CN109116555A - A kind of design method of the free-form surface lens for inclined surface illumination - Google Patents

Abstract

The invention discloses a design method of a free-form surface lens used for inclined plane illumination. It belongs to the field of non-imaging optical technology. The invention sets the specific optical path structure of the free-form surface lens according to the lighting requirements, designs a free-form surface that meets the predetermined lighting requirements according to the law of refraction and the law of energy conservation, and designs a free-form surface that meets the predetermined lighting requirements, so that the outgoing light of the light source is deflected by the free-form surface. The target illumination area on the inclined surface produces a predetermined illumination spot, such as a rectangular illumination spot with the word "ZJU" and a uniform rectangular illumination spot. The emergent surface of the free-form surface lens is a free-form surface, and the incident surface is a spherical surface, and the free-form surface is obtained by fitting discrete data points with a curved surface. The invention has compact and simple structure, good shaping effect, high energy utilization rate, strong practicability and wide application range. The free-form lens can be realized by injection molding technology with optical resin and other materials.

Description

A Design Method of Free-form Surface Lens for Inclined Surface Illumination

technical field

The present invention relates to the technical field of non-imaging optics and lighting, and in particular, to a design method of a free-form surface lens for inclined surface lighting.

Background technique

Compared with traditional optical surfaces, free-form surfaces have a very high degree of design freedom, which can greatly improve the ability and flexibility of manipulating light. Using free-form surfaces to control the light field can obtain an optical system with a compact structure and excellent performance. More importantly, it can realize a new optical system that cannot be realized by traditional optical surfaces. The extremely free and flexible surface structure of free-form surfaces brings us opportunities but also brings great design challenges. The key point and difficulty of free-form surface lighting is how to control the light according to the requirements (given the distribution of incident light and the distribution of outgoing light). ) to inverse the free-form surface shape.

Among the existing beam shaping methods for free-form surfaces, the Raymapping method proposed in Chinese Patent No. 200910046129.5 predefines the mapping relationship between incident light rays and outgoing light rays according to energy conservation, and then obtains the surface shape by numerical solution. In the Ray mapping method, the integrability of the mapping relationship determines the continuity of the surface. Since it is difficult to obtain a mapping relationship that satisfies the integrable condition in free-form surface beam shaping, the free-form surface is discontinuous or the actual light distribution and target light are There is a big difference between the distributions. The MA (Monge-Ampère, MA) method proposed in Chinese patent 201210408729.3 converts a single free-form surface shaping problem into an MA equation according to the law of energy conservation and refraction, and obtains the numerical solution of the beam shaping problem by numerically solving the MA equation. Compared with the Ray mapping method, the MA method can obtain continuous free-form surfaces, and the actual light distribution is in good agreement with the target light distribution. The Supporting quadric method discretizes a continuous light distribution, and uses many quadric surfaces (such as paraboloids, ellipsoids, etc.) to construct free-form surfaces to obtain an approximate solution to the beam shaping problem. Although the above methods have been widely studied, they also face a common problem: the above-mentioned design methods are only suitable for coaxial beam shaping applications, that is, shaping applications in which the optical axis of the incident beam and the optical axis of the outgoing beam are coincident, and cannot be applied to off-axis beam shaping. The off-axis beam shaping here means that the target surface of the beam shaping application is an inclined illumination surface, that is, the angle between the French pattern of the illumination surface and the optical axis of the beam shaping system is greater than zero degrees. Compared with on-axis beam shaping, off-axis oblique illumination surface beam shaping has broader application prospects.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a design method of a free-form surface lens for inclined plane illumination.

The technical scheme of the present invention is as follows:

(1) Setting the optical path structure of the free-form surface lens, the incident surface of the free-form surface lens adopts a spherical surface, the exit surface is a free-form surface, and the light source is located at the center of the sphere of the incident surface; after the light source is refracted by the free-form surface lens, the target is obtained on the inclined illumination surface Illuminance distribution; free-form surface design of free-form surface lens according to initial design parameters;

(2) The global rectangular coordinate system xyz is established with the light source S as the coordinate origin, and the position of the point P on the free-form surface of the free-form surface lens determined in step (1) is expressed in spherical coordinates as Taking the intersection point B ₃ of the oblique illumination surface and the z-axis as the coordinate origin, establish a local coordinate system x ₁ y ₁ z ₁ on the oblique illumination surface, and make the x axis of the global coordinate system xyz and the local coordinate system x ₁ y ₁ z ₁ The direction of the x ₁ axis is the same; the angle between the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ and the z axis of the global coordinate system xyz is β, β≠0°; when from the z axis of the global coordinate system xyz to the local When the z ₁ axis of the coordinate system x ₁ y ₁ z ₁ rotates counterclockwise, β<0; when the z 1 axis from the z axis of the global coordinate system xyz to the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ is clockwise When rotating, β >0; the coordinates of the landing point T of the outgoing light on the oblique illumination surface in the global coordinate system xyz are expressed as (t _x , t _y , t _z ), and in the local coordinate system x ₁ y ₁ z ₁ The coordinates are expressed as (t _x1 , t _y1 , t _z1 ); the vector P is the position vector of the point P, which is a vector pointing to the point P from the origin of the global Cartesian coordinate system; the vector T is the position vector of the point T, which is a The vector pointing from the origin of the global Cartesian coordinate system to the point T; according to the law of refraction O=n×I+P ₁ ×N, the unit direction vector O=(O _x , O _y , O _z ) of the emitted light can be obtained, and established Coordinate relationship between point P and target point T

Among them, P _x , P _y and P _z are the three components of the position vector P of the point P; O _x , O _y and O _z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point unit normal vector at P, The angle α is the angle between the vector I and the vector N; n is the refractive index of the material used for the free-form surface lens;

(3) The coordinate relationship between the point P and the target point T obtained according to step (2) also needs to satisfy the equation of the inclined illumination surface in the global coordinate system:

At _x +Ct _z +D=0

Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point _B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; the global coordinate of the target point T is further obtained according to this equation

(4) According to the coordinate relationship between the point P and the target point T obtained in step (2), there are the following coordinate transformation relationships

where J(T) is the Jacobi matrix of the position vector T,

(5) According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, The deflection of the beamlet by the free-form surface lens satisfies the following energy relation

in, is the intensity distribution of the light source, E(t _x1 , t _y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens;

(6) While the free-form surface satisfies the energy transfer equation in step (5), it must also ensure that the boundary rays of the light beam are deflected by the free-form surface and enter the boundary of the illumination area of the target surface, that is, the following boundary conditions are satisfied

Among them, Ω ₁ represents the total solid angle of the light beam incident on the free-form surface lens, Ω ₂ represents the target illumination area on the oblique illumination surface, and are the boundaries of regions Ω ₁ and Ω ₂ , respectively;

(7) Simultaneously solve the energy transfer equation in step (5) and the boundary conditions in step (6) to obtain a set of discrete data points, which can be used for inclined surfaces by surface fitting of the set of data points. The freeform surface profile of the freeform lens for illumination.

Preferably, the refractive index of each area of the free-form surface lens is the same; the surrounding medium of the free-form surface lens is air.

Preferably, the free-form surface lens is a shaping lens after the light source, that is, a secondary lens.

Compared with the prior art, the present invention has the following beneficial effects:

1) The design method of the free-form surface lens for inclined surface illumination proposed by the present invention can realize accurate regulation of beam distribution on the inclined illumination surface;

2) The design method of the free-form surface lens for inclined surface illumination proposed by the present invention can significantly improve the energy utilization rate of the beam shaping system and realize energy saving;

3) The design method of the free-form surface lens for inclined surface illumination proposed by the present invention can promote the wide application of free-form surfaces in semiconductor lighting and semiconductor laser beam shaping;

4) The design method of the free-form surface lens for inclined surface illumination proposed by the present invention can obtain a continuously machinable free-form surface surface;

5) The design method of the free-form surface lens for inclined surface lighting proposed by the present invention has high design efficiency and can realize complex lighting tasks.

Description of drawings

Figure 1 is a schematic diagram of the design of a free-form surface lens;

Fig. 2 is the optical structure of free-form surface lens;

Fig. 3 is a free-form surface lens as a beam shaping secondary lens;

Fig. 4 is the model of the free-form surface lens in the embodiment;

FIG. 5 is an illuminance distribution diagram on an inclined illumination surface in an embodiment.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings.

The specific steps of the design method of the free-form surface lens for inclined surface illumination are as follows:

(1) Setting the optical path structure of the free-form surface lens, the incident surface of the free-form surface lens adopts a spherical surface, the exit surface is a free-form surface, and the light source is located at the center of the sphere of the incident surface; after the light source is refracted by the free-form surface lens, the target is obtained on the inclined illumination surface Illuminance distribution; free-form surface design according to initial design parameters;

(2) The global rectangular coordinate system xyz is established with the light source S as the coordinate origin, and the position of the point P on the free-form surface of the free-form surface lens determined in step (1) is expressed in spherical coordinates as Taking the intersection point B ₃ of the oblique illumination surface and the z-axis as the coordinate origin, establish a local coordinate system x ₁ y ₁ z ₁ on the oblique illumination surface, and make the x axis of the global coordinate system xyz and the local coordinate system x ₁ y ₁ z ₁ The direction of the x ₁ axis is the same; the angle between the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ and the z axis of the global coordinate system xyz is β; when from the z axis of the global coordinate system xyz to the local coordinate system x ₁ y When the z ₁ axis of ₁ z ₁ rotates counterclockwise, β &lt;0; when the z 1 axis from the z axis of the global coordinate system xyz to the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ rotates clockwise, β &gt; 0. The coordinates of the landing point T of the outgoing light on the oblique illumination surface in the global coordinate system xyz are expressed as (t _x , t _y , t _z ), and the coordinates under the local coordinate system x ₁ y ₁ z ₁ are expressed as (t _x1 ,t _y1 ,t _z1 ). The vector P is the position vector of the point P, which is a vector pointing to the point P from the origin of the global coordinate system; the vector T is the position vector of the point T, which is a vector pointing to the point T from the origin of the global coordinate system; see Figure 1 , according to the law of refraction O=n×I+P ₁ ×N, obtain the unit direction vector O=(O _x , O _y , O _z ) of the emitted light, and establish the coordinate relationship between the point P and the target point T

Among them, P _x , P _y and P _z are the three components of the position vector P of the point P; O _x , O _y and O _z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point Unit French at P, The angle α is the angle between the vector I and the vector N; n is the refractive index of the material used for the free-form lens, and the medium around the free-form lens is air;

(3) The coordinate relationship between the point P and the target point T obtained according to step (2) also needs to satisfy the equation of the inclined illumination surface in the global coordinate system, and the following relationship

At _x +Ct _z +D=0

Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point _B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; further obtain the global coordinate of the target point T according to this relationship

(4) According to step (3), the global coordinates (t _x , t _y , t _z ) of the point P are obtained, and the local coordinates (t _x1 , t z ) of the point P are obtained from the transformation relationship between the global coordinates and the local coordinates of the point P t _y1 ,t _z1 ), there is the following relation

(5) According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, The deflection of the beamlet by the free-form surface lens satisfies the following energy relation

in, is the intensity distribution of the light source, E(t _x1 , t _y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens;

(6) While the free-form surface satisfies the energy transfer equation in step (5), it must also ensure that the boundary rays of the light beam are deflected by the free-form surface and enter the boundary of the illumination area of the target surface, that is, the following boundary conditions are satisfied

Among them, Ω ₁ represents the total solid angle of the light beam incident on the free-form surface lens, Ω ₂ represents the target illumination area on the oblique illumination surface, and are the boundaries of regions Ω ₁ and Ω ₂ , respectively;

(7) Simultaneously solve the energy transfer equation in step (5) and the boundary conditions in step (6) to obtain a set of discrete data points, and a free-form surface can be obtained by performing surface fitting on the set of data points.

The incident surface S1 of the free-form curved lens is a spherical surface, and the exit surface S2 is a free-form curved surface, see FIG. 2 . The free-form surface lens is a shaping lens after the light source, that is, a secondary lens, see FIG. 3 .

Example: The free-form surface lens is proposed to adopt the structure type shown in FIG. 3 , the incident surface S1 is a spherical surface, the exit surface S2 is a free-form surface, and the light source is located at the center of the sphere of the incident surface S1. The light source is a Lambertian light source with a cosine intensity distribution, assuming that the intensity distribution of the light source satisfies It is required that the outgoing beam of the light source is deflected by the free-form surface lens to generate a rectangular illumination spot with the word "ZJU" in the target illumination area of the inclined illumination surface. The letters and the rectangular background are required to be uniformly illuminated, and the illuminance ratio of the two is 2. According to the lighting spot requirements, the illuminance distribution E(t _x1 , t _y1 ) of the target lighting area on the inclined lighting surface in step (5) can be determined. The z-coordinate of the vertex of the spherical surface S1 of the incident surface is 12mm, the z-coordinate of the vertex of the free-form surface S2 of the output surface is 25mm, the z-coordinate of the intersection point _B3 of the oblique illumination surface and the z-axis of the global coordinate system xyz is 600mm, and the z-coordinate of the oblique illumination surface is 600mm. The angle of inclination is β=42°; the length and width of the rectangular illumination spot are both 800mm, the refractive index of the free-form surface lens is n=1.4935, the medium around the lens is air, and the maximum exit angle of the light source incident on the free-form surface lens is

According to the law of refraction O=n×I+P ₁ ×N, the unit direction vector O=(O _x , O _y , O _z ) of the emitted light is obtained, and the coordinate relationship between the point P and the target point T is established

Among them, P _x , P _y and P _z are the three components of the position vector P of the point P; O _x , O _y and O _z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point Unit French at P, The angle α is the angle between the vector I and the vector N. The coordinate relationship between the point P and the target point T also needs to satisfy the equation of the inclined illumination surface in the global coordinate system, which has the following relationship

At _x +Ct _z +D=0

Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point _B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; further obtain the global coordinate of the target point T according to this relationship

From the global coordinates (t _x , _ty , t _z ) of the point P, and the transformation relationship between the global coordinates and the local coordinates of the point P, the local coordinates (t _x1 , t _y1 , t _z1 ) of the point P are obtained, there are The following relation

According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, the free-form surface lens. The deflection of the beamlet satisfies the following energy relation

in, is the intensity distribution of the light source, E(t _x1 , t _y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens. Further simplifying the energy transfer equation, the following elliptical Monge-Ampère equation can be obtained

Among them, ρ _θθ , and are ρ with respect to the angle θ and The second partial and mixed partial derivatives of , the coefficients In order to ensure the shape of the target illumination area on the oblique illumination surface, certain boundary conditions need to be applied.

in and area respectively and Ω ₂ ={(x,y)|-400mm≤x≤400mm,-400mm≤y≤400mm} boundary.

For such a highly nonlinear partial differential equation, only its numerical solution can be obtained. First, it is necessary to discretize the region Ω ₁ where the light beam incident on the free-form surface lens is located to obtain a set of discrete grid points, and each grid node corresponds to a partial differential equation; then, the difference is used to replace the partial differential equation in The energy transfer equation and boundary conditions can be converted into a nonlinear equation system; finally, a set of discrete data points can be obtained by solving the nonlinear equation system using Newton's method. The free-form surface can be obtained by performing surface fitting on the set of discrete data points in CAD software, so that the free-form surface lens model can be constructed, as shown in FIG. 4 . Trace the light rays on the free-form surface lens model, and obtain the illuminance distribution diagram on the inclined target illumination surface, as shown in Figure 5. The illuminance distribution diagram clearly shows that the ratio of the illuminance of the letter to the background illuminance is 2, and the design method of the free-form surface lens for inclined surface illumination proposed by the present invention effectively realizes the complex target illumination.

It can be seen from the embodiments that the design method of the free-form surface lens for inclined surface illumination proposed by the present invention can realize complex lighting requirements, obtain a continuous free-form surface, and realize the machinability of the free-form surface, which has significant practical significance. .

Claims (3)

1. a design method for the free-form surface lens of inclined plane illumination, it is characterized in that concrete steps are as follows: (1) Setting the optical path structure of the free-form surface lens, the incident surface of the free-form surface lens adopts a spherical surface, the exit surface is a free-form surface, and the light source is located at the center of the sphere of the incident surface; after the light source is refracted by the free-form surface lens, the target is obtained on the inclined illumination surface Illuminance distribution; free-form surface design of free-form surface lens according to initial design parameters; (2) The global rectangular coordinate system xyz is established with the light source S as the coordinate origin, and the position of the point P on the free-form surface of the free-form surface lens determined in step (1) is expressed in spherical coordinates as Taking the intersection point B ₃ of the oblique illumination surface and the z-axis as the coordinate origin, establish a local coordinate system x ₁ y ₁ z ₁ on the oblique illumination surface, and make the x axis of the global coordinate system xyz and the local coordinate system x ₁ y ₁ z ₁ The direction of the x ₁ axis is the same; the angle between the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ and the z axis of the global coordinate system xyz is β, β≠0°; when from the z axis of the global coordinate system xyz to the local When the z ₁ axis of the coordinate system x ₁ y ₁ z ₁ rotates counterclockwise, β<0; when the z 1 axis from the z axis of the global coordinate system xyz to the z ₁ axis of the local coordinate system x ₁ y ₁ z ₁ is clockwise When rotating, β >0; the coordinates of the landing point T of the outgoing light on the oblique illumination surface in the global coordinate system xyz are expressed as (t _x , t _y , t _z ), and in the local coordinate system x ₁ y ₁ z ₁ The coordinates are expressed as (t _x1 , t _y1 , t _z1 ); the vector P is the position vector of the point P, which is a vector pointing to the point P from the origin of the global Cartesian coordinate system; the vector T is the position vector of the point T, which is a The vector pointing from the origin of the global Cartesian coordinate system to the point T; according to the law of refraction O=n×I+P ₁ ×N, the unit direction vector O=(O _x , O _y , O _z ) of the emitted light can be obtained, and established Coordinate relationship between point P and target point T Among them, P _x , P _y and P _z are the three components of the position vector P of the point P; O _x , O _y and O _z are the three components of the unit direction vector O of the outgoing ray at the point P; N is the free-form surface at the point unit normal vector at P, The angle α is the angle between the vector I and the vector N; n is the refractive index of the material used for the free-form surface lens; (3) The coordinate relationship between the point P and the target point T obtained according to step (2) also needs to satisfy the equation of the inclined illumination surface in the global coordinate system: At _x +Ct _z +D=0 Among them, A=sinβ, C=cosβ and D=-C×L, L is the z-coordinate of the intersection point _B3 of the z-axis of the oblique illumination surface and the global coordinate system xyz; the global coordinate of the target point T is further obtained according to this equation (4) According to the coordinate relationship between the point P and the target point T obtained in step (2), there are the following coordinate transformation relationships where J(T) is the Jacobi matrix of the position vector T, (5) According to the law of local energy conservation, without considering the energy loss, it is required that any light beam emitted by the light source is deflected by the free-form surface lens and all its energy is transmitted to the target illumination area on the inclined illumination surface, that is, The deflection of the beamlet by the free-form surface lens satisfies the following energy relation in, is the intensity distribution of the light source, E(t _x1 , t _y1 ) is the illuminance distribution of the target illumination area on the oblique illumination surface, J(T) is the Jacobi matrix of the position vector T, 0≤θ≤2π, in is the maximum divergence angle of the light beam incident on the free-form surface lens; (6) While the free-form surface satisfies the energy transfer equation in step (5), it must also ensure that the boundary rays of the light beam are deflected by the free-form surface and enter the boundary of the illumination area of the target surface, that is, the following boundary conditions are satisfied Among them, Ω ₁ represents the total solid angle of the light beam incident on the free-form surface lens, Ω ₂ represents the target illumination area on the oblique illumination surface, and are the boundaries of regions Ω ₁ and Ω ₂ , respectively; (7) Simultaneously solve the energy transfer equation in step (5) and the boundary conditions in step (6) to obtain a set of discrete data points, which can be used for inclined surfaces by surface fitting of the set of data points. The freeform surface profile of the freeform lens for illumination. 2 . The method for designing a free-form surface lens for inclined surface illumination according to claim 1 , wherein the refractive index of each area of the free-form surface lens is the same; and the surrounding medium of the free-form surface lens is air. 3 . 3 . The method for designing a free-form surface lens for inclined surface illumination according to claim 1 , wherein the free-form surface lens is a shaping lens after the light source, that is, a secondary lens. 4 .