Freeform lens design method and system for expanding surface light source beam control

Abstract

The present invention discloses a design method and system for a free-form lens for expanding the beam control of an extended surface light source, which relates to the field of non-imaging optics. The present invention divides the extended surface light source into a number of small-scale light sources that can be regarded as point light sources, constructs a Monge-Ampère equation based on Snell's law and energy conservation; calculates the energy contribution of each divided independent small-scale light source on the observation plane, and calculates the illumination distribution according to the energy contribution of each small-scale light source; establishes a free-form lens beam control model for the extended surface light source, performs numerical solution, and obtains a free-form lens that meets the predetermined illumination requirements. The present invention can efficiently integrate and control the beam distribution of the extended light source, while improving the energy utilization rate, realizing a compact system structure. The system can be widely applied to a variety of optical application scenarios, including high-efficiency lighting, optical sensing, and other fields that require a compact structure and precise beam control.

Description

Technical Field

[0001] The present invention relates to the technical field of non-imaging optics and extended light sources, and particularly to a free-form lens design method and system for beam control of an extended surface light source. Background Art

[0002] An extended surface light source is a type of light source with a certain luminous area and diverse emission beam directions. Compared with a point light source, the distribution of its emitted light rays is more complex and the spatial coherence is lower, increasing the difficulty of precise beam control. The extended surface light source can achieve efficient utilization of light energy and compactness and miniaturization of the optical system. The beam control technology of such light sources has broad application prospects in LED lighting, automotive lamps, display backlights, and vision inspection systems. However, the beam control of the extended surface light source is relatively complex, and the traditional optical design method based on the assumption of a point light source is difficult to directly apply. Its main challenges include: (1) The large luminous surface of the light source results in a wide beam angle distribution, making it difficult to achieve high-uniformity illumination through simple optical elements; (2) There are non-uniformities in the luminous intensity and angle distribution of the light source, and an accurate light energy mapping relationship needs to be constructed to meet the illuminance requirements of the observation plane; (3) The design of the free-form surface needs to consider the compactness, efficiency of the optical system, and uniform control of the beam, while the traditional analytical or empirical methods have limitations in high-precision free-form surface modeling. Therefore, for the free-form surface optical design of an extended light source, a more accurate mathematical model needs to be constructed to optimize beam control and improve the performance of the optical system.

[0003] Among the existing free-form surface optical design methods for extended light sources, Patent CN202210607568 proposes a double free-form surface light homogenizing lens design method, which improves the uniformity and energy utilization rate of the beam by iteratively solving the discrete points of the free-form surface; Patent CN202311344003 adopts weighted superposition and feedback optimization, combines the particle swarm algorithm to optimize the weight factor of the lens busbar, realizes the automated optical system design, and improves the calculation efficiency and beam control accuracy; Patent CN202410904784 uses the snake optimization algorithm to optimize the free-form surface shape, realizing efficient light energy utilization and high-uniformity illumination. These methods have made progress in aspects such as beam control accuracy, application of optimization algorithms, and calculation efficiency, but there is still room for optimization in large-scale optical free-form surface solving, calculation stability of non-linear equations, and system compactness. Summary of the Invention

[0004] The purpose of the present invention is to solve the deficiencies in the technology and provide a free-form lens design method and system for beam control of an extended surface light source.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention first provides a method for designing a free-form surface lens for regulating the light beam of an extended surface light source, wherein the free-form surface lens is used to regulate the light beam of a specified extended surface light source to achieve a preset target light intensity distribution on an observation plane; the method comprises the following steps:

[0007] 1) Divide the specified extended surface light source into several independent and non-overlapping small-scale light sources, and regard each small-scale light source as a point light source;

[0008] 2) According to Snell's law and energy conservation and the specified incident surface shape of the free-form lens, the Monge-Ampere equation is constructed. The Monge-Ampere equation is used to describe the energy distribution of the light beam during the deflection and regulation process of the free-form lens;

[0009] 3) According to the Monge-Ampere equation corresponding to each small-scale light source, calculate the energy contribution of each small-scale light source on the observation plane, and calculate the illumination distribution according to the energy contribution of each small-scale light source;

[0010] 4) According to the preset target light intensity distribution on the observation plane, a free-form surface lens beam control model for the extended surface light source is constructed, and the corresponding free-form surface lens output surface data points are obtained by numerical solution, and then the corresponding free-form surface lens is constructed.

[0011] In the above design process, the extended surface light source is pre-specified, the observation plane and the target light intensity distribution thereon are also pre-given, the incident surface of the free-form surface lens is pre-given, and the exit surface of the free-form surface lens is the free-form surface to be designed. The design method obtains the exit surface surface data points of the free-form surface lens that meet the above settings, and then constructs the corresponding free-form surface lens.

[0012] On the other hand, the present invention also provides a beam control system for an extended surface light source, which includes an extended surface light source, a free-form surface lens and an observation plane; the exit surface of the free-form surface lens is a free-form surface, and the free-form surface lens is used to control the beam of the extended light source to achieve a preset light intensity distribution on the observation plane; the free-form surface lens is designed using the aforementioned method.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] 1. Aiming at the characteristics of the extended light source, the present invention adopts a light source segmentation method to discretize it into multiple small-scale light sources, and explicitly introduces the spatial position information of the light source into the Monge-Ampere equation. This method can not only accurately describe the light energy distribution of the extended light source, but also effectively solve the problems of beam divergence and uneven energy transmission caused by the large light-emitting surface, making the free-form surface design more in line with the actual optical system requirements, thereby improving the beam control accuracy and system adaptability.

[0015] 2. The present invention establishes the global illuminance distribution of the observation plane, calculates the barycenter interpolation of control points on the basis of splitting light sources, making the energy contributions of small-scale light sources more uniform in space, and reducing the calculation errors caused by local energy mutations. Subsequently, an energy superposition strategy for multiple light sources is adopted to make the global illuminance distribution more accurately match the brightness requirements of the observation plane, and combined with the optimization solution of free form surfaces, an optical system design with high uniformity and high energy utilization rate is realized, thereby enhancing the stability of free form surface design and the beam control accuracy.

[0016] 3. By constructing a large-scale Monge-Ampère equation set and solving it in combination with the Newton iteration method, the present invention can make full use of second-order partial derivative information to accelerate the convergence of the solution. Compared with traditional optimization methods, the present invention avoids the computational complexity of high-dimensional numerical integration, reduces the accumulation of local errors through global illuminance modeling and interpolation optimization, and significantly improves the convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is the design schematic diagram of a free form surface lens for expanding a surface light source;

[0019] Figure 2 It is the schematic diagram of barycenter interpolation calculation in obtaining the global illuminance distribution model;

[0020] Figure 3 It is the schematic diagram of the principle of free form surface beam control for expanding a light source;

[0021] Figure 4 It is the free form surface lens model in the embodiment;

[0022] Figure 5 It is the illuminance distribution diagram on the illumination surface after the beam of the expanded light source in the embodiment is controlled. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] To make the objectives, technical solutions and advantages of the present invention clearer and more complete, the following will further illustrate the present invention with reference to the drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0024] In this text, the terms "comprising", "including" or any other variants thereof are intended to cover non-exclusive inclusion. In addition to the listed elements, other elements not expressly listed may also be included.

[0025] In this text, the directional terms such as front, back, top, bottom, etc. are defined based on the positions of the components in the drawings and their positions relative to each other, solely for the sake of clarity and convenience in expressing the technical solution. It should be understood that the use of these directional terms should not limit the scope of protection claimed in this application.

[0026] Figure 1 It is a schematic design diagram of a freeform lens for expanding a surface light source. In the design method of the freeform lens for beam control of the surface light source, the surface light source is divided into several independent and non-overlapping small-scale light sources during the modeling process, and it is ensured that all light source positions are covered and there are no overlapping areas. The ratio of the distance between the incident surface of the freeform lens and the divided small-scale light sources to the maximum size of the small-scale light sources is greater than 5 to ensure that the divided small-scale light sources can be approximated as point light sources. As Figure 1 shown, the surface light source 101 is divided into multiple independent and non-overlapping small-scale light sources, such as the sub-light source 102. The sub-light source satisfies the "five-fold rule" and can be regarded as a point light source. The light rays emitted by this light source are regulated by the freeform lens 103 and fall on the target illumination plane 104, and at the falling point (t x1 , t y1 , 0) in the local coordinate system, a specific illuminance E(t x1 , t y1 ) acts. Each sub-light source will construct a Monge-Ampère equation for describing the deflection of the light beam by the optical freeform surface and its energy conservation and distribution according to Snell's law and energy conservation.

[0027] The specific steps of the design method of the present invention are as follows:

[0028] 1) Divide the specified surface light source into several independent and non-overlapping small-scale light sources according to the division requirements introduced above, and regard each small-scale light source as a point light source;

[0029] Among them, when dividing the extended light source, all the light-emitting positions of the surface light source are covered by the small-scale light sources, and there are no overlapping areas among the small-scale light sources.

[0030] 2) Construct a Monge-Ampère equation according to Snell's law, energy conservation, and the specified incident surface profile of the freeform lens. The Monge-Ampère equation is used to describe the energy distribution during the deflection and regulation of the light beam by the freeform lens;

[0031] Specifically, in this embodiment, step 2) can be implemented according to the following sub-steps:

[0032] 2.1) Coordinate system establishment: Establish a global rectangular coordinate system xyz, and define the coordinates of each independent small light source S in the coordinate system xyz as (s x , s y , 0); Set the coordinates of point P on the free surface serving as the lens exit surface in the coordinate system xyz as (p x , p y , p z ); Set the coordinates of point T on the observation plane in the global coordinate system xyz as (t x , t y , t z ), and the coordinates in the local coordinate system x1y1z1 of the observation plane as (t x1 , t y1 , 0); Define the normal vector of the free surface at point P as O = (O x , O y , O z );

[0033] 2.2) Observation plane equation setting: The observation plane is a preset plane in three-dimensional space, and the equation of this plane in the global coordinate system is

[0034]

[0035] where A = sinβcosα, B = sinβsinα, C = cosβ, D = -C × L, where β is the angle between the z1 axis in the local coordinate system x1y1z1 and the z axis in the global coordinate system xyz, α is the angle between the x1 axis in the local coordinate system x1y1z1 and the x axis in the global coordinate system xyz, and L is the distance from the intersection of the z axes of the local coordinate system x1y1z1 and the global coordinate system xyz to the origin;

[0036] 2.3) Light path calculation: According to Snell's law, set the light path equation from the light source point through the incident surface of the free surface lens to point P on the exit surface and then to the target point T on the observation plane, and calculate the coordinates of point T in the global coordinate system xyz:

[0037]

[0038] 2.4) According to steps 2.2) and 2.3), point T must satisfy both the plane equation and the coordinate relationship equation at the same time. Further combine, simplify, and transform the coordinate system to obtain the coordinates of the target point T in the local coordinate system x1y1z1:

[0039] where E = cosα, F = sinα;

[0040] 2.5) According to the law of conservation of energy, the energy emitted by the small-scale light source is passed through the free-form lens and generates an illuminance distribution on the observation plane. The integrated energy of the two remains consistent. Therefore, the energy constraint relationship for a ray on the small-scale light source falling on a point on the observation plane can be obtained;

[0041] Specifically, the energy constraint relationship is:

[0042]

[0043] Among them, is the luminance distribution of the small-scale light source, is the tilt angle in the spherical coordinate system, is the azimuth angle; |JT1| is the coordinate transformation Jacobian matrix from the coordinate (t x1 , t y1 , 0) on the observation plane to the free-form lens; |JT2| is respectively the coordinate transformation Jacobian matrix from the light source position (s x , s y , 0)); E(t x1 , t y1 ) is the illuminance value generated by the small-scale light source at the coordinate (t x1 , t y1 , 0);

[0044] 2.6) According to the local coordinates (t x1 , t y1 , 0) of the target point T calculated in step 2.4), combined with the energy constraint relationship in step 2.5), calculate the illuminance value E(t x , t y ) at a point (t x1 , t y1 , 0) on the observation plane after passing through the free-form lens from the light source position (s x1 , s y1 ), and further simplify to obtain the Monge-Ampère equation.

[0045] 3) According to the Monge-Ampère equations corresponding to each small-scale light source, calculate the energy contribution of each small-scale light source on the observation plane, and calculate the light distribution according to the energy contributions of each small-scale light source;

[0046] In this embodiment, the specific steps of step 3) are as follows:

[0047] 3.1) Data sampling: Based on the illuminance values of each independent small-scale light source, obtain the illuminance distribution data on the observation plane, and define the coordinate distribution of the landing points of each independent light source S i on the observation plane as (t xi , tyi , 0);

[0048] 3.2) Control point setting: Taking the center position of the extended light source as the reference, trace the light rays from the discrete points (p x , p y , p z ) on the exit surface of the freeform lens to the observation plane to obtain the control coordinate points (t xc , t yc , 0), and use them as the reference points for subsequent interpolation calculations;

[0049] 3.3) Constructing the spatial division grid: Based on the grid formed by the landing coordinates of the independent light source S i (t xi , t yi ), divide the observation plane into multiple non - overlapping grid cells, such that any reference point (t xc , t yc , 0) falls into at least one grid cell. As shown in Figure 1 and 2 , in this embodiment, the grid cells are selected as triangles. However, it should be noted that the grid cell types of the present invention can be polygons such as triangles, quadrilaterals, pentagons, etc. The subsequent embodiments will only take triangles as an example for detailed description.

[0050] 3.4) Calculating the interpolation weights: For each target control point (t xc , t yc , 0), determine the corresponding illuminance values (E1, E2, E3) of the vertex coordinates (tr1, tr2, tr3) of the triangle it is in, and calculate the barycentric weight w of this reference point with respect to grid vertex j i,j

[0051] 3.5) Interpolation calculation: Use the area - ratio weight method to calculate the illuminance value of the control point:

[0052]

[0053] Thus, construct the illuminance distribution E i at the control point positions on the observation plane for each independent light source S i (t xc , t yc ).

[0054] Figure 2 is a schematic diagram of the barycentric interpolation calculation in obtaining the global illuminance distribution model. Figure 3 is a schematic diagram of the principle of freeform beam control for an extended light source. From Figure 3It can be seen that after the extended light source 301 passes through the freeform lens 302, the light beams at different positions on the extended light source have different regulation effects, and the final regulation result is obtained by the combined action of the light rays at different positions. Therefore, it is necessary to calculate the energy contribution of each segmented small-scale light source on the observation plane and perform interpolation and superposition.

[0055] 4) According to the preset target light intensity distribution on the observation plane, construct a freeform lens beam regulation model for the extended surface light source, and perform numerical solution to obtain the data points of the exit surface shape of the corresponding freeform lens, and then construct the corresponding freeform lens.

[0056] In this embodiment, step 4) includes the following steps:

[0057] 4.1) Global illuminance distribution construction: Based on the illumination light rays of multiple small-scale light sources S i on the observation plane, establish the global illuminance distribution E global (t xc , t yc ):

[0058]

[0059] where N is the total number of small-scale light sources obtained by dividing the extended surface light source. So far, the process of calculating E global (t xc , t yc ) is the global illuminance distribution on the observation plane;

[0060] 4.2) Target illuminance distribution setting: Set the expected illuminance distribution E disire (t xc , t yc ) of the observation plane, and calculate the expected illuminance distribution E d,i (t xc , t yc ) corresponding to each light source according to the contribution of each small-scale light source to the global illuminance, satisfying:

[0061]

[0062] 4.3) Nonlinear equation system construction: According to the steps of calculating the illuminance at the target point for each light source S i in the light ray regulation process on the freeform lens, it can be expressed as the linear transformation superposition of multiple Monge-Ampère equations.

[0063] Substitute the E d,i (t xc , t yc ) calculated in step 4.2) into the above formula to obtain the equation representing the deviation between the actual radiant illuminance and the target radiant illuminance:

[0064]

[0065] Combined with E obtained in step 4.2) i (t xc , t yc ), and E d,i (t xc , t yc ), accurately describe the light ray control process on the free - form lens, and finally form a large - scale Monge - Ampère equation system;

[0066] 4.4) Numerical solution: Use the Newton iteration method or other numerical methods applicable to non - linear elliptic equation systems to solve the above equation system, calculate and update the free - form surface shape until the global error meets the convergence criterion, and finally form the free - form surface shape for controlling the extended light source beam. Example: Figure 4 It is the free - form lens model in the example. The boundary of the free - form surface is rectangular, the size of the free - form lens is 18mm×18mm×4mm, the incident surface is a plane, the exit surface is the designed free - form surface, the extended light source is located 7mm directly below the free - form surface, and the extended light source is a 1.3mm×1.3mm surface light source. It is required that the beam of the extended light source generates a circular illumination spot with an "Ω" on the observation plane after being controlled by the free - form lens. In the example, it is required that the background is uniformly illuminated, and the ratio between the letter pattern and the illuminance is 3. The designed illumination distance is 250mm, and the diameter of the circular illumination spot after control is 250mm. The refractive index of the free - form lens is 1.49386, and the medium around the lens is air. Model and solve according to the above method, and finally obtain a free - form lens that meets the design conditions and is applicable to an extended light source with a size of 1.3mm×1.3mm and a distance of 7mm from the lens, as shown in Figure 4 .

[0067] Figure 5 It is the illuminance distribution diagram on the illumination plane after the extended light source beam is controlled in the example. By performing Monte Carlo ray tracing on the free - form lens model, the illuminance distribution diagram is obtained on the observation plane, clearly showing that an illumination spot with a ratio of letter illuminance to uniform background illuminance of 3 is achieved. The example effectively realizes the design of the free - form surface for controlling the extended light source beam.

[0068] In summary, the present invention realizes the precise design of freeform surfaces and beam control for large-area area light sources by constructing a large-scale non-linear Monge-Ampère equation system applicable to extended light sources and combining the comprehensive processing of light source segmentation, global illuminance interpolation, and boundary conditions. The embodiments show that the freeform surface lens designed by the present invention exhibits high efficiency and stability in meeting various lighting requirements (such as the letter shape, uniform light spot, and different illuminance ratios in the embodiments), significantly improving the light energy utilization rate and lighting uniformity of extended light sources. Since the present invention has been specifically optimized in key aspects such as optical modeling, numerical iteration, and physical constraints, it can also ensure fast convergence and high-precision control in complex optical environments. Thus, it can be seen that the technical solution of the present invention has a wide range of applications and high reliability, can effectively solve the design problems of large-area extended light sources that are difficult to handle by traditional point-source methods, and has significant engineering application value and potential for industrial promotion.

Claims

1. A freeform lens design method for expanding the beam control of a surface light source, characterized in that The freeform lens is used to regulate the light beam of a specified extended surface light source to achieve a preset target light intensity distribution on the observation plane; the design method includes the following steps: 1) Divide the specified extended surface light source into several independent and non-overlapping small-scale light sources, and regard each small-scale light source as a point light source; 2) Construct a Monge-Ampère equation according to Snell's law, energy conservation, and the specified surface shape of the incident surface of the freeform lens. The Monge-Ampère equation is used to describe the energy distribution during the deflection and regulation of the light beam by the freeform lens; 3) Calculate the energy contribution of each small-scale light source on the observation plane according to the Monge-Ampère equation corresponding to each small-scale light source, and calculate the illumination distribution according to the energy contribution of each small-scale light source; 4) Construct a freeform lens beam regulation model for the extended surface light source according to the preset target light intensity distribution on the observation plane, and perform numerical solution to obtain the data points of the surface shape of the exit surface of the corresponding freeform lens, and then construct the corresponding freeform lens.

2. The design method according to claim 1, characterized in that, When dividing the extended light source in step 1), the light-emitting positions of all extended surface light sources are covered by small-scale light sources, and there are no overlapping areas among the small-scale light sources.

3. The design method according to claim 1, wherein The ratio of the distance between the incident surface of the freeform lens and the divided small-scale light source to the maximum size of the small-scale light source is greater than 5.

4. The design method according to claim 1, characterized in that The said step 2) includes the following steps: 21) Establish a global rectangular coordinate system xyz, and define the coordinates of each independent small-scale light source S in the coordinate system xyz as (s x , s y , 0); Set the coordinates of the point P on the free surface that serves as the exit surface of the lens in the coordinate system xyz as (p x , p y , p z ); Set the coordinates of the point T on the observation plane in the global coordinate system xyz as (t x , t y , t z ), and the coordinates in the local coordinate system x1y1z1 of the observation plane as (t x1 , t y1 , 0); Define the normal vector of the free surface at point P as O = (O x , O y , O z ); 22) Set the observation plane equation. The observation plane is a preset plane in three-dimensional space, and the equation of this plane in the global coordinate system is: ； where A, B, C, and D are the coefficients of the plane equation; 23) According to Snell's law, set the light path equation from the light source point passing through the incident surface of the freeform lens and reaching the point P on the exit surface and then hitting the target point T on the observation plane, and calculate the coordinates of point T in the global coordinate system xyz: ； 24) According to steps 22) and 23), point T must satisfy both the plane equation and the coordinate relation equation simultaneously. Further combine, simplify, and transform the coordinate system to obtain the coordinates of the target point T in the local coordinate system x1y1z1 of the observation plane as (t x1 , t y1 , 0); 25) According to energy conservation, the energy emitted by the small-scale light source passes through the freeform lens and then generates an illumination distribution on the observation plane, and the integrated energies of the two are consistent. Therefore, the energy constraint relationship of a ray on the small-scale light source falling on a point on the observation plane can be obtained; 26) According to the local coordinates (t x1 , t y1 , 0) of the target point T calculated in step 24), combined with the energy constraint relationship in step 25), calculate the illuminance value E(t x , s y , 0) of a point (t x1 , t y1 , 0) on the observation plane after passing through the free-form lens from the light source position (s x1 , t y1 ), and further simplify to obtain the Monge-Ampère equation.

5. The design method according to claim 4, characterized in that, provided that α is the angle between the x1 axis in the local coordinate system x1y1z1 of the observation plane and the x axis in the global coordinate system xyz, β is the angle between the z1 axis in the local coordinate system x1y1z1 of the observation plane and the z axis in the global coordinate system xyz, and L is the distance from the intersection of the z axes of the local coordinate system x1y1z1 and the global coordinate system xyz to the origin; Then the coefficients A = sinβcosα, B = sinβsinα, C = cosβ, D = -C×L of the plane equation in step 22); In step 24), the coordinate values satisfy: ； where the coefficients E = cosα, F = sinα.

6. The design method according to claim 4, wherein The energy constraint relationship in step 25) is: ； Among them, is the brightness distribution of the small-scale light source, is the tilt angle in the spherical coordinate system, is the azimuth angle; |JT1| is the Jacobian matrix of the coordinate transformation from the coordinate (t x1 , t y1 , 0) on the observation plane to the free-form lens; |JT2| is respectively the Jacobian matrix of the coordinate transformation from the light source position (s x , s y , 0)) to the free-form lens; E(t x1 , t y1 ) is the illuminance value generated by the small-scale light source at the coordinate (t x1 , t y1 , 0).

7. The design method according to claim 1, characterized in that In step 3), the calculation of the energy contribution of each small-scale light source on the observation plane includes the following steps: 31) Based on the illuminance values of each independent small-scale light source, obtain the illuminance distribution data on the observation plane, and define the landing point coordinate distribution of each independent light source S i on the observation plane as (t xi , t yi , 0); 32) Taking the center position of the extended light source as a reference, ray tracing is performed from discrete points (p x , p y , p z ) on the exit surface of the freeform lens to the observation plane to obtain the control coordinate points (t xc , t yc , 0), which are used as reference points for subsequent interpolation calculations; 33) Based on the distribution of the landing point coordinates (t xi , t yi ), perform spatial partitioning to divide the observation plane into multiple non-overlapping grid cells, such that any reference point (t xc , t yc , 0) falls into at least one grid cell; 34) For each reference point (t xc , t yc , 0), determine the coordinates of the vertices of the grid formed by the landing coordinates of the independent light source S i , and the corresponding illuminance values E i,j of tr i,j , where the subscript i represents the serial number of the independent light source S i , the subscript j represents the vertex serial number of the grid cell, and calculate the centroid weight w i,j of this reference point relative to the grid vertex j; 35) Calculate the illumination value of the reference point according to the centroid weight: ； Each independent light source S is thus constructed i at the position of the control point on the observation plane, the light intensity distribution E i (t xc , t yc ).

8. The design method according to claim 7, wherein The type of grid cell in step 33) is triangle, quadrilateral or pentagon.

9. The design method according to claim 7, wherein Step 4) includes the following steps: 41) Based on the illumination light rays of multiple small-scale light sources S i on the observation plane, establish the global illuminance distribution E global (t xc , t yc ) on the observation plane: ； where N is the total number of small-scale light sources obtained by dividing the extended surface light source; 42) Set the expected illuminance distribution E of the observation plane disire (t xc ,t yc ), and calculate the expected illuminance distribution E corresponding to each small-scale light source according to the contribution of each small-scale light source to the global illuminance d,i (t xc ,t yc ), satisfying: ； 43) Each light source S i The light ray regulation process on the freeform lens is represented as a superposition of linear transformations of multiple Monge-Ampère equations; Substitute the E d,i (t xc ,t yc ) calculated in step 42) into the above formula to obtain an equation characterizing the deviation between the actual irradiance and the target irradiance: ； Combined with E obtained in step 42) i (t xc ,t yc ), and E d,i (t xc ,t yc ), accurately describe the light control process on the free-form lens, and finally form a large-scale Monge-Ampère equation system; 44) Solve the above large-scale Monge-Ampère equations, update the free-form surface shape using the Newton iteration method, and finally form the free-form surface shape of the lens for regulating the extended light source beam.

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