CN103196066B - Led narrow beam illumination optical system and design method - Google Patents

Led narrow beam illumination optical system and design method Download PDF

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CN103196066B
CN103196066B CN201310140657.3A CN201310140657A CN103196066B CN 103196066 B CN103196066 B CN 103196066B CN 201310140657 A CN201310140657 A CN 201310140657A CN 103196066 B CN103196066 B CN 103196066B
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light
lens
point
angle
curve
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CN103196066A (en
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张尚超
张顺清
袁卫星
扬东建
梅杰
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深圳市实益达科技股份有限公司
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Abstract

本发明公开一种窄光束LED照明光学系统及其设计方法,以自由曲面透镜和自由曲面反射杯对COB型LED光源发出的光进行区域化互补控制;自由曲面透镜控制COB型LED光源发出的小角度的光,自由曲面反射杯控制COB型LED光源发出的大角度的光。 Disclosed is a narrow beam LED illumination optical system and a design method, a free-form surface lens and the free surface of the reflective cup regionate complementary control COB type light emitted from the LED light source; free curved surface lens control small COB type LED light emitted light beam angle, the free surface of the reflective cup COB type LED control light emitted at large angles. 本发明结合透镜和反射杯的各自优点,克服了单纯用反射杯或者透镜无法利用所有光线的缺点。 The present invention combines the advantages of each lens and the reflective cup, overcome the shortcomings of the reflective cup with a simple lens or not the use of the light. 并运用菲涅尔透镜将小角度光线汇聚,使光学系统达到轻、薄和小的效果,减小透镜中心厚度,提高光效率;同时,将阶梯状微结构透镜运用于透镜内侧面,实现同一套光学系统适用于不同尺寸大小的COB型光源。 Using the Fresnel lens and the light converging angle small, the optical system to reach the light, thin and small effects to reduce the lens center thickness, improving the light efficiency; Meanwhile, the stepped lenticular lens used in the side surface, to achieve the same the optical system is adapted to set COB type light sources of different sizes.

Description

窄光束LED照明光学系统及其设计方法 Narrow beam LED illumination optical system and design method

技术领域 FIELD

[0001] 本发明涉及LED照明光学系统,尤其涉及一种用于多芯片集成式高功率LED (C0B 型LED)的二次光学系统,以及实现小角度窄光出射效果的一种设计方法,属于非成像光学 [0001] The present invention relates to a LED illumination system, and particularly to the secondary optical system for a multi-chip integrated high-power LED (LED C0B type), and to realize a small narrow angle light emission effect of a design method, belongs non-imaging optics

技术领域。 Technology.

背景技术 Background technique

[0002] LED光源本身是一个近似的朗伯光源,难以满足各种照明用途的需求,因此必须根据不同的应用场合,针对LED光源设计不同的光学系统,对LED光源发出的光进行整形,进行光能量的二次分布。 [0002] LED light source itself is an approximate Lambertian source, it is difficult to meet the needs of lighting applications, it is necessary depending on the application, an LED light source for different design of the optical system, light emitted from the LED light source is shaped, were secondary distribution of light energy.

[0003] 随着电路板上直接芯片封装(C0B)技术的发展,其高功率密度、色度均匀及体积小等特点,使C0B型LED光源越来越多的应用到商业照明中。 [0003] With the circuit board direct chip package (C0B) technology development, its high power density, uniform color and small volume, more and more LED light sources applied to C0B commercial type lighting. C0B型LED光源面积较单颗LED 光源大很多,将数十颗LED芯片集成封装时,光源面积能达到到25mm*25mm,该光源的优势在于大大降低了LED光源的数量,减小了灯具面积,降低灯具成本,较低的色容差使应用灯具具有较好的颜色一致性。 C0B type LED light source than the area of ​​a single LED light source much larger when dozens LED chip integrated package, the light source can reach the area of ​​25mm * 25mm, the advantage that the light source is greatly reduced number of LED light sources, reducing the area of ​​the lamp , reduce lighting costs, lower color tolerance errand lighting applications having good color consistency.

[0004] 然而,面向C0B型光源的二次光学设计却较为困难。 [0004] However, the secondary light source optical design for C0B but difficult. 目前大多数专利的设计方法均基于近似点光源的设计,而C0B型LED属于扩展光源,点光源设计方法不再适用于C0B型LED。 Most methods are based on the patented design similar design point light source, and C0B belonging to an expanded type LED light source, a point light source method is no longer applicable to the design type LED C0B.

[0005] 目前采用的光学系统多为反射杯,但其控制光线的能力有限,对于小角度的光线无法进行很好的控制,想要达到小角度精确照明的配光效果,往往需要较大的体积,且容易产生杂散光,使得接收面功能区域的相对光利用率较低。 [0005] It is an optical system using a multi-reflective cup, but is limited in its ability to control light, the light for a small angle can not be well controlled, to achieve the desired small angle light distribution accurate illumination effects, often require larger volume, and easy generation of stray light, such that light utilization efficiency is relatively low functional area receiving surface.

[0006] 面向单颗LED的小型TIR (total internal reflection)透镜可以较好的完成窄光束配光要求,但当其应用于C0B型LED光源时,出光效果会产生严重畸变。 [0006] For small single LED TIR (total internal reflection) lens may be better to complete the optical requirements of narrow beam, but it applies to C0B type LED light source, the light effect will produce serious distortion. 而普通透镜通常只能对LED光源发出的与其光轴成一定角度以内的光线调整方向,无法控制大角度的光线,也存在接收面功能区域的相对光利用率较低的问题。 Usually only an ordinary lens and the LED light source to its optical axis to adjust the direction of light within a certain angle, the light can not control large angle, there is a relatively low light receiving surface functional area utilization problems.

[0007] 因此,如何解决C0B型LED光源配光难的问题,实现窄光束精确照明的功能及其设计方法,是LED照明技术领域,尤其是用于商业照明领域亟待解决的问题。 [0007] Therefore, how to solve the problem with C0B type LED light source is difficult to achieve the design functionality and precise method of narrow-beam illumination, the LED lighting technology, especially for commercial lighting problem to be solved.

发明内容 SUMMARY

[0008] 本发明的目的在于提供一种针对C0B型LED光源的光能量进行合理分配的窄光束LED照明光学系统及其设计方法。 [0008] The object of the present invention is to provide a rational allocation for type LED light energy C0B narrow beam LED light source of the illumination optical system and its design method.

[0009] 本发明要解决的技术问题在于,针对如何提高LED灯具的光能利用率,提供一种以C0B型LED为光源的配光系统,实现小角度的重点照明,并且实现照明区域较高的光度均匀性和色度均匀性的效果。 [0009] The present invention is to solve the technical problem how to improve the energy efficiency of the LED lamp, the light distribution system to provide C0B type LED light source, to achieve a small angle of accent lighting, the illumination area and achieve a higher uniformity and color uniformity of an effect luminosity. 主要解决原有传统反射器式或透镜式光学系统的缺陷与不足。 Mainly to solve the defects and deficiencies existing traditional-type reflector or a lens optical system. [0010] 本发明的技术方案如下: [0010] aspect of the present invention is as follows:

[0011] 一种窄光束LED照明光学系统,包括C0B型LED光源、自由曲面透镜以及自由曲面反射杯;所述自由曲面透镜和自由曲面反射杯对C0B型LED光源发出的光进行区域化控制;其中,自由曲面透镜控制COB型LED光源发出的小角度的光,自由曲面反射杯控制COB 型LED光源发出的大角度的光。 [0011] A narrow beam LED illumination optical system including an LED light source C0B type free-form surface lens and a free-form surface reflector cup; light from the free curved surface lens and the free surface of the reflective cup C0B type LED light source is controlled regionalization; wherein the free curved surface lens control COB type small-angle LED light emitted by a light, free-form surface reflector cup large angle light control type LED COB light emitted.

[0012] 其中一种结构为:所述自由曲面透镜设置在自由曲面反射杯的内部杯底并与自由曲面反射杯相连,所述C0B型LED光源设置在自由曲面反射杯的内部杯底与自由曲面透镜的内腔所围成的空间之内。 [0012] One of the structure: the free-form surface lens is disposed in the interior of the cup base and the free surface of the reflective cup is connected with the free surface of the reflective cup, the inside bottom of the cup with the free C0B type LED light source provided at the free surface of the reflective cup lumen within the curved lens of the space surrounded.

[0013] 所述C0B型LED光源发出的0度至α度的光线透过自由曲面透镜顶部,均匀分布在β度以内;所述C0B型LED光源发出的α度到90度的光线透过自由曲面透镜侧壁,经过自由曲面反射杯内表面反射,分布在照明区域内。 [0013] [alpha] of 0 degrees to light the LED light source type C0B through the top of the free-form surface lens, uniformly distributed within β degrees; [alpha] of the C0B type LED light source 90 to light through free curved lens sidewall, through the free surface of the reflective surface of the reflective cup, the distribution within the illumination area.

[0014] 所述自由曲面透镜包括透镜顶部、透镜侧壁和透镜底部;所述透镜顶部由内表面和外表面组成;所述透镜顶部外表面是上凸或下凹的自由曲面。 [0014] The free-form surface lens includes a lens top, side walls and a bottom lens of the lens; the top of the lens by the inner surface and an outer surface composition; free-form surface lens of said top outer surface is convex or concave. 所述透镜顶部外表面制成菲涅尔透镜。 The top surface of the outer lens made of a Fresnel lens.

[0015] 所述自由曲面反射杯的内表面为镀层处理。 Inner surface of the [0015] surface of the reflective cup consisting of plating. 所述自由曲面反射杯的内表面为鳞甲结构,所述鳞甲高度不高于0. 05mm。 The inner surface of the free-form surface of the reflective cup structure scales, the scales height of not more than 0. 05mm.

[0016] 本发明还提供一种权利要求1所述的窄光束LED照明光学系统的设计方法,以光源所在平面为X轴,中垂线为y轴建立坐标系,以光源中心为原点,设扩展光源半径为R,生成透镜自由曲面以及反射杯自由曲面; [0016] The present invention also provides a design method of claim 1, said narrow beam LED illumination optical system, the light source plane where the X axis, the coordinate system is established perpendicular to the y-axis, the center of the light source as an origin, provided extended source of radius R, generate free-form surface lens and the free surface of the reflective cup;

[0017] 生成透镜自由曲面的步骤如下: [0017] The step of generating free-form surface lens as follows:

[0018] 1)设Η为LED光源左边缘札的光线与y轴的交点,坐标为(0, H); [0018] 1) provided Η ray intersection with the y axis is the left edge of the LED light source sheaf, coordinates (0, H);

[0019] 2)根据光源尺寸D (D=2R),取第一次折射光线上的点\作为透镜外表面曲线的起始点,并使X〇点处的法线]^坚直向上; [0019] 2) The source size D (D = 2R), taking the first point on the refracted light \ as a starting point of the curve of the outer surface of the lens, and the normal at the point X〇] ^ Kennedy straight on;

[0020] 3 )根据光学扩展量守恒式β [0020] 3) According to etendue conservation of formula β

[0021] 2//xy)= J Ιάβ -β [0021] 2 // xy) = J Ιάβ -β

[0022] 求出投射宽度L ;其中,D为光源直径,β为出射光线与y轴夹角,η为光学材料的折射率; [0022] obtaining a projection width L; where, D is the diameter of the light source, β is the angle between the outgoing light and the axis y, η is the refractive index of the optical material;

[0023] 4)直线a为札出射光线,取与其距离L的直线b作为光源边缘艮的出射光线,在直线b上取点YQ ; [0023] 4) A is a straight sheaf emitted light, therewith taking a straight line distance L b as a light source edge of the light exit Gen taken YQ point on the straight line b;

[0024] 5 )根据折射定律矢量形式 [0024] 5) The vector form of the law of refraction

[0025] ULBU UU L麗I LIULK UU [0025] ULBU UU L Korea I LIULK UU

[1 + «2 - 2ni0m hi)]'2 N = OuI - nln [1 + 2 «- 2ni0m hi)] '2 N = OuI - nln

[0026] 求出l点得法线方向}^ ;其中&和$分别为出射和入射光线单位矢量,$为界面法线单位矢量; LH.-U.SIS LUJ. [0026] Fa line direction points obtained l ^}; and wherein & $, respectively, and the incident light emission unit vector $ is the unit vector normal to the interface; LH.-U.SIS LUJ.

[0027] 6)根据I的坐标以及它们的法线方向和&,插值一条连续曲线,使之通LltLUI. LIUU 过X〇和Y〇,同时在这两点满足法线方向和」;由此可以拟定一条连续曲线ΧΛ)作为计算起始曲线; [0027] 6) The coordinates I and their normal direction and &, interpolating a continuous curve, making it pass through X〇 LltLUI LIUU Y〇 and, at the same time satisfy these two points and the normal direction ";. Thus can develop a continuous curve ΧΛ) is calculated as the initial curve;

[0028] 7)将初始曲线划分η小段,得到曲线上的n+1点,分别为X。 [0028] 7) The initial curve into η, yielding an n + 1 point on the curve, respectively X. 〜Xn,对应未知曲线的点Y〇〜Y n ; ~Xn, n corresponding point Y〇~Y unknown curve;

[0029] 8)取\较近一点\,出射光线为直线c,把距直线c为L的直线d作为艮经透镜折射后的另一条光线;计算出直线d与I点得切线的交点t,根据折射定律矢量形式计算出t点得法线方向;同样根据的坐标以及它们的法线方向,插值三次曲线; [0029] 8) Take \ near point \, emergent ray is a straight line c, the pitch line c to the L linearly d as another light Burgundy by a lens refracted; calculating an intersection point t a straight line d and the point I have tangent , is calculated according to the law of refraction vector form Fa t-point line direction; the same according to the coordinates of a normal direction thereof, the cubic curve interpolation;

[0030] 9)取&较近一点X2,依次类推计算,使用同步多曲面法计算剩下的点,直到α的范围在40°〜45°为止,最终得到透镜截面曲线; [0030] 9) & taken near point X2, and so on is calculated, using the calculated remaining points simultaneous multi-surface method, until α is in the range of 40 ° ~45 ° until the final lens obtained profile curve;

[0031] 生成反射杯自由曲面的步骤如下: [0031] The step of generating free-form surface reflector cups as follows:

[0032] 1)确定初始线段Α&,从与y轴夹角最大光线开始考虑,这一簇光线对应屏幕上的起始点为^,初始入射光线经过反射到达Γι ;根据边缘光线理论,&发出的某一条光线入射到初始曲线端点&也会被反射到Γι,则曲线段ΑΑ是以艮和Γι为两个焦点椭圆的部分曲线;角θ ρ角Θ i分别为出射光线Anrn、Bnrn与光轴y的夹角; [0032] 1) determining an initial [alpha] & segment, starting from the maximum angle between the light axis y considered, which corresponds to the starting point of a cluster of light on the screen is ^, after the initial incident light reaches the reflective Γι; The theory of the marginal ray, emitted & a light is incident to an initial curve will be reflected to the terminal & Γι, the curve segment is ΑΑ Gen Γι and two curved portions of focus of the ellipse; angle θ ρ angle Θ i respectively emitted light Anrn, Bnrn optical axis angle y;

[0033] 2)设光源亮度为B,而发出与y轴夹角较小而直接照射在屏幕上而产生的照度可由 [0033] 2) set the light source luminance is B, the y-axis angle and emits less directly irradiated on the screen illuminance can be generated

[0034] 厂{/) = j" /)* · COS 沒.ί.消="Ω 得至IJ。 [0034] Plant {/) = j "/) * · COS no .ί. Cancellation =" Ω have to IJ.

[0035] 角的大小由Γι的照度决定;出射光线ΑιΓι与y轴的夹角吣由Ai的坐标确定,^接受到的照度可由光源直接照射的能量减去反射器反射的能量得到,即 [0035] The size of the angle is determined by the illuminance Γι; Qin emitted light ΑιΓι included angle with the y axis is determined by the coordinates of Ai, ^ illuminance received by the energy source is directly irradiated by subtracting the energy reflected by the reflector is obtained, i.e.,

[0036] Er=E_B Ω =B (sin Θ r-sin Θ 丄) [0036] Er = E_B Ω = B (sin Θ r-sin Θ Shang)

[0037] 得到出射光线ΒΛ与y轴的夹角Θ i并得到Bl点的坐标,初始曲线AA方程即可确定; [0037] emergent ray ΒΛ obtained with the y axis and with an angle Θ i of the coordinates of the point Bl, to determine initial curve equation AA;

[0038] 3)从札点发出与y轴夹角稍小的光线,入射到曲线AA上的A2点,从曲线方程上可求出A2的坐标以及其法向量%,由反射定律可得到其反射光线,设反射光线入射到屏幕上的点为r2,出射光线A2r2与y轴的夹角t可确定;由光通量守恒得到出射光线B 2r2与y轴的夹角Θ i,即确定r2光线接收锥的另外一个边界的光线,其与氏点的切线交于B2,作为新的曲线点; [0038] 3) issue point A2 smaller angle with the y axis of the light incident on the AA from Sapporo curve point, the curve equation can be obtained from the coordinates of the normal vector thereof and A2%, which can be obtained by the law of reflection reflected light, provided the reflected light is incident to a point on the screen is r2, the outgoing light A2r2 with the y axis angle t can be determined; by the flux conservation to obtain an exit beam B 2r2 included angle Θ i y-axis, i.e., to determine r2 light receiving another boundary of the light cone, which is tangent to the cross's point B2, a new curve points;

[0039] 4)光源从边缘艮发出的光线RA经反射的反射光线为B2r2,根据反射定律,B 2的坐标和法向量也可确定;反射器Ap2的轮廓可以确定,再考虑由&点发出的与y轴夹角更小的光线,重复以上步骤,轮廓线将不断扩展,直至达到所要求的边界为止。 [0039] 4) emitted from the light source edge RA Burgundy reflected light is reflected B2r2, according to the law of reflection, normal vector coordinates and B 2 can also be determined; Ap2 reflector profile can be determined, and then consider & emitted from point the y-axis angle less light, repeating the above steps, the contour line will continue to expand until it reaches the required boundaries.

[0040] 本发明的有益技术效果是: [0040] Advantageous effects of the invention are:

[0041] 本发明结合透镜和反射杯的各自优点,克服了单纯用反射杯或者透镜无法利用所有光线的缺点。 Invention combines the respective advantages of the lens and the reflective cup [0041] present, overcomes the drawbacks with a simple lens or reflective cup can not use all the light. 运用菲涅尔透镜将小角度光线汇聚,使光学系统达到轻、薄和小的效果,减小透镜中心厚度,提高光效率。 Using the small angle Fresnel lenses converging the light, the optical system to reach the light, thin and small effects to reduce the lens center thickness, improve the light efficiency. 阶梯状微结构透镜运用于透镜内侧面,实现同一套光学系统适用于不同尺寸大小的C0B型光源。 Stepped lenticular lens used in the side surface, to realize C0B light source for different sizes of the same set of optics.

[0042] 本发明附加的优点将在下面具体实施方式部分的描述中给出,部分将从下面的描述中变得明显,或通过本发明的实践了解到。 Additional advantages of the invention [0042] The present description will be given in the Detailed Description below, from the following description in part be apparent from, or learned by practice of the present invention.

附图说明 BRIEF DESCRIPTION

[0043] 图1是本发明光学系统的结构示意图。 [0043] FIG. 1 is a schematic view of the optical system of the present invention.

[0044] 图2是透镜自由曲面的生成过程图。 [0044] FIG 2 is a free-form surface lens generation process of FIG.

[0045] 图3是反射杯自由曲面的生成过程图。 [0045] FIG. 3 is a process of generating free-form surface reflector cup of FIG.

具体实施方式 Detailed ways

[0046] 下面结合附图对本发明的具体实施方式做进一步说明。 [0046] The following drawings further illustrate specific embodiments of the present invention binds.

[0047] 如图1所示,本发明的光学系统由C0B型LED光源1、自由曲面透镜2、自由曲面反射杯3三部分构成。 [0047] As shown in FIG. 1, the optical system of the present invention is a free-form surface lens 2, the free surface of the reflective cup 3 is made of three parts C0B type LED light source. 自由曲面透镜2和自由曲面反射杯3对C0B型LED光源1发出的光进行区域化控制。 Free-form surface lens and a free-form surface reflector cup 2 C0B light type LED light emitted by the three pairs of a regional control.

[0048] 在图1所示的实施例中,自由曲面透镜2设置在自由曲面反射杯3的内部杯底并与自由曲面反射杯3相连。 [0048] In the embodiment illustrated in Figure 1, the free-form surface lens 2 arranged at the free surface of the reflective cup inside the cup bottom 3 and connected to the free surface of the reflective cup 3. C0B型LED光源1设置在自由曲面反射杯3的内部杯底与自由曲面透镜2的内腔所围成的空间之内。 C0B type LED light source 1 is disposed within the inner lumen of the free surface of the reflective cup and the cup bottom 3 of the free-form surface lens 2 surrounded by the space within.

[0049] 其中,C0B型LED光源1采用市售的大功率型(10W〜60W)光源,发光面较大,发光面直径的选择范围为l〇mm〜25mm。 [0049] wherein, C0B type LED light source 1 using a commercially available high-power type (10W~60W) light source, a light emitting surface is larger, the light emitting surface diameter selected in the range l〇mm~25mm.

[0050] 自由曲面透镜2的功能为:将COB型LED光源1发出的0度-α度(α通常取45 度)的光线均匀分布在β度以内,根据相应的C0B型LED光源1发光区域直径D,结合边缘光线理论,设计出尺寸合理的自由曲面透镜2。 Function [0050] The free-form surface lens 2 is: 0 ° -α ° light rays ([alpha] typically takes 45 degrees) of the COB type LED light source 1 emits uniformly distributed within β degrees, a light emitting region according to the corresponding type LED light source C0B the diameter D, in conjunction with the marginal ray theory, design a reasonable size of the free surface of the lens 2.

[0051] 自由曲面透镜2包含三部分,透镜顶部、透镜侧壁和透镜底部。 [0051] The free-form surface lens 2 comprises three parts, the top of the lens, the lens side walls and a bottom of the lens.

[0052] 透镜顶部由内外两个自由曲面组成。 [0052] The top lens consisting of two inner and outer curved surfaces. 透镜顶部内表面可以是球面、上凹或下凸的自由曲面,透镜顶部外表面可以是上凸或下凹的自由曲面。 The top inner surface of the lens may be spherical, concave or convex lower free-form surface, the top outer surface of the lens may be a free curved surface concave or convex.

[0053] 透镜顶部外表面可以做成菲涅尔透镜,减小透镜厚度,提高照射区域中心光强的同时,节省了材料。 [0053] The top outer surface of the lens can be made into a Fresnel lens, the lens thickness is reduced to improve the irradiation intensity of the center region at the same time, saving material.

[0054] 透镜内侧壁可以是普通圆柱形内腔面,也可以是阶梯状圆柱形内腔面,透镜外侧壁是球面或者自由曲面。 [0054] The inner lens may be generally cylindrical sidewall surface of the lumen may be a stepped cylindrical interior surface, the outer sidewall is a spherical lens or a free curved surface.

[0055] 透镜底部圆直径大小可调,根据C0B型LED光源1发光区域直径D大小,选择普通圆柱形内腔或阶梯状圆柱形内腔。 [0055] The bottom lens diameter size is adjustable according to the size of the diameter D of the light emitting region 1 C0B type LED light source, to select a generally cylindrical stepped bore or cylindrical cavity.

[0056] 自由曲面反射杯3的功能为:控制C0B型LED光源1发出的大角度光线,S卩α度到90度的光线透过自由曲面透镜2侧面,再经过自由曲面反射杯3内侧反射,根据照明距离,将大角度的出射光线控制在所要求大小的照明区域内。 [0056] The function of the free surface of the reflective cup is 3: control type LED C0B high angle light rays emitted from the light source 1, S Jie α degrees to 90 degrees of light through free-form surface lens 2 side, and then through the inner free surface of the reflective cup 3 reflected the illumination range, large outgoing angle of light is controlled within the desired size of the illumination area.

[0057] 自由曲面反射杯3的内表面为镀层处理,实现镜面发射,为解决眩光问题,将微结构(如鳞甲结构)作用于反射杯内侧,鳞甲高度不高于0. 〇5_。 [0057] The inner surface of the free-form surface reflector cups 3 for plating processing, transmitting mirror, to solve the problem of glare, the microstructure (e.g. Linked Structure) acting on the inner side of the reflective cup, the height of not more than 0.5 scales 〇5_.

[0058] 本发明的主旨思想是将C0B型LED光源1发出的光分区域设计,小角度的光由自由曲面透镜2控制,大角度的光由自由曲面反射杯3控制。 [0058] The gist of the idea of ​​the invention is to design a light subregion, a small angle C0B type LED light source 1 emits light 2 is controlled by a free-form surface lens, the third light controlled by a free-form surface of the reflective cup high angle. 图1中的实施例是本发明的一种可行结构,但本发明不限于上述结构。 Example Figure 1 is a possible structure of the present invention, but the present invention is not limited to the above structure.

[0059] 自由曲面透镜2能较好的控制偏离光轴的小角度光线,但当入射光线的角度大于临界角时,将产生全发射,这种局限性使得自由曲面透镜2光学效率降低;相反,自由曲面反射杯3能较好的控制偏离光轴的大角度光线,对小角度光线却无法精确控制。 When [0059] The free-form surface lens 2 can better control the small angle off the optical axis of the light, but the incident angle of the line is greater than the critical angle, total reflection generated, this limitation such that a free curved surface lens to reduce optical efficiency; conversely , the free surface of the reflective cup 3 can better control the high angle light rays off the optical axis, but can not accurately control the small angle rays.

[0060] 自由曲面透镜2与自由曲面反射杯3互补的特性是本发明的思想来源。 [0060] 2 free-form surface lens and the free surface of the reflective cup 3 is thought characteristic complementary to the source of the present invention. 本发明提出的照明系统能应用于多种LED灯具,如LED投射灯、LED工矿灯、LED筒灯等。 An illumination system proposed by the present invention can be applied to various LED lamps, such as LED projection lamp, LED mining light, LED downlight.

[0061] 在上述照明系统中,要实现窄光束的LED照明,要对自由曲面透镜2的透镜顶部外表面,以及自由曲面反射杯3的曲线进行合理的设计。 [0061] In the lighting system, to realize a narrow beam LED lighting lens to the outer surface of the top free-form surface lens 2, and the curve of the free surface of the reflective cup 3 is reasonable design. 下面给出自由曲面透镜2的透镜顶部外表面,以及自由曲面反射杯3的一种设计方法(或生成方法)。 The outer surface of the top lens surface of the lens 2 below gives free, and free-form surface reflector cup Design Method (or generation method) 3. 其余诸如自由曲面透镜2的透镜顶部内表面、透镜侧壁以及透镜底部的设计则可遵循现有技术。 Remaining free curved surface such as the top of the lens surface design lens 2, the lens side walls and a bottom of the lens can follow the prior art.

[0062] 透镜自由曲面的生成方法如下: [0062] The method of generating a free curved surface of the lens as follows:

[0063] 如图2所示,以光源所在平面为X轴,中垂线为y轴建立坐标系,以光源中心为原点。 [0063] As shown in FIG. 2, the light source plane where the X axis, the vertical y-axis coordinate system is established, as the light source center to an origin. 设扩展光源半径为R,面1和面2分别为透镜顶部的内外表面,确定自由曲面步骤如下: Extended source is disposed a radius R, and the surface 1 to surface 2, respectively inner and outer surface of the top of the lens, the step of free-form surface is determined as follows:

[0064] 1)设Η为LED光源左边缘札的光线与y轴交点,坐标为(0, H)。 [0064] 1) provided with the y axis intersection Η light LED light source of the left edge of the sheaf, coordinates (0, H).

[0065] 2)根据光源尺寸D (D=2R),适当取第一次折射光线上的某一点\作为透镜外表面曲线的起始点,并使X。 [0065] 2) The source size D (D = 2R), take the appropriate start of a certain point the first refractive \ as an outer curved surface of the lens on the light, and X. 点处的法线竖直向上。 Normal at a point vertically upward.

[0066] 3)根据光学扩展量守恒式β [0066] 3) According to etendue conservation of formula β

[0067] 2nxD= J Ldfi -β [0067] 2nxD = J Ldfi ​​-β

[0068] 求出投射宽度L。 [0068] obtaining the projection width L.

[0069] 其中,D为光源直径,β为出射光线与y轴夹角,η为光学材料的折射率。 [0069] where, D is the diameter of the light source, β is the angle between the outgoing light and the axis y, η is the refractive index of the optical material.

[0070] 4)直线a为札出射光线,取与其距离L的直线b作为光源边缘艮的出射光线,直线b上适当取一点Y。 [0070] 4) A is a straight sheaf outgoing light, taking as its source a straight edge distance L b Gen outgoing light, to take the appropriate point on the straight line b Y. .

[0071] 5)根据折射定律矢量形式 [0071] 5) The vector form of the law of refraction

[0072] ULHJI LIU UU tlUUI 1111 [0072] ULHJI LIU UU tlUUI 1111

[1 + /r - 2f}{Oui //0ll 2 · N = Out - nln [1 + / r - 2f} {Oui // 0ll 2 · N = Out - nln

[0073] 可求出YQ点得法线方向。 [0073] can be obtained YQ point Fa line direction.

[0074] 其中和$分别为出射和入射光线单位矢量,$为界面法线单位矢量。 [0074] and wherein the exit and $ are incident ray unit vector $ is the unit vector normal to the interface. LiLfLfti ULiU LiLfLfti ULiU

[0075] 6)根据I的坐标以及它们的法线方向和」,插值一条连续曲线(通常取LK.ILK.L ULIU. 三次曲线),使之通过X〇和Y〇,同时在这两点满足法线方向和。 [0075] 6) The I coordinate and a normal direction thereof and "interpolating a continuous curve (usually taken LK.ILK.L ULIU. Cubic), and so by X〇 Y〇, while these two and to meet the normal direction. 由此可以拟定一条连续曲线XdYt!作为计算起始曲线。 Whereby a continuous curve drawn XdYt! Calculated as the initial curve.

[0076] 7)将初始曲线划分η小段,得到曲线上的n+1点,分别为X。 [0076] 7) The initial curve into η, yielding an n + 1 point on the curve, respectively X. 〜Xn,对应未知曲线的点Y〇〜Yn。 ~Xn, Y〇~Yn unknown curve corresponding point.

[0077] 8)取\较近一点\,出射光线为直线c,把距直线c为L的直线d作为艮经透镜折射后的另一条光线。 [0077] 8) Take \ point close \, is emergent ray line c, the distance L of the straight line c to d as another light rays refracted by a lens of Burgundy. 计算出直线d与I点得切线的交点(即I),根据折射定律矢量形式计算出t点得法线方向。 I calculate the straight line d and the tangent point of intersection obtained (i.e. I), the t-point is calculated according to the law of refraction Fa line direction vector form. 同样根据&,t的坐标以及它们的法线方向,插值三次曲线。 Also according to the coordinates &, t, and the normal direction thereof, parametric cubic curves.

[0078] 9)取&较近一点X2,依次类推计算,可以计算机迭代计算,使用同步多曲面法计算剩下的点,直到α的范围在40°〜45°为止(角度可根据实际情况进行微调),最终得到透镜截面曲线。 [0078] 9) & taken near one o'clock X2, and so calculated, the computer can be iterated, using the simultaneous multi-point rest surface method, until the range of α (angle according to the actual situation up in 40 ° ~45 ° trimming), to give a final lens profile curve.

[0079] 在计算允许的情况下,初始曲线上点的数量选的越多,模型准确度越高。 [0079] In the case of calculating the allowable number of selected points on the initial curve, the more accurate the higher model.

[0080] 经透镜侧面出射的大角度光线由反射杯控制。 [0080] emitted by a lens side is controlled by the high angle light rays reflecting cup.

[0081] 反射杯自由曲面的生成方法如下:如图3所示, [0081] The method of generating a free curved surface of the reflective cup is as follows: As shown in FIG 3,

[0082] 1)先确定一段初始线段APi (其中&的坐标是根据具体的应用一开始就确定的), 从与y轴夹角最大光线开始考虑。 [0082] 1) to determine the period of the initial segment APi (wherein & coordinate is a specific application determines the beginning), starting from the maximum y-axis angle rays considered. 这一簇光线对应屏幕上的起始点为^,初始入射光线札心经过反射到达ri。 This starting point on the screen corresponding to the light ^ cluster, the initial incident light reaches the reflection through core sheaf ri. 可根据边缘光线理论,&发出的某一条光线入射到初始曲线端点也会被反射到巧,则曲线段AiBi是以艮和巧为两个焦点椭圆的部分曲线。 According to the marginal ray theory, a certain & incident light emitted to the initial end of a curve will be reflected to the coincidence, the portion of the curve is a curve segments AiBi Gen Qiao and two focus of the ellipse. 角〜、角分别为出射光线A nrn、Bnrn与光轴y的夹角。 ~ Angle, angles of light exiting angle A nrn, Bnrn optical axis y.

[0083] 2)设光源亮度为B,而发出与y轴夹角较小而直接照射在屏幕上而产生的照度可由 [0083] 2) set the light source luminance is B, the y-axis angle and emits less directly irradiated on the screen illuminance can be generated

[0084] /;(,) = j /i · cos 沒.ί/61 = 5Ω 得到。 [0084] /; (,) = j / i · cos not .ί / to give 61 = 5Ω.

[0085] 角的大小由Γι的照度决定。 [0085] The size is determined by the angle of illumination Γι. 出射光线ΑιΓι与y轴的夹角吣可由Ai的坐标确定,^接受到的照度可由光源直接照射的能量减去反射器反射的能量得到,即 Emergent ray ΑιΓι Qin angle with the y axis of coordinates determined by Ai, ^ received directly irradiated by the illumination energy source minus the energy reflected by the reflector is obtained, i.e.,

[0086] Er=E_B Ω =B (sin Θ r-sin Θ 丄) [0086] Er = E_B Ω = B (sin Θ r-sin Θ Shang)

[0087] 可求得出射光线ΒΛ与y轴的夹角Θ i,并可得到&点的坐标,初始曲线A#方程即可确定。 [0087] The exit angle of the light obtained can be evaluated with the y axis ΒΛ Θ i, and to obtain the coordinates of the point &, A # to determine initial curve equation.

[0088] 3)从札点发出与y轴夹角稍小的光线,入射到曲线AA上的A2点,从曲线方程上可求出a2的坐标以及其法向量瓦;,由反射定律可得到其反射光线,设反射光线入射到屏幕上的点为r2,出射光线A2r2与y轴的夹角t可确定。 [0088] 3) emitted from the point A2 sheaf point smaller angle with the y axis of the light incident on the AA curve, the curve equation can be derived from the coordinates and a2 whose normal vector W; can be obtained by the law of reflection reflected light, the reflected light is incident is provided on the screen to point r2, A2r2 emergent ray angle t with the y axis can be determined. 由光通量守恒可求得出射光线B 2r2 与y轴的夹角Θ i,即可确定r2光线接收锥的另外一个边界的光线,其与&点的切线交于B2,可作为新的曲线点。 Conservation of the luminous flux emitted beam B 2r2 stars can be evaluated with the y axis angle Θ i, to determine the acceptance cone of light rays r2 another boundary, a tangent which intersects the point & B2, as a new profile point.

[0089] 4)光源从边缘艮发出的光线RA经反射的反射光线为B2r2,根据反射定律,B 2的坐标和法向量也可确定。 [0089] 4) from the light rays emitted by the RA edge Gen reflected light is reflected B2r2, according to the law of reflection, B 2 coordinates and normal vectors can also be determined. 反射器AiB2的轮廓可以确定,再考虑由&点发出的与y轴夹角更小的光线,重复以上步骤,轮廓线将不断扩展,直至达到所要求的边界为止。 AiB2 reflector profile can be determined, and then the angle between the axis y considered less light emitted by the point & Repeat the above steps, the contour line will continue to expand until it reaches the required boundaries.

[0090] 此设计方法可根据光源大小来设定边缘光线点的坐标,并可根据需求多远的照射面来确定照明区域的大小,并且可以与透镜控制的较小角度光线进行完美的重合。 [0090] This design method may be set according to the size of the source point coordinates of the edge ray, and can be determined according to the size of the illumination area far demand irradiation surface, and can be perfectly coincide with the smaller angle lens control light. 由于反射器的曲线方程是有各个反射点确定的,范围变动性可调,能够较好对大角度出射的光线进行收光。 Since the curve equation of the reflector is determined by the respective reflection points, the variation range of adjustable, can be better for large angle light rays emitted light received.

具体实施方式[0091] : DETAILED DESCRIPTION [0091]:

[0092] 下面给出上述设计方法的一个具体实施例。 A design method is given above [0092] The following specific examples.

[0093] 1)确定光源尺寸参数D的大小(D可取10mm〜25mm),确定透镜高度Η的大小(20mm〈H〈30mm),确定分光角度α的大小(40° <α〈45° ),确定出光角度β的大小(4° <β〈9° )。 [0093] 1) determining the size of the source size parameter D (D preferably 10mm~25mm), to determine the size of the lens height Η (20mm <H <30mm), the angle [alpha] is determined spectral magnitude (40 ° <α <45 °), determining the size of the beam angle beta] (4 ° <β <9 °). β β

[0094] 2)根据光学扩展两守恒式λ#,计算出投射宽度L。 [0094] 2) The optical extension two conserved formula λ #, calculate a projection width L. _β L1L1LI11 _β L1L1LI11

[0095] 3)在面2上取一点\作为透镜外表面曲线的起始点,并使\点处的法线;V.坚直-λ〇向上,出射光线角度为β,根据距离L和β的大小确定I点位置。 [0095] 3) taken in a plane that 2 \ as a starting point of the curve of the outer surface of the lens, and \ normal at the point;. V Kennedy -λ〇 straight upward, the light outgoing angle beta], according to the distance L and beta] I magnitude determining position. 根据折射定律矢量形式mu Liu uii mu iju , h Λ , 1认;**·* The vector form of the law of refraction mu Liu uii mu iju, h Λ, 1 recognized; * * *

[1 + ¥-2"((}"/.]/,)]12.# = 0?"-,,办求出丫。点法线方向况3.。。 [1 + ¥ -2 "((}" /.]/,)] 12. # = 0 "-? ,, do Ah point normal direction determined conditions ... 3.

[0096] 4)拟定一条连续曲线ΧΛ作为计算起始曲线,将曲线划分η小段,得到曲线上得η+1点,分别为X。 [0096] 4) develop a continuous curve as the calculation start ΧΛ curve, the curve into small pieces η, η have obtained one point on the curve +, respectively X. 〜Χη,对应未知曲线的点Υ。 ~Χη, Υ corresponding point unknown curve. 〜Υη。 ~Υη.

[0097] 5)取\较近一点Xi,出射光线角度为β,根据L和β的大小确定Yi点位置。 [0097] 5) takes \ that close Xi, outgoing light angle β, is determined in accordance with the position of the point Yi and the size L of beta]. 同样根据折射定律矢量形式计算出t点法线方向,插值曲线。 The same point normal direction t is calculated, the interpolation curve according to the law of refraction vector form.

[0098] 6)取较近一点,依次类推计算,可以计算机迭代计算,使用同步多曲面法计算剩下的点,直到α =45°为止,最终得到透镜截面曲线。 [0098] 6) taken near point, and so calculated, the computer can be iterated, using the simultaneous multi-point rest surface method, up until α = 45 °, to give a final lens profile curve.

[0099] 7)将计算得到的离散点导入到机械建模软件(如:Rhinoceros、UG等)中,连接成一条自由曲线,对称旋转得到透镜实体模型。 [0099] 7) the calculated discrete points into mechanical modeling software (eg: Rhinoceros, UG, etc.), is connected to a free curve, rotationally symmetrical lenses to give a solid model.

[0100] 8)为节省材料,提高中心光强,不改变透镜顶部曲率,将透镜顶部外表面采用菲涅尔透镜。 [0100] 8) In order to save material and improve the central light intensity, the top of the lens without changing the curvature of the lens outer surface with the top Fresnel lens.

[0101] 9)确定照射距离S=l. 2m,根据β的大小,确定目标面上的照明范围半径rmax大小, rmax=SXtan3。 [0101] 9) determines the irradiation distance S = l. 2m, depending on the size of β, the illumination radius rmax determined size of the target surface, rmax = SXtan3.

[0102] 10)确定一段初始线段AA,初始入射光线RA经过反射到达Γι,根据边缘光线理论,艮发出的某一条光线入射到初始曲线&也会被反射到 [0102] 10) determining an initial period of a line segment AA, RA after the initial incident light reaches the reflection Γι, based on the edge ray theory, a ray a emitted incident Gen & initial curve will be reflected to the

[0103] 11)设光源亮度为Β,在屏幕上而产生的照度计算如下: [0103] 11) is provided as the light source luminance Β, calculated illuminance on the screen is generated as follows:

[0104] /:'(/) = |5· COS ^·£/6> = ΛΩ [0104] /: '(/) = | 5 · COS ^ · £ / 6> = ΛΩ

[0105] ri接受到的照度可由光源透过透镜后照射的能量减去反射器反射的能量得到,即 [0105] ri received illumination through energy irradiation by light energy reflected by the reflector after subtracting the lens obtained, i.e.,

[0106] Er=E_B Ω =B (sin Θ r-sin Θ 丄) [0106] Er = E_B Ω = B (sin Θ r-sin Θ Shang)

[0107] 可求出角Θ i和&点的坐标,确定曲线方程A%。 [0107] can be obtained angle Θ i and & coordinate point determined curve equation A%.

[0108] 12)从札点发出与y轴夹角稍小的光线,入射到曲线AA上的A2点,由曲线方程AA求出A2的坐标以及其法向量%,由反射定律得到其反射光线,对应屏幕上的点为r2, 确定A2r2与y轴的夹角t的大小。 [0108] 12) issuing point A2 smaller angle with the y axis of the light incident on the curve AA from Sapporo point coordinates determined by the curve equation AA and its normal vector A2%, obtained by the law of reflection reflected light a point on the screen corresponding to r2, to determine the size of the angle t A2r2 with the y axis. 由光通量守恒可求出,即可确定1*2光线接收锥的另外一个边界的光线,其与&点的切线交于B2,作为新的曲线点。 Conservation of luminous flux can be obtained, the light can be determined light acceptance cone 1 * 2 another boundary, a tangent which intersects the point & B2, as a new profile point.

[0109] 13)从光源边缘艮发出的光线R,B2经反射的反射光线为B2r 2,根据反射定律,B2的坐标和法向量也可确定。 [0109] 13) R light emitted from the light source edge of Burgundy, B2 reflected light is reflected B2r 2, according to the law of reflection, B2 coordinates and normal vectors can also be determined. 反射器AiB2的轮廓可以确定,再考虑由&点发出的与y轴夹角更小的光线,重复以上步骤,轮廓线将不断扩展,直到与y轴夹角减小为45度停止,得到最终的反射杯曲线。 AiB2 reflector profile can be determined, and then the angle between the axis y considered less light emitted by the point & Repeat the above steps, the contour line will continue to expand until it is reduced to an angle of 45 degrees with the y-axis is stopped, to give a final the reflective cup curve.

[0110] 14)将计算得到的反射杯曲线对称旋转得到反射杯实体模型。 [0110] 14) The reflector cups curve calculated rotational symmetric reflective cup to give a solid model.

[0111] 15)为改善出光效果,在不改变反射杯曲率的情况下,将鳞甲结构作用于反射杯内侧面。 [0111] 15) In order to improve the effect of light, without changing the curvature of the reflective cup, the scales on the side surface of the structure acting reflective cup.

[0112] 16)透镜模型与反射杯模型结合,得到最终的LED照明光学系统,如图1所示。 [0112] 16) lens model and the reflective cup binding model, to give a final LED lighting optical system, as shown in FIG.

[0113] 17)采用直径15mm的C0B型LED光源,运用得到的LED配光系统,最终在照明距离S=l. 2m处,形成30cm〜40cm左右的均勻光斑。 [0113] 17) with a diameter of 15mm C0B type LED light source, the light distribution system using LED obtained, the final illumination range S = l. 2m, the formation of a uniform spot of about 30cm~40cm. 半光强出光全角为16度,中心光强达7500cd/klm。 Full light intensity half angle 16 degrees, the central light intensity of 7500cd / klm.

[0114] 以上所述的仅是本发明的优选实施方式,本发明不限于以上实施例。 [0114] The above embodiment is merely a preferred embodiment of the present invention, the present invention is not limited to the above embodiments. 可以理解,本领域技术人员在不脱离本发明的基本构思的前提下直接导出或联想到的其他改进和变化, 均应认为包含在本发明的保护范围之内。 It will be appreciated that those skilled in the art, or derived directly associate other modifications and variations without departing from the basic premise of the concept of the invention shall be considered to be within the scope of the present invention.

Claims (1)

1. 一种窄光束LED照明光学系统的设计方法,其特征在于:以光源所在平面为X轴,中垂线为y轴建立坐标系,以光源中心为原点,设扩展光源半径为R,生成透镜自由曲面以及反射杯自由曲面; 生成透镜自由曲面的步骤如下: 1) 设Η为LED光源左边缘氏的光线与y轴的交点,坐标为(0, H); 2) 根据光源尺寸D(D = 2R),取第一次折射光线上的点\作为透镜外表面曲线的起始点,并使X〇点处的法线^坚直向上; 3) 根据光学扩展量守恒式β 2/?xD=丨-β 求出投射宽度L;其中,D为光源直径,β为出射光线与y轴夹角,η为光学材料的折射率; 4) 直线a为&出射光线,取与其距离L的直线b作为光源边缘艮的出射光线,在直线b上取点YQ ; 5) 根据折射定律矢量形式[1 + n~ - 2n(0ui in)]12 N = Οιιί - nIn 求出Υ〇点得法线方向其中^和$分别为出射和入射光线单位矢量,元为界面法线单位矢量; 6 Design method for narrow beam LED illumination optical system, wherein: the light source plane where the X-axis, the y-axis perpendicular to the coordinate system established to the light source center as an origin, an extended light source is provided for the radius R, to generate lens free-form surface and a reflective cup consisting of a curved surface; the step of generating a lens free curved surface as follows: 1) set Η intersection of the LED left edge's source light and the y-axis, coordinates (0, H); 2) the light source size D ( D = 2R), taking the first refractive starting point \ as an outer curved surface of the lens on the light, and the solid vertical ^ normal at point X〇; 3) according to etendue conservation of formula β 2 /? Shu xD = -β projection width L is obtained; wherein, D is the diameter of the light source, the light emitted beta] is the angle between the y-axis, [eta] is the refractive index of the optical material; 4) is a linear light emitted & taken its distance L as the light source edge of the straight line b Gen outgoing light taking YQ point on the straight line b;. 5) in accordance with the law of refraction vector form [1 + n ~ - 2n (0ui in)] 12 N = Οιιί - nIn point Fa line determined Υ〇 and wherein the direction of $ ^ respectively and the incident light emission unit vector normal to the interface element is a unit vector; 6 ) 根据的坐标以及它们的法线方向<和&,插值一条连续曲线,使之通过\ 和I,同时在这两点满足法线方向%和% ;由此可以拟定一条连续曲线作为计算起始曲线; 7) 将初始曲线ΧΛ划分η小段,得到曲线上的η+1点,分别为X。 ) And according to the coordinates of a normal direction thereof <and & interpolating a continuous curve, so that by \ and I, while the normal direction of these two points satisfies% and%; can thus be prepared as a continuous curve calculation start curve; 7) dividing the initial curve η ΧΛ, yielding an η + 1 on the curve points respectively X. 〜Χη,对应未知曲线的点Υ〇〜Υη ; 8) 取\较近一点Xi,出射光线为直线c,把距直线c为L的直线d作为艮经透镜折射后的另一条光线;计算出直线d与I点得切线的交点t,根据折射定律矢量形式计算出t 点得法线方向;同样根据&,t的坐标以及它们的法线方向,插值三次曲线; 9) 取&较近一点X2,依次类推计算,使用同步多曲面法计算剩下的点,直到α的范围在40°〜45°为止,最终得到透镜截面曲线; 生成反射杯自由曲面的步骤如下: 1) 确定初始线段APi,从与y轴夹角最大光线开始考虑,这一簇光线对应屏幕上的起始点为A,初始入射光线经过反射到达Γι ;根据边缘光线理论,&发出的某一条光线入射到初始曲线端点&也会被反射到Γι,则曲线段APi是以艮和Γι为两个焦点椭圆的部分曲线;角L、角Θ i分别为出射光线Anrn、Bnrn与光轴y的夹角; 2) 设光源亮度为B, ~Χη, Υ〇~Υη unknown curve corresponding point; 8) Take \ near one o'clock Xi, is emergent ray line c, the distance L of the straight line c to d as another light after refracted by a lens Burgundy; calculated I d and the straight line intersection of the tangent point t obtained, calculated according to the law of refraction vector form Fa t-point line direction; according to the same coordinates &, t, and the normal direction thereof, cubic interpolation; 9) & taken near a point X2 , and so calculated, using the calculated surface normal simultaneous multi remaining points until α in the range of 40 ° ~45 ° until the final lens profile curve obtained; the step of generating the free surface of the reflective cup are as follows: 1) determining an initial segment APi, from the maximum y-axis angle rays began to consider that the starting point on the screen corresponding to the light cluster a, the initial incident light reaches the reflector through Γι; theory based on the edge ray, a & emitted light is incident to an initial end of a curve is also & will be reflected to Γι, the curve segments Gen APi is partially curved and Γι two focus of the ellipse; angle L, angle Θ i respectively emitted light Anrn, Bnrn angle with the optical axis of y; 2) disposed light source luminance is B, 发出与y轴夹角较小而直接照射在屏幕上而产生的照度可由E (r) = / B · cos θ · d θ = Β Ω 得到; 角的大小由Γι的照度决定;出射光线ΑΛ与y轴的夹角吣由Ai的坐标确定, rl接受到的照度可由光源直接照射的能量减去反射器反射的能量得到,即Er = EB Ω = B (sin Θ r-sin Θ J 得到出射光线ΒιΓι与y轴的夹角Θ i并得到Bl点的坐标,初始曲线APi方程即可确定; 3) 从札点发出与y轴夹角稍小的光线,入射到曲线AA上的A2点,从曲线方程上可求出A2的坐标以及其法向量ϊ^,由反射定律可得到其反射光线,设反射光线入射到屏幕上的点为r2,出射光线A2r2与y轴的夹角吣可确定;由光通量守恒得到出射光线B 2r2与y轴的夹角Θ i,即确定r2光线接收锥的另外一个边界的光线,其与&点的切线交于B2,作为新的曲线点; 4) 光源从边缘艮发出的光线RA经反射的反射光线为B2r2,根据反射 It emits y-axis angle is small and directed onto the screen illuminance produced by E (r) = / B · cos θ · d θ = Β Ω obtained; determined by the size of the angle of illumination Γι; and emergent ray ΑΛ Qin angle determined by the y-axis coordinates of Ai, rl energy received directly irradiated by the illumination light source reflector reflects energy subtracted obtained, i.e. Er = EB Ω = B (sin Θ r-sin Θ J emergent ray obtained an angle Θ i ΒιΓι obtained with the y axis and the coordinates of the points Bl, APi to determine initial curve equation; 3) issue point A2 smaller angle with the y axis of the light incident on the AA from Sapporo curve point, from curve equation can be obtained on the coordinates A2 and its normal vector ϊ ^, obtained by the law of reflection reflected light, the reflected light is incident to a point located on the screen is r2, the outgoing light A2r2 Qin angle with the y axis can be determined; the light flux conservation to obtain an exit beam B 2r2 with the y axis angle Θ i, i.e., determining light r2 light acceptance cone of the other boundary, which is tangent to & points intersect at B2, as a new profile point; 4) a light source from Gen RA edge light emitted reflected light is reflected B2r2, the reflected 律,B2的坐标和法向量也可确定;反射器Ap 2的轮廓可以确定,再考虑由&点发出的与y轴夹角更小的光线,重复以上步骤,轮廓线将不断扩展,直至达到所要求的边界为止。 Law, B2 coordinates and normal vectors can also be determined; Ap contour reflector 2 can be determined, then the angle between the axis y considered less light emitted by the point & Repeat the above steps, the contour line will continue to expand until it reaches the Until the required boundaries.
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