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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CN102890342B (en
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李海峰
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

Design method of free-form surface optical element for point light source light distribution
Technical Field
The invention relates to the technical field of non-imaging optics and illumination, in particular to a design method of a free-form surface optical element for point light source light distribution.
Background
An optical curved surface is designed according to the intensity distribution of a point light source (such as an LED) and the target illumination requirement to realize the preset light distribution requirement, which is a reverse design problem and is always a hotspot and difficulty of non-imaging optical research. The free-form surface has the advantages of flexible spatial layout, design freedom degree and the like, and the free-form surface not only can greatly simplify the structure of an optical system, but also can easily realize complex illumination requirements, so the free-form surface design plays a very important role in solving the reverse problem.
Currently, free-form surfaces are often designed using an optimized design and a "Partial Differential Equation (PDE)" approach to solve this inverse illumination problem. The optimization design reduces the evaluation function by continuously changing the optimization variables by means of a certain optimization algorithm until a curved surface meeting the design requirement is obtained. Lighting optimization typically requires pursuing a large number of rays in each optimization iteration to reduce the simulation statistical noise, and the results of the optimization design are very dependent on the selection of the optimization variables, the construction of the evaluation functions, and the optimization algorithm. For a complex illumination, thousands of discrete data points are typically required to construct a free-form surface, which is not achievable with an optimal design. The design idea of the PDE method is to convert the inverse design problem into a system of first-order partial differential equations and to construct a free-form surface by numerically solving the system of equations. Compared with the optimization design, the PDE method has higher design efficiency and can realize complex illumination requirements, and the PDE method is the research focus of free-form surface design all the time. Chinese patent 200910046129.5 proposes a design method for a point light source light distribution lens, which constructs a first order partial differential equation set that a curved surface satisfies according to the law of refraction, then selects an energy topological relation to determine the energy mapping relation between the light source and the target illumination, and then solves the first order partial differential equation set by numerical values to obtain a free-form surface form. One key step in designing a free-form surface using this PDE method is to first establish an energy mapping between the light source and the target illumination. The integrability of the energy mapping relation determines the continuity of the free-form surface, and the continuous free-form surface can be obtained only by the energy mapping relation meeting the integrability condition. Some easily-obtained energy mapping relations often do not meet the integrable condition, and only discontinuous free-form surfaces can be obtained at the moment. For example, chinese patent 200910046129.5 adopts a variable separable mapping relationship to realize rectangular illumination, and as a result, only discontinuous free-form surfaces can be obtained, which undoubtedly presents great difficulty for practical processing.
Disclosure of Invention
The invention aims to provide a design method of a free-form surface optical element for point light source light distribution.
The design method of the free-form surface optical element for point light source light distribution comprises the following specific steps:
(1) setting the structure of the free-form surface optical element, and carrying out free-form surface design on the free-form surface optical element according to initial design parameters;
(2) establishing a rectangular coordinate system by taking the light source as the origin of coordinates, and expressing the coordinates of any point P on the free-form surface, which is required to be designed by the free-form surface optical element determined in the step (1), by using spherical coordinatesCoordinates of a target point T on the target illumination surface corresponding to the point P are expressed as T (x, y, z) in rectangular coordinates; the vector P is a vector of the position of the point P and is a vector pointing from the origin to the point P, and the vector T is a vector of the position of the point T and is a vector pointing from the origin to the point T according to the law of refraction noO=niI+P1N, establishing a coordinate relation between the point P and the target 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, the vector
Figure BDA00002293243000023
Px、PyAnd PzThree components of vector P; i isx、IyAnd IzIs a unit direction vector of incident light
Figure BDA00002293243000024
Three components of (a); n is a radical ofx、NyAnd NzIs the unit normal vector N = (N) of the free-form surface at point Px,Ny,Nz) The three components of (a) and (b),
Figure BDA00002293243000025
Figure BDA00002293243000026
and PθRespectively position vector P in relation to angle
Figure BDA00002293243000027
And the partial derivative of θ;
Figure BDA00002293243000028
the angle alpha is the included angle of the vector I and the vector N; n isiAnd noThe refractive index of the material used for the free-form surface optical element and the refractive index of the medium around the free-form surface optical element are respectively;
(3) according to the law of conservation of energy, the energy relation between the emergent light energy of the light source and the light energy received by the target illumination area is established, under the condition of not considering energy loss, the emergent energy of the light source received by the free-form surface optical element is required to be equal to the energy reaching the target illumination area, and the energy can meet the relational expression
Figure BDA00002293243000029
Wherein,
Figure BDA000022932430000210
as the intensity distribution of the light source, E (x, y) is the illuminance distribution of the target illumination area on the illumination surface, R denotes the target illumination area, and Ω denotes the total solid angle of light incident on the free-form surface optical element;
(4) according to the coordinate relationship between the point P and the target point T obtained in the step (2), the following coordinate transformation relationship exists
Figure BDA00002293243000031
Wherein J (T) is a Jacobi matrix of the position vector T,
Figure BDA00002293243000032
(5) substituting the coordinate transformation relation in the step (4) into the energy equation in the step (3) and removing the integral number to obtain an energy transmission equation for describing the free-form surface optical element
Figure BDA00002293243000033
Wherein theta is more than or equal to 0 and less than or equal to 2 pi,
Figure BDA00002293243000034
(6) the free-form surface meets the energy transmission equation in the step (5), and simultaneously ensures that boundary light rays emitted by the light source enter the boundary of the target surface illumination area after being deflected by the free-form surface, namely the following boundary conditions are met
Figure BDA00002293243000035
Wherein,
Figure BDA00002293243000036
and
Figure BDA00002293243000037
the boundaries of regions Ω and R, respectively;
(7) and (4) solving the energy transmission equation in the step (5) and the boundary condition in the step (6) simultaneously to obtain a group of discrete data points on the free-form surface, and performing surface fitting on the group of discrete data points to obtain the free-form surface model.
The free-form surface optical element has two types of reflection type and refraction type; n iso＝-1,ni1 corresponds to a reflection type free-form optical element, no1 corresponds to a free-form optical element of a refractive type. The reflection-type free-form surface optical element is only provided with one curved surface, and the curved surface is a free-form surface. The outer surface of the refraction type free-form surface optical element is a free-form surface, and the inner surface of the refraction type free-form surface optical element is a spherical surface or a plane. The refraction type free-form surface optical element is an external packaging lens of an LED chip, namely an LED primary optical element. The refraction type free-form surface optical element is a shaping lens behind an LED light source, namely an LED secondary optical element. Compared with the prior art, the invention has the beneficial effects that:
1) the design method of the free-form surface optical element for point light source (LED) light distribution can obtain a continuous free-form surface shape;
2) the design method of the free-form surface optical element for point light source (LED) light distribution provided by the invention has high design efficiency and can realize complex illumination tasks;
drawings
FIG. 1 is a schematic diagram of a free-form optical element design;
FIG. 2 is a reflective structure of a free-form optical element;
FIG. 3 is a refractive structure of a free-form optical element;
FIG. 4 is a free-form optical element with a refractive structure as an LED primary optical element;
FIG. 5 is a free-form optical element having a refractive structure as an LED secondary optical element;
FIG. 6 is a schematic diagram of discretization of an acquisition region in example 1;
fig. 7 is a model of a refractive free-form optical element in example 1;
FIG. 8 shows the illumination spots on the illumination surface of the object in example 1;
FIG. 9 is a graph of the illuminance on the illuminated target surface in example 1;
fig. 10 is a model of a refractive free-form optical element in example 2;
FIG. 11 shows the illumination spots on the illumination surface of the object in example 2;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the accompanying drawings.
The design method of the free-form surface optical element for point light source light distribution comprises the following specific steps:
(1) setting the structure of the free-form surface optical element, and carrying out free-form surface design on the free-form surface optical element according to initial design parameters;
(2) establishing a rectangular coordinate system by taking the light source as the origin of coordinates, and expressing the coordinates of any point P on the free-form surface, which is required to be designed by the free-form surface optical element determined in the step (1), by using spherical coordinatesCoordinates of a target point T on the target illumination surface corresponding to the point P are expressed as T (x, y, z) in rectangular coordinates; the vector P is the position vector of the point P and is the vector pointing from the origin to the point P, and the vector T is the position vector of the point T and is the vector pointing from the origin to the point T, see FIG. 1, according to the law of refraction noO=niI+P1N, establishing a coordinate relation between the point P and the target 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 the vectorMeasurement of
Figure BDA00002293243000043
Px、PyAnd PzThree components of vector P; i isx、IyAnd IzIs a unit direction vector of incident light
Figure BDA00002293243000051
Three components of (a); n is a radical ofx、NyAnd NzIs the unit normal vector N = (N) of the free-form surface at point Px,Ny,Nz) The three components of (a) and (b),
Figure BDA00002293243000052
Figure BDA00002293243000053
and PθRespectively position vector P in relation to angleAnd the partial derivative of θ;
Figure BDA00002293243000055
the angle alpha is the included angle of the vector I and the vector N; n isiAnd noThe refractive index of the material used for the free-form surface optical element and the refractive index of the medium around the free-form surface optical element are respectively;
(3) according to the law of conservation of energy, the energy relation between the emergent light energy of the light source and the light energy received by the target illumination area is established, under the condition of not considering energy loss, the emergent energy of the light source received by the free-form surface optical element is required to be equal to the energy reaching the target illumination area, and the energy can meet the relational expression
Figure BDA00002293243000056
Wherein,
Figure BDA00002293243000057
as the intensity distribution of the light source, E (x, y) is the illuminance distribution of the target illumination area on the illumination surface, R denotes the target illumination area, and Ω denotes the total solid angle of light incident on the free-form surface optical element;
(4) according to the coordinate relationship between the point P and the target point T obtained in the step (2), the following coordinate transformation relationship exists
Figure BDA00002293243000058
Wherein J (T) is a Jacobi matrix of the position vector T,
Figure BDA00002293243000059
(5) substituting the coordinate transformation relation in the step (4) into the energy equation in the step (3) and removing the integral number to obtain an energy transmission equation for describing the free-form surface optical element
Figure BDA000022932430000510
Wherein theta is more than or equal to 0 and less than or equal to 2 pi,
Figure BDA000022932430000511
(6) the free-form surface meets the energy transmission equation in the step (5), and simultaneously ensures that boundary light rays emitted by the light source enter the boundary of the target surface illumination area after being deflected by the free-form surface, namely the following boundary conditions are met
Wherein,
Figure BDA00002293243000062
and
Figure BDA00002293243000063
the boundaries of regions Ω and R, respectively;
(7) and (4) solving the energy transmission equation in the step (5) and the boundary condition in the step (6) simultaneously to obtain a group of discrete data points on the free-form surface, and performing surface fitting on the group of discrete data points to obtain the free-form surface model.
The free-form surface optical element has two types of reflection type and refraction type; n iso＝-1,ni1 corresponds to a reflection type free-form optical element, no1 corresponds to a free-form optical element of a refractive type. The reflection type free-form surface optical element has only one curved surface which is a free-form surface, and the free-form surface is shown in figure 2. The outer surface S1 of the refractive free-form optical element is a free-form surface, and the inner surface S2 is a spherical surface or a plane, as shown in fig. 3. The refraction type free-form surface optical element is an external packaging lens of an LED chip, namely an LED primary optical element, and is shown in figure 4. The refractive free-form optical element is a shaping lens behind the LED light source, i.e. an LED secondary optical element, see fig. 5.
Example 1: the free-form optical element is designed to have the structure shown in fig. 3, the inner surface S2 is a spherical surface, and the outer surface S1 is a free-form surface, so the design is focused on how to design the outer surface S1 of the free-form optical element. The light source adopts an LED with Lambertian intensity distribution, and the intensity distribution of the LED satisfies the condition that the intensity in the optical axis direction is 1
Figure BDA00002293243000064
The LED light is distributed through the free-form surface lens to generate a circular illumination with a ZJU character on a target illumination surface. The letter and the circular background are required to be uniformly illuminated, and the ratio of the illumination intensity of the letter and the circular background is 2.The z coordinate of the vertex of the free-form surface S1 on the outer surface is 20mm, the distance from the light source LED to the target illumination surface is 300mm, the radius of the circular illumination light spot is 150mm, and the refractive index of the free-form surface lens is ni=1.4935, the medium around the lens is air no=1, maximum exit angle of light source incident on free-form surface lens
Figure BDA00002293243000065
According to the law of refraction noO=niI+P1N, a coordinate relationship between the point P and the target point T can be established
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, the vector
Figure BDA00002293243000067
Px、PyAnd PzThree components of vector P; i isx、IyAnd IzIs a unit direction vector of incident light
Figure BDA00002293243000068
Three components of (a); n is a radical ofx、NyAnd NzIs fromFrom the unit normal vector N = (N) of the surface at point Px,Ny,Nz) The three components of (a) and (b),
Figure BDA000022932430000610
and PθRespectively position vector P in relation to angle
Figure BDA000022932430000611
And the partial derivative of θ;
P 1 = n o 1 - n i 2 n o 2 ( 1 - cos 2 α ) - n i cos α , the angle α is the angle between vector I and vector N.
According to the law of conservation of energy, the energy relation between the emergent light energy of the light source and the light energy received by the target illumination area is established. Under the condition of not considering energy loss, the emergent energy of the light source received by the free-form surface optical element is required to be equal to the energy reaching the target illumination area, namely the energy meets the relational expression
Figure BDA00002293243000072
Where R represents the target illumination area and Ω represents the total solid angle of light incident on the free-form optical element. According to the coordinate relationship between the point P and the target point T, there is the following coordinate transformation relationship
Figure BDA00002293243000073
Wherein J (T) is a Jacobi matrix of the position vector T,the coordinate transformation relation is substituted into the energy relation formula to obtain an energy transmission equation for describing the free-form surface optical element
Figure BDA00002293243000075
Wherein theta is more than or equal to 0 and less than or equal to 2 pi,
Figure BDA00002293243000076
further simplifying the energy transmission equation to obtain the following elliptical type Monge-Ampere equation
Where ρ isθθ、
Figure BDA00002293243000078
And
Figure BDA00002293243000079
respectively ρ about the angles θ and
Figure BDA000022932430000710
second order partial derivatives and mixed partial derivatives, coefficients
Figure BDA000022932430000711
In order to ensure the shape of the target illumination area, certain boundary conditions are applied
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
And
Figure BDA000022932430000714
are respectively regions
Figure BDA000022932430000715
And R = { (x, y) | x2+y2≤1502The boundary of.
For such a mathematical problem, only a numerical solution can be found. It is first necessary to discretize the region Ω of the light incident on the free-form surface lens, i.e., to discretize the region Ω
Each one of which isCorresponding to a mesh node, the mesh points located on the boundary are called boundary points, and the mesh points inside the region are internal nodes. Taking the sub-area of the area located in the first quadrant as an example, the sub-area is shown in fig. 6 after discretization. Then, the difference format is used to replace the corresponding partial derivatives in the energy transfer equation and the boundary conditions. For internal nodes, a nine-point difference method is adopted
Figure BDA00002293243000083
The nine-point method has second-order precision, and can adopt second-order front difference or rear difference formula according to the position of boundary 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 corresponding difference formula is adopted, so that the energy transmission equation and the boundary condition can be converted into a nonlinear equation set, and then the nonlinear equation set is solved by a Newton method to obtain a group of discrete data points. And performing surface fitting on the group of discrete data points in CAD software to obtain a free-form surface, so that a free-form surface lens model can be constructed, and the free-form surface lens model is shown in an attached figure 7. For the free-form surface lens model tracing light, an illumination light spot is obtained on a target illumination surface, see the attached figure 8. To facilitate the analysis of the simulation results, the illumination curve on the target illumination surface is plotted with the line y =50mm, see fig. 9. The illumination curve clearly shows that the ratio of the illumination of the letters to the background illumination is 2, and the design method of the free-form surface optical element for the light distribution of the point light source (LED) effectively realizes the complex target illumination.
Example 2: the free-form optical element is designed to have the structure shown in fig. 3, the inner surface S2 is a spherical surface, and the outer surface S1 is a free-form surface, so the design is focused on how to design the outer surface of the free-form optical element. The light source adopts an LED with Lambertian intensity distribution, and the intensity distribution of the LED satisfies the condition that the intensity in the optical axis direction is 1
Figure BDA00002293243000087
The LED light is distributed through the free-form surface lens to generate uniform rectangular illumination on a target illumination surface. The z coordinate of the vertex of the free curved surface S1 on the outer surface is 7mm, and the LED is illuminated from the targetThe distance between the surfaces is 200mm, the length-width ratio of the rectangular illumination light spot is 4:3, the width of the light spot is 250mm, and the refractive index of the free-form surface lens is ni=1.4935 refractive index of medium around free-form lens no=1, maximum exit angle of light source incident on free-form surface lens
Figure BDA00002293243000088
The free-form surface lens model is obtained by using the design method of the free-form surface optical element for point light source (LED) light distribution provided by the invention, and is shown in figure 10. For the model tracing light, an illumination spot is obtained on the target illumination surface, see fig. 11. The design method of the free-form surface optical element for point light source (LED) light distribution effectively realizes the preset rectangular illumination.
According to the two embodiments, the design method of the free-form surface optical element for point light source (LED) light distribution can meet complex illumination requirements, can obtain continuous free-form surfaces, achieves machining of the free-form surfaces, and has obvious practical significance.

Claims (6)

1. A design method of a free-form surface optical element for point light source light distribution is characterized by comprising the following specific steps:
(1) setting the structure of the free-form surface optical element, and carrying out free-form surface design on the free-form surface optical element according to initial design parameters;
(2) establishing a rectangular coordinate system by taking the light source as the origin of coordinates, and expressing the coordinates of any point P on the free-form surface, which is required to be designed by the free-form surface optical element determined in the step (1), by using spherical coordinates
Figure FDA00002293242900011
Coordinates of a target point T on the target illumination surface corresponding to the point P are expressed as T (x, y, z) in rectangular coordinates; the vector P is a vector of the position of the point P and is a vector pointing from the origin to the point P, and the vector T is a vector of the position of the point T and is a vector pointing from the origin to the point T according to the law of refraction noO＝niI+P1N, establishing a coordinate relation between the point P and the target 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, the vector
Figure FDA00002293242900013
Px、PyAnd PzThree components of vector P; i isx、IyAnd IzIs a unit direction vector of incident light
Figure FDA00002293242900014
Three components of (a); n is a radical ofx、NyAnd NzIs the unit normal vector N = (N) of the free-form surface at point Px,Ny,Nz) The three components of (a) and (b),
Figure FDA00002293242900015
Figure FDA00002293242900016
and PθRespectively position vector P in relation to angle
Figure FDA00002293242900017
And the partial derivative of θ;
Figure FDA00002293242900018
the angle alpha is the included angle of the vector I and the vector N; n isiAnd noThe refractive index of the material used for the free-form surface optical element and the refractive index of the medium around the free-form surface optical element are respectively;
(3) according to the law of conservation of energy, the energy relation between the emergent light energy of the light source and the light energy received by the target illumination area is established, under the condition of not considering energy loss, the emergent energy of the light source received by the free-form surface optical element is required to be equal to the energy reaching the target illumination area, and the energy can meet the relational expression
Figure FDA00002293242900019
Wherein,
Figure FDA000022932429000110
as the intensity distribution of the light source, E (x, y) is the illuminance distribution of the target illumination area on the illumination surface, R denotes the target illumination area, and Ω denotes the total solid angle of light incident on the free-form surface optical element;
(4) according to the coordinate relationship between the point P and the target point T obtained in the step (2), the following coordinate transformation relationship exists
Figure FDA00002293242900021
Wherein J (T) is a Jacobi matrix of the position vector T,
Figure FDA00002293242900022
(5) substituting the coordinate transformation relation in the step (4) into the energy equation in the step (3) and removing the integral number to obtain an energy transmission equation for describing the free-form surface optical element
Figure FDA00002293242900023
Wherein theta is more than or equal to 0 and less than or equal to 2 pi,
Figure FDA00002293242900024
(6) the free-form surface meets the energy transmission equation in the step (5), and simultaneously ensures that boundary light rays emitted by the light source enter the boundary of the target surface illumination area after being deflected by the free-form surface, namely the following boundary conditions are met
Figure FDA00002293242900025
Wherein,
Figure FDA00002293242900026
andthe boundaries of regions Ω and R, respectively;
(7) and (4) solving the energy transmission equation in the step (5) and the boundary condition in the step (6) simultaneously to obtain a group of discrete data points on the free-form surface, and performing surface fitting on the group of discrete data points to obtain the free-form surface model.
2. The method according to claim 1, wherein the free-form optical element has a free-form surfaceReflective and refractive; n iso＝-1,ni1 corresponds to a reflection type free-form optical element, no1 corresponds to a free-form optical element of a refractive type.
3. The method according to claim 2, wherein the reflection-type free-form optical element has only one free-form surface, and the free-form surface is a free-form surface.
4. The method of claim 2, wherein the outer surface (S1) of the refractive free-form optical element is a free-form surface, and the inner surface (S2) is a spherical surface or a flat surface.
5. The method as claimed in claim 4, wherein the refractive free-form optical element is an external package lens of an LED chip, i.e. an LED primary optical element.
6. The method as claimed in claim 4, wherein the refractive free-form optical element is a shaping lens behind the LED light source, i.e. an LED secondary optical element.
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WO2021093669A1 (en) * 2019-11-11 2021-05-20 苏州欧普照明有限公司 Lighting device and lighting system
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JP2018120206A (en) * 2017-01-23 2018-08-02 セイコーエプソン株式会社 Lighting system and projector
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