CN102890342A - Method for designing free-form surface optical element for point light source distribution - Google Patents

Method for designing free-form surface optical element for point light source distribution Download PDF

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CN102890342A
CN102890342A CN2012104087293A CN201210408729A CN102890342A CN 102890342 A CN102890342 A CN 102890342A CN 2012104087293 A CN2012104087293 A CN 2012104087293A CN 201210408729 A CN201210408729 A CN 201210408729A CN 102890342 A CN102890342 A CN 102890342A
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optics element
form surface
freeform optics
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energy
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CN102890342B (en
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吴仍茂
张雅琴
刘鹏
王会会
杨洋
侯佳
郑臻荣
刘旭
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Zhejiang University ZJU
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Abstract

The invention discloses a method for designing a free-form surface optical element for point light source distribution and belongs to the technical field of non-imaging optics. The method comprises the following steps of: setting a specific structure of the free-form surface optical element according to the design requirements, and designing a free-form surface which meets the preset illumination requirements according to the refraction law and the energy conservation in a computer-assisted mode, so that emergent light of a light source is deflected through the free-form surface and generates preset illumination light spots in a target illumination area, such as circular illumination light spots with ZJU words and uniform rectangular illumination light spots. A certain surface of the free-form surface optical element is a free-form surface, and the free-form surface is obtained through a surface fitting discrete point. The method has the high design efficiency, can realize the complicated illumination and can obtain a continuous free-form surface, and the surface can be machined; and moreover, refractive and reflective free-form surface optical elements can be realized by means of an injection molding technology by using materials such as optical resins.

Description

A kind of method for designing of the freeform optics element for the pointolite luminous intensity distribution
Technical field
The present invention relates to nonimaging optics and lighting technical field, relate in particular to a kind of method for designing of the freeform optics element for the pointolite luminous intensity distribution.
Background technology
Intensity distributions and target illumination according to pointolite (such as LED) require light distribution requirements that optical surface is realized being scheduled to of design, and this is a reverse engineer problem, is focus and the difficult point of nonimaging optics research always.Because free form surface has the flexibly advantage such as space layout and design freedom, adopt free form surface not only can greatly simplify the structure of optical system, also can easily realize complicated lighting requirement, so Random Curved Surface Designing there is very important effect to solving this Reverse Problem.
At present, usually adopt optimal design and " Partial Differential Equation (PDE) " method to design free form surface to solve this reverse illumination problem.Optimal design reduces evaluation function until the curved surface that obtains to meet design requirement by certain optimized algorithm by continuous change optimized variable.Illumination is optimized and usually to be required to pursue and attack a large amount of light reducing to simulate statistical noise in each Optimized Iterative, and the result of optimal design depends on structure and the optimized algorithm of the choosing of optimized variable, evaluation function very much.For the illumination of a complexity, usually need thousands of discrete data points to make up free form surface, this is that optimal design can't realize.The design philosophy of PDE method is that this reverse engineer problem is changed into a first order PDE system, and makes up free form surface by this system of equations of numerical solution.The optimal design of comparing, the PDE method has higher design efficiency, and can realize complicated lighting requirement, and the PDE method all is the research emphasis of Random Curved Surface Designing all the time.Chinese patent 200910046129.5 has proposed a kind of method for designing for the pointolite light-distribution lens, the method constructs the first order PDE system that curved surface satisfies according to refraction law, then a selected energy topological relation is determined the energy mapping relations between light source and the target illumination, obtains free-curved-surface-type by this first order PDE system of numerical solution afterwards.Adopting a committed step of this kind PDE method design free form surface is the energy mapping relations that need set up first between light source and the target illumination.The integrability of these energy mapping relations has determined the continuity of free form surface, only has the energy mapping relations that satisfy integrability condition just can obtain continuous free form surface.Some energy mapping relations of easily obtaining are often discontented can amass condition completely, and can only obtain discontinuous free form surface this moment.Adopted a kind of mapping relations of variable separable to realize rectangular illumination such as Chinese patent 200910046129.5, the result can only obtain discontinuous free form surface, and this has proposed a very large difficult problem for undoubtedly actual processing.
Summary of the invention
The object of the present invention is to provide a kind of method for designing of the freeform optics element for the pointolite luminous intensity distribution.
The method for designing concrete steps of freeform optics element that are used for the pointolite luminous intensity distribution are as follows:
(1) structure of freeform optics element is set, according to the initial designs parameter it is carried out Random Curved Surface Designing;
(2) set up rectangular coordinate system take light source as true origin, the coordinate of any point P on the free form surface of the required design of the determined freeform optics element of step (1) is expressed as with spherical coordinates The coordinate of the impact point T corresponding with a P is expressed as T (x, y, z) with rectangular coordinate on the target illumination face; Vector P is the position vector of some P, is a vector that is pointed to some P by initial point, and vector T is the position vector of some T, is a vector that is pointed to some T by initial point, according to refraction law n oO=n iI+P 1N sets up the coordinate relation between some P and the impact point T
x = P x + ( z - P z ) n i I x + P 1 N x n i I z + P 1 N z y = P y + ( z - P z ) n i I y + P 1 N y n i I z + P 1 N z
Wherein, vector
Figure BDA00002293243000023
P x, P yAnd P zThree components for vector P; I x, I yAnd I zBe incident ray unit's direction vector
Figure BDA00002293243000024
Three components; N x, N yAnd N zFor free form surface is vowed N=(N in the per unit system at a P place x, N y, N z) three components,
Figure BDA00002293243000025
Figure BDA00002293243000026
And P θBe respectively position vector P about angle
Figure BDA00002293243000027
Partial derivative with θ;
Figure BDA00002293243000028
Angle [alpha] is the angle of vector I and vector N; n iAnd n oBe respectively the refractive index of freeform optics element material therefor and the refractive index of freeform optics component ambient medium;
(3) according to law of conservation of energy, set up the energy relationship between the luminous energy that light source outgoing luminous energy and target illumination zone receive, in the situation that do not consider energy loss, the light source outgoing energy that requires the freeform optics element to receive equates with the energy in arrival target illumination zone, and namely energy satisfies relational expression
Figure BDA00002293243000029
Wherein,
Figure BDA000022932430000210
Be the intensity distributions of light source, E (x, y) is the Illumination Distribution in target illumination zone on the illuminated area, and R represents the target illumination zone, and Ω represents to incide total solid angle of the light on the freeform optics element;
(4) the some P and the relation of the coordinate between the impact point T that obtain according to step (2) have following coordinate transform relation
Figure BDA00002293243000031
Wherein, J (T) is the Jacobi matrix of position vector T,
Figure BDA00002293243000032
(5) coordinate transform in the step (4) is concerned the energy equation of substitution step (3) and removes the sign of integration, obtain describing the Energy Transfer equation of freeform optics element
Figure BDA00002293243000033
Wherein, 0≤θ≤2 π,
Figure BDA00002293243000034
(6) to guarantee also in the Energy Transfer equation of free form surface in satisfying step (5) that the boundary rays of light source outgoing incides the border of target face field of illumination behind the free form surface deviation, namely satisfy with downstream condition
Figure BDA00002293243000035
Wherein,
Figure BDA00002293243000036
With
Figure BDA00002293243000037
Be respectively the border of regional Ω and R;
(7) to the boundary condition simultaneous solution in the Energy Transfer equation in the step (5) and the step (6), obtain one group of discrete data point on the free form surface, by being carried out surface fitting, this group data point can obtain FREEFORM SURFACE MODEL.
Described freeform optics element has two types of reflection-type and refractive; n o=-1, n iThe freeform optics element of=1 corresponding reflection-type, n oThe freeform optics element of=1 corresponding refractive.Described reflection-type freeform optics element only has a curved surface, and this curved surface is free form surface.The outside surface of described refractive freeform optics element is free form surface, and inside surface is sphere or plane.Described refractive freeform optics element is the outer enclosure lens of led chip, i.e. optical element of LED.Described refractive freeform optics element is the shaping lens after the led light source, i.e. LED secondary optics element.The beneficial effect that the present invention compared with prior art has is:
1) method for designing of the freeform optics element that is used for pointolite (LED) luminous intensity distribution of the present invention's proposition can obtain continuous free-curved-surface-type;
2) the method for designing design efficiency of the freeform optics element that is used for pointolite (LED) luminous intensity distribution of the present invention's proposition is high, can realize complicated illumination task;
Description of drawings
Fig. 1 is the design concept figure of freeform optics element;
Fig. 2 is the reflection type structure of freeform optics element;
Fig. 3 is the refractive structure of freeform optics element;
Fig. 4 is the freeform optics element with refractive structure as an optical element of LED;
Fig. 5 is the freeform optics element with refractive structure as LED secondary optics element;
Fig. 6 is value discrete region schematic diagram among the embodiment 1;
Fig. 7 is the model of the refractive freeform optics element among the embodiment 1;
Fig. 8 is the illumination hot spot on the target illumination face among the embodiment 1;
Fig. 9 is the illumination curve figure on the target illumination face among the embodiment 1;
Figure 10 is the model of the refractive freeform optics element among the embodiment 2;
Figure 11 is the illumination hot spot on the target illumination face among the embodiment 2;
Embodiment
For making purpose of the present invention, technical scheme and advantage clearer, further specify the present invention below in conjunction with accompanying drawing.
The method for designing concrete steps of freeform optics element that are used for the pointolite luminous intensity distribution are as follows:
(1) structure of freeform optics element is set, according to the initial designs parameter it is carried out Random Curved Surface Designing;
(2) set up rectangular coordinate system take light source as true origin, the coordinate of any point P on the free form surface of the required design of the determined freeform optics element of step (1) is expressed as with spherical coordinates The coordinate of the impact point T corresponding with a P is expressed as T (x, y, z) with rectangular coordinate on the target illumination face; Vector P is the position vector of some P, is a vector that is pointed to some P by initial point, and vector T is the position vector of some T, is a vector that is pointed to some T by initial point, referring to accompanying drawing 1, according to refraction law n oO=n iI+P 1N sets up the coordinate relation between some P and the impact point T
x = P x + ( z - P z ) n i I x + P 1 N x n i I z + P 1 N z y = P y + ( z - P z ) n i I y + P 1 N y n i I z + P 1 N z
Wherein, vector
Figure BDA00002293243000043
P x, P yAnd P zThree components for vector P; I x, I yAnd I zBe incident ray unit's direction vector
Figure BDA00002293243000051
Three components; N x, N yAnd N zFor free form surface is vowed N=(N in the per unit system at a P place x, N y, N z) three components,
Figure BDA00002293243000052
Figure BDA00002293243000053
And P θBe respectively position vector P about angle Partial derivative with θ;
Figure BDA00002293243000055
Angle [alpha] is the angle of vector I and vector N; n iAnd n oBe respectively the refractive index of freeform optics element material therefor and the refractive index of freeform optics component ambient medium;
(3) according to law of conservation of energy, set up the energy relationship between the luminous energy that light source outgoing luminous energy and target illumination zone receive, in the situation that do not consider energy loss, the light source outgoing energy that requires the freeform optics element to receive equates with the energy in arrival target illumination zone, and namely energy satisfies relational expression
Figure BDA00002293243000056
Wherein,
Figure BDA00002293243000057
Be the intensity distributions of light source, E (x, y) is the Illumination Distribution in target illumination zone on the illuminated area, and R represents the target illumination zone, and Ω represents to incide total solid angle of the light on the freeform optics element;
(4) the some P and the relation of the coordinate between the impact point T that obtain according to step (2) have following coordinate transform relation
Figure BDA00002293243000058
Wherein, J (T) is the Jacobi matrix of position vector T,
Figure BDA00002293243000059
(5) coordinate transform in the step (4) is concerned the energy equation of substitution step (3) and removes the sign of integration, obtain describing the Energy Transfer equation of freeform optics element
Figure BDA000022932430000510
Wherein, 0≤θ≤2 π,
Figure BDA000022932430000511
(6) to guarantee also in the Energy Transfer equation of free form surface in satisfying step (5) that the boundary rays of light source outgoing incides the border of target face field of illumination behind the free form surface deviation, namely satisfy with downstream condition
Wherein,
Figure BDA00002293243000062
With
Figure BDA00002293243000063
Be respectively the border of regional Ω and R;
(7) to the boundary condition simultaneous solution in the Energy Transfer equation in the step (5) and the step (6), obtain one group of discrete data point on the free form surface, by being carried out surface fitting, this group data point can obtain FREEFORM SURFACE MODEL.
Described freeform optics element has two types of reflection-type and refractive; n o=-1, n iThe freeform optics element of=1 corresponding reflection-type, n oThe freeform optics element of=1 corresponding refractive.Described reflection-type freeform optics element only has a curved surface, and this curved surface is free form surface, referring to accompanying drawing 2.The outside surface S1 of described refractive freeform optics element is free form surface, and inside surface S2 is sphere or plane, referring to accompanying drawing 3.Described refractive freeform optics element is the outer enclosure lens of led chip, i.e. optical element of LED is referring to accompanying drawing 4.Described refractive freeform optics element is the shaping lens after the led light source, i.e. LED secondary optics element is referring to accompanying drawing 5.
Embodiment 1: the freeform optics element intends adopting structure type as shown in Figure 3, and inside surface S2 adopts sphere, and outside surface S1 is free form surface, therefore the design focuses on how designing the outside surface S1 of this freeform optics element.Light source adopts has the LED that intensity is lambertian distribution, and the intensity of supposing its optical axis direction is 1, and then the intensity distributions of this LED satisfies
Figure BDA00002293243000064
The LED bright dipping produces the circular illumination with " ZJU " printed words at the target illumination face behind this light distribution of freeform lens.Require letter and circular background to be Uniform Illumination, and both illumination ratio is 2.The z coordinate on the summit of outside surface free form surface S 1 is 20mm, and the distance of light source led distance objective illuminated area is 300mm, and the radius of circular illumination hot spot is 150mm, and the refractive index of free-form surface lens is n i=1.4935, the lens surrounding medium is that air is n o=1, the maximum shooting angle of light source that incides on the free-form surface lens is
Figure BDA00002293243000065
According to refraction law n oO=n iI+P 1N can set up the coordinate relation between a P and the impact point T
x = P x + ( z - P z ) n i I x + P 1 N x n i I z + P 1 N z y = P y + ( z - P z ) n i I y + P 1 N y n i I z + P 1 N z
Wherein, vector
Figure BDA00002293243000067
P x, P yAnd P zThree components for vector P; I x, I yAnd I zBe incident ray unit's direction vector
Figure BDA00002293243000068
Three components; N x, N yAnd N zFor free form surface is vowed N=(N in the per unit system at a P place x, N y, N z) three components,
Figure BDA000022932430000610
And P θBe respectively position vector P about angle
Figure BDA000022932430000611
Partial derivative with θ;
P 1 = n o 1 - n i 2 n o 2 ( 1 - cos 2 α ) - n i cos α , Angle [alpha] is the angle of vector I and vector N.
According to law of conservation of energy, set up the energy relationship between the luminous energy that light source outgoing luminous energy and target illumination zone receive.In the situation that do not consider energy loss, the light source outgoing energy that requires the freeform optics element to receive equates with the energy that arrives the target illumination zone, and namely energy satisfies relational expression
Figure BDA00002293243000072
Wherein, R represents the target illumination zone, and Ω represents to incide total solid angle of the light on the freeform optics element.According to the relation of the coordinate between a P and the impact point T, following coordinate transform relation is arranged
Figure BDA00002293243000073
Wherein, J (T) is the Jacobi matrix of position vector T, Bring this coordinate transform relation into Energy Transfer equation that above-mentioned energy relationship formula can obtain describing the freeform optics element
Figure BDA00002293243000075
Wherein, 0≤θ≤2 π,
Figure BDA00002293243000076
Further this Energy Transfer equation of abbreviation can obtain following ellipse Monge-Amp é re equation
Wherein, ρ θ θ,
Figure BDA00002293243000078
With
Figure BDA00002293243000079
Respectively ρ about angle θ and
Figure BDA000022932430000710
Second-order partial differential coefficient and mixed partial derivative, coefficient
Figure BDA000022932430000711
For guaranteeing the shape in target illumination zone, also need apply certain boundary condition
x = P x + ( z - P z ) n i I x + P 1 N x n i I z + P 1 N z y = P y + ( z - P z ) n i I y + P 1 N y n i I z + P 1 N z : ∂ Ω → ∂ R
Wherein
Figure BDA000022932430000713
With
Figure BDA000022932430000714
Be respectively the zone
Figure BDA000022932430000715
And R={ (x, y) | x 2+ y 2≤ 150 2The border.
For such mathematical problem, can only try to achieve its numerical solution.At first need and to incide the regional Ω discretize at the light place on the free-form surface lens, namely
Each Corresponding grid node, limitrophe net point is called frontier point, and the net point of intra-zone is internal node.The subregion that is positioned at first quartile take this zone is example, and this subregion is seen accompanying drawing 6 after discretize.Afterwards, adopt difference scheme to substitute corresponding local derviation item in energy transmission equation and the boundary condition.For internal node, adopt 9 method of difference
Figure BDA00002293243000083
9 methods have second order accuracy, for keeping precision consistent, can adopt front difference or the rear poor formula of second order according to the position of frontier point for boundary condition
ρ θ = ρ i + 1 , n - ρ i - 1 , n 2 h 1 ,
Figure BDA00002293243000085
At each node
Figure BDA00002293243000086
The place adopts corresponding difference formula, then can convert Energy Transfer equation and boundary condition to a Nonlinear System of Equations, adopts afterwards this Nonlinear System of Equations of Newton Algorithm can obtain one group of discrete data point.In CAD software, this group discrete data point is carried out surface fitting and can obtain free form surface, thereby can construct this free-form surface lens model, see accompanying drawing 7.To free-form surface lens model Geometrical Optics, obtain the hot spot that throws light at the target illumination face, see accompanying drawing 8.For ease of analog result is analyzed, the illumination curve on the render target illuminated area on the straight line y=50mm is seen accompanying drawing 9.This illumination curve clearly illustrates that, the illumination of letter and the ratio of background illuminance are 2, the method for designing of the freeform optics element that is used for pointolite (LED) luminous intensity distribution proposed by the invention effectively realized should complexity target illumination.
Embodiment 2: the freeform optics element intends adopting structure type as shown in Figure 3, and inside surface S2 adopts sphere, and outside surface S1 is free form surface, therefore the design focuses on how designing the outside surface of this freeform optics element.Light source adopts has the LED that intensity is lambertian distribution, and the intensity of supposing its optical axis direction is 1, and then the intensity distributions of this LED satisfies
Figure BDA00002293243000087
The LED bright dipping produces a uniform rectangular illumination at the target illumination face behind this light distribution of freeform lens.The z coordinate on the summit of outside surface free form surface S 1 is 7mm, and the distance of LED distance objective illuminated area is 200mm, and the length-width-ratio of rectangular illumination hot spot is the wide 250mm of being of 4:3 and hot spot, and the refractive index of free-form surface lens is n i=1.4935, the refractive index of free-form surface lens surrounding medium is n o=1, the maximum shooting angle of light source that incides on the free-form surface lens is
Figure BDA00002293243000088
Utilize the method for designing of the freeform optics element that is used for pointolite (LED) luminous intensity distribution proposed by the invention, obtain the model of this free-form surface lens, see accompanying drawing 10.To the model Geometrical Optics, obtain the hot spot that throws light at the target illumination face, see accompanying drawing 11.The method for designing of the freeform optics element that is used for pointolite (LED) luminous intensity distribution proposed by the invention has realized this predetermined rectangular illumination effectively.
By two embodiment as can be known, adopt the method for designing of the freeform optics element that is used for pointolite (LED) luminous intensity distribution proposed by the invention can realize complicated lighting requirement, can obtain continuous free form surface, realize processing of free form surface, have significant practical significance.

Claims (6)

1. method for designing that is used for the freeform optics element of pointolite luminous intensity distribution is characterized in that concrete steps are as follows:
(1) structure of freeform optics element is set, according to the initial designs parameter it is carried out Random Curved Surface Designing;
(2) set up rectangular coordinate system take light source as true origin, the coordinate of any point P on the free form surface of the required design of the determined freeform optics element of step (1) is expressed as with spherical coordinates
Figure FDA00002293242900011
The coordinate of the impact point T corresponding with a P is expressed as T (x, y, z) with rectangular coordinate on the target illumination face; Vector P is the position vector of some P, is a vector that is pointed to some P by initial point, and vector T is the position vector of some T, is a vector that is pointed to some T by initial point, according to refraction law n oO=n iI+P 1N sets up the coordinate relation between some P and the impact point T
x = P x + ( z - P z ) n i I x + P 1 N x n i I z + P 1 N z y = P y + ( z - P z ) n i I y + P 1 N y n i I z + P 1 N z
Wherein, vector
Figure FDA00002293242900013
P x, P yAnd P zThree components for vector P; I x, I yAnd I zBe incident ray unit's direction vector
Figure FDA00002293242900014
Three components; N x, N yAnd N zFor free form surface is vowed N=(N in the per unit system at a P place x, N y, N z) three components,
Figure FDA00002293242900015
Figure FDA00002293242900016
And P θBe respectively position vector P about angle
Figure FDA00002293242900017
Partial derivative with θ;
Figure FDA00002293242900018
Angle [alpha] is the angle of vector I and vector N; n iAnd n oBe respectively the refractive index of freeform optics element material therefor and the refractive index of freeform optics component ambient medium;
(3) according to law of conservation of energy, set up the energy relationship between the luminous energy that light source outgoing luminous energy and target illumination zone receive, in the situation that do not consider energy loss, the light source outgoing energy that requires the freeform optics element to receive equates with the energy in arrival target illumination zone, and namely energy satisfies relational expression
Figure FDA00002293242900019
Wherein,
Figure FDA000022932429000110
Be the intensity distributions of light source, E (x, y) is the Illumination Distribution in target illumination zone on the illuminated area, and R represents the target illumination zone, and Ω represents to incide total solid angle of the light on the freeform optics element;
(4) the some P and the relation of the coordinate between the impact point T that obtain according to step (2) have following coordinate transform relation
Figure FDA00002293242900021
Wherein, J (T) is the Jacobi matrix of position vector T,
Figure FDA00002293242900022
(5) coordinate transform in the step (4) is concerned the energy equation of substitution step (3) and removes the sign of integration, obtain describing the Energy Transfer equation of freeform optics element
Figure FDA00002293242900023
Wherein, 0≤θ≤2 π,
Figure FDA00002293242900024
(6) to guarantee also in the Energy Transfer equation of free form surface in satisfying step (5) that the boundary rays of light source outgoing incides the border of target face field of illumination behind the free form surface deviation, namely satisfy with downstream condition
Figure FDA00002293242900025
Wherein,
Figure FDA00002293242900026
With Be respectively the border of regional Ω and R;
(7) to the boundary condition simultaneous solution in the Energy Transfer equation in the step (5) and the step (6), obtain one group of discrete data point on the free form surface, by being carried out surface fitting, this group data point can obtain FREEFORM SURFACE MODEL.
2. the method for designing of a kind of freeform optics element for the pointolite luminous intensity distribution according to claim 1 is characterized in that described freeform optics element has two types of reflection-type and refractive; n o=-1, n iThe freeform optics element of=1 corresponding reflection-type, n oThe freeform optics element of=1 corresponding refractive.
3. the method for designing of a kind of freeform optics element for the pointolite luminous intensity distribution according to claim 2 is characterized in that described reflection-type freeform optics element only has a curved surface, and this curved surface is free form surface.
4. the method for designing of a kind of freeform optics element for the pointolite luminous intensity distribution according to claim 2 is characterized in that the outside surface (S1) of described refractive freeform optics element is free form surface, and inside surface (S2) is sphere or plane.
5. the method for designing of a kind of freeform optics element for the pointolite luminous intensity distribution according to claim 4 is characterized in that described refractive freeform optics element is the outer enclosure lens of led chip, i.e. optical element of LED.
6. the method for designing of a kind of freeform optics element for the pointolite luminous intensity distribution according to claim 4 is characterized in that described refractive freeform optics element is the shaping lens after the led light source, i.e. LED secondary optics element.
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