x₁，y₀)对应的步长Δx₁：2.1.4) Use the formula in step 2.1.2) to calculate the step size Δx ₁ corresponding to the point (x ₁ , y ₀ ) on the illumination plane:

${Δx Δx}_{11} = = E E. (({Δu Δu}_{11})) {| |}_{u u = = {u u}_{11}} / / {&Integral; &Integral;}_{x x = = {x x}_{11}} L L ((x x,, y the y)) | | J J ((x x,, y the y)) | | dy dy;;$

2.1.5)令u₂＝u₁+Δu₁，x₂＝x₁+Δx₁，利用步骤2.1.1)和步骤2.1.2)中的公式，获得点光源发出的另一条光线与照度平面上的另一个点的能量对应关系：(u₂，v₀)对应于(x₂，y₀)；2.1.5) Let u ₂ =u ₁ +Δu ₁ , x ₂ =x ₁ +Δx ₁ , use the formulas in step 2.1.1) and step 2.1.2) to obtain another ray from the point light source and the illuminance plane The energy correspondence of another point on : (u ₂ , v ₀ ) corresponds to (x ₂ , y ₀ );

2.1.6)重复步骤2.1.1)～2.1.5)，叠代计算得到光源光线和照度平面上的点形成的一个能量纵向对应关系 $U_{v_{0}} = h (X_{y_{0}})$ 以及ΔX，其中：2.1.6) Repeat steps 2.1.1) to 2.1.5), iteratively calculate and obtain an energy longitudinal correspondence between the light source light and the points on the illuminance plane $u_{v_{0}} = h (x_{{the y}_{0}})$ and ΔX, where:

${U u}_{{v v}_{00}} = = {{(({u u}_{00},, {v v}_{00})),, (({u u}_{11},, {v v}_{00})),, . . . . . . . . . . . . (({u u}_{n no},, {v v}_{00}))}}$

${X x}_{{y the y}_{00}} = = {{(({x x}_{00},, {y the y}_{00})),, (({x x}_{11},, {y the y}_{00})),, . . . . . . . . . . . . (({x x}_{n no},, {y the y}_{00}))}}$

ΔX＝{Δx₀，Δx₁，......Δx_n}；ΔX={Δx ₀ , Δx ₁ ,...Δx _n };

2.2)建立以上述纵向对应关系上的点为初始点的n+1个光线和照度平面上的点的能量横向对应关系：2.2) Establish the energy horizontal correspondence between n+1 light rays and points on the illuminance plane with the point on the above-mentioned longitudinal correspondence as the initial point:

2.2.1)从上述纵向对应关系 $U_{v_{0}} = h (X_{y_{0}})$ 中取初始点(u₀，v₀)和初始步长Δv₀，计算光线(u₀，v₀)在(Δu₀，Δv₀)范围内具有的能量大小：2.2.1) From the above vertical correspondence $u_{v_{0}} = h (x_{{the y}_{0}})$ Take the initial point (u ₀ , v ₀ ) and the initial step size Δv ₀ , and calculate the energy of the ray (u ₀ , v ₀ ) within the range (Δu ₀ , Δv ₀ ):

$E E. (({Δu Δu}_{00},, {Δv Δv}_{00})) {| |}_{((u u = = {u u}_{00},, v v = = {v v}_{00}))} = = I I (({u u}_{00},, {v v}_{00})) | | J J (({u u}_{00},, {v v}_{00})) | | {Δu Δu}_{00} {Δv Δv}_{00};;$

2.2.2)计算照度平面上的初始点(x₀，y₀)对应的步长Δy₀：2.2.2) Calculate the step size Δy ₀ corresponding to the initial point (x ₀ , y ₀ ) on the illumination plane:

${Δy Δy}_{00} = = \frac{E E. (({Δu Δu}_{00},, {Δv Δv}_{00})) {| |}_{((u u = = {u u}_{00},, v v = = {v v}_{00}))}}{L L (({x x}_{00},, {y the y}_{00})) | | J J (({x x}_{00},, {y the y}_{00})) | | {Δx Δx}_{00}};;$

2.2.3)令v₁＝v₀+Δv₀，y₁＝y₀+Δy₀得到点光源一条光线与照度平面上的一个点的能量对应关系：(u₀，v₁)对应于(x₀，y₁)；2.2.3) Set v ₁ =v ₀ +Δv ₀ , y ₁ =y ₀ +Δy ₀ to obtain the energy correspondence between a light ray of a point light source and a point on the illuminance plane: (u ₀ , v ₁ ) corresponds to (x ₀ ,y ₁ );

2.2.4)根据步骤2.2.1)的公式计算光线(u₀，v₁)在(Δu₀，Δv₁)范围内具有的能量大小：2.2.4) Calculate the energy of light (u ₀ , v ₁ ) within the range of (Δu ₀ , Δv ₁ ) according to the formula in step 2.2.1):

$E E. (({Δu Δ u}_{00},, {Δv Δv}_{11})) {| |}_{((u u = = {u u}_{00},, v v = = {v v}_{11}))} = = I I (({u u}_{00},, {v v}_{11})) | | J J (({u u}_{00},, {v v}_{11})) | | {Δu Δ u}_{00} {Δv Δv}_{11};;$

2.2.5)根据步骤2.2.2)的公式计算照度平面上的(x₀，y₁)对应的步长Δy₁：2.2.5) Calculate the step size Δy ₁ corresponding to (x ₀ , y ₁ ) on the illumination plane according to the formula in step 2.2.2):

${Δy Δy}_{11} = = \frac{E E. (({Δu Δu}_{00},, {Δv Δv}_{11})) {| |}_{((u u = = {u u}_{00},, v v = = {v v}_{11}))}}{L L (({x x}_{00},, {y the y}_{11})) | | J J (({x x}_{00},, {y the y}_{11})) | | {Δx Δx}_{00}};;$

2.2.6)令v₂＝v₁+Δv₀，y₂＝y₁+Δy₁得到点光源的另一条光线与照度平面上的另一个点的能量对应关系：(u₀，v₂)对应于(x₀，y₂)；2.2.6) Set v ₂ =v ₁ +Δv ₀ , y ₂ =y ₁ +Δy ₁ to obtain the energy correspondence between another ray of the point light source and another point on the illuminance plane: (u ₀ , v ₂ ) corresponds to at (x ₀ , y ₂ );

2.2.7)重复利用步骤2.2.1)和2.2.2)中的公式，叠代计算得到点光源出射光线和照度平面上的点的一个能量横向对应关系 $V_{u_{0}} = Y_{x_{0}},$ 其中 $V_{u_{0}} = {(u_{0}, v_{0}), (u_{0}, v_{1}), . . . . . . (u_{0}, v_{m})},$ $Y_{x_{0}} = {(x_{0}, y_{0}), (x_{0}, y_{1}), . . . . . . (x_{0}, y_{m})};$ 2.2.7) Repeatedly use the formulas in steps 2.2.1) and 2.2.2) to iteratively calculate an energy horizontal correspondence between the light emitted by the point light source and the point on the illuminance plane $V_{u_{0}} = Y_{x_{0}},$ in $V_{u_{0}} = {(u_{0}, v_{0}), (u_{0}, v_{1}), . . . . . . (u_{0}, v_{m})},$ $Y_{x_{0}} = {(x_{0}, {the y}_{0}), (x_{0}, {the y}_{1}), . . . . . . (x_{0}, {the y}_{m})};$

2.2.8)重复步骤2.2.1～2.2.7)，计算得到以纵向对应关系上的n+1个点为初始点的n+1个能量横向对应关系，其中每一条横向曲线的求解采用ΔX＝{Δx₀，Δx₁，......Δx_n}中相应的一个步长作为离散点在x方向上的步长2.2.8) Repeat steps 2.2.1 to 2.2.7) to calculate n+1 energy horizontal correspondences with n+1 points on the vertical correspondence as the initial point, where each horizontal curve is solved using ΔX ＝{Δx ₀ , Δx ₁ ,...Δx _n } a corresponding step size as the step size of the discrete point in the x direction

${V V}_{{u u}_{00}} = = g g (({Y Y}_{{x x}_{00}})),,$ ${V V}_{u u 00} = = {{(({u u}_{00},, {v v}_{00})),, (({u u}_{00},, {v v}_{11})),, . . . . . . . . . . . . (({u u}_{00},, {v v}_{m m}))}},,$ ${Y Y}_{{x x}_{00}} = = {{(({x x}_{00},, {y the y}_{00})),, (({x x}_{00},, {y the y}_{11})),, . . . . . . . . . . . . (({x x}_{00},, {y the y}_{m m}))}}$

${V V}_{{u u}_{11}} = = g g (({Y Y}_{{x x}_{11}})),,$ ${V V}_{{u u}_{11}} = = {{(({u u}_{11},, {v v}_{00})),, (({u u}_{11},, {v v}_{11})),, . . . . . . . . . . . . (({u u}_{11},, {v v}_{m m}))}},,$ ${Y Y}_{{x x}_{11}} = = {{(({x x}_{11},, {y the y}_{00})),, (({x x}_{11},, {y the y}_{11})),, . . . . . . . . . . . . (({x x}_{11},, {y the y}_{m m}))}}$

${V V}_{{u u}_{n no}} = = g g (({Y Y}_{{x x}_{n no}})),,$ ${V V}_{{u u}_{n no}} = = {{(({u u}_{n no},, {v v}_{00})),, (({u u}_{n no},, {v v}_{11})),, . . . . . . . . . . . . (({u u}_{11},, {v v}_{m m}))}},,$ ${Y Y}_{{x x}_{n no}} = = {{(({x x}_{n no},, {y the y}_{00})),, (({x x}_{n no},, {y the y}_{11})),, . . . . . . . . . . . . (({x x}_{n no},, {y the y}_{m m}))}};;$

3)透镜表面数据点的叠代求解：3) Iterative solution of lens surface data points:

3.1)透镜表面的一条纵向曲线的确定：3.1) Determination of a longitudinal curve of the lens surface:

3.1.1)根据光源和照度平面的纵向对应关系 $U_{v_{0}} = h (X_{y_{0}}),$ 在光源上选择一条初始的光线对应于照度平面上的一个初始位置P₀₀(x₀，y₀)；3.1.1) According to the longitudinal correspondence between the light source and the illumination plane $u_{v_{0}} = h (x_{{the y}_{0}}),$ Select an initial ray on the light source Corresponding to an initial position P ₀₀ (x ₀ , y ₀ ) on the illumination plane;

3.1.2)在初始光线的传播路径上选择一个初始点S₀₀作为光学表面的起始点；3.1.2) Select an initial point S ₀₀ on the propagation path of the initial light as the starting point of the optical surface;

3.1.3)利用初始点S₀₀和在照度平面上的对应位置P₀₀求出在点S₀₀处的出射光线的方向矢量 ${\overset{&RightArrow;}{O}}_{00} = \overset{&RightArrow;}{S_{00} P_{00}},$ 根据折射定律求出在S₀₀点表面应该具有的法向矢量

3.1.3) Use the initial point S ₀₀ and the corresponding position P ₀₀ on the illuminance plane to obtain the direction vector of the outgoing light at the point S ₀₀

{\overset{&Right Arrow;}{o}}_{00} = \overset{&Right Arrow;}{S_{00} P_{00}},

According to the law of refraction, find the normal vector that the surface should have at point S ₀₀

${\overset{&RightArrow; &Right Arrow;}{N N}}_{0000} = = {n no}_{11} * * {\overset{&RightArrow; &Right Arrow;}{I I}}_{0000} - - {n no}_{22} * * {\overset{&RightArrow; &Right Arrow;}{O o}}_{0000};;$

或根据反射定律求出在S₀₀点表面应该具有的法向矢量

Or calculate the normal vector that the surface should have at point S ₀₀ according to the law of reflection

${\overset{&RightArrow; &Right Arrow;}{N N}}_{0000} = = {\overset{&RightArrow; &Right Arrow;}{I I}}_{0000} - - {\overset{&RightArrow; &Right Arrow;}{O o}}_{0000};;$

3.1.4)根据光源和照度平面的纵向对应关系在光源上选择第二条出射光线

对应照度平面P₁₀(x₁，y₀)点，根据S₀₀点表面的法向矢量

得到S₀₀点的切平面T₀₀；3.1.4) Select the second outgoing ray on the light source according to the longitudinal correspondence between the light source and the illumination plane

Corresponding to the illuminance plane P ₁₀ (x ₁ , y ₀ ) point, according to the normal vector of the surface at point S ₀₀

Obtain the tangent plane T ₀₀ of point S ₀₀ ;

3.1.5)求出光线

经过传播与S₀₀点的切平面T₀₀的交点位置S₁₀；3.1.5) Calculate the light

The intersection position S ₁₀ of the tangent plane T ₀₀ after propagation and the point S ₀₀ ;

3.1.6)结合照度平面的对应点P₁₀，求出点S₁₀的出射光线的方向矢量 ${\overset{&RightArrow;}{O}}_{10} = \overset{&RightArrow;}{S_{10} P_{10}},$ 根据折射定律求出在S₁₀点表面应该具有的法向矢量

3.1.6) Combining with the corresponding point P ₁₀ on the illuminance plane, calculate the direction vector of the outgoing light at point S ₁₀

{\overset{&Right Arrow;}{o}}_{10} = \overset{&Right Arrow;}{S_{10} P_{10}},

According to the law of refraction, find the normal vector that the surface at point S ₁₀ should have

${\overset{&RightArrow; &Right Arrow;}{N N}}_{1010} = = {n no}_{11} * * {\overset{&RightArrow; &Right Arrow;}{I I}}_{1010} - - {n no}_{22} * * {\overset{&RightArrow; &Right Arrow;}{O o}}_{1010};;$

或根据反射定律求出在S₀₀点表面应该具有的法向矢量

：Or calculate the normal vector that the surface should have at point S ₀₀ according to the law of reflection

:

${\overset{&RightArrow; &Right Arrow;}{N N}}_{1010} = = {\overset{&RightArrow; &Right Arrow;}{I I}}_{1010} - - {\overset{&RightArrow; &Right Arrow;}{O o}}_{1010};;$

3.1.7)根据光源和照度平面的纵向对应关系在光源上继续选择出射光线，根据步骤3.1.2)～3.1.6)步，求出透镜表面一条纵向曲线上的离散数据点S₀₀，S₁₀……S_n0，及每一点对应的出射光线的法向矢量

即确定了透镜表面的一条纵向曲线；3.1.7) According to the longitudinal correspondence between the light source and the illumination plane, continue to select the outgoing light on the light source, and according to steps 3.1.2) to 3.1.6), obtain the discrete data points S ₀₀ , S on a longitudinal curve on the lens surface ₁₀ ……S _n0 , and the normal vector of the outgoing light corresponding to each point

That is, a longitudinal curve of the lens surface is determined;

3.2)以透镜表面的纵向曲线上的离散点作为初始点的n+1条横向曲线的求解：3.2) take the discrete point on the longitudinal curve of the lens surface as the solution of the n+1 transverse curves of the initial point:

3.2.1)从上述透镜表面的纵向曲线上取一初始点S₀₀，作为一条横向曲线的初始点，根据光源和照度平面的能量横向对应关系选择S₀₀点邻近的一条入射光线

对应的照度平面上的点P0₁(x₀，y₁)；3.2.1) Take an initial point S ₀₀ from the longitudinal curve of the above-mentioned lens surface as the initial point of a horizontal curve, and select an incident ray adjacent to the S ₀₀ point according to the energy horizontal correspondence between the light source and the illuminance plane

Point P0 ₁ (x ₀ , y ₁ ) on the corresponding illumination plane;

3.2.2)求出光线经过传播与S₀₀点的切平面T₀₀的交点位置S₀₁；3.2.2) Calculate the light The intersection position S ₀₁ of the tangent plane T ₀₀ after propagation and the point S ₀₀ ;

3.2.3)该点对应于照度平面上的点P₀₁(x₀，y₁)，从而求出S₀₁点光线的出射光线的方向矢量 ${\overset{&RightArrow;}{O}}_{01} = \overset{&RightArrow;}{S_{01} P_{01}},$ 根据折射定律求出在S₀₁点表面应该具有的法向矢量

3.2.3) This point corresponds to the point P ₀₁ (x ₀ , y ₁ ) on the illuminance plane, so as to obtain the direction vector of the outgoing ray of the ray at point S ₀₁

{\overset{&Right Arrow;}{o}}_{01} = \overset{&Right Arrow;}{S_{01} P_{01}},

According to the law of refraction, find out the normal vector that the surface at point S ₀₁ should have

${\overset{&RightArrow; &Right Arrow;}{N N}}_{0101} = = {n no}_{11} * * {\overset{&RightArrow; &Right Arrow;}{I I}}_{0101} - - {n no}_{22} * * {\overset{&RightArrow; &Right Arrow;}{O o}}_{0101};;$

或根据反射定律求出在S₀₁点表面应该具有的法向矢量

Or find out the normal vector that the surface at point S ₀₁ should have according to the law of reflection

${\overset{&RightArrow; &Right Arrow;}{N N}}_{0101} = = {\overset{&RightArrow; &Right Arrow;}{I I}}_{0101} - - {\overset{&RightArrow; &Right Arrow;}{O o}}_{0101};;$

3.2.4)根据光源和照度平面的横向对应关系在光源上继续依次选择邻近的出射光线

根据步骤3.2.1)～3.2.4)，求出以透镜表面的一条纵向曲线上的点S₀₀为初始点的一条横向曲线上的离散数据点S₀₀，S₀₁……S_0m，及每一点对应的法向矢量

{\overset{&RightArrow;}{N}}_{00}, {\overset{&RightArrow;}{N}}_{01} \cdot \cdot \cdot \cdot \cdot \cdot {\overset{&RightArrow;}{N}}_{0 m};

3.2.4) According to the horizontal correspondence between the light source and the illuminance plane, continue to select the adjacent outgoing rays on the light source in turn

According to steps 3.2.1) to 3.2.4), the discrete data points S ₀₀ , S ₀₁ ... S _0m on a horizontal curve with the point S ₀₀ on a longitudinal curve of the lens surface as the initial point, and each The normal vector corresponding to a point

{\overset{&Right Arrow;}{N}}_{00}, {\overset{&Right Arrow;}{N}}_{01} &Center Dot; &Center Dot; &Center Dot; &Center Dot; &Center Dot; &Center Dot; {\overset{&Right Arrow;}{N}}_{0 m};

3.2.5)继续依次选择初始点S₁₀……S_n0，根据步骤3.2.1～3.2.4)，求解得到以透镜上的纵向曲线上的所有以离散点S₀₀……S_n0为初始点的n+1条横向曲线上的离散点及该点具有的法向矢量，则透镜表面的所有数据点及其法向矢量求解完毕，即确定了一个透镜的表面。3.2.5) Continue to select the initial points S ₁₀ ... S _n0 in turn, according to steps 3.2.1 ~ 3.2.4), solve all the discrete points S ₀₀ ... S _n0 on the longitudinal curve on the lens as initial points Discrete points on the n+1 horizontal curves and the normal vectors of the points, then all the data points and their normal vectors on the lens surface are solved, that is, the surface of a lens is determined.

在上述初始化中，所述坐标系(u，v)和坐标系(x，y)采用同一个原点。坐标系(u，v)可以采用球坐标或极坐标。所述光源的出光方向上的初始光线

选择边缘的光线或中心的光线，照度平面上的初始点(x₀，y₀)为与所述初始光线对应的边缘位置的点(x₀，y₀)或中心位置的点。In the above initialization, the coordinate system (u, v) and the coordinate system (x, y) adopt the same origin. The coordinate system (u, v) can adopt spherical coordinates or polar coordinates. The initial light in the light emitting direction of the light source

Select the edge ray or the center ray, and the initial point (x ₀ , y ₀ ) on the illuminance plane is the point (x ₀ , y ₀ ) at the edge position or the point at the center position corresponding to the initial ray.

在光线的传播路径中，当存在给定表面时，In the ray's propagation path, when there is a given surface,

步骤3.1.2)改为：初始光线追迹过给定表面后，在传播路径上选择一个初始点S₀₀作为光学表面的起始点；Step 3.1.2) is changed to: After the initial ray traces a given surface, select an initial point S ₀₀ on the propagation path as the starting point of the optical surface;

步骤3.1.5)改为：求出光线

追迹过给定表面后，经过传播与S₀₀点的切平面T₀₀的交点位置S₁₀；步骤3.2.2)改为：求出光线

追迹过给定表面后，经过传播与S₀₀点的切平面T₀₀的交点位置S₀₁。Step 3.1.5) is changed to: Find the light

After the given surface has been traced, the intersection position S ₁₀ of the tangent plane T ₀₀ through propagation and point S ₀₀ ; step 3.2.2) is changed to: Find the ray

After tracing a given surface, the intersection position S 01 of the tangent plane T ₀₀ of the propagating point S ₀₀ and the point S ₀₀ is passed.

本发明所述的设计方法而设计的透镜，其特征在于，具有中部凹陷的花生壳型外表面。The lens designed according to the design method of the present invention is characterized in that it has a peanut shell-shaped outer surface with a central depression.

本发明所述的设计方法而设计的透镜，其特征在于，具有三条以上棱的球形外表面。The lens designed by the design method of the present invention is characterized in that it has a spherical outer surface with more than three ribs.

试验证明，根据本发明的设计方法能够根据照度分布的需要设计三维透镜，充分利用光源的能量，从而节省能源，具有广阔的应用前景。Tests have proved that the design method of the present invention can design a three-dimensional lens according to the requirement of illuminance distribution, fully utilize the energy of the light source, thereby saving energy, and has broad application prospects.

附图说明： Description of drawings:

图1是对光源能量和照明区域能量的纵向划分的示意图；Fig. 1 is a schematic diagram of longitudinal division of light source energy and illumination area energy;

图2是对光源能量和照明区域的能量的横向划分示意图；Fig. 2 is a schematic diagram of the horizontal division of the energy of the light source and the energy of the lighting area;

图3是根据纵向划分得到浸没透镜纵向曲线数据点的示意图；Fig. 3 is a schematic diagram of obtaining data points of the longitudinal curve of the immersion lens according to the longitudinal division;

图4是根据横向划分得到浸没透镜横向曲线数据点的示意图；Fig. 4 is a schematic diagram of obtaining the data points of the lateral curve of the immersion lens according to the lateral division;

图5是根据透镜的横向曲线上的数据点生成透镜表面的一横向曲线；Fig. 5 is to generate a transverse curve of the lens surface according to the data points on the transverse curve of the lens;

图6是将一系列横向曲线拟合成为一个光学表面；Fig. 6 is a series of transverse curves fitted into an optical surface;

图7是存在两个给定折射球面的时候，透镜表面数据的示意图；Fig. 7 is a schematic diagram of lens surface data when there are two given refraction spheres;

图8是根据中国道路照明标准，对照明区域和朗伯光源的能量划分示意图；Figure 8 is a schematic diagram of the energy division of the lighting area and the Lambertian light source according to the Chinese road lighting standard;

图9是根据图8的划分方法得到的浸没透镜；Fig. 9 is the immersion lens obtained according to the dividing method in Fig. 8;

图10是根据图8的划分方法得到的芯片具有一次封装的透镜；Fig. 10 is a chip obtained according to the division method of Fig. 8 with a lens of primary packaging;

图11是对正六边形照度区域和朗伯光源的能量划分方法；Fig. 11 is the energy division method to regular hexagonal illuminance area and Lambertian light source;

图12是根据图11的划分方法设计的浸没透镜；Fig. 12 is the immersion lens designed according to the dividing method of Fig. 11;

图13是一个5×5透镜阵列的排布；Fig. 13 is the arrangement of a 5 * 5 lens array;

图14是本方法的流程图。Figure 14 is a flowchart of the method.

具体实施方式： Detailed ways:

本发明是基于能量守恒的原理，将点光源的出光方向的能量与照度平面的能量先进行分割，将二者的能量以若干离散点的形式进行一一对应，然后根据这种对应关系，叠带求解出对应于两个能量对应关系之间的光学系统表面离散数据点的坐标和出光方向，从而确定了透镜表面的形状。The present invention is based on the principle of energy conservation, divides the energy of the light output direction of the point light source and the energy of the illuminance plane first, and makes a one-to-one correspondence between the energy of the two in the form of several discrete points, and then according to this correspondence, superimposed The coordinates of the discrete data points on the surface of the optical system corresponding to the relationship between the two energies and the direction of the light are obtained by solving it, thereby determining the shape of the lens surface.

能量单元划分方法，首先被使用在形成给定的光强分布中，见(W.A.Parkyn，“采用外微分几何的方法设计照明透镜”，Proc.SPIE，vol 3482，pp.191-193(1998).)，在本发明提出的方法中，能量单元划分方法被进一步推广成为点对点的映射关系，并且可以用来形成给定的照度分布。这种能量划分方法适用于光源尺寸相对与光学系统比较小的情况。由于在划分的过程中，两个变量被分离处理，因此这种方法也可以认为是变量分离的方法。The energy unit division method was first used to form a given light intensity distribution, see (W.A.Parkyn, "Designing Illumination Lens Using the Method of External Differential Geometry", Proc.SPIE, vol 3482, pp.191-193(1998) .), in the method proposed by the present invention, the energy unit division method is further extended to a point-to-point mapping relationship, and can be used to form a given illuminance distribution. This energy division method is suitable for situations where the size of the light source is relatively small compared with the optical system. Because in the process of division, two variables are treated separately, this method can also be considered as a method of variable separation.

假设从光源发出的，在我们考虑范围中的光，都入射到给定照度的平面上，根据能量守恒定律可以得到：Assuming that the light emitted from the light source and in the range we consider is incident on the plane with a given illuminance, according to the law of energy conservation, we can get:

${&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} I I ((\overset{&RightArrow; &Right Arrow;}{L L})) dΩ dΩ = = {&Integral; &Integral; &Integral; &Integral;}_{D D.} L L ((\overset{&RightArrow; &Right Arrow;}{p p})) ds ds - - - - - - ((11))$

在式(1)中

表示光线的方向，点光源的光强角分布在

方向为

表示目标平面上的点位置，在

点位置的给定照度为Ω代表从光源发出光线的立体角范围，D代表在目标平面上的照射范围。In formula (1)

Indicates the direction of the light, and the light intensity angle distribution of the point light source is in

Direction is

Indicates the point position on the target plane, in

The given illuminance at the point position is Ω represents the solid angle range of the light emitted from the light source, and D represents the irradiation range on the target plane.

光学系统中的反射表面或者折射表面实际上是来实现从光源到照射平面上的一个映射 $γ : \overset{&RightArrow;}{l} &RightArrow; \overset{&RightArrow;}{p},$ 如果映射γ连续可微，可以将上述积分方程转换成为微分方程：γ的物理含义就是 $γ : \overset{&RightArrow;}{l} &RightArrow; \overset{&RightArrow;}{p}$ The reflective surface or refractive surface in the optical system is actually to achieve a mapping from the light source to the illumination plane $γ : \overset{&Right Arrow;}{l} &Right Arrow; \overset{&Right Arrow;}{p},$ If the mapping γ is continuous and differentiable, the above integral equation can be transformed into a differential equation: the physical meaning of γ is $γ : \overset{&Right Arrow;}{l} &Right Arrow; \overset{&Right Arrow;}{p}$

$L L ((\overset{&RightArrow; &Right Arrow;}{p p})) = = I I ((\overset{&RightArrow; &Right Arrow;}{l l})) / / | | J J ((γ γ ((\overset{&RightArrow; &Right Arrow;}{l l})))) | | - - - - - - ((22))$

其中表示定义的映射γ具有的雅可比行列式的大小。in Indicates the size of the Jacobian that the defined map γ has.

现在利用能量划分的方法求解一个从光源到目标平面的映射，根据能量守恒公式(1)，对光源出光方向采用(u，v)坐标系进行描述，对照度平面的位置采用(x，y)坐标系进行描述可以得到：Now use the method of energy division to solve a mapping from the light source to the target plane. According to the energy conservation formula (1), the (u, v) coordinate system is used to describe the light output direction of the light source, and the (x, y) coordinate system is used to describe the position of the illumination plane. The coordinate system can be described as follows:

I(u，v)|J(u，v)|dudv＝L(x，y)|J(x，y)|dxdy (3)I(u, v)|J(u, v)|dudv＝L(x, y)|J(x, y)|dxdy (3)

其中为J(u，v)采用(u，v)坐标系需要将du·dv换算为单位面积的雅可比行列式Among them, J(u, v) adopts (u, v) coordinate system and needs to convert du dv to the Jacobian determinant of unit area

|J(x，y)|为采用(x，y)坐标系需要将dx·dy换算为单位面积的雅可比行列式|J(x, y)| In order to use the (x, y) coordinate system, it is necessary to convert dx·dy to the Jacobian determinant of the unit area

将光源的能量沿着u线(沿v线也可以)划分成一系列的能量区域同时将相应的目标平面能量沿着x线(沿y线也可以)划分成一系列能量区域，可以得到：The energy of the light source is divided into a series of energy regions along the u line (along the v line) and the corresponding target plane energy is divided into a series of energy regions along the x line (along the y line), which can be obtained:

(∫I(u，v)|J(u，v)|dv)du＝(∫L(x，y)|J(x，y)|dy)dx (4)(∫I(u, v)|J(u, v)|dv)du＝(∫L(x, y)|J(x, y)|dy)dx (4)

方程(4)是一个一阶常微分方程f(u)du＝g(x)dx，给定初始条件后就可以采用数值计算的方法叠代求解。求解出来得到能量的纵向对应关系U＝h(X)，相同的方法可以得出横向对应关系V＝m(Y)。Equation (4) is a first-order ordinary differential equation f(u)du=g(x)dx, which can be solved iteratively by numerical calculation method after initial conditions are given. Solve it to get the vertical correspondence relation of energy U=h(X), and the same method can obtain the horizontal correspondence relation V=m(Y).

将方程(4)代入方程(3)中可以得到：Substituting equation (4) into equation (3) gives:

$I I ((u u,, v v)) | | J J ((u u,, v v)) | | du du = = L L ((x x,, y the y)) | | J J ((x x,, y the y)) | | \frac{&Integral; &Integral; I I ((u u,, v v)) | | J J ((u u,, v v)) | | du du}{&Integral; &Integral; L L ((x x,, y the y)) | | J J ((x x,, y the y)) | | dx dx} dx dx - - - - - - ((55))$

从方程(4)和(5)中得到的实际上是一个满足具有雅可比行列式的方程(3)要求的点到点的映射关系。这种映射的定义中，关键是对用于表示光线方向的变量(u，v)和表示照度位置的变量(x，y)进行分别的对应，在划分中，可以采用不同的正交曲线进行分割，如极坐标曲线或者直角坐标曲线。通过上述能量的划分后，就建立起了从光源到照度平面的网格格点一一对应关系。从光源发出的光线，经过光学表面后，就被投射到照度平面上相应的对应位置。What is obtained from equations (4) and (5) is actually a point-to-point mapping relationship that satisfies the requirement of equation (3) with Jacobian determinant. In the definition of this mapping, the key is to separately correspond to the variable (u, v) used to represent the direction of the light and the variable (x, y) representing the position of the illuminance. In the division, different orthogonal curves can be used for Segmentation, such as a polar curve or a Cartesian curve. After the above division of energy, the one-to-one correspondence between the grid points from the light source to the illuminance plane is established. The light emitted from the light source, after passing through the optical surface, is projected to the corresponding corresponding position on the illuminance plane.

基于以上原理，本发明设计的方法在计算机中运行，本方法首先利用能量守恒的关系在点光源出光方向上确定一条由若干离散点构成的一条纵向曲线，相应的在照度平面上也确定一条由相等的离散点构成的纵向曲线，形成能量的纵向对应关系，然后以纵向曲线上的离散点为起始点，采用同样的方法构成由若干离散点构成的若干条横向曲线，形成能量的横向对应关系，从而将光源出光方向与照度平面划分为若干个离散点组成的能量对应的面；然后从两个从两个能量对应的面之间取一个点作为透镜(光学系统)表面计算的起始点，采用叠带方法，计算出透镜表面的所有离散点的坐标和出光方向，从而确定了一个透镜表面。具体步骤见发明内容。Based on the above principles, the method designed by the present invention runs in the computer. This method first utilizes the relationship of energy conservation to determine a longitudinal curve composed of several discrete points in the direction of light output of the point light source, and correspondingly determines a curve composed of several discrete points on the illuminance plane. The vertical curve composed of equal discrete points forms the vertical corresponding relationship of energy, and then takes the discrete point on the longitudinal curve as the starting point, and uses the same method to form several horizontal curves composed of several discrete points to form the horizontal corresponding relationship of energy , so that the light emitting direction of the light source and the illuminance plane are divided into surfaces corresponding to the energy composed of several discrete points; and then a point is taken from two surfaces corresponding to the two energies as the starting point for the calculation of the surface of the lens (optical system), The coordinates and light-emitting directions of all discrete points on the lens surface are calculated by using the superimposed band method, thereby determining a lens surface. See the summary of the invention for the specific steps.

在上述步骤中，坐标系(u，v)和(x，y)最好采用同一个原点，以便后续计算，作为点光源出光方向的坐标，坐标系(u，v)可以是球坐标或极坐标等，而照度平面一般采用直角坐标。In the above steps, the coordinate system (u, v) and (x, y) preferably use the same origin for subsequent calculations. As the coordinates of the light emitting direction of the point light source, the coordinate system (u, v) can be spherical coordinates or polar coordinates Coordinates, etc., while the illuminance plane generally adopts rectangular coordinates.

初始点的选择是一个非常重要的设计参数，只有合理的选择初始点的位置，如将光源的u参数的边界值和照度平面x参数的边界值或者u参数的中心值和照度平面x参数的中心值进行对应，才可能得到合理的对应关系。在步骤中，初始步长的给定取决于对光源划分的密度，划分越密，得到的近似解越精确，也可以先选择一个初始的步长Δx，计算得到相应的Δu。The selection of the initial point is a very important design parameter, only the position of the initial point is reasonably selected, such as the boundary value of the u parameter of the light source and the boundary value of the x parameter of the illuminance plane or the center value of the u parameter and the x parameter of the illuminance plane Only by corresponding to the central value can a reasonable corresponding relationship be obtained. In the step, the initial step size depends on the density of the division of the light source. The denser the division, the more accurate the approximate solution can be obtained. You can also choose an initial step size Δx and calculate the corresponding Δu.

初始步长Δu₀……Δu_n，Δv₀……Δv_n的确定与离散点的个数n+1、m+1有关，设计者可根据需要的照度区域的形状和大小以及透镜表面的大小来确定离散点的个数和初始步长，离散点越多，步长则越小，反之越大。The determination of the initial step size Δu ₀ ... Δu _n , Δv ₀ ... Δv _n is related to the number of discrete points n+1, m+1, and the designer can choose according to the shape and size of the required illumination area and the size of the lens surface To determine the number of discrete points and the initial step size, the more discrete points, the smaller the step size, and vice versa.

初始光线和初始点(x₀，y₀)的选择，从便于计算的角度考虑应选择边缘或中心位置的点。initial light and the selection of the initial point (x ₀ , y ₀ ), considering the ease of calculation, the edge or center point should be selected.

在透镜表面数据点的叠带求解中，初始的光线

的选择不一定是

可以是能量对应关系中的任意一点，但为了便于计算，选择

作为初始光线比较合适。当已经求出一条纵向曲线后，应以该纵向曲线上的点为起始点，求解一系列横向曲线，可以从S₀₀，S₁₀……S_n0中选择任意一点来求解，只要将所有以这些点为起始点的横向曲线求解出来即可，不一定按秩序求解。In the band solution for lens surface data points, the initial ray

The choice is not necessarily

It can be any point in the energy correspondence, but for the convenience of calculation, choose

It is more suitable as the initial light. When a longitudinal curve has been obtained, a series of transverse curves should be solved with the point on the longitudinal curve as the starting point. You can choose any point from S ₀₀ , S ₁₀ ... S _n0 to solve it, as long as all of these Point as the starting point of the horizontal curve can be solved, not necessarily in order.

在步骤3.1.3)、3.1.6)、3.2.3)中，采用折射定律是光线直接经过光学元件照射到照度平面的情况，采用反射定律是光线先照射到反射表面，然后反射到照度平面的情况。In steps 3.1.3), 3.1.6), and 3.2.3), the law of refraction is used when the light directly passes through the optical element and irradiates the illuminance plane, and the law of reflection is that the light first irradiates the reflective surface and then reflects to the illuminance plane Case.

在应用本方法的一些设计中，采用的有些光源需要进行一次封装，即光源发出的光需要穿过一些给定的表面，如LED光源实际使用中为了提高LED的出光效率和使用方便，需要预先对LED芯片进行一次封装，如采用球透镜的封装方式，同时为了配合光源的一次封装，在透镜的下表面也有一个球形的凹槽，因此设计的光学系统需要考虑到存在的一些给定的表面，如球面或者平面。为了实现上述光源和照度平面的一一映射，需要先将光源发出的光线追迹过这些给定的表面。对于已知的光学表面，光线从该光学表面的一侧具有折射率为n₁的介质中入射到另一侧具有折射率为n₂的介质中，可以很容易求出光线和已知光学表面的交点位置P，从而得到在P点位置的法线方向，然后可以利用折射定律求出光线离开给定的光学表面后的出射光线方向。In some designs using this method, some light sources used need to be packaged once, that is, the light emitted by the light source needs to pass through some given surfaces. The LED chip is packaged once, such as using a ball lens package. At the same time, in order to match the primary package of the light source, there is also a spherical groove on the lower surface of the lens. Therefore, the designed optical system needs to take into account the existence of some given surfaces. , such as a sphere or a plane. In order to realize the above-mentioned one-to-one mapping between the light source and the illuminance plane, it is necessary to trace the light rays emitted by the light source through these given surfaces. For a known optical surface, light is incident from a medium with a refractive index n ₁ on one side of the optical surface to a medium with a refractive index n ₂ on the other side, it is easy to obtain the ray and the known optical surface The intersection point position P, so as to obtain the normal direction at point P, and then use the law of refraction to find the direction of the outgoing light after the light leaves a given optical surface.

存在给定的光学表面时，初始化参数还应包括：给定光学表面的位置和法向矢量，给定光学材料的反射率和折射率。光源发出的光线需要追迹过一系列给定的光学表面，最后得到出射光线，利用出射光线来确定透镜表面数据点。因此只需要在步骤3中的3.1.2)，3.1.5)，3.1.7)前加入追迹光线的过程。给定的光学表面为s₁……s_k，光源发出的入射光线为

，人别和一系列光学表面相交于ins₁……ins_t，最终得到出射光线

光线追迹给定表面的方法是成3.1.7)前加入追迹光线的过程。给定的光学表面为s₁……s_k，光源发出的入射光线为分别熟的现有技术，可参考(R.Courant，LBers，J.J.Stoker“Modern Geometrical Optics(现代几何光学)”，Interscience Publishers，Inc，New York)文献。When there is a given optical surface, the initialization parameters should also include: the position and normal vector of the given optical surface, the reflectivity and refractive index of the given optical material. The light rays emitted by the light source need to trace through a series of given optical surfaces, and finally get the outgoing rays, which are used to determine the data points on the lens surface. Therefore, it is only necessary to add the process of tracing rays before 3.1.2), 3.1.5), and 3.1.7) in step 3. The given optical surface is s ₁ ... s _k , and the incident light emitted by the light source is

, people intersect with a series of optical surfaces at ins ₁ ... ins _t , and finally get the outgoing rays

The method of ray tracing a given surface is added to the process of tracing rays before 3.1.7). The given optical surface is s ₁ ... s _k , and the incident light emitted by the light source is For the well-known prior art, reference may be made to (R. Courant, LBers, JJStoker "Modern Geometrical Optics (Modern Geometrical Optics)", Interscience Publishers, Inc, New York) literature.

存在给定的光学表面时，能量的划分方法同没有给定光学表面的情况是一样的，因为能量划分确定的是光源和照度平面的对应关系，而光学系统的作用就是来实现这个对应关系。When there is a given optical surface, the division method of energy is the same as that without a given optical surface, because the energy division determines the correspondence between the light source and the illumination plane, and the function of the optical system is to realize this correspondence.

根据上述的设计方法，得到了透镜表面离散的数据点，包括每一个点的坐标和在该点的法向矢量。在光源划分采用的正交参数(u，v)和照度平面划分采用的正交参数(x，y)实际上在光学表面也诱导了一个自然的参数表示(p，q)，第i条p线为由具有相同的第一角标i，即(S_i1，S_i2……S_in)，的数据点构成的曲线，p线方向和曲面的横向曲线一致；第j条q线为由具有相同的第二角标j，即(S_1j，S_2j……S_nj)，的数据点构成的曲线，q线方向和曲面的纵向曲线一致。过每一个数据点具有沿着过该点的p线方向，并且和法线方向垂直的切线

根据NURBS(非均匀有理样条曲线)理论，可以根据每条横向曲线上的点坐标和切线方向，求出光滑的过这些点并且具有给定切线方向的横向曲线。相临的两条横向曲线之间可以生成一个过两条横向曲线上的点，并且具有和这些点上给定的法线方向的一个小曲面片，。将这些小曲面片连接起来，就构成了透镜的完整表面。According to the above-mentioned design method, discrete data points on the lens surface are obtained, including the coordinates of each point and the normal vector at the point. The orthogonal parameters (u, v) used in the light source division and the orthogonal parameters (x, y) used in the illumination plane division actually induce a natural parameter representation (p, q) on the optical surface, the i-th p The line is a curve composed of data points with the same first index i, namely (S _i1 , S _i2 ... S _in ), the direction of the p line is consistent with the transverse curve of the surface; the jth q line is composed of The curve formed by the data points of the same second subscript j, namely (S _1j , S _2j . . . S _nj ), has the same direction of the q-line as the longitudinal curve of the curved surface. Each data point has a tangent line along the p-line direction passing through the point and perpendicular to the normal direction

According to the NURBS (Non-Uniform Rational Spline) theory, a smooth transverse curve passing through these points and having a given tangent direction can be obtained according to the point coordinates and tangent direction on each transverse curve. A small surface patch can be generated between two adjacent transverse curves that passes through the points on the two transverse curves and has the normal direction given by these points. Connecting these small curved pieces makes up the complete surface of the lens.

下面结合附图进行详细的说明：Carry out detailed explanation below in conjunction with accompanying drawing:

图1.(a)表示对光源(110)能量的纵向分块，采用一系列纵向u曲线(120)将光源的能量分割成为不同的能量块(130)，110表示点光源。(b)表示对相应的照度区域的纵向能量分块，采用一系列横向x(140)曲线将照度区域的能量分割成为不同的能量块(150)，在照度区域和光源上对应的能量分块(130)和(150)中含有相同的能量大小。Figure 1. (a) shows the longitudinal division of the energy of the light source (110), using a series of longitudinal u-curves (120) to divide the energy of the light source into different energy blocks (130), and 110 represents a point light source. (b) represents the vertical energy block of the corresponding illuminance area, using a series of horizontal x (140) curves to divide the energy of the illuminance area into different energy blocks (150), and the corresponding energy block on the illuminance area and the light source (130) and (150) contain the same energy magnitude.

图2.(a)表示在分块的基础上，对光源的能量的横向划分。采用一系列的纵向V曲线(210)将光源的能量分成不同的小单元(220)。(b)表示在分块的基础上，对照度区域的能量的横向划分。采用一系列的纵向y曲线(230)将光源的能量分成不同的小单元(240)。在照度区域和光源上对应的能量单元格中含有相同的能量大小。Figure 2. (a) shows the horizontal division of the energy of the light source on the basis of the block. A series of longitudinal V-curves (210) are used to divide the energy of the light source into different small units (220). (b) represents the horizontal partitioning of the energy of the illumination region on a block basis. A series of longitudinal y-curves (230) are used to divide the energy of the light source into different small units (240). The corresponding energy cells on the illuminance area and the light source contain the same amount of energy.

图3表示根据光源和照度平面的纵向划分，利用方程(4)，求出光学曲面的一条纵向曲线，(a)图中的点380、390表示光学透镜表面的一条纵向曲线上的离散的点，是根据下述方法生成的，结合图3(b)进行说明：Fig. 3 represents according to the longitudinal division of light source and illumination plane, utilizes equation (4), obtains a longitudinal curve of optical curved surface, point 380,390 in (a) figure represents the discrete point on a longitudinal curve of optical lens surface , is generated according to the following method, which is illustrated in conjunction with Figure 3(b):

1)根据光源和照度平面的纵向对应关系在光源(300)上选择一条初始的光线

(310)，对应于照度平面上的一个初始位置P₁₁(380)，在初始光线的传播路径上选择一个初始点S₁₁(311)作为光学表面的起始点；1) Select an initial ray on the light source (300) according to the longitudinal correspondence between the light source and the illumination plane

(310), corresponding to an initial position P ₁₁ (380) on the illuminance plane, select an initial point S ₁₁ (311) as the starting point of the optical surface on the propagation path of the initial light;

2)利用初始点S₁₁(311)和在照度平面上的对应位置P₁₁(380)就可以得到出射光线的方向矢量

{\overset{&RightArrow;}{O}}_{10} = \overset{&RightArrow;}{S_{11} P_{11}};

2) Using the initial point S ₁₁ (311) and the corresponding position P ₁₁ (380) on the illumination plane, the direction vector of the outgoing light can be obtained

{\overset{&Right Arrow;}{o}}_{10} = \overset{&Right Arrow;}{S_{11} P_{11}};

3)根据折射定律(6)求出在该点表面应该具有的法向矢量的方向

3) According to the law of refraction (6), find out the direction of the normal vector that the surface should have at this point

4)在S₁₁点的切平面T₁₁(340)上，根据邻近的第2条入射光线

求出和T₁₁(340)的交点S₁₂(351)点的位置，结合照度平面的对应点P₁₂(390)；4) On the tangent plane T ₁₁ (340) at point S ₁₁ , according to the adjacent second incident ray

Obtain the position of the intersection point S ₁₂ (351) with T ₁₁ (340), and combine the corresponding point P ₁₂ (390) of the illuminance plane;

5)根据折射定律(6)，求出在S₁₂点的法向矢量的方向

5) According to the law of refraction (6), find out the direction of the normal vector at S ₁₂ points

6)根据上述叠代方法求出一条透镜表面纵向曲线上的离散数据点。6) Calculate discrete data points on a longitudinal curve of the lens surface according to the above iterative method.

当用于划分光源和照度平面的网格足够细的时候，可以近似认为后一个点的位置位于前一个点的切平面上而不改变曲线的C1光滑性。When the grid used to divide the light source and illuminance plane is fine enough, it can be approximated that the position of the latter point is located on the tangent plane of the previous point without changing the C1 smoothness of the curve.

图4表示根据光源和照度平面的横向分割V_u＝g(Y_x)，利用光学纵向曲线上的数据点作为初始点，求出图4(a)所示的透镜表面的横向曲线，结合图4(b)、图4(c)：Fig. 4 shows that according to the transverse division V _u =g(Y _x ) of the light source and the illuminance plane, using the data points on the optical longitudinal curve as the initial point, the transverse curve of the lens surface shown in Fig. 4(a) is obtained, combined with Fig. 4(b), Figure 4(c):

1)从纵向曲线上选取一点S₁₁(311)作为一条横向曲线的初始点；1) Select a point S ₁₁ (311) from the longitudinal curve as the initial point of a transverse curve;

2)入射光线

(410)和S₁₁(311)点的切平面(340)相交于一点S₂₁(411)，其对应于照度平面上的点为P₂₁(420)，从而求出光线的出射方向为

2) Incident light

(410) and the tangent plane (340) of S ₁₁ (311) point intersect at a point S ₂₁ (411), which corresponds to the point on the illuminance plane as P ₂₁ (420), thereby obtaining the outgoing direction of the light as

3)根据折射定律求出表面在S₂₁(440)点具有的法向矢量；3) obtain the normal vector that surface has at S ₂₁ (440) point according to the law of refraction;

4)与纵向曲线上的离散点的求解方式相同，叠代求解出光学表面的一条横向曲线上的离散点。4) In the same way as the solution of the discrete points on the longitudinal curve, the discrete points on a transverse curve of the optical surface are solved iteratively.

以纵向曲线上的每一个点生成出一条横向曲线，这一系列横向曲线的离散点覆盖了光学透镜的表面，可以用来生成光学表面，见图4(c)。Each point on the longitudinal curve generates a horizontal curve, and the discrete points of this series of horizontal curves cover the surface of the optical lens, which can be used to generate an optical surface, as shown in Figure 4(c).

图5表示横向曲线上的数据点和法线，得到了光滑的横向曲线(510)，横向曲线在每一点具有指定的切线方向。Figure 5 shows the data points and normals on the transverse curve resulting in a smooth transverse curve (510) with a specified tangent direction at each point.

图6表示两条相邻的横向曲线(510)上的相邻的离散点形成一个小的曲面片(610)，由相临的曲面片连接则成为一个完整的透镜表面(620)。Fig. 6 shows that adjacent discrete points on two adjacent transverse curves (510) form a small curved surface sheet (610), and a complete lens surface (620) is formed by connecting adjacent curved surface sheets.

图7表示在给定两个球表面的时候求出能量分配的表面设计：Figure 7 shows the surface design for finding the energy distribution given two spherical surfaces:

1)光线追迹过两个给定的球形表面(700)，得到出射光线

(710)；1) The ray is traced through two given spherical surfaces (700), and the outgoing ray is obtained

(710);

2)在光线

(710)上选取一点S₁₁(711)作为设计的初始点，根据能量映射的要求得到在S₁₁点的法线方向(720)；2) In light

On (710), select a point S ₁₁ (711) as the initial point of design, obtain the normal direction (720) at S ₁₁ points according to the requirement of energy mapping;

3)光线

(730)追迹过两个给定的球形表面后，和过S₁₁点的切平面相交于S₁₂(731)，根据能量映射的要求，求出在S₁₂点的法线方向(740)；3) light

(730) After tracing two given spherical surfaces, intersect the tangent plane passing through _S11 at _S12 (731), and calculate the normal direction at _S12 according to the requirements of energy mapping (740) ;

4)叠代求出光学透镜表面的一条纵向曲线的离散数据点和离散法向矢量；4) iteratively obtain discrete data points and discrete normal vectors of a longitudinal curve of the optical lens surface;

5)利用纵向曲线上面的点作为横向曲线的初始参数，求出表面的一系列横向曲线上的离散数据点。5) Using the points on the longitudinal curve as the initial parameters of the transverse curve to obtain discrete data points on a series of transverse curves of the surface.

本方法的一个重要应用是根据中国道路照明要求，设计满足照度分布的透镜。在本方法的一个具体实施例中，采用的光源是大功率白光LED，光源的光强具有朗伯形分布。根据路灯照明标准要求，光源离路面的距离是9m，照明范围是以光源为中心的10m×40m矩形范围内的路面，形成均匀的照度分布。An important application of this method is to design a lens that satisfies the illuminance distribution according to the road lighting requirements in China. In a specific embodiment of the method, the light source used is a high-power white LED, and the light intensity of the light source has a Lambertian distribution. According to the requirements of street lighting standards, the distance between the light source and the road surface is 9m, and the lighting range is the road surface within a 10m×40m rectangular range centered on the light source, forming a uniform illuminance distribution.

图8(a)中，照度平面被先沿着长度方向(810)划分成为N₁块，然后在宽度方向(820)上将每一块内分成N₂个能量单元；图8(b)中只考虑一部分的朗

型光源能量，光源首先被一簇纵向曲线(830)相应分成N₁份能量块，每一块和对应照度平面上的能量块具有相同的能量大小，考虑的经度角u的取值范围(840)为(-90⁰，90⁰)共180⁰；用另一簇垂直于这簇纵向曲线的横向曲线(850)对光源进行切片，将光源能量进一步分成N₂份小的能量单元，每一个能量单元同照度平面上对应的能量单元具有相同的能量大小，考虑得纬度角v的取值范围(860)为(-80⁰，80⁰)共160⁰ In Figure 8(a), the illuminance plane is first divided into N ₁ blocks along the length direction (810), and then each block is divided into N ₂ energy units in the width direction (820); in Figure 8(b) only consider part of lang

Type light source energy, the light source is first divided into N ₁ energy blocks by a cluster of longitudinal curves (830), each block has the same energy size as the energy block on the corresponding illuminance plane, and the value range of the longitude angle u considered (840) It is (-90 ⁰ , 90 ⁰ ) a total of 180 ⁰ ; use another group of horizontal curves (850) perpendicular to this group of longitudinal curves to slice the light source, and further divide the light source energy into N ₂ small energy units, each energy The unit has the same energy size as the corresponding energy unit on the illuminance plane, and the value range (860) of the latitude angle v is considered to be (-80 ⁰ , 80 ⁰ ) in total 160 ⁰

图9(a)是根据本方法叠带计算得到的浸没透镜的前视图，(910)是透镜的上表面，(920)是透镜的支撑柱面；图9(b)是得到的透镜的俯视图，一个LED芯片(930)通过环氧树脂和透镜的下表面封在了一起。芯片发出的光直接入射到透镜的表面上。这种结构因为具有很少的折射表面，具有低损耗的特点。Fig. 9 (a) is the front view of the immersion lens calculated according to this method, (910) is the upper surface of the lens, (920) is the support cylinder of the lens; Fig. 9 (b) is the top view of the obtained lens , an LED chip (930) is sealed together with the lower surface of the lens through epoxy resin. The light emitted by the chip is directly incident on the surface of the lens. This structure is characterized by low loss because it has few refractive surfaces.

图10(a)是根据本方法得到的具有一次封装的透镜侧视图，(1010)是透镜的上表面，LED芯片被一次封装在一个半球型小透镜(1030)中，在透镜的底部也相应的设计一个半球表面(1020)将芯片的光引导进入大透镜中，同时引线(1040)可以从透镜底面和基板(1050)的缝隙中引出。图10(b)是得到的透镜的俯视图。这种结构因为芯片和透镜是分离的，因此具有安装方便的特点。该透镜表面呈花生壳外型，该外型的中部有横轴和纵轴，该形状是相对于横轴和纵轴完全对称的。Figure 10(a) is a side view of the lens with primary packaging obtained according to this method, (1010) is the upper surface of the lens, and the LED chip is packaged in a small hemispherical lens (1030) at one time, and the bottom of the lens is also corresponding The design of a hemispherical surface (1020) guides the light of the chip into the large lens, and at the same time, the lead (1040) can be drawn out from the gap between the bottom surface of the lens and the substrate (1050). Fig. 10(b) is a plan view of the obtained lens. This structure is easy to install because the chip and the lens are separated. The surface of the lens is in the shape of a peanut shell, and the middle part of the shape has a horizontal axis and a vertical axis, and the shape is completely symmetrical with respect to the horizontal axis and the vertical axis.

另一个具体实施例是形成一个正六边型的照度分布设计，由于六角型分布的照度容易拼接，可以方便的用于一些景观照明和道路照明等通用照明应用中。在本具体实施例中，设计的高度为5m，正六边行的外接圆半径为7m。Another specific embodiment is to form a regular hexagonal illuminance distribution design, since the illuminance of the hexagonal distribution is easy to splice, it can be conveniently used in some general lighting applications such as landscape lighting and road lighting. In this specific embodiment, the designed height is 5m, and the radius of the circumscribed circle of the regular hexagonal row is 7m.

图11(a)是对照度平面的能量划分，采用极坐标的方法首先沿着径向(1110)将光源划分成为N₁能量块，在沿着极角的方向(1120)进一步的将每一个能量块划分成为N₂能量单元，从而得到N₁×N₂的网格点；(b)图是对光源能量的划分方法，首先沿着经度的方向(1130)将朗伯型光源的能量分成相应的N₁能量块，每一块和对应照度平面上的能量块具有相同的能量大小，考虑的经度角度取值范围(1140)为(-90⁰，90⁰)共180⁰；其次再沿着纬度的方向(1150)进一步将每一个分块的能量相应的划分成为N₂小的能量单元，每一个能量单元同照度平面上对应的能量单元具有相同的能量大小，纬度角取值范围(1160)为(-80⁰，80⁰)共160⁰，从而也得到了N₁×N₂对应网格点。Figure 11(a) is the energy division of the illumination plane. Using the method of polar coordinates, the light source is first divided into N ₁ energy blocks along the radial direction (1110), and each of them is further divided along the direction of the polar angle (1120). The energy block is divided into N ₂ energy units, so as to obtain N ₁ × N ₂ grid points; (b) is the division method of light source energy, firstly, along the direction of longitude (1130), the energy of Lambertian light source is divided into Corresponding N ₁ energy blocks, each block has the same energy size as the energy block on the corresponding illuminance plane, and the value range (1140) of longitude and angle considered is (-90 ⁰ , 90 ⁰ ) a total of 180 ⁰ ; followed by The direction of latitude (1150) further divides the energy of each block into _N2 small energy units, each energy unit has the same energy size as the corresponding energy unit on the illuminance plane, and the value range of latitude angle (1160 ) is (-80 ⁰ , 80 ⁰ ) a total of 160 ⁰ , thus also obtaining N ₁ ×N ₂ corresponding grid points.

图12(a)是根据本发明的叠带计算方法得到的透镜前视图的形状，考虑正六边形的对称性，和光源位于正多边形的中心正上方，透镜上表面的六分之一份如(1220)，芯片(1210)和透镜通过环氧树脂封装成为一体，(b)图是得到透镜的俯视图。图中的透镜形状是有六条边的球形，相对于照度平面，这六条棱是对称的。根据照度平面的设计，透镜的形状也可以是三棱、四棱或更多棱的球形形状。Fig. 12 (a) is the shape of the front view of the lens obtained according to the calculation method of overlapping bands of the present invention, considering the symmetry of the regular hexagon, and the light source is positioned directly above the center of the regular polygon, and one-sixth of the upper surface of the lens is as (1220), the chip (1210) and the lens are encapsulated into one body through epoxy resin, and the figure (b) is a top view of the obtained lens. The shape of the lens in the figure is a sphere with six sides, and these six sides are symmetrical with respect to the illuminance plane. According to the design of the illuminance plane, the shape of the lens can also be a spherical shape with three edges, four edges or more edges.

通常单个LED芯片的总光通量是有限的，不能达到相关的照度要求值，可以根据具体的需要将多个芯片和透镜排成阵列，共同完成给定的照度要求，因为每一个透镜都在整个照明范围内形成一个同给定照度成比例的照度分布，因此排布阵列非常的方便，具体需要调整的只是透镜和芯片的个数。Usually the total luminous flux of a single LED chip is limited and cannot meet the required illuminance value. Multiple chips and lenses can be arranged in an array according to specific needs to jointly complete a given illuminance requirement, because each lens is in the entire lighting An illuminance distribution proportional to the given illuminance is formed within the range, so it is very convenient to arrange the array, and only the number of lenses and chips needs to be adjusted.

图13是一个5×5的透镜的阵列，采用的透镜(1310)是根据国家照度标准设计的路灯透镜模型。FIG. 13 is a 5×5 lens array, and the lens (1310) used is a street lamp lens model designed according to the national illuminance standard.

总而言之，基于分离变量原理的三维光学表面设计的关键是：In summary, the key to the design of 3D optical surfaces based on the principle of separation of variables is:

1)采用分离变量的方法确定横向和纵向的能量对应关系；1) Use the method of separating variables to determine the horizontal and vertical energy correspondence;

2)利用横向和纵向的能量对应关系得到透镜表面的数据点2) Obtain the data points of the lens surface by using the horizontal and vertical energy correspondences

图14是基于分离变量划分方法的三维给定照度分布设计的基本流程图：主要包括给定初始输入参数、求解映射对应关系、纵向曲线的求解、横向曲线的求解和最后光学表面的生成这些部分。由于求解纵向曲线只需要纵向对应关系，求解横向曲线只需要横向对应关系，所以图中的步骤也可改为1，2，4，3，5，6，并不影响光学系统的设计。Figure 14 is the basic flow chart of the three-dimensional given illuminance distribution design based on the separation of variable division method: mainly including the given initial input parameters, solving the mapping correspondence, solving the longitudinal curve, solving the transverse curve and finally generating these parts of the optical surface . Since only the longitudinal correspondence is needed to solve the longitudinal curve, and only the horizontal correspondence is needed to solve the transverse curve, the steps in the figure can also be changed to 1, 2, 4, 3, 5, 6 without affecting the design of the optical system.

根据本发明的设计方法设计的透镜可以具有非旋转对称性的形状，能在一个目标平面上形成给定的照度分布设计，充分利用光源的能量，从而节省能源。根据设计原理要求，光源的尺寸要远小于光学系统的尺寸，代表未来发展趋势的LED光源成为一种合适的照明设计光源。另一个优点是每一个光学系统都可以在整个照明区域内形成一个同给定照度成比例的照度分布，因此可以根据具体的照度要求和光源的光通量水平，将光源和透镜排成阵列，共同形成一个给定的照度分布。本发明与现有的照明技术相比，具有高效、节能和使用灵活方便的特点，在各种照明场合，如道路照明，景观照明和显示器背光源照明等，都有广阔的应用前景。The lens designed according to the design method of the present invention can have a non-rotational symmetrical shape, can form a given illuminance distribution design on a target plane, fully utilize the energy of the light source, and thus save energy. According to the requirements of the design principle, the size of the light source should be much smaller than the size of the optical system, and the LED light source, which represents the future development trend, has become a suitable light source for lighting design. Another advantage is that each optical system can form an illuminance distribution proportional to the given illuminance in the entire lighting area, so the light source and the lens can be arranged in an array according to the specific illuminance requirements and the luminous flux level of the light source to jointly form A given illuminance distribution. Compared with the existing lighting technology, the present invention has the characteristics of high efficiency, energy saving, flexible and convenient use, and has broad application prospects in various lighting occasions, such as road lighting, landscape lighting and display backlight lighting.

Claims

1, a kind of method for designing of two-dimension optical lens is characterized in that, this method contains the following steps of moving in computing machine:

1) initialization:

For the light direction of light source set up a coordinate system (u, v), for the point on the illumination plane set up a coordinate system (x, y);

An initial light (u on the given light source light direction ₀, v ₀), an initial point (x on the given illumination plane ₀, y ₀);

The number m+1 of discrete point in the energy corresponding relation is walked crosswise in number n+1 of discrete point in given vertical energy corresponding relation,

Wherein n and m are natural number;

Step delta u between the given source light ₀Δ u _n, Δ v _oΔ v _m

The refractive index n of given lens material ₁Refractive index n with air ₂

2) light source and illumination plane are carried out the correspondence division of energy:

2.1) set up with the light direction of light source and a vertical corresponding relation of the point on the illumination plane:

2.1.1) calculating source light (u ₀, v ₀), at Δ u ₀The energy size that has in the scope:

E ({Δu}_{0}) |_{u = u_{0}} = {&Integral;}_{u = u_{0}} I (u, v) | J (u, v) | dv \cdot {Δu}_{0},

Wherein 1 (u v) is a light source (u, the v) light intensity magnitude on the direction,

For adopt (u, v) coordinate system need be scaled dudv the Jacobian of unit area;

2.1.2) calculate the point (x on the illumination plane ₀, y ₀) corresponding step delta x ₀:

{Δx}_{0} = E ({Δu}_{0}) |_{u = u_{0}} / {&Integral;}_{x = x_{0}} L (x, y) | J (u, v) | dy,

Wherein L (x, y) be illustrated on the illumination plane (x, the y) brightness value at some place, For adopt (x, y) coordinate system need be scaled dxdy the Jacobian of unit area;

2.1.3) make u ₁=u ₀+ Δ u ₀, x ₁=x ₀+ Δ x ₀Thereby, the light that obtains that pointolite sends and the energy corresponding relation of a point on the illumination plane: (u ₁, v ₀) corresponding to (x ₁, y ₀);

2.1.3) utilize step 2.1.1) and in formula compute ray (u ₁, v ₀) at Δ u ₁The energy size that has in the scope:

E ({Δu}_{1}) |_{u = u_{1}} = {&Integral;}_{u = u_{1}} I (u, v) | J (u, v) | dv \cdot {Δu}_{1};

2.14) utilize step 2.1.2) and in formula calculate point (x on the illumination plane ₁, y ₀) corresponding step delta x ₁:

{Δx}_{1} = E ({Δu}_{1}) |_{u = u_{1}} / {&Integral;}_{x = x_{1}} L (x, y) | J (u, v) | dy;

2.1.5) make u ₂=u ₁+ Δ u ₁, x ₂=x ₁+ Δ x ₁, utilize step 2.1.1) and step 2.1.2) in formula, obtain another light that pointolite sends and the energy corresponding relation of another point on the illumination plane: (u ₂, v ₀) corresponding to (x ₂, y ₀);

2.1.6) repeating step 2.1.1)～2.1.5), iterate a vertical corresponding relation of energy of the some formation that calculates on source light and the illumination plane

U_{v_{0}} = h (X_{y_{0}})

And Δ X, wherein:

U_{v_{0}} = {(u_{0}, v_{0}), (u_{1}, v_{0}), . . . . . . (u_{n}, v_{0})}

X_{y_{0}} = {(x_{0}, y_{0}), (x_{1}, y_{0}), . . . . . . (x_{n}, y_{0})}

Δ X={ Δ x ₀, Δ x ₁... Δ x _n;

2.2) to set up with the point on above-mentioned vertical corresponding relation be n+1 the light of initial point and the horizontal corresponding relation of energy of the point on the illumination plane:

2.2.1) from above-mentioned vertical corresponding relation

U_{v_{0}} = h (X_{y_{0}})

In get initial point (u ₀, v ₀) and initial step length Δ v ₀, compute ray (u ₀, v ₀) at (Δ u ₀, Δ v ₀) the energy size that has in the scope:

E ({Δu}_{0}, {Δv}_{0}) |_{(u = u_{0}, v = v_{0})} = I (u_{0}, v_{0}) | J (u_{0}, v_{0}) | {Δu}_{0} {Δv}_{0};

2.2.2) calculate the initial point (x on the illumination plane ₀, y ₀) corresponding step delta y ₀:

{Δy}_{0} = \frac{E ({Δu}_{0}, {Δv}_{0}) |_{(u = u_{0}, v = v_{0})}}{L (x_{0}, y_{0}) | J (x_{0}, y_{0}) | {Δx}_{0}};

2.2.3) make v ₁=v ₀+ Δ v ₀, y ₁=y ₀+ Δ y ₀Obtain the energy corresponding relation of a point on light of pointolite and the illumination plane:

(u ₀, v ₁) corresponding to (x ₀, y ₁);

2.2.4) according to step 2.2.1) and formula compute ray (u ₀, v ₁) at (Δ u ₀, Δ v ₁) the energy size that has in the scope:

E ({Δu}_{0}, {Δv}_{1}) |_{(u = u_{0}, v = v_{1})} = I (u_{0}, v_{1}) | J (u_{0}, v_{1}) | {Δu}_{0} {Δv}_{1};

2.2.5) according to step 2.2.2) and formula calculate (x on the illumination plane ₀, y ₁) corresponding step delta y ₁:

{Δy}_{1} = \frac{E ({Δu}_{0}, {Δv}_{1}) |_{(u = u_{0}, v = v_{1})}}{L (x_{0}, y_{1}) | J (x_{0}, y_{1}) | {Δx}_{0}};

2.2.6) make v ₂=v ₁+ Δ v ₀, y ₂=y ₁+ Δ y ₁Obtain another light of pointolite and the energy corresponding relation of another point on the illumination plane: (u ₀, v ₂) corresponding to (x ₀, y ₂);

2.2.7) recycling step 2.2.1) and 2.2.2) in formula, iterate a horizontal corresponding relation of energy of the point that calculates on pointolite emergent ray and the illumination plane

V_{u_{0}} = Y_{x_{0}},

Wherein

V_{u_{0}} = {(u_{0}, v_{0}), (u_{0}, v_{1}), . . . . . . (u_{0}, v_{m})},

Y_{x_{0}} = {(x_{0}, y_{0}), (x_{0}, y_{1}), . . . . . . (x_{0}, y_{m})};

2.2.8) repeating step 2.2.1～2.2.7), calculating with the n+1 on vertical corresponding relation point is n+1 the horizontal corresponding relation of energy of initial point, wherein finding the solution of each bar horizontal curve adopted Δ X={ Δ x ₀, Δ x ₁... Δ x _nIn a corresponding step-length as the step-length of discrete point on the x direction

V_{u_{0}} = g (Y_{x_{0}}),

Vu ₀＝{(u ₀，v ₀)，(u ₀，v ₁)，......(u ₀，v _m)}，

Y_{x_{0}} = {(x_{0}, y_{0}), (x_{0}, y_{1}), . . . . . . (x_{0}, y_{m})}

V_{u_{1}} = g (Y_{x_{1}}),

V_{u_{1}} = {(u_{1}, v_{0}), (u_{1}, v_{1}), . . . . . . (u_{1}, v_{m})},

Y_{x_{1}} = {(x_{1}, y_{0}), (x_{1}, y_{1}), . . . . . . (x_{1}, y_{m})}

V_{u_{n}} = g (Y_{x_{n}}),

V_{u_{n}} = {(u_{n}, v_{0}), (u_{n}, v_{1}), . . . . . . (u_{n}, v_{m})},

Y_{x_{n}} = {(x_{n}, y_{0}), (x_{n}, y_{1}), . . . . . . (x_{n}, y_{m})};

3) iterating of lens surface data point found the solution:

3.1) the determining of a vertical curve of lens surface:

3.1.1) according to vertical corresponding relation on light source and illumination plane

U_{v_{0}} = h (X_{y_{0}})

, on light source, select an initial light

, corresponding to an initial position P on the illumination plane ₀₀(x ₀, y ₀);

3.1.2) initial point S of selection on the travel path of initial light ₀₀Starting point as optical surface;

3.1.3) utilize initial point S ₀₀With the correspondence position P on the illumination plane ₀₀Obtain at a S ₀₀The direction vector of the emergent ray at place

{\overset{&RightArrow;}{O}}_{00} = \overset{&RightArrow;}{S_{00} P_{00}},

Obtain at S according to refraction law ₀₀The normal vector that the some surface should have

{\overset{&RightArrow;}{N}}_{00} = n_{1} * {\overset{&RightArrow;}{I}}_{00} - n_{2} * {\overset{&RightArrow;}{O}}_{00};

Or obtain at S according to reflection law ₀₀The normal vector that the some surface should have

:

{\overset{&RightArrow;}{N}}_{00} = {\overset{&RightArrow;}{I}}_{00} - {\overset{&RightArrow;}{O}}_{00};

3.1.4) on light source, select the second emergent ray according to vertical corresponding relation on light source and illumination plane Corresponding illumination plane P ₁₀(x ₁, y ₀) point, according to S ₀₀The normal vector on some surface

, obtain S ₀₀The section T of point ₀₀

3.1.5) obtain light

Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₁₀

3.1.6) in conjunction with the corresponding point P on illumination plane ₁₀, obtain a S ₁₀The direction vector of emergent ray

{\overset{&RightArrow;}{O}}_{10} = \overset{&RightArrow;}{S_{10} P_{10}}

, obtain at S according to refraction law ₁₀The normal vector that the some surface should have

{\overset{&RightArrow;}{N}}_{10} = n_{1} * {\overset{&RightArrow;}{I}}_{10} - n_{2} * {\overset{&RightArrow;}{O}}_{10};

{\overset{&RightArrow;}{N}}_{10} = {\overset{&RightArrow;}{I}}_{10} - {\overset{&RightArrow;}{O}}_{10};

3.1.7) on light source, continue to select emergent ray according to vertical corresponding relation on light source and illumination plane, according to step 3.1.2)～3.1.6) go on foot, obtain the discrete data point S on vertical curve of lens surface ₀₀, S ₁₀S _N0, and the normal vector of the emergent ray of every bit correspondence , promptly determined a vertical curve of lens surface;

3.2) with the finding the solution of the discrete point on vertical curve of lens surface as the n+1 bar horizontal curve of initial point:

3.2.1) get an initial point S from vertical curve on said lens surface ₀₀,, select S according to the horizontal corresponding relation of the energy on light source and illumination plane as the initial point of a horizontal curve ₀₀The incident ray that point is contiguous , the some P on the corresponding illumination plane ₀₁(x ₀, y ₁);

3.2.2) obtain light

Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

3.2.3) this is corresponding to the some P on the illumination plane ₀₁(x ₀, y ₁), thereby obtain S ₀₁The direction vector of the emergent ray of some light

{\overset{&RightArrow;}{O}}_{01} = \overset{&RightArrow;}{S_{01} P_{01}},

Obtain at S according to refraction law ₀₁The normal vector that the some surface should have

{\overset{&RightArrow;}{N}}_{01} = n_{1} * {\overset{&RightArrow;}{I}}_{01} - n_{2} * {\overset{&RightArrow;}{O}}_{01};

Or obtain at S according to reflection law ₀₁The normal vector that the some surface should have

{\overset{&RightArrow;}{N}}_{01} = {\overset{&RightArrow;}{I}}_{01} - {\overset{&RightArrow;}{O}}_{01};

3.2.4) on light source, continue to select successively contiguous emergent ray according to the horizontal corresponding relation on light source and illumination plane

According to step 3.2.1)～3.2.4), obtain with the some S on the vertical curve of lens surface ₀₀Be the discrete data point S on the horizontal curve of initial point ₀₀, S ₀₁S _0m, and the normal vector of every bit correspondence

{\overset{&RightArrow;}{N}}_{01} \cdot \cdot \cdot \cdot \cdot \cdot {\overset{&RightArrow;}{N}}_{0 m};

3.2.5) continue to select successively initial point S ₁₀S _N0,, find the solution and obtain with on the vertical curve on the lens all with discrete point S according to step 3.2.1～3.2.4) ₀₀S _N0Be the normal vector that the discrete point on the n+1 bar horizontal curve of initial point and this point have, then all data points of lens surface and normal vector thereof are found the solution and are finished, and have promptly determined the surface of lens.

2, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, described coordinate system (u, v) and coordinate system (x y) adopts same initial point.

3, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, (u v) is spherical coordinates or polar coordinates to described coordinate system.

4, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, and the initial light (u on the light direction of described light source ₀, v ₀) select the light at edge or the light at center, the initial point (x on the illumination plane ₀, y ₀) be the point (x of the marginal position corresponding with described initial light ₀, y ₀) or the point of center.

5, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, when having given surface, and step 3.1.2) change into: after preliminary ray trace is crossed given surface, on travel path, select an initial point S ₀₀Starting point as optical surface;

Step 3.1.5) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S10;

Step 3.2.2) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

6, the method for designing according to claim 1 and lens that design is characterized in that having the peanut shell mould outside surface of medial recess.

7, the method for designing according to claim 1 and lens that design is characterized in that having the spherical outer surface of three above ribs.