An extended LED light source free-form lens design method

Abstract

The present application belongs to the technical field of optical design, and particularly relates to a design method of an extended LED light source free-form lens. The design method comprises the following steps: constructing an initial lens structure according to a point light source; obtaining an irradiation surface illumination distribution by using an optical tracing technology to construct a global evaluation function; weighting and superimposing lens generatrix by using a particle swarm algorithm; obtaining a new lens generatrix by using a feedback optimization algorithm; adding the obtained new lens generatrix to the weighted and superimposed lens generatrix, and iterating the foregoing steps to solve an optimal weight factor group. The present application realizes cross-software communication interconnection through an interface provided by simulation and programming software, not only automatically optimizes a design process, but also improves an upper limit of an optimization effect while having a high working efficiency.

Description

Technical Field

[0001] This invention belongs to the field of optical design technology, specifically relating to a design method for a freeform surface optical system. Background Technology

[0002] Freeform surfaces are complex surfaces with non-rotational symmetry properties. They are typically represented by adding additional modified polynomials to rotationally symmetric surfaces (such as spheres, ellipsoids, hyperbolas, or parabolas). Due to their rich design freedom, freeform surfaces are more convenient for optimizing various aberrations in optical system design, thereby achieving high-performance optical systems. They have wide applications in deep space exploration, microscopic resolution, and spectral analysis.

[0003] Freeform optical surfaces are widely used in non-imaging optical systems, especially in LED lighting design. LED light sources have advantages such as low energy consumption, high efficiency, small size, and long lifespan, and are widely used in various lighting fields such as road lighting, automotive lighting, and indoor lighting.

[0004] In the design of freeform surface non-imaging systems, secondary light distribution design methods based on extended light sources mainly include the "Synchronous Multisurface (SMS)" method and the "Generalized Function Method." The SMS method directly obtains the surface shape of the target system by solving a series of partial differential equations, while the "Generalized Function Method" achieves uniform illumination by discretizing the extended light source into multiple point sources. However, the SMS method requires solving complex partial differential equations, making it difficult and offering weaker control over intermediate rays; the "Generalized Function Method" is also complex and has lower luminous efficiency. More automated and powerful freeform surface optical system design methods can foster the design of higher-performance freeform surface optical systems, which is of great significance for the development of high-performance freeform surface optical systems. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a design method for freeform lenses of extended LED light sources based on weighted superposition and feedback optimization. This method enables fully automated design and optimization of freeform lenses given initial system parameters, and ultimately provides an optical system design that meets the requirements.

[0006] The extended LED light source freeform lens design method provided by this invention employs weighted superposition and feedback optimization techniques. The specific steps are as follows:

[0007] Step 1: Construct the initial lens structure; treat the LED light source as a Lambertian point source and sample the light source according to equal luminous flux; sample the irradiation surface by dividing it into equal areas; map the light source sampling to the irradiation surface sampling; apply the vector form of the law of refraction to each sampling point to obtain the normal vector of that point, and then extend its tangent direction to the intersection point with the next sampling angle, which is the next sampling point; iteratively calculate the coordinates of all sampling points on the generatrix; fit the sampling points to obtain the initial structure of the freeform lens;

[0008] Step 2: Construct a global evaluation function; use the irradiance non-uniformity of the irradiated surface obtained by optical simulation lens couple to evaluate the quality of the weighting factor, and its independent variable is the weighting factor of each bus in the bus list.

[0009] Step 3, weighted superposition of lens generatrices; after obtaining the lens generatrices obtained from the point light source, translate and copy them by an appropriate distance as members of the list; use the weight factor of each member in the list as an optimization variable and traverse the entire multidimensional space; judge the quality of its current position by the fitness of each particle itself, and find the optimal value of the weight factor.

[0010] Step 4: Feedback optimization of lens generatrix; based on the actual and expected irradiance distribution of the target surface, readjust the grid distribution of the target surface or the solid angle division of the light source; establish a new mapping relationship between the target surface irradiance and the light source energy; establish a new lens based on the new mapping relationship between the target surface irradiance and the light source energy;

[0011] Step 5: Iteratively solve for the optimal weight factor set; evaluate whether the lens obtained in Step 3 meets the design requirements based on the evaluation function constructed in Step 2; if it does, output the lens and its weight factors; if it does not, perform feedback optimization; add the lens bus obtained in Step 4 to the lens bus list in Step 3, perform PSO optimization, and evaluate whether the obtained lens meets the design requirements based on the evaluation function constructed in Step 2; repeat Step 3 to Step 5 until the lens meets the design requirements, and output the final obtained lens and its weight factor set.

[0012] Furthermore, in step 1, an initial lens structure is constructed. This initial lens is an ideal lens designed based on a point light source, with its upper surface being a freeform surface and its lower surface being a concave sphere, assuming the point light source is located at the center of the sphere. The advantage lies in treating the extended light source as a point light source in the initial design structure, enabling the rapid acquisition of an optimized lens surface generatrix based on the initial conditions; the upper surface being a freeform surface and the lower surface being a sphere allows for optimization design focusing solely on the upper surface while ignoring the lower surface, significantly reducing the difficulty of optimization.

[0013] Furthermore, in step 2, a global evaluation function is constructed based on the irradiance distribution generated by each lens on the irradiation surface. The magnitude of the evaluation function is linearly related to the irradiance uniformity. Its advantage lies in the fact that the evaluation function is closely related to the optimization variables, and the process of finding the optimal weighting factors can be transformed into finding the maximum value of the evaluation function through an algorithm, simplifying the solution process.

[0014] Furthermore, in step 3, the lens genes are weighted and superimposed. Based on the initial structure constructed in step 1, displacement replication is performed to obtain a list of lens genes to be weighted. Each gene has its corresponding weight factor. The values ​​of all weight factors are collectively referred to as a particle in the PSO algorithm, which traverses the solution space to search for the optimal solution. Its advantage lies in the fact that the Particle Swarm Optimization (PSO) algorithm is based on an iterative method, which narrows the search range by finding relatively optimal positions for particles, thus achieving a fast convergence search effect.

[0015] Furthermore, in step 4, the lens generatrix is ​​optimized through feedback. If the lens obtained after step 3 does not meet the design requirements, it is optimized through feedback. This feedback optimization process is an overoptimization, involving multiple feedback optimizations based on the irradiance distribution results of a single simulation, allowing the optimization results to appropriately exceed expectations. Its advantage lies in enabling lenses that do not meet the design requirements in step 3 to escape local optima.

[0016] Furthermore, in step 5, the optimal weight factor set is iteratively solved. When adding the lens obtained in step 4 to the lens generatrix list in step 3, a particle in the PSO process is defined rather than randomly assigned a value, which is the weight distribution obtained in the previous optimization and the lens generatrix weight added in step 4. Its advantage is that it allows the particle swarm optimization algorithm to remember the optimal position of the previous cycle, effectively accelerating its convergence speed.

[0017] The positive and progressive effects of this invention are as follows:

[0018] The design method of this invention, based on obtaining the lens fitting curve through weighted superposition, further improves the optimizability of the lens by using a feedback optimization method; optimizes the weight factors of each surface through the particle swarm optimization algorithm to minimize the evaluation function based on the uniformity of illumination on the target surface; and realizes cross-software communication and interconnection through the interface provided by simulation and programming software, which not only realizes a fully automated optimization design process, but also improves the upper limit of optimization effect while maintaining high work efficiency. Attached Figure Description

[0019] Figure 1 This is a flowchart of the extended LED light source freeform surface lens design method based on weighted superposition and feedback optimization according to the present invention.

[0020] Figure 2This is a schematic diagram illustrating the principle of the weighted superposition design method involved in this invention.

[0021] Figure 3 This is a schematic diagram illustrating the principle of the feedback optimization design method involved in this invention. In the diagram, (a) shows the irradiance distribution of the target surface before feedback optimization, and (b) shows the irradiance distribution of the target surface after feedback optimization.

[0022] Figure 4 The figures show a comparison of the results before and after optimization in an embodiment of the present invention. (a) shows the irradiance distribution of the target surface before optimization, and (b) shows the irradiance distribution of the target surface after optimization. Detailed Implementation

[0023] The present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0024] An extended LED light source freeform lens design method based on weighted superposition and feedback optimization, the process of which is as follows: Figure 1 As shown. By calculating the optimal solution of the weighting factors of each busbar, a freeform surface lens that meets the design requirements is obtained. The specific steps are as follows:

[0025] Step 1, construct the initial lens structure. The specific steps are as follows:

[0026] Step S1.1: Consider the LED light source as a Lambertian point light source, its expression is:

[0027] I(θ)=I0cosθ, (1)

[0028] Where I0 is the luminous intensity distribution in the direction perpendicular to the normal of the light source surface, and θ is the emission angle of the light ray;

[0029] Divide the energy space of the light source into N = 30 equal parts. The ring between two adjacent sampling angles of the Lambertian point source contains 1 / 30 of the total luminous flux, denoted as φ0:

[0030]

[0031] The magnitude of each sampling angle θ can be obtained from the above formula;

[0032] Step S1.2: Divide the target surface into a set of circles with different radii, each with an area of ​​equal area. The area of ​​the annulus between two adjacent circles is S0.

[0033]

[0034] Where R is the radius of the entire target surface, specifically, R = 700 mm, r i Let i be the radius of the circles divided by equal area, where i ranges from 1 to 30. The radius of each circle can be calculated as follows:

[0035]

[0036] By mapping each sampling angle to a circle, the normal vector of each sampling point is calculated using the vector form of the law of refraction.

[0037]

[0038] Where n is the refractive index of the material, For the emitted light, For the incident light ray, It is the normal vector;

[0039] Step S1.3: After obtaining the normal vector of the first point, extend its tangent direction and the intersection point with the next sampling angle to obtain the second point of the lens generatrix. By iterating in this way, all sampling points on the generatrix can be obtained, thus obtaining the initial lens structure.

[0040] Step 2, construct the global evaluation function;

[0041] The positional quality of particles is evaluated by the irradiance non-uniformity U of the irradiated surface obtained through a simulated lens, with the independent variables being the weighting coefficients w1, w2, w3, w4, w5, ..., w of each generatrix. add , where w add Given the weight coefficients of the surface obtained from feedback optimization, the evaluation function can be written as:

[0042] F0(w1,w2,…,w i ,w add )=1-U, (6)

[0043] It can be observed that the objective evaluation function F is related to the optimization variables w1, w2, ..., w i If the values ​​are closely related to and linearly related to U, then the process of finding the optimal weighting factor can be transformed into finding the maximum value of the evaluation function F using the particle swarm optimization algorithm, which is very simple to solve.

[0044] Step 3, weighted superposition of lens genes, the specific operation steps are as follows:

[0045] Step S3.1: Define the generatrix list; after obtaining the lens generatrix from the point light source, translate and copy it by a suitable distance, and assign weight factors w1, w2, w3, w4, and w5 to the five obtained generatrixes S1, S2, S3, S4, and S5 respectively to obtain five new weighted generatrixes S′1, S′2, S′3, S′4, and S′5; define the sampling ray L, divide the range from 0 to π / 2 into M = 30 parts, and the i-th ray L... i The angle between the x-axis and the positive x-axis is:

[0046]

[0047] The number of buses needs to be chosen appropriately. Too few buses will result in an unsatisfactory optimization effect due to too few optimization variables, while too many buses will lead to a decrease in optimization efficiency and a slower convergence speed. Therefore, we choose 5 here.

[0048] Ray L i The ray L intersects the generatrixes S′1, S′2, S′3, S′4, and S′5 at points P1, P2, P3, P4, and P5 respectively. Since the generatrixes are also composed of points, the ray L needs to be determined first when calculating the intersection point P. i Between which two points on the busbar S′1 should L be calculated? i The intersection point between the lines connecting the two points is point P1[x1(i), 0, z1(i)]. Then, by adding the coordinates of P1, P2, P3, P4, and P5, we can obtain the points on the final weighted lens generatrix S. The coordinates of each point on the generatrix can be represented as:

[0049]

[0050] Wherein, the weighting factor w1+w2+w3+w4+w5=1; rotating the obtained generatrix S by 360° yields a new freeform lens based on an LED extended light source, such as... Figure 2 As shown;

[0051] Step S3.2: Treat w1, w2, w3, w4, and w5 as a single particle and use the particle swarm optimization algorithm (Reference 1) to find the weight factor set for the optimal solution. All particles are searched in a five- or six-dimensional space (after the first round of iteration, a new feedback optimization surface is added to the generatrix list, increasing the number of variables from five to six). The fitness of each particle is used to determine the quality of its current position, and the best position experienced and the current best position of the entire population are remembered. The fitness is obtained using the evaluation function constructed in Step 2. After traversing the entire particle swarm, if a particle's current best position is closer to the optimal value than the overall optimal position, then the optimal position of this population is updated to that position. The relevant parameter settings for the particle swarm optimization algorithm are shown in Table 1.

[0052] Table 1 Parameters of PSO

[0053] Particle number of population N 20 Optimization times T 30 Dimensions of particle D 5or 6 <![CDATA[Leaning factor C1]]> 2 <![CDATA[Leaning factor C2]]> 2 Inertia weightω 0.6

[0054] Step 4, feedback optimization of the lens busbar, the specific operation steps are as follows:

[0055] Step S4.1: Calculate the deformation coefficient of each annular region; use simulation software to track the optimized lens, and the average irradiance of each concentric annular region on the target surface is... Where the subscript i represents the number of the annular cell region on the target surface, and the number in the superscript parentheses represents the number of feedback optimizations; then the received optical flux on the target surface is:

[0056]

[0057] In the formula, S is the total area on the target surface. Let i be the area of ​​the i-th ring in the m-th feedback optimization. Transforming the above equation, we get:

[0058]

[0059] Define the deformation coefficient

[0060]

[0061] Then we can obtain:

[0062]

[0063] Therefore, in the (m+1)th feedback optimization:

[0064]

[0065] Step S4.2: According to Adjusting the area of ​​the ring-shaped mesh cells and reconstructing the mapping relationship yields a new lens. The feedback optimization process involves over-optimization; multiple feedback optimizations are performed based on the irradiance distribution results of a single simulation, allowing the optimization results to appropriately exceed expectations, resulting in a new lens generatrix. Figure 3 As shown.

[0066] Step 5: Iteratively solve for the optimal set of weight factors. The specific steps are as follows:

[0067] Step S5.1: Use the evaluation function defined in step 2 to evaluate whether the lens meets the design requirements. If it does, output the result; if it does not, repeat steps 3 to 5.

[0068] Step S5.2: Add the lens generatrix obtained in step S4.2 to the surface list in step S3.1. In the next round of PSO optimization in step S3.2, modify the position of one of the randomly distributed particles to:

[0069] (w1 / 2,w2 / 2,w3 / 2,w4 / 2,w5 / 2,1 / 2), (14)

[0070] Then return to step 3 and continue optimizing until the target evaluation function U of the lens obtained after this weight allocation and superposition meets the requirements. Stop the loop, output the lens result, and compare the effects before and after optimization. Figure 4as shown.

[0071] References

[0072] 1, P. Zhou et al., "Application of particle swarm optimization in the design of a mono-capillary X-ray lens," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 953, p. 163077, 2020 / 02 / 11 / 2020, doi: https: / / doi.org / 10.1016 / j.nima.2019.163077.

Claims

1. A method for designing freeform surface lenses for LED light sources, characterized in that, The weighted superposition and feedback optimization techniques are employed, and the specific steps are as follows: Step 1: Construct the initial lens structure; treat the LED light source as a Lambertian point source and sample the light source according to equal luminous flux; sample the irradiation surface by dividing it into equal areas; map the light source sampling to the irradiation surface sampling; apply the vector form of the law of refraction to each sampling point to obtain the normal vector of that point, and then extend its tangent direction to the intersection point with the next sampling angle, which is the next sampling point; iteratively calculate the coordinates of all sampling points on the generatrix; fit the sampling points to obtain the initial structure of the freeform lens; Step 2, construct the global evaluation function; The quality of the weighting factor is evaluated by using the irradiation non-uniformity of the irradiated surface obtained by optical simulation lens, with the independent variable being the weighting factor of each bus in the bus list. Step 3, weighted superposition of lens generatrices; after obtaining the lens generatrices obtained from the point light source, translate and copy them by an appropriate distance as members of the list; use the weight factor of each member in the list as an optimization variable and traverse the entire multidimensional space; judge the quality of its current position by the fitness of each particle itself, and find the optimal value of the weight factor. Step 4: Feedback optimization of lens generatrix; based on the actual and expected irradiance distribution of the target surface, readjust the grid distribution of the target surface or the solid angle division of the light source; establish a new mapping relationship between the target surface irradiance and the light source energy; establish a new lens based on the new mapping relationship between the target surface irradiance and the light source energy; Step 5: Iteratively solve for the optimal weight factor set; evaluate whether the lens obtained in Step 3 meets the design requirements based on the evaluation function constructed in Step 2; if it does, output the lens and its weight factors; if it does not, perform feedback optimization; add the lens generatrix obtained in Step 4 to the lens generatrix list in Step 3, perform PSO optimization, and evaluate whether the obtained lens meets the design requirements based on the evaluation function constructed in Step 2; repeat Steps 3 to 5 until the lens meets the design requirements, and output the final obtained lens and its weight factor set. Step 4, which involves optimizing the feedback lens bus, includes the following specific steps: Step S4.1: Calculate the deformation coefficient of each annular region: Use simulation software to trace the optimized lens. The average irradiance of each concentric annular region on the target surface is... Where the subscript i represents the number of the annular cell region on the target surface, and the number in the superscript parentheses is the number of feedback optimizations; then the received light flux on the target surface is: ， （9） In the formula, S is the total area on the target surface. Let i be the area of ​​the i-th ring in the m-th feedback optimization. Transforming the above equation, we get: ， （10） Define the deformation coefficient : ， （11） Then we get: , (12) Therefore, in the (m+1)th feedback optimization: ， （13） Step S4.2: According to Adjusting the area of ​​the annular mesh cells and reconstructing the mapping relationship yields a new lens. The feedback optimization process is an over-optimization process, where multiple feedback optimizations are performed based on the irradiance distribution results of a single simulation, allowing the optimization results to appropriately exceed expectations, resulting in a new lens generatrix.

2. The design method according to claim 1, characterized in that, Step 1 describes the construction of the initial lens structure, and the specific operation steps are as follows: Step S1.1: Consider the LED light source as a Lambertian point light source, its expression is: ， （1） in, The luminous intensity distribution is perpendicular to the normal direction of the light source surface. The angle at which the light rays emerge; Dividing the energy space of the light source into N equal parts, the ring between two adjacent sampling angles of the Lambertian point light source contains The total luminous flux is denoted as . : ， （2） Each sampling angle can be obtained from the above formula. Size; Step S1.2: Divide the target surface into a set of circles with different radii, each with an area equal to that of the surrounding ring. : ， （3） Where R is the radius of the entire target surface. Let i be the radius of the circles divided by equal areas, where i is 1 to N. The radius of each circle is calculated as follows: ， （4） By mapping each sampling angle to a circle, the normal vector of each sampling point is calculated using the vector form of the law of refraction. ， （5） Where n is the refractive index of the material, For the emitted light, For the incident light ray, It is the normal vector; Step S1.3: After obtaining the normal vector of the first point, extend its tangent direction and the intersection point with the next sampling angle to obtain the second point of the lens generatrix. By iterating in this way, all sampling points on the generatrix are obtained, thus obtaining the initial lens structure.

3. The design method according to claim 2, characterized in that, Step 2, which involves constructing the global evaluation function, specifically includes: The positional quality of particles is evaluated by the irradiance non-uniformity U of the irradiated surface obtained through a simulated lens, with the independent variable being the weighting coefficient of each generatrix. , , ,in To assign weight coefficients to the surfaces obtained through feedback optimization, the evaluation function is written as: ， （6） Objective evaluation function With optimization variables , , , Closely related to and If linearly correlated, then the process of finding the optimal weighting factor is transformed into finding the evaluation function using the PSO algorithm. The problem of finding the maximum value.

4. The design method according to claim 3, characterized in that, The weighted superposition lens bus mentioned in step 3 is specifically operated as follows: Step S3.1: Define the generatrix list. After obtaining the lens generatrix from the point light source, translate and copy it by an appropriate distance to obtain the five generatrixes. , , , , Each assigned a weighting factor , , , , Five new weighted busbars were obtained. ; Define the sampling ray L, and set 0~ The range is divided into M parts, and the i-th ray... The angle between the x-axis and the positive x-axis is: ， （7） ray respectively with the busbar Intersect at , , , , Since the generatrix is ​​also composed of points, the ray is first determined during the calculation of the intersection point P. Passing through the busbar Between which two points, calculate again? The intersection of the lines connecting the two points is called point A. [ ,0, ] ; and then the obtained , , , , By adding the coordinates, we obtain the points on the lens generatrix S after the final weighted superposition. The coordinates of each point on the generatrix are represented as follows: ， （8） Among them, weighting factors Rotate the obtained generatrix S by 360° to obtain a new freeform lens based on an LED extended light source. Step S3.2: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] , , , , As a particle, the optimal solution's weight factor set is found using the particle swarm optimization algorithm. All particles search in a five- or six-dimensional space, and the quality of their current position is determined by their own fitness. The best positions they have experienced and the current best position of the entire swarm are also remembered. The fitness is obtained by the evaluation function constructed in step 2. After traversing the entire particle swarm, if there is a particle whose current best position is closer to the optimal value than the overall best position, then the optimal position of this swarm is updated to that position.

5. The design method according to claim 4, characterized in that, Step 5 involves iteratively solving for the optimal weight factor set, and the specific steps are as follows: Step S5.1: Use the evaluation function defined in step 2 to evaluate whether the lens meets the design requirements. If it does, output the result; if it does not, repeat steps 3 to 5. Step S5.2: Add the lens generatrix obtained in step S4.2 to the surface list in step S3.

1. In the next round of PSO optimization in step S3.2, modify the position of one of the randomly distributed particles to: ， （14） Then return to step 3 and continue optimizing until the target evaluation function U of the lens obtained after the weight allocation and superposition meets the requirements. Stop the loop and output the result of the lens.

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