CN109445093A - A kind of LED free-form surface lens array apparatus for inclined surface Uniform Illumination - Google Patents
A kind of LED free-form surface lens array apparatus for inclined surface Uniform Illumination Download PDFInfo
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Abstract
本发明公开了一种用于倾斜面均匀照明的LED自由曲面透镜阵列装置,属于非成像光学和激光光束整形技术领域。包含若干按行和列均匀排布的自由曲面透镜单元(U)和LED光源单元(V);每个自由曲面透镜单元(U)形状相同,且每颗LED光源单元(V)也相同,自由曲面透镜单元(U)和LED光源单元(V)的数量相同,且一一对应;每颗LED光源单元和相应的自由曲面透镜单元的光轴重合,LED光源单元的出光经相应的自由曲面透镜单元偏折后在倾斜照明面上产生预定的均匀光分布,自由曲面透镜单元可以用光学树脂等材料借助注塑成型技术来实现。本发明结构紧凑、简单;整形效果好,能量利用率高;实用性强,应用范围广。
The invention discloses an LED free-form surface lens array device used for uniform illumination of inclined surfaces, belonging to the technical field of non-imaging optics and laser beam shaping. It includes a number of free-form surface lens units (U) and LED light source units (V) evenly arranged in rows and columns; each free-form surface lens unit (U) has the same shape, and each LED light source unit (V) is also the same, free The number of curved lens units (U) and LED light source units (V) are the same and correspond one-to-one; the optical axes of each LED light source unit and the corresponding free-form curved lens unit are coincident, and the light emitted from the LED light source unit passes through the corresponding free-form curved lens. After the unit is deflected, a predetermined uniform light distribution is generated on the inclined illumination surface, and the free-form surface lens unit can be realized by injection molding technology with materials such as optical resin. The invention has compact and simple structure, good shaping effect, high energy utilization rate, strong practicability and wide application range.
Description
技术领域technical field
本发明涉及非成像光学及照明技术领域,尤其涉及一种用于倾斜面均匀照明的LED自由曲面透镜阵列装置。The invention relates to the technical field of non-imaging optics and lighting, in particular to an LED free-form surface lens array device used for uniform illumination of inclined surfaces.
背景技术Background technique
区别于传统同轴照明,倾斜照明解除了同轴限制,大大提升了光照的灵活性,在实际中有着广泛的应用,如城市道路照明、隧道照明、城市景观亮化等。为了提高光照强度,实际中的倾斜照明系统一般通过阵列一组光束整形透镜单元构成。由于每个光束整形透镜单元相同,因此设计倾斜照明系统的关键在于设计单个的光束整形透镜单元。光束整形透镜单元借助一定的光学曲面,对光源的出光进行重新的分配。在相比较传统的光学曲面,自由曲面具有极高的设计自由度,可极大提高操控光的能力和灵活性。采用自由曲面进行光束调控,可获得结构紧凑、性能优异的光学系统,更为重要的,可实现传统光学曲面无法实现的新型倾斜照明系统。自由曲面极其自由灵活的面型结构在给我们带来机遇的同时也带了很大的设计挑战,自由曲面照明的关键点和难点在于如何根据光操控要求(给定入射光分布和出射光分布)来反求自由曲面面型。Different from traditional coaxial lighting, oblique lighting removes the coaxial limitation and greatly improves the flexibility of lighting. It has a wide range of applications in practice, such as urban road lighting, tunnel lighting, and urban landscape lighting. In order to improve the light intensity, an actual oblique lighting system is generally constituted by an array of a group of beam shaping lens units. Since each beam-shaping lens unit is identical, the key to designing an oblique illumination system is to design a single beam-shaping lens unit. The beam shaping lens unit redistributes the light emitted from the light source by means of a certain optical curved surface. Compared with traditional optical surfaces, freeform surfaces have a very high degree of design freedom, which can greatly improve the ability and flexibility of manipulating light. The use of free-form surfaces for beam regulation can obtain an optical system with a compact structure and excellent performance, and more importantly, a new oblique lighting system that cannot be achieved by traditional optical surfaces can be realized. The extremely free and flexible surface structure of free-form surfaces not only brings us opportunities, but also brings great design challenges. The key point and difficulty of free-form surface lighting is how to control the light according to the requirements (given the distribution of incident light and the distribution of outgoing light). ) to inverse the free-form surface shape.
在现有的自由曲面光束整形方法中,中国专利200910046129.5提出的Raymapping方法根据能量守恒预先定义入射光线和出射光线之间的映射关系,然后通过数值求解得到曲面面型。在Ray mapping方法中,映射关系的可积性决定了曲面的连续性,由于在自由曲面光束整形中很难获得一个满足可积条件的映射关系,导致自由曲面不连续或实际光分布和目标光分布之间存在很大的差异。中国专利201210408729.3提出的MA(Monge-Ampère,MA)方法根据能量守恒和折射定律,将单个自由曲面整形问题转化成MA方程,并通过数值求解MA方程得到光束整形问题的数值解。相比较Ray mapping方法,MA方法可得到连续的自由曲面,实际光分布和目标光分布吻合较好。Supporting quadric方法将一个连续的光分布离散化,并采用许多二次曲面面片(如:抛物面、椭球面等)来构建自由曲面面型,以此求得光束整形问题的近似解。上述方法在同轴自由曲面光束整形中已得到广泛的研究,然而尚无法很好地解决非同轴的倾斜照明问题。将同轴设计的照明系统用于倾斜面照明,势必导致倾斜面上的实际光分布显著偏离预定的光分布,无法满足实际倾斜照明要求;无法实现能量的有效分配,势必造成能量浪费。Among the existing beam shaping methods for free-form surfaces, the Raymapping method proposed in Chinese Patent No. 200910046129.5 predefines the mapping relationship between incident rays and outgoing rays according to energy conservation, and then obtains the surface shape by numerical solution. In the Ray mapping method, the integrability of the mapping relationship determines the continuity of the surface. Since it is difficult to obtain a mapping relationship that satisfies the integrable condition in free-form surface beam shaping, the free-form surface is discontinuous or the actual light distribution and target light There is a big difference between the distributions. The MA (Monge-Ampère, MA) method proposed in Chinese patent 201210408729.3 converts a single free-form surface shaping problem into an MA equation according to the law of energy conservation and refraction, and obtains the numerical solution of the beam shaping problem by numerically solving the MA equation. Compared with the Ray mapping method, the MA method can obtain continuous free-form surfaces, and the actual light distribution is in good agreement with the target light distribution. The Supporting quadric method discretizes a continuous light distribution, and uses many quadric surfaces (such as paraboloids, ellipsoids, etc.) to construct free-form surfaces, so as to obtain an approximate solution to the beam shaping problem. The above methods have been widely studied in beam shaping of coaxial free-form surfaces, but they cannot solve the problem of non-coaxial oblique illumination. Using a coaxially designed lighting system for inclined surface lighting will inevitably cause the actual light distribution on the inclined surface to significantly deviate from the predetermined light distribution, which cannot meet the actual inclined lighting requirements; it cannot achieve effective energy distribution, which will inevitably lead to energy waste.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于克服现有技术的不足,提供一种用于倾斜面均匀照明的自由曲面透镜阵列装置。The purpose of the present invention is to overcome the deficiencies of the prior art and provide a free-form surface lens array device for uniform illumination of inclined surfaces.
所述的用于倾斜面均匀照明的LED自由曲面透镜阵列装置包含若干按行和列均匀排布的自由曲面透镜单元(U)和LED光源单元(V);每个自由曲面透镜单元(U)形状相同,且每颗LED光源单元(V)也相同,自由曲面透镜单元(U)和LED光源单元(V)的数量相同,且一一对应;每颗LED光源单元和相应的自由曲面透镜单元的光轴重合,LED光源单元的出光经相应的自由曲面透镜单元偏折后在倾斜照明面上产生预定的均匀光分布;所述的自由曲面透镜单元的具体设计步骤如下:The LED free-form surface lens array device for uniform illumination of inclined surfaces includes a number of free-form surface lens units (U) and LED light source units (V) uniformly arranged in rows and columns; each free-form surface lens unit (U) The shape is the same, and each LED light source unit (V) is also the same, the number of free-form lens units (U) and LED light source units (V) are the same, and correspond one-to-one; each LED light source unit and the corresponding free-form surface lens unit The optical axis of the LED light source unit coincides, and the light emitted from the LED light source unit is deflected by the corresponding free-form surface lens unit to produce a predetermined uniform light distribution on the inclined illumination surface; the specific design steps of the free-form surface lens unit are as follows:
(1)设置自由曲面透镜的光路结构,光源经自由曲面透镜的入射面进入自由曲面透镜;从自由曲面透镜的出射面射出,并在倾斜照明面上产生预定的均匀光分布;所述的出射面为自由曲面;根据初始设计参数对自由曲面透镜进行自由曲面设计;(1) The optical path structure of the free-form surface lens is set, and the light source enters the free-form surface lens through the incident surface of the free-form surface lens; it is emitted from the exit surface of the free-form surface lens, and a predetermined uniform light distribution is generated on the inclined illumination surface; The surface is a free-form surface; the free-form surface lens is designed according to the initial design parameters;
(2)以光源S为坐标原点建立全局直角坐标系xyz,对步骤(1)所确定的自由曲面透镜的自由曲面上点P的位置用球坐标表示为以倾斜照明面和z轴的交点B3为坐标原点,在倾斜照明面上建立局部坐标系x1y1z1,并使全局坐标系xyz的x轴和局部坐标系x1y1z1的x1轴方向相同;局部坐标系x1y1z1的z1轴和全局坐标系xyz的z轴的夹角为β,β≠0°;当从全局坐标系xyz的z轴到局部坐标系x1y1z1的z1轴为逆时针方向旋转时,β<0;当从全局坐标系xyz的z轴到局部坐标系x1y1z1的z1轴为顺时针方向旋转时,β>0;出射光线在倾斜照明面上的落点T在全局坐标系xyz下的坐标表示为(tx,ty,tz),在局部坐标系x1y1z1下的坐标表示为(tx1,ty1,tz1);矢量P为点P的位置矢量,是一个由全局直角坐标系的原点指向点P的矢量;矢量T为点T的位置矢量,是一个由全局直角坐标系的原点指向点T的矢量;根据折射定律O=n×I+P1×N,求得出射光线的单位方向向量O=(Ox,Oy,Oz),并建立点P和目标点T之间的坐标关系(2) The global rectangular coordinate system xyz is established with the light source S as the coordinate origin, and the position of the point P on the free-form surface of the free-form surface lens determined in step (1) is expressed in spherical coordinates as Taking the intersection point B 3 of the oblique illumination surface and the z-axis as the coordinate origin, establish a local coordinate system x 1 y 1 z 1 on the oblique illumination surface, and make the x axis of the global coordinate system xyz and the local coordinate system x 1 y 1 z 1 The direction of the x 1 axis is the same; the angle between the z 1 axis of the local coordinate system x 1 y 1 z 1 and the z axis of the global coordinate system xyz is β, β≠0°; when from the z axis of the global coordinate system xyz to the local When the z 1 axis of the coordinate system x 1 y 1 z 1 rotates counterclockwise, β<0; when the z 1 axis from the z axis of the global coordinate system xyz to the z 1 axis of the local coordinate system x 1 y 1 z 1 is clockwise When rotating, β>0; the coordinates of the landing point T of the outgoing light on the oblique illumination surface in the global coordinate system xyz are expressed as (t x , t y , t z ), and in the local coordinate system x 1 y 1 z 1 The coordinates of t are expressed as (t x1 , t y1 , t z1 ); the vector P is the position vector of point P, which is a vector pointing to the point P from the origin of the global Cartesian coordinate system; the vector T is the position vector of point T, which is a The vector pointing from the origin of the global Cartesian coordinate system to the point T; according to the law of refraction O=n×I+P 1 ×N, the unit direction vector O=(O x , O y , O z ) of the emitted light can be obtained, and established Coordinate relationship between point P and target point T
其中,Px、Py和Pz为点P位置矢量P的三个分量;Ox、Oy和Oz为点P处出射光线单位方向向量O的三个分量;N为自由曲面在点P处的单位法矢,角度α是矢量I和矢量N的夹角;n为自由曲面透镜所用材料的折射率;Among them, P x , P y and P z are the three components of the position vector P of the point P; O x , O y and O z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point unit normal vector at P, The angle α is the angle between the vector I and the vector N; n is the refractive index of the material used for the free-form surface lens;
(3)根据步骤(2)得到的点P和目标点T之间的坐标关系还需满足倾斜照明面在全局坐标系下的方程:(3) The coordinate relationship between the point P and the target point T obtained according to step (2) also needs to satisfy the equation of the inclined illumination surface in the global coordinate system:
Atx+Ctz+D=0At x +Ct z +D=0
其中,A=sinβ、C=cosβ以及D=-C×L,L为倾斜照明面与全局坐标系xyz的z轴交点B3的z坐标;根据该方程进一步得到目标点T的全局坐标Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; the global coordinate of the target point T is further obtained according to this equation
(4)根据步骤(2)得到的点P和目标点T之间的坐标关系,有以下坐标变换关系(4) According to the coordinate relationship between the point P and the target point T obtained in step (2), there are the following coordinate transformation relationships
其中,J(T)为位置矢量T的Jacobi矩阵, where J(T) is the Jacobi matrix of the position vector T,
(5)根据局部能量守恒定律,在不考虑能量损失的情况下,要求由光源出射的任意一条细光束经自由曲面透镜偏折后其所有能量被传输至倾斜照明面上的目标照明区域,即自由曲面透镜对细光束的偏折满足以下能量关系式(5) According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, The deflection of the beamlet by the free-form surface lens satisfies the following energy relation
其中,为光源的强度分布,E(tx1,ty1)为倾斜照明面上目标照明区域的照度分布,J(T)为位置矢量T的Jacobi矩阵,0≤θ≤2π,其中为入射到自由曲面透镜的光束的最大发散角;in, is the intensity distribution of the light source, E(t x1 , t y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens;
(6)自由曲面在满足步骤(5)中的能量传输方程的同时还要保证光束的边界光线经自由曲面偏折后入射到目标面照明区域的边界,即满足以下边界条件(6) While the free-form surface satisfies the energy transfer equation in step (5), it must also ensure that the boundary rays of the light beam are deflected by the free-form surface and enter the boundary of the illumination area of the target surface, that is, the following boundary conditions are satisfied
其中,Ω1表示入射到自由曲面透镜上的光束的总立体角,Ω2表示倾斜照明面上目标照明区域,和分别为区域Ω1和Ω2的边界;Among them, Ω 1 represents the total solid angle of the light beam incident on the free-form surface lens, Ω 2 represents the target illumination area on the oblique illumination surface, and are the boundaries of regions Ω 1 and Ω 2 , respectively;
(7)对步骤(5)中的能量传输方程和步骤(6)中的边界条件联立求解,得到一组离散数据点,通过对该组数据点进行曲面拟合即可得到用于倾斜面照明的自由曲面透镜的自由曲面面型。(7) Simultaneously solve the energy transfer equation in step (5) and the boundary conditions in step (6) to obtain a set of discrete data points, which can be used for inclined surfaces by surface fitting of the set of data points. The freeform surface profile of the freeform lens for illumination.
优选的,所述的自由曲面透镜的入射面(S1)为球面,每颗LED光源单元位于其对应的自由曲面透镜的入射面球心处。Preferably, the incident surface ( S1 ) of the free-form curved lens is a spherical surface, and each LED light source unit is located at the spherical center of the incident surface of the corresponding free-form curved lens.
优选的,所述的自由曲面透镜各区域的折射率相同;自由曲面透镜周围介质为空气。Preferably, the refractive index of each area of the free-form surface lens is the same; the surrounding medium of the free-form surface lens is air.
优选的,所述的自由曲面透镜是光源之后的整形透镜,即二次透镜。Preferably, the free-form surface lens is a shaping lens after the light source, that is, a secondary lens.
本发明与现有技术相比具有的有益效果是:Compared with the prior art, the present invention has the following beneficial effects:
1)本发明提出的用于倾斜面均匀照明的自由曲面透镜阵列装置可在倾斜的照明面上实现预定的均匀光分布;1) The free-form surface lens array device for uniform illumination of inclined surfaces proposed by the present invention can achieve predetermined uniform light distribution on the inclined illumination surfaces;
2)本发明提出的用于倾斜面均匀照明的自由曲面透镜阵列装置可实现对LED出射光束的有效调控,获得较高的能量利用率;2) The free-form surface lens array device for the uniform illumination of the inclined surface proposed by the present invention can realize the effective regulation of the LED outgoing beam and obtain a higher energy utilization rate;
3)本发明提出的用于倾斜面均匀照明的自由曲面透镜阵列装置可促进自由曲面在半导体照明中的应用;3) The free-form surface lens array device for uniform illumination of inclined surfaces proposed by the present invention can promote the application of free-form surfaces in semiconductor lighting;
4)本发明提出的用于倾斜面均匀照明的自由曲面透镜阵列装置有助于形成高效节能的半导体照明技术。4) The free-form surface lens array device for uniform illumination of inclined surfaces proposed by the present invention is helpful to form a high-efficiency and energy-saving semiconductor lighting technology.
附图说明Description of drawings
图1为用于倾斜面均匀照明的自由曲面透镜阵列装置的结构示意图;1 is a schematic structural diagram of a free-form surface lens array device for uniform illumination of inclined surfaces;
图2为自由曲面透镜单元的设计原理图;Fig. 2 is the design principle diagram of the free-form surface lens unit;
图3为自由曲面透镜单元的光学结构;Fig. 3 is the optical structure of free-form surface lens unit;
图4为作为LED光束整形二次透镜的自由曲面透镜单元;4 is a free-form surface lens unit as a secondary lens for LED beam shaping;
图5为实施例中的自由曲面透镜单元的模型;Fig. 5 is the model of the free-form surface lens unit in the embodiment;
图6为实施例中自由曲面透镜单元在倾斜照明面上的照明光斑;Fig. 6 is the illumination spot of the free-form surface lens unit on the inclined illumination surface in the embodiment;
图7为实施例中自由曲面透镜阵列装置的模型;7 is a model of a free-form surface lens array device in an embodiment;
图8为实施例中自由曲面透镜阵列装置在倾斜照明面上的照明光斑。FIG. 8 is an illumination light spot on an oblique illumination surface of the free-form surface lens array device in the embodiment.
具体实施方式Detailed ways
为使本发明的目的、技术方案及优点更加清楚,下面将结合附图进一步说明本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings.
用于倾斜面均匀照明的LED自由曲面透镜阵列装置包含由按行和列均匀排布的自由曲面透镜单元U所构成的LED自由曲面透镜阵列,参见附图1;每个自由曲面透镜单元形状相同,且每颗LED光源单元(V)也相同,自由曲面透镜单元(U)和LED光源单元(V)的数量相同,且一一对应;LED光源的出光经相应的自由曲面透镜单元偏折后在倾斜照明面上产生预定的均匀光分布;自由曲面透镜单元的具体设计步骤如下:The LED free-form surface lens array device for uniform illumination of inclined surfaces includes an LED free-form surface lens array composed of free-form surface lens units U uniformly arranged in rows and columns, see Figure 1; each free-form surface lens unit has the same shape , and each LED light source unit (V) is also the same, the number of free-form surface lens units (U) and LED light source units (V) are the same, and correspond one-to-one; the light emitted by the LED light source is deflected by the corresponding free-form surface lens unit. A predetermined uniform light distribution is generated on the inclined illumination surface; the specific design steps of the free-form surface lens unit are as follows:
(1)设置自由曲面透镜的光路结构,所述自由曲面透镜的入射面采用球面,出射面为自由曲面,光源位于入射面的球心处;光源经自由曲面透镜折射后在倾斜照明面得到目标照度分布;根据初始设计参数对其进行自由曲面设计;(1) Setting the optical path structure of the free-form surface lens, the incident surface of the free-form surface lens adopts a spherical surface, the exit surface is a free-form surface, and the light source is located at the spherical center of the incident surface; the light source is refracted by the free-form surface lens and obtains the target on the inclined illumination surface Illuminance distribution; free-form surface design according to initial design parameters;
(2)以光源S为坐标原点建立全局直角坐标系xyz,对步骤(1)所确定的自由曲面透镜的自由曲面上点P的位置用球坐标表示为以倾斜照明面和z轴的交点B3为坐标原点,在倾斜照明面上建立局部坐标系x1y1z1,并使全局坐标系xyz的x轴和局部坐标系x1y1z1的x1轴方向相同;局部坐标系x1y1z1的z1轴和全局坐标系xyz的z轴的夹角为β;当从全局坐标系xyz的z轴到局部坐标系x1y1z1的z1轴为逆时针方向旋转时,β<0;当从全局坐标系xyz的z轴到局部坐标系x1y1z1的z1轴为顺时针方向旋转时,β>0。出射光线在倾斜照明面上的落点T在全局坐标系xyz下的坐标表示为(tx,ty,tz),在局部坐标系x1y1z1下的坐标表示为(tx1,ty1,tz1)。矢量P为点P的位置矢量,是一个由全局坐标系的原点指向点P的矢量;矢量T为点T的位置矢量,是一个由全局坐标系的原点指向点T的矢量;参见附图2,根据折射定律O=n×I+P1×N,求得出射光线的单位方向向量O=(Ox,Oy,Oz),并建立点P和目标点T之间的坐标关系(2) The global rectangular coordinate system xyz is established with the light source S as the coordinate origin, and the position of the point P on the free-form surface of the free-form surface lens determined in step (1) is expressed in spherical coordinates as Taking the intersection point B 3 of the oblique illumination surface and the z-axis as the coordinate origin, establish a local coordinate system x 1 y 1 z 1 on the oblique illumination surface, and make the x axis of the global coordinate system xyz and the local coordinate system x 1 y 1 z 1 The direction of the x 1 axis is the same; the angle between the z 1 axis of the local coordinate system x 1 y 1 z 1 and the z axis of the global coordinate system xyz is β; when from the z axis of the global coordinate system xyz to the local coordinate system x 1 y When the z 1 axis of 1 z 1 rotates counterclockwise, β<0; when the z 1 axis from the z axis of the global coordinate system xyz to the z 1 axis of the local coordinate system x 1 y 1 z 1 rotates clockwise, β> 0. The coordinates of the landing point T of the outgoing light on the oblique illumination surface in the global coordinate system xyz are expressed as (t x , t y , t z ), and the coordinates under the local coordinate system x 1 y 1 z 1 are expressed as (t x1 ,t y1 ,t z1 ). The vector P is the position vector of the point P, which is a vector pointing to the point P from the origin of the global coordinate system; the vector T is the position vector of the point T, which is a vector pointing to the point T from the origin of the global coordinate system; see Figure 2 , according to the law of refraction O=n×I+P 1 ×N, obtain the unit direction vector O=(O x , O y , O z ) of the emitted light, and establish the coordinate relationship between the point P and the target point T
其中,Px、Py和Pz为点P位置矢量P的三个分量;Ox、Oy和Oz为点P处出射光线单位方向向量O的三个分量;N为自由曲面在点P处的单位法式,角度α是矢量I和矢量N的夹角;n为自由曲面透镜所用材料的折射率,自由曲面透镜周围介质为空气;Among them, P x , P y and P z are the three components of the position vector P of the point P; O x , O y and O z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point Unit French at P, The angle α is the angle between the vector I and the vector N; n is the refractive index of the material used for the free-form lens, and the medium around the free-form lens is air;
(3)根据步骤(2)得到的点P和目标点T之间的坐标关系还需满足倾斜照明面在全局坐标系下的方程,有以下关系(3) The coordinate relationship between the point P and the target point T obtained according to step (2) also needs to satisfy the equation of the inclined illumination surface in the global coordinate system, and the following relationship
Atx+Ctz+D=0At x +Ct z +D=0
其中,A=sinβ、C=cosβ以及D=-C×L,L为倾斜照明面与全局坐标系xyz的z轴交点B3的z坐标;根据该关系进一步得到目标点T的全局坐标Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; further obtain the global coordinate of the target point T according to this relationship
(4)根据步骤(3)得到点P的全局坐标(tx,ty,tz),并由点P的全局坐标和局部坐标之间的变换关系得到点P的局部坐标(tx1,ty1,tz1),有以下关系式(4) According to step (3), the global coordinates (t x , t y , t z ) of the point P are obtained, and the local coordinates (t x1 , t z ) of the point P are obtained from the transformation relationship between the global coordinates and the local coordinates of the point P t y1 ,t z1 ), there is the following relation
(5)根据局部能量守恒定律,在不考虑能量损失的情况下,要求由光源出射的任意一条细光束经自由曲面透镜偏折后其所有能量被传输至倾斜照明面上的目标照明区域,即自由曲面透镜对细光束的偏折满足以下能量关系式(5) According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, The deflection of the beamlet by the free-form surface lens satisfies the following energy relation
其中,为光源的强度分布,E(tx1,ty1)为倾斜照明面上目标照明区域的照度分布,J(T)为位置矢量T的Jacobi矩阵,0≤θ≤2π,其中为入射到自由曲面透镜单元的光束的最大发散角;in, is the intensity distribution of the light source, E(t x1 , t y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens unit;
(6)自由曲面在满足步骤(5)中的能量传输方程的同时还要保证光束的边界光线经自由曲面偏折后入射到目标面照明区域的边界,即满足以下边界条件(6) While the free-form surface satisfies the energy transfer equation in step (5), it must also ensure that the boundary rays of the light beam are deflected by the free-form surface and enter the boundary of the illumination area of the target surface, that is, the following boundary conditions are satisfied
其中,Ω1表示入射到自由曲面透镜上的光束的总立体角,Ω2表示倾斜照明面上目标照明区域,和分别为区域Ω1和Ω2的边界;Among them, Ω 1 represents the total solid angle of the light beam incident on the free-form surface lens, Ω 2 represents the target illumination area on the oblique illumination surface, and are the boundaries of regions Ω 1 and Ω 2 , respectively;
(7)对步骤(5)中的能量传输方程和步骤(6)中的边界条件联立求解,得到一组离散数据点,通过对该组数据点进行曲面拟合即可得到自由曲面单元。(7) Simultaneously solve the energy transfer equation in step (5) and the boundary conditions in step (6) to obtain a set of discrete data points, and a free-form surface element can be obtained by performing surface fitting on the set of data points.
所述的自由曲面透镜单元的入射面S1为球面,出射面S2为自由曲面,参见附图3。所述的自由曲面透镜单元是LED光源之后的整形透镜,即LED二次透镜,参见附图4。The incident surface S1 of the free-form curved lens unit is a spherical surface, and the exit surface S2 is a free-form curved surface, see FIG. 3 . The free-form surface lens unit is a shaping lens after the LED light source, that is, the LED secondary lens, see FIG. 4 .
实施例:自由曲面透镜单元拟采用如附图3所示的结构类型,入射面S1采用球面,出射面S2为自由曲面,LED光源位于入射面S1的球心处,并假定该LED光源的强度分布满足要求光源的出射光束经该自由曲面透镜偏折后在倾斜照明面的目标照明区域产生一个均匀的矩形照明光斑。入射面球面S1的顶点的z坐标为12mm,出射面自由曲面S2的顶点的z坐标为25mm,倾斜照明面和全局坐标系xyz的z轴的交点B3的z坐标为3000mm,倾斜照明面的倾斜角度β=34°;矩形照明光斑的长为4000mm,宽为5000mm,自由曲面透镜的折射率为n=1.4935,透镜周围介质为空气,入射到自由曲面透镜上的光源最大出射角度为 Example: The free-form surface lens unit intends to adopt the structure type shown in Figure 3, the incident surface S1 adopts a spherical surface, the exit surface S2 is a free-form surface, the LED light source is located at the center of the sphere of the incident surface S1, and it is assumed that the intensity of the LED light source distribution satisfies It is required that the outgoing beam of the light source is deflected by the free-form surface lens to generate a uniform rectangular illumination spot in the target illumination area of the inclined illumination surface. The z-coordinate of the vertex of the spherical surface S1 of the incident surface is 12mm, the z-coordinate of the vertex of the free-form surface S2 of the output surface is 25mm, the z-coordinate of the intersection point B3 of the oblique illumination surface and the z-axis of the global coordinate system xyz is 3000mm, and the z-coordinate of the oblique illumination surface is 3000mm. The angle of inclination is β=34°; the length of the rectangular illumination spot is 4000mm, the width is 5000mm, the refractive index of the free-form surface lens is n=1.4935, the medium around the lens is air, and the maximum outgoing angle of the light source incident on the free-form surface lens is
根据折射定律O=n×I+P1×N,求得出射光线的单位方向向量O=(Ox,Oy,Oz),并建立点P和目标点T之间的坐标关系According to the law of refraction O=n×I+P 1 ×N, the unit direction vector O=(O x , O y , O z ) of the emitted light is obtained, and the coordinate relationship between the point P and the target point T is established
其中,Px、Py和Pz为点P位置矢量P的三个分量;Ox、Oy和Oz为点P处出射光线单位方向向量O的三个分量;N为自由曲面在点P处的单位法式,角度α是矢量I和矢量N的夹角。点P和目标点T之间的坐标关系还需满足倾斜照明面在全局坐标系下的方程,有以下关系Among them, P x , P y and P z are the three components of the position vector P of the point P; O x , O y and O z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point Unit French at P, The angle α is the angle between the vector I and the vector N. The coordinate relationship between the point P and the target point T also needs to satisfy the equation of the inclined illumination surface in the global coordinate system, which has the following relationship
Atx+Ctz+D=0At x +Ct z +D=0
其中,A=sinβ、C=cosβ以及D=-C×L,L为倾斜照明面与全局坐标系xyz的z轴交点B3的z坐标;根据该关系进一步得到目标点T的全局坐标Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; further obtain the global coordinate of the target point T according to this relationship
由点P的全局坐标(tx,ty,tz),并由点P的全局坐标和局部坐标之间的变换关系得到点P的局部坐标(tx1,ty1,tz1),有以下关系式From the global coordinates (t x , ty , t z ) of the point P, and the transformation relationship between the global coordinates and the local coordinates of the point P, the local coordinates (t x1 , t y1 , t z1 ) of the point P are obtained, there are The following relation
根据局部能量守恒定律,在不考虑能量损失的情况下,要求由光源出射的任意一条细光束经自由曲面透镜偏折后其所有能量被传输至倾斜照明面上的目标照明区域,即自由曲面透镜对细光束的偏折满足以下能量关系式According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, the free-form surface lens. The deflection of the beamlet satisfies the following energy relation
其中,为光源的强度分布,E(tx1,ty1)为倾斜照明面上目标照明区域的照度分布,J(T)为位置矢量T的Jacobi矩阵,0≤θ≤2π,其中为入射到自由曲面透镜的光束的最大发散角。进一步化简该能量传输方程,可得到以下椭圆型Monge-Ampère方程in, is the intensity distribution of the light source, E(t x1 , t y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens. Further simplifying the energy transfer equation, the following elliptical Monge-Ampère equation can be obtained
其中,ρθθ、和分别是ρ关于角度θ和的二阶偏导数和混合偏导数,系数为保证倾斜照明面上目标照明区域的形状,还需施加一定的边界条件Among them, ρ θθ , and are ρ with respect to the angle θ and The second partial and mixed partial derivatives of , the coefficients In order to ensure the shape of the target illumination area on the oblique illumination surface, certain boundary conditions need to be applied.
其中和分别为区域和的边界。in and area respectively and border.
对于这样一个高度非线性的偏微分方程,只能求得其数值解。首先需要将入射到自由曲面透镜上的光束所在的区域Ω1离散化,得到一组离散的网格点,并且在每个网格节点对应一个偏微分方程;之后,采用差分替代偏微分方程中的一阶偏导数和二阶偏导数,则可将能量传输方程和边界条件转换成一个非线性方程组;最后,采用牛顿法求解该非线性方程组即可得到一组离散数据点。在CAD软件中对该组离散数据点进行曲面拟合即可得到自由曲面,从而可构建出该自由曲面透镜模型,见附图5。对自由曲面透镜模型追迹光线,在倾斜目标照明面上得到照度分布图,见附图6。随后,将自由曲面透镜单元沿全局坐标系xyz的x轴和y轴排布成一个3×3的自由曲面透镜阵列,自由曲面透镜单元在x轴和y轴方向上的阵列间距均为50mm,见附图7。对自由曲面透镜阵列模型追迹光线,在倾斜目标照明面上得到照度分布图,见附图8。该照度分布图清楚地表明,本发明所提出的用于倾斜面均匀照明的自由曲面透镜阵列有效地实现了预定的目标照明。For such a highly nonlinear partial differential equation, only its numerical solution can be obtained. First, it is necessary to discretize the region Ω 1 where the light beam incident on the free-form surface lens is located to obtain a set of discrete grid points, and each grid node corresponds to a partial differential equation; then, the difference is used to replace the partial differential equation in The energy transfer equation and boundary conditions can be converted into a nonlinear equation system; finally, a set of discrete data points can be obtained by solving the nonlinear equation system using Newton's method. A free-form surface can be obtained by performing surface fitting on the set of discrete data points in CAD software, so that the free-form surface lens model can be constructed, as shown in FIG. 5 . Trace the light rays on the free-form surface lens model, and obtain the illuminance distribution diagram on the inclined target illumination surface, as shown in Figure 6. Subsequently, the free-form surface lens units are arranged along the x-axis and y-axis of the global coordinate system xyz into a 3×3 free-form surface lens array, and the array spacing of the free-form surface lens units in the x-axis and y-axis directions is both 50mm. See Figure 7. Trace the light rays on the free-form surface lens array model, and obtain the illuminance distribution diagram on the inclined target illumination surface, as shown in Figure 8. The illuminance distribution diagram clearly shows that the free-form surface lens array proposed by the present invention for uniform illumination of inclined surfaces effectively achieves the predetermined target illumination.
由实施例可知,采用本发明所提出的用于倾斜面均匀照明的自由曲面透镜阵列可在倾斜照明面上实现预定的光分布,可获得连续的自由曲面,实现了自由曲面的可加工,具有显著的实际意义。It can be seen from the examples that the use of the free-form surface lens array for uniform illumination of the inclined surface proposed by the present invention can realize a predetermined light distribution on the inclined illumination surface, obtain a continuous free-form surface, realize the machinability of the free-form surface, and have the advantages of significant practical significance.
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