Free-form surface lens design method and system based on spherical iteration

Abstract

The invention discloses a free-form surface lens design method and system based on spherical iteration. The method comprises the following steps: constructing an initial lens structure; constructing a non-uniform irradiation weight factor; calculating coordinates of all surface points on the generatrix based on a spherical iteration method; calculating adjacent surface points in the latitude direction by using a spherical surface iteration method; fitting in the longitude and latitude directions in the spatial point cloud by using a B spline curve to form a curved surface grid of the outer surface of the lens; performing curved surface fitting on a lens curved surface grid based on a least square method to form a lens outer surface molded surface, splicing a set hemispherical inner surface with the lens outer surface, constructing a lens entity for optical simulation verification, and returning to adjust the non-uniform irradiation weight factor if it is judged that a simulation result deviates from expected illumination irradiation. And if not, outputting a lens entity result. According to the method, the iteration deviation angle is reduced through spherical iteration, and the design period of the free-form surface lens is shortened.

Description

Technical Field

[0001] The present invention relates to the technical field of lens design, and in particular to a free-form surface lens design method and system based on spherical surface iteration. Background Art

[0002] At present, the optical design of lighting systems mainly uses the free-form surface design method based on microelement mapping to design the optical surface, so as to solve the corresponding relationship between the energy of the light source and the lighting surface requirements, and solve the energy distribution problem with the maximum light energy utilization rate. However, in this design method, the shaping design of the free-form surface is mainly based on the section iteration. The current main design tools, such as LightTools, Code V, TracePro, ASAP and other software, mainly use section iteration to perform surface configuration based on the vector of the spatial point position in the free-form surface shaping method. However, the section iteration is a method of determining the tangent plane according to the normal vector of the previous point, and taking the intersection of the next incident light and the tangent plane as the surface data of the lens surface. During the iteration process, due to the lack of restrictions on the outgoing light at the next iteration point, the tangent plane iteration will cause the deviation of the normal vector at the free-form surface mesh node from the expected normal vector (iteration deviation angle). As the iteration continues, the iteration deviation angle gradually increases, causing the direction of the outgoing light to be far from the expected direction, which ultimately leads to the degradation of lighting quality. In existing software, users need to continuously try and make errors, and after a long period of adjustment, the established design goals can be achieved. The whole process is time-consuming and labor-intensive; moreover, the uniformity of the adjusted optical energy distribution cannot be guaranteed. Summary of the invention

[0003] In order to overcome the defects and shortcomings of the prior art, the present invention provides a free-form surface lens design method and system based on spherical iteration. The present invention uses spherical iteration to replace the cut surface iteration, increases the restriction of the outgoing light at the next iteration point, and reduces the iteration deviation angle, thereby fundamentally solving the problem of lighting quality degradation. This method can be widely used in various simulation software, reducing the time cost of users' repeated trial and error, and greatly shortening the design cycle of free-form surface lenses.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention provides a free-form surface lens design method based on spherical surface iteration, comprising the following steps:

[0006] Constructing an initial lens structure;

[0007] Construct non-uniform irradiation weighting factors;

[0008] Set the initial lens size, set the coordinates of the outer surface of the lens in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, and calculate the coordinates of all surface points on the generatrix based on the spherical iteration method;

[0009] According to the coordinates of all surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points;

[0010] In each spherical iteration, the center and radius of the sphere iteration are reversely solved with the expected normal vector at each node, and the free-form surface data is calculated with the sphere iteration;

[0011] After all lens surface points are calculated, a space point cloud is formed. Using the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens.

[0012] Based on the least squares method, the lens surface mesh is fitted to form the outer surface profile of the lens. The set inner surface of the hemispherical surface is spliced ​​with the outer surface of the lens to construct the lens entity and perform optical simulation verification. If it is determined that the simulation result deviates from the expected illumination irradiation, the adjustment of the non-uniform irradiation weight factor is returned and the lens surface points are constructed. Otherwise, the lens entity result is output.

[0013] As a preferred technical solution, the construction of the initial lens structure specifically includes:

[0014] The LED light source is regarded as a Lambertian point light source. The light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area. The light source mesh and the irradiated surface mesh are matched.

[0015] As a preferred technical solution, the construction of the non-uniform irradiation weight factor specifically includes:

[0016] The irradiation non-uniform weight factor is set at each point on the grid divided into equal areas of the irradiation surface, and the weight factor is adjusted according to the irradiation surface energy demand required by the user. When the irradiation surface energy distribution is uniform, all weight factors are 1.

[0017] As a preferred technical solution, the coordinates of all surface points on the generatrix are calculated based on the spherical iteration method, specifically including:

[0018] With the center of the sphere on the straight line determined by the normal vector of the previous point, the radius R of the sphere is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free-form surface coordinate point P i,j (P i,jx ,P i,jy ,P i,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface;

[0019] Determine the incident light vector based on the solid angle divided by the light source for:

[0020]

[0021] Among them, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the serial number of the γ direction, and j represents the serial number of the θ direction;

[0022] The deviation between the center of the sphere and the origin of the XYZ coordinate system is:

[0023] a=RN i,jx -P i,jx

[0024] b=RN i,jy -P i,jy

[0025] c=RN i,jz -P i,jz

[0026] Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes;

[0027] Transform the straight line determined by the next incident ray into the coordinate system ORΦ determined by the center of the sphere;

[0028] The next incident light line is determined by the incident light vector:

[0029]

[0030] The straight line is expressed in the X'Y'Z' coordinate system as:

[0031]

[0032] Then express it as a spherical coordinate system with X'Y'Z' as the reference coordinate system:

[0033]

[0034] Among them, γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system respectively;

[0035] make:

[0036]

[0037] The spherical coordinate system with X'Y'Z' as the base coordinate system is decomposed into:

[0038]

[0039] The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively;

[0040] Based on the first point P of the free-form surface lens 0,i The coordinates and normal vector of P are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1 Coordinates, using Snell's law to determine P 0,i+1 Point Normal Vector Again, the spherical iteration method is used to calculate P 0,i+1 Spherical equation of a point;

[0041] The first curve of the free-form surface is obtained by iteration along the meridian direction.

[0042] As an optimal technical solution, the binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively, specifically including:

[0043] Solve γ' and θ' based on inner iteration:

[0044] The interval of θ' is determined according to the intersection of the incident light and the circle: and Determine cosγ' as:

[0045]

[0046] sinγ' is expressed as:

[0047]

[0048] Use θ', sinγ', and cosγ' to solve the function:

[0049] A=Rnsinθ'sinγ'-bn-mRcosθ'+cm

[0050] With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine θ' and γ' as the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends;

[0051] Solve R based on outer iteration:

[0052] Calculate the surface coordinate point P determined by γ', θ', and R in XYZ i+1,j :

[0053]

[0054] Using the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector:

[0055]

[0056] Solving using Snell's law

[0057]

[0058] P i+1,j Surface normal vector of a point for:

[0059]

[0060] Sure and The angle between two vectors:

[0061]

[0062] Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases, and iteratively solve γ', θ', and R to make sinλ<ε R , the iteration ends.

[0063] The present invention also provides a free-form surface lens design system based on spherical iteration, comprising: an initial lens structure construction module, a weight factor construction module, a lens surface point construction module, a surface mesh construction module, a lens entity construction module, an optical simulation verification module, and a lens entity result output module;

[0064] The initial lens structure building module is used to build an initial lens structure;

[0065] The weight factor construction module is used to construct a non-uniform irradiation weight factor;

[0066] The lens surface point construction module is used to construct lens surface points, and specifically includes:

[0067] Set the initial lens size, set the coordinates of the outer surface of the lens in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, and calculate the coordinates of all surface points on the generatrix based on the spherical iteration method;

[0068] According to the coordinates of all surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points;

[0069] In each spherical iteration, the center and radius of the sphere iteration are reversely solved with the expected normal vector at each node, and the free-form surface data is calculated with the sphere iteration;

[0070] The curved surface mesh construction module is used to construct the curved surface mesh of the outer surface of the lens, and specifically includes:

[0071] After all lens surface points are calculated, a space point cloud is formed. Using the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens.

[0072] The lens entity construction module is used to perform surface fitting on the lens surface mesh based on the least square method to form the lens outer surface profile, splice the set hemispherical inner surface with the lens outer surface to construct the lens entity;

[0073] The optical simulation verification module is used to perform optical simulation verification. If it is determined that the simulation result deviates from the expected illumination irradiation, it returns to adjust the non-uniform irradiation weight factor and constructs the lens surface points. Otherwise, the lens entity result is output through the lens entity result output module.

[0074] As a preferred technical solution, the initial lens structure building module is used to build the initial lens structure, specifically including:

[0075] The LED light source is regarded as a Lambertian point light source. The light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area. The light source mesh and the irradiated surface mesh are matched.

[0076] As a preferred technical solution, the weight factor construction module is used to construct a non-uniform irradiation weight factor, specifically including:

[0077] The irradiation non-uniform weight factor is set at each point on the grid divided into equal areas of the irradiation surface, and the weight factor is adjusted according to the irradiation surface energy demand required by the user. When the irradiation surface energy distribution is uniform, all weight factors are 1.

[0078] As a preferred technical solution, the coordinates of all surface points on the generatrix are calculated based on the spherical iteration method, specifically including:

[0079] With the center of the sphere on the straight line determined by the normal vector of the previous point, the radius R of the sphere is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free-form surface coordinate point P i,j (P i,jx ,P i,jy ,Pi,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface;

[0080] Determine the incident light vector based on the solid angle divided by the light source for:

[0081]

[0082] Among them, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the serial number of the γ direction, and j represents the serial number of the θ direction;

[0083] The deviation between the center of the sphere and the origin of the XYZ coordinate system is:

[0084] a=RN i,jx -P i,jx

[0085] b=RN i,jy -P i,jy

[0086] c=RN i,jz -P i,jz

[0087] Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes;

[0088] Transform the straight line determined by the next incident ray into the coordinate system ORΦ determined by the center of the sphere;

[0089] The next incident light line is determined by the incident light vector:

[0090]

[0091] The straight line is expressed in the X'Y'Z' coordinate system as:

[0092]

[0093] Then express it as a spherical coordinate system with X'Y'Z' as the reference coordinate system:

[0094]

[0095] Among them, γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system respectively;

[0096] make:

[0097]

[0098] The spherical coordinate system with X'Y'Z' as the base coordinate system is decomposed into:

[0099]

[0100] The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively;

[0101] Based on the first point P of the free-form surface lens 0,i The coordinates and normal vector of P are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1 Coordinates, using Snell's law to determine P 0,i+1 Point Normal Vector Again, the spherical iteration method is used to calculate P 0,i+1 Spherical equation of a point;

[0102] The first curve of the free-form surface is obtained by iteration along the meridian direction.

[0103] As an optimal technical solution, the binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively, specifically including:

[0104] Solve γ' and θ' based on inner iteration:

[0105] The interval of θ' is determined according to the intersection of the incident light and the circle: and Determine cosγ' as:

[0106]

[0107] sinγ' is expressed as:

[0108]

[0109] Use θ', sinγ', and cosγ' to solve the function:

[0110] A=Rnsinθ'sinγ'-bn-mRcosθ'+cm

[0111] With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine θ' and γ' as the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends;

[0112] Solve R based on outer iteration:

[0113] Calculate the surface coordinate point P determined by γ', θ', and R in XYZ i+1,j :

[0114]

[0115] Using the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector:

[0116]

[0117] Solving using Snell's law

[0118]

[0119] P i+1,j Surface normal vector of a point for:

[0120]

[0121] Sure and The angle between two vectors:

[0122]

[0123] Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases, and iteratively solve γ', θ', and R to make sinλ<ε R , the iteration ends.

[0124] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0125] In view of the problems that the iteration error of the section iteration algorithm in the existing free-form surface molding design leads to the degradation of lighting quality, long design cycle, complicated design process, etc., the present invention uses spherical iteration to replace the section iteration, increases the restriction of the outgoing light of the next iteration point, and reduces the iteration deviation angle, thereby fundamentally solving the problem of lighting quality degradation. It can be widely used in various simulation software, reduces the time cost of users' repeated trial and error, and greatly shortens the design cycle of free-form surface lenses. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 It is a schematic flow chart of the free-form surface lens design method based on spherical surface iteration of the present invention;

[0127] Figure 2It is a schematic diagram of the spherical iteration process of the present invention on the coordinate system;

[0128] Figure 3 It is a schematic diagram of the spherical iterative solution process based on the dichotomy method of the present invention;

[0129] Figure 4 It is a schematic diagram of the spherical iterative configuration of the present invention;

[0130] Figure 5 A schematic diagram of the design requirements for the example comparison between spherical iteration and tangent iteration;

[0131] Figure 6 The figure is a schematic diagram of the lens entity model and size comparison;

[0132] Figure 7 (a) is a schematic diagram of the spherical iterative lens spot;

[0133] Figure 7 (b) is a schematic diagram of the cut surface iterative lens spot;

[0134] Figure 8 (a) is a schematic diagram of the illumination distribution of the spherical iterative lens spot;

[0135] Figure 8 (b) is a schematic diagram of the illumination distribution of the lens spot after cross-section iteration;

[0136] Fig. 9 This is a schematic diagram for comparing the illumination distribution of circular light spots simulated by the lens. DETAILED DESCRIPTION

[0137] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0138] Example 1

[0139] like Figure 1 As shown, this embodiment provides a free-form surface lens design method based on spherical surface iteration, taking the inner surface as a hemispherical surface as an example, specifically comprising the following steps:

[0140] S1: construct the initial lens structure;

[0141] The LED light source is regarded as a Lambertian point light source, and the light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area, and the light source mesh and the irradiated surface mesh are matched;

[0142] S2: Construct non-uniform irradiation weight factor;

[0143] Set the irradiation unevenness weight factor at each point on the grid divided by equal area on the irradiation surface, and adjust the weight factor according to the irradiation surface energy demand required by the user. When the energy distribution of the irradiation surface is uniform, all weight factors are 1;

[0144] S3: Set the initial lens size, set the coordinates of the lens outer surface in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, apply the spherical iteration method to the next lens surface point calculation, and then use the calculated lens surface point to calculate the next surface point using the spherical iteration method, and iterate in sequence until the coordinates of all surface points on the generatrix are iteratively calculated;

[0145] The corresponding relationship between the LED energy microelement and the illumination surface microelement can determine the incident and outgoing light vectors at each microelement node, and the normal vector of each node can be calculated according to Snell's law. However, the normal vector cannot determine the coordinates of the free-form surface, which requires an iterative method to iteratively calculate the coordinates of each node point by point. Although the existing section iteration method can solve the coordinates of each point, the section iteration lacks the restriction condition of the outgoing light direction of the next iteration point, which causes the normal vector at the next iteration point to deviate from the expected normal vector, resulting in inaccurate free-form surface configuration; in order to eliminate the iteration deviation angle, this embodiment uses a spherical iteration method, and in each iteration, the expected normal vector at each node is used to reversely solve the center and radius of the sphere iteration, and then the iterative sphere is used to calculate the free-form surface data. Due to the restriction conditions added in the iterative process, the iteration deviation angle can be avoided, thereby fundamentally solving the problem of low surface configuration accuracy caused by the iteration deviation angle.

[0146] like Figure 2 As shown, the sphere center is on the straight line determined by the normal vector of the previous point, and the sphere radius R is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free surface coordinate point P i,j (P i,jx ,P i,jy ,P i,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface;

[0147] First, the incident light vector can be determined based on the solid angle divided by the light source for:

[0148]

[0149] Wherein, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the number of the γ direction, and j represents the number of the θ direction.

[0150] Since the center of the sphere is set at With P i,j (P i,jx ,P i,jy ,P i,jz ), so first assume that the radius of the sphere is R, so the deviation between the center of the sphere and the origin of the XYZ coordinate system is:

[0151] a=RN i,jx -P i,jx (2-34)

[0152] b=RN i,jy -P i,jy

[0153] c=RN i,jz -P i,jz

[0154] Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes.

[0155] Since the next coordinate point on the free surface is determined by the intersection of the next incident light ray and the sphere, and considering that the representation of a straight line in a spherical coordinate system is much simpler than that of a circle in a rectangular coordinate system, the straight line determined by the next incident light ray is converted into the coordinate system ORΦ determined by the center of the sphere.

[0156] The next incident light line is determined by the incident light vector:

[0157]

[0158] The straight line is expressed in the X'Y'Z' coordinate system as:

[0159]

[0160] Then it is expressed as a spherical coordinate system with X'Y'Z' as the reference coordinate system:

[0161]

[0162] Where γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system, respectively.

[0163] To simplify the above formula, let:

[0164]

[0165] Then equation (2-37) can be decomposed into:

[0166]

[0167] The unknown quantities in this system of equations are γ', θ', and R. The three unknown quantities cannot be determined using only this system of equations. According to the idea of ​​spherical iteration, there is another equation that should be Snell's law. The outgoing light vector in Snell's law is determined by γ', θ', and R. i,j (P i,jx ,P i,jy ,P i,jz ) point and the position Q of the expected outgoing light i,j (Q i,jx ,Q i,jy ,Q i,jz ). Snell's law contains the dot product of the incident light vector and the outgoing light vector. Therefore, directly using Snell's law and the above two equations to establish a system of equations to solve γ', θ', and R will make the solution process extremely complicated and it is difficult to write a general solution.

[0168] In order to enable the computer to successfully solve the three variables γ', θ', and R, this embodiment uses the dichotomy method in numerical approximation to solve these three variables respectively.

[0169] The binary method is a quick way to reduce the root interval, such as Figure 3 As shown, the solution process based on the dichotomy method in this embodiment is:

[0170] Assume f(x) is a continuous function, f(a)<0, f(b)>0, so [a,b] is a root interval. Let [a,b]=[a0,b0], the first calculation of the midpoint and its function value f(x1), then f(a0)f(x1)<0, so we get a new root interval [a0,x1]=[a1,b1] and

[0171] Calculate the midpoint for the second time and its function value f(x2), then f(a1)f(x2)>0, so we get a new root interval [x2,x1]=[a2,b2] and

[0172] Continue like this, and calculate the midpoint for the nth time and its function value f(x n ). At this time, by judging the sign of the endpoint function value, we can get the new root interval [a n ,b n ]and

[0173] So, in [a n ,b n], for example, take a n or b n (One of them is x n ) or other (such as the midpoint) as the root x of the equation * The approximate value of

[0174]

[0175] According to the idea of ​​dichotomy, solving γ', θ', and R requires inner and outer iterations. The inner iteration mainly solves γ' and θ', and the outer iteration mainly solves R. First, the inner iteration algorithm is described:

[0176] According to the intersection of the incident light and the circle, the interval of θ' can be determined as and If the normal vector N of the previous point i,jz <0, otherwise First, let's discuss N i,jz <0: First, a given θ'∈(a i ,b i ) (usually the midpoint is chosen), and substituting into equation (2-39) cosγ' can be determined:

[0177]

[0178] At the same time, sinγ' can be expressed as

[0179]

[0180] Then use θ', sinγ', and cosγ' to solve the function

[0181] A=Rnsinθ'sinγ'-bn-mRcosθ'+cm (2-43)

[0182] With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine that θ' and γ' are the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends.

[0183] At the beginning of the peripheral iteration, a given R is used to solve the corresponding θ' and γ' values. Then the coordinates of the point are calculated using the calculated θ' and γ' values, and the angle sinλ between the surface normal vector and the refraction normal vector is calculated to see if it is less than the error ε. R To calculate the surface normal and refraction normal of this point, we first need to calculate the surface coordinate point P determined by γ', θ', and R in XYZ. i+1,j :

[0184]

[0185] Then use the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector:

[0186]

[0187] Solving using Snell's law

[0188]

[0189] Since the iteration is performed on the sphere, P i+1,j Surface normal vector of a point for:

[0190]

[0191] Sure and The angle between two vectors:

[0192]

[0193] Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases. Then iterate until γ', θ', and R are found so that sinλ<ε R , the iteration ends.

[0194] Among them, the inner iteration of determining γ' and θ' is to perform the following numerical optimization:

[0195] min:|A|<ε θ (2-51)

[0196]

[0197] External iteration is to perform numerical optimization on R:

[0198]

[0199] like Figure 4 As shown, referring to the iterative method of the tangent plane iteration method, the seed line is first obtained, and then all the free surface coordinate points are iteratively obtained along the latitude direction.

[0200] Using P 0,i The coordinates and normal vector of the point are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1 Coordinates. Since P 0,i+1 The coordinates are determined, then through P 0,i+1 The incident light of a point With the outgoing light vector That is to say, using Snell's law, P can be determined 0,i+1 Point Normal Vector Then, the spherical iteration method is used to calculate P 0,i+1 The spherical equation of a point.

[0201] According to the above method, the first curve of the free-form surface, i.e., the seed line, can be obtained by iterating along the meridian direction. Then, the coordinates of each node of the seed line are used as the base point, and the spherical surface is iterated in the latitude direction to determine all the nodes of the free-form surface mesh. When all the nodes of all lenses are determined, a smooth free-form surface can be formed by surface lofting.

[0202] S4: Based on all the surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points;

[0203] S5: After all lens surface points are calculated, a space point cloud is formed. According to the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens.

[0204] S6: Use the least squares method to fit the lens surface mesh to form the lens outer surface profile; then splice the set hemispherical inner surface with the lens outer surface to construct the lens entity and import it into the simulation software for optical simulation verification. If the simulation result deviates from the expected lighting irradiation, return to step S2, adjust the non-uniform irradiation weight factor, and then construct the lens surface points.

[0205] like Figure 5 As shown, this embodiment further illustrates the design requirements of the spherical iteration and the tangent iteration example. The light emitted by the LED is irradiated to the screen at a distance of 80mm through the free-form surface lens, forming a circular illumination spot with a radius of 150mm. The illumination distribution within the circular spot is required to be uniform. The designed lens height is 5mm, the lens material is pmma, the refractive index n=1.49, the LED chip is 1×1×0.1mm, and it is assumed that the light emitted by the LED is a Lambertian light intensity distribution;

[0206] According to the design requirements, the light source energy and the target illumination surface are divided into micro-elements and the corresponding relationship of light energy is established. The light source energy is divided into micro-elements of equal luminous flux, and the target illumination surface is divided into micro-elements of equal area. The number of micro-element divisions is equal and one-to-one. In the Rhino software, the free-form surface data is calculated by spherical iteration and section iteration, and then fitted into a surface. The inner surface of the lens is designed as the inner surface of a hemisphere with the LED as the center, and the lens entity is formed by combining the outer surface of the free-form surface. Figure 6 As shown in FIG. 1 , the outer surface contour dimensions of the free-form surface lens calculated by the two design methods are compared. Due to the symmetry of the circular spot lens, only the rotation generatrix is ​​shown in the figure.

[0207] like Figure 6 As shown, at the starting stage of iteration (0mm~3mm on the X-axis), the spherical iteration lens contour is outside the cut surface iteration lens contour, with a size difference of 0.001~0.015mm; while at the ending stage of iteration (6mm~5.6mm on the X-axis), the circular iteration lens contour is inside the cut surface iteration lens contour, with a size difference of 0.001~0.025mm.

[0208] According to the design requirements of the spherical iteration and the cross-section iteration comparison example, the lighting system of two lenses is established and simulated in Tracepro. The simulation uses 1 million rays for tracing. Figure 7 As shown in (a), the circular spot is formed by the free-form surface lens designed by the spherical iteration method. Figure 7 (b) shows the circular light spot formed by the free-form surface lens designed by the facet iteration method. It can be seen that the light spot illumination of the lens of the spherical iteration method is very uniform, which is very close to the design expectation, while the light spot illumination of the lens of the facet iteration method has obvious light and dark changes, which is far from the design expectation. In terms of light energy utilization, the lens of the spherical iteration method is 90.2%, and the lens of the facet iteration is only 70.1%, that is, the lens calculated by the spherical iteration method can basically transfer all the light energy emitted by the LED to the target plane, and the light energy transfer and distribution are close to the design expectation.

[0209] like Figure 8 (a) and (b) show the axial symmetric illumination distribution of the spherical iteration lens and the facet iteration lens, respectively. It can be seen that the illumination distribution of the spherical iteration lens spot varies around its average value, with little fluctuation, and its illumination uniformity is 90.1%; while the illumination distribution of the facet iteration lens spot varies greatly, and its illumination uniformity is less than 40%.

[0210] To further verify the effectiveness of the design method, the target circular spot is set as R, and R changes gradually from 60 mm to 200 mm, as shown in the following example. Fig. 9 As shown, the design effects of the cut surface iteration and the spherical iteration are compared and contrasted.

[0211] The results show that when the R value is small, the surface formed by the slice iteration will cause serious spot unevenness. As the R value increases, the effect gradually improves. However, the overall uniformity of the spherical iteration always remains at a high level and does not change with the change of the R value.

[0212] The results show that this design method has a high practical effect, can greatly reduce design errors, and enables users to obtain better design results in a very short time.

[0213] Example 2

[0214] This embodiment provides a free-form surface lens design system based on spherical surface iteration, which is used to implement the free-form surface lens design method based on spherical surface iteration of the above-mentioned embodiment 1, and the system includes: an initial lens structure construction module, a weight factor construction module, a lens surface point construction module, a surface mesh construction module, a lens entity construction module, an optical simulation verification module, and a lens entity result output module;

[0215] In this embodiment, the initial lens structure building module is used to build the initial lens structure;

[0216] In this embodiment, the weight factor construction module is used to construct a non-uniform irradiation weight factor;

[0217] In this embodiment, the lens surface point construction module is used to construct lens surface points, specifically including:

[0218] Set the initial lens size, set the coordinates of the outer surface of the lens in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, and calculate the coordinates of all surface points on the generatrix based on the spherical iteration method;

[0219] According to the coordinates of all surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points;

[0220] In each spherical iteration, the center and radius of the sphere iteration are reversely solved with the expected normal vector at each node, and the free-form surface data is calculated with the sphere iteration;

[0221] In this embodiment, the curved surface mesh construction module is used to construct the curved surface mesh of the outer surface of the lens, specifically including:

[0222] After all lens surface points are calculated, a space point cloud is formed. Using the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens.

[0223] In this embodiment, the lens entity construction module is used to perform surface fitting on the lens surface mesh based on the least squares method to form the lens outer surface profile, and to splice the set hemispherical inner surface with the lens outer surface to construct the lens entity;

[0224] In this embodiment, the optical simulation verification module is used to perform optical simulation verification. If it is determined that the simulation result deviates from the expected illumination irradiation, the non-uniform irradiation weight factor is adjusted and the lens surface points are constructed. Otherwise, the lens entity result is output through the lens entity result output module.

[0225] In this embodiment, the initial lens structure construction module is used to construct the initial lens structure, specifically including:

[0226] The LED light source is regarded as a Lambertian point light source. The light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area. The light source mesh and the irradiated surface mesh are matched.

[0227] In this embodiment, the weight factor construction module is used to construct the non-uniform irradiation weight factor, which specifically includes:

[0228] The irradiation non-uniform weight factor is set at each point on the grid divided into equal areas of the irradiation surface, and the weight factor is adjusted according to the irradiation surface energy demand required by the user. When the irradiation surface energy distribution is uniform, all weight factors are 1.

[0229] In this embodiment, the coordinates of all surface points on the generatrix are calculated based on the spherical iteration method, specifically including:

[0230] With the center of the sphere on the straight line determined by the normal vector of the previous point, the radius R of the sphere is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free-form surface coordinate point P i,j (P i,jx ,P i,jy ,P i,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface;

[0231] Determine the incident light vector based on the solid angle divided by the light source for:

[0232]

[0233] Among them, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the serial number of the γ direction, and j represents the serial number of the θ direction;

[0234] The deviation between the center of the sphere and the origin of the XYZ coordinate system is:

[0235] a=RN i,jx -P i,jx

[0236] b=RN i,jy -P i,jy

[0237] c=RN i,jz -P i,jz

[0238] Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes;

[0239] Transform the straight line determined by the next incident ray into the coordinate system ORΦ determined by the center of the sphere;

[0240] The next incident light line is determined by the incident light vector:

[0241]

[0242] The straight line is expressed in the X'Y'Z' coordinate system as:

[0243]

[0244] Then express it as a spherical coordinate system with X'Y'Z' as the reference coordinate system:

[0245]

[0246] Among them, γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system respectively;

[0247] make:

[0248]

[0249] The spherical coordinate system with X'Y'Z' as the base coordinate system is decomposed into:

[0250]

[0251] The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively;

[0252] Based on the first point P of the free-form surface lens 0,i The coordinates and normal vector of P are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1Coordinates, using Snell's law to determine P 0,i+1 Point Normal Vector Again, the spherical iteration method is used to calculate P 0,i+1 Spherical equation of a point;

[0253] The first curve of the free-form surface is obtained by iteration along the meridian direction.

[0254] In this embodiment, the binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively, which specifically includes:

[0255] Solve γ' and θ' based on inner iteration:

[0256] The interval of θ' is determined according to the intersection of the incident light and the circle: and Determine cosγ' as:

[0257]

[0258] sinγ' is expressed as:

[0259]

[0260] Use θ', sinγ', and cosγ' to solve the function:

[0261] A=Rnsinθ'sinγ'-bn-mRcosθ'+cm

[0262] With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine θ' and γ' as the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends;

[0263] Solve R based on outer iteration:

[0264] Calculate the surface coordinate point P determined by γ', θ', and R in XYZ i+1,j :

[0265]

[0266] Using the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector:

[0267]

[0268] Solving using Snell's law

[0269]

[0270]

[0271] P i+1,j Surface normal vector of a point for:

[0272]

[0273] Sure and The angle between two vectors:

[0274]

[0275] Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases, and iteratively solve γ', θ', and R to make sinλ<ε R , the iteration ends.

[0276] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A free-form surface lens design method based on spherical iteration, characterized in that: The steps include: Constructing an initial lens structure; Construct non-uniform irradiation weighting factors; Set the initial lens size, set the coordinates of the outer surface of the lens in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, and calculate the coordinates of all surface points on the generatrix based on the spherical iteration method; According to the coordinates of all surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points; In each spherical iteration, the center and radius of the sphere iteration are reversely solved with the expected normal vector at each node, and the free-form surface data is calculated with the sphere iteration; After all lens surface points are calculated, a space point cloud is formed. Using the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens. Based on the least squares method, the lens surface mesh is fitted to form the outer surface profile of the lens. The set inner surface of the hemispherical surface is spliced ​​with the outer surface of the lens to construct the lens entity and perform optical simulation verification. If it is determined that the simulation result deviates from the expected illumination irradiation, the adjustment of the non-uniform irradiation weight factor is returned and the lens surface points are constructed. Otherwise, the lens entity result is output.

2. The free-form surface lens design method based on spherical surface iteration according to claim 1, characterized in that: The constructing of the initial lens structure specifically includes: The LED light source is regarded as a Lambertian point light source. The light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area. The light source mesh and the irradiated surface mesh are matched.

3. The free-form surface lens design method based on spherical iteration according to claim 2, characterized in that: The constructing of the non-uniform irradiation weight factor specifically includes: The irradiation non-uniform weight factor is set at each point on the grid divided into equal areas of the irradiation surface, and the weight factor is adjusted according to the irradiation surface energy demand required by the user. When the irradiation surface energy distribution is uniform, all weight factors are 1.

4. The free-form surface lens design method based on spherical surface iteration according to claim 1, characterized in that: The coordinates of all surface points on the generatrix are calculated based on the spherical iteration method, including: With the center of the sphere on the straight line determined by the normal vector of the previous point, the radius R of the sphere is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free-form surface coordinate point P i,j (P i,jx ,P i,jy ,P i,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface; Determine the incident light vector based on the solid angle divided by the light source for: Among them, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the serial number of the γ direction, and j represents the serial number of the θ direction; The deviation between the center of the sphere and the origin of the XYZ coordinate system is: a=RN i,jx -P i,jx b=RN i,jy -P i,jy c=RN i,jz -P i,jz Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes; Transform the straight line determined by the next incident ray into the coordinate system ORΦ determined by the center of the sphere; The next incident light line is determined by the incident light vector: The straight line is expressed in the X'Y'Z' coordinate system as: Then express it as a spherical coordinate system with X'Y'Z' as the reference coordinate system: Among them, γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system respectively; make: The spherical coordinate system with X'Y'Z' as the base coordinate system is decomposed into: The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively; Based on the first point P of the free-form surface lens 0,i The coordinates and normal vector of P are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1 Coordinates, using Snell's law to determine P 0,i+1 Point Normal Vector Again, the spherical iteration method is used to calculate P 0,i+1 Spherical equation of a point; The first curve of the free-form surface is obtained by iteration along the meridian direction.

5. The free-form surface lens design method based on spherical surface iteration according to claim 4, characterized in that: The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively, including: Solve γ' and θ' based on inner iteration: The interval of θ' is determined according to the intersection of the incident light and the circle: and Determine cosγ' as: sinγ' is expressed as: Use θ', sinγ', and cosγ' to solve the function: A=Rnsinθ'sinγ'-bn-mRcosθ'+cm With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine θ' and γ' as the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends; Solve R based on outer iteration: Calculate the surface coordinate point P determined by γ', θ', and R in XYZ i+1,j : Using the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector: Solving using Snell's law P i+1,j Surface normal vector of a point for: Sure and The angle between two vectors: Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases, and iteratively solve γ', θ', and R to make sinλ<ε R , the iteration ends.

6. A free-form surface lens design system based on spherical iteration, characterized in that: include: Initial lens structure building module, weight factor building module, lens surface point building module, surface mesh building module, lens entity building module, optical simulation verification module, lens entity result output module; The initial lens structure building module is used to build an initial lens structure; The weight factor construction module is used to construct a non-uniform irradiation weight factor; The lens surface point construction module is used to construct lens surface points, and specifically includes: Set the initial lens size, set the coordinates of the outer surface of the lens in the axis direction to correspond to the lens size, use the set point on the axis as the first lens surface point, and calculate the coordinates of all surface points on the generatrix based on the spherical iteration method; According to the coordinates of all surface points on the generatrix, the spherical iteration method is used again in the latitude direction to calculate the adjacent surface points; In each spherical iteration, the center and radius of the sphere iteration are reversely solved with the expected normal vector at each node, and the free-form surface data is calculated with the sphere iteration; The curved surface mesh construction module is used to construct the curved surface mesh of the outer surface of the lens, and specifically includes: After all lens surface points are calculated, a space point cloud is formed. Using the calculation order, the longitude and latitude directions in the space point cloud are fitted with B-spline curves to form a surface mesh of the outer surface of the lens. The lens entity construction module is used to perform surface fitting on the lens surface mesh based on the least square method to form the lens outer surface profile, splice the set hemispherical inner surface with the lens outer surface to construct the lens entity; The optical simulation verification module is used to perform optical simulation verification. If it is determined that the simulation result deviates from the expected illumination irradiation, it returns to adjust the non-uniform irradiation weight factor and constructs the lens surface points. Otherwise, the lens entity result is output through the lens entity result output module.

7. The free-form surface lens design system based on spherical surface iteration according to claim 6, characterized in that: The initial lens structure building module is used to build an initial lens structure, and specifically includes: The LED light source is regarded as a Lambertian point light source. The light source is meshed according to equal luminous flux, and the irradiated surface is meshed according to equal area. The light source mesh and the irradiated surface mesh are matched.

8. The free-form surface lens design system based on spherical surface iteration according to claim 7, characterized in that: The weight factor construction module is used to construct a non-uniform irradiation weight factor, specifically including: The irradiation non-uniform weight factor is set at each point on the grid divided into equal areas of the irradiation surface, and the weight factor is adjusted according to the irradiation surface energy demand required by the user. When the irradiation surface energy distribution is uniform, all weight factors are 1.

9. The free-form surface lens design system based on spherical surface iteration according to claim 6, characterized in that: The coordinates of all surface points on the generatrix are calculated based on the spherical iteration method, including: With the center of the sphere on the straight line determined by the normal vector of the previous point, the radius R of the sphere is solved in real time, so that the intersection of the sphere and the next incident light ray determines the next free-form surface coordinate point P i,j (P i,jx ,P i,jy ,P i,jz ), the normal vector determined by the point and the position of the outgoing ray The normal vector of the sphere at this coordinate point The angle sinλ between them is used as the judgment condition. If sinλ is less than the given error ε, then P is determined. i,j is the coordinate point on the free surface; Determine the incident light vector based on the solid angle divided by the light source for: Among them, γ represents the azimuth angle of the incident light vector, θ represents the zenith angle of the incident light vector, i represents the serial number of the γ direction, and j represents the serial number of the θ direction; The deviation between the center of the sphere and the origin of the XYZ coordinate system is: a=RN i,jx -P i,jx b=RN i,jy -P i,jy c=RN i,jz -P i,jz Among them, a, b, and c are the offsets of the sphere center position and the origin of the XYZ coordinate system in the directions of the three coordinate axes; Transform the straight line determined by the next incident ray into the coordinate system ORΦ determined by the center of the sphere; The next incident light line is determined by the incident light vector: The straight line is expressed in the X'Y'Z' coordinate system as: Then express it as a spherical coordinate system with X'Y'Z' as the reference coordinate system: Among them, γ' and θ' are the azimuth and zenith angles of the ORΦ coordinate system respectively; make: The spherical coordinate system with X'Y'Z' as the base coordinate system is decomposed into: The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively; Based on the first point P of the free-form surface lens 0,i The coordinates and normal vector of P are determined using the spherical iteration algorithm. 0,i The spherical equation of the point and the next incident light vector The intersection point with the spherical equation is determined as the second point P of the free-form surface lens. 0,i+1 Coordinates, using Snell's law to determine P 0,i+1 Point Normal Vector Again, the spherical iteration method is used to calculate P 0,i+1 Spherical equation of a point; The first curve of the free-form surface is obtained by iteration along the meridian direction.

10. The free-form surface lens design system based on spherical surface iteration according to claim 6, characterized in that: The binary method in numerical approximation is used to solve the three variables γ', θ', and R respectively, including: Solve γ' and θ' based on inner iteration: The interval of θ' is determined according to the intersection of the incident light and the circle: and Determine cosγ' as: sinγ' is expressed as: Use θ', sinγ', and cosγ' to solve the function: A=Rnsinθ'sinγ'-bn-mRcosθ'+cm With |A|<ε θ To determine the target, we gradually make |A| approach the target |A|<ε according to the idea of ​​dichotomy. θ , and finally determine θ' and γ' as the desired approximate values. When |A| reaches the target |A|<ε θ When , the inner iteration ends; Solve R based on outer iteration: Calculate the surface coordinate point P determined by γ', θ', and R in XYZ i+1,j : Using the surface coordinate point P i+1,j The Q on the target screen corresponding to that point i+1,j Point Request Unit vector: Solving using Snell's law P i+1,j Surface normal vector of a point for: Sure and The angle between two vectors: Use sinλ to determine whether the target is reached, and Determine whether R increases or decreases, and iteratively solve γ', θ', and R to make sinλ<ε R , the iteration ends.

Images