Method for generating and optimizing optical spline surface

Abstract

The invention discloses a method for generating and optimizing an optical spline surface, which comprises the following steps of: establishing an initial optical spline surface according to initial parameters by taking a surface parallel to target light as an XY surface and a direction vertical to the target light as a Z-axis direction, and selecting an initial control point; optimizing in an XY plane: adjusting the control points by utilizing the surface element coefficients until the deviation of the surface element coefficients at the four vertex angles of each control point is within 1%; and adjusting the optical spline surface according to the new control point. And optimization in the Z-axis direction: adjusting the control points by using the normal vectors until the Z value deviation between the curved surface normal vectors of the adjacent control points and the target normal vector is within 1% under the same X value and Y value, and adjusting the optical spline surface according to the new control points. The calculation process of the optical free-form surface is simplified, the control points of the free-form surface are adjusted according to calculation of local parameters around the control points, process data are reduced, computer memory is saved, and calculation efficiency is improved.

Description

Technical Field

[0001] The invention relates to the field of optical technology, and in particular to a method for generating and optimizing an optical spline surface. Background Art

[0002] The light distribution after the light source passes through the optical spline surface and reaches the projection surface is related to the refractive index of the incident medium, the refractive index of the exiting medium, and the curved surface shape of the optical spline surface. In order to enable the incident light to be projected through the optical spline surface to form a specific light distribution area, it is necessary to calculate the curved surface shape of the optical spline surface to ensure that the light intensity in the required light distribution area reaches the maximum value. For example, the incident light is a uniformly incident rectangular light source, and the target light is a cross-shaped area. Therefore, the four corners of the rectangular light source are invalid light areas. If the optical spline surface is a plane, the exiting light is also a rectangular light distribution. The light intensity distributed in the cross-shaped area will be greatly weakened, and the light efficiency is low.

[0003] The traditional optical spline surface calculation method is to divide the optical surface into a large number of facets, and it is necessary to traverse and calculate the area and energy of each facet. The length and width of the facet must be small enough to ensure the accuracy of area / energy calculation. This makes the number of facets huge, occupies a large amount of memory, and the traversal speed is slow. For example, the invention patent "A design method for a point light source light distribution lens" with patent application number CN 200910046129.5 adopts a ray mapping method, and the specific steps are as follows: (1) set the initial structure of the free surface, (2) set the spatial energy distribution of the light source and the lens output light energy, (3) establish the relationship equation between the incident light vector and the output light vector, (4) combine the equations obtained in step 3 and step 2 to obtain the discrete points of the lens free surface, (5) fit the discrete points to obtain the surface, and obtain the entity from the surface. This solution requires the establishment and solution of the optical surface. It is necessary to first solve the surface discrete data points of the optical surface, and then fit the discrete points to form the surface. For example, the invention patent "Automobile Lighting Projection Module" with patent application number CN202111638887.3 discloses a module and design method for realizing dynamic projection effects using free-form surfaces. The design method involved is also to first establish an initial point, and then calculate the coordinates of the adjacent points based on the coordinates of the known points and the local normal vector of the surface at the known points, and gradually calculate the point coordinates and surface shape of the entire free-form surface.

[0004] Therefore, it is necessary to design a spline surface calculation method with low computational complexity, small memory usage and high computational accuracy. Summary of the invention

[0005] In order to solve the technical problems of large amount of calculation, complicated calculation process and slow calculation speed in the optical spline surface calculation method in the prior art, the present invention provides a method for generating and optimizing optical spline surface to solve the above problems.

[0006] The technical solution adopted by the present invention to solve its technical problem is: a method for generating and optimizing an optical spline surface, comprising the following steps: taking the surface of parallel target light as the XY plane, taking the direction of perpendicular target light as the Z axis direction, establishing an initial optical spline surface according to initial parameters, and selecting initial control points.

[0007] Optimize in the XY plane: Use the facet coefficients to adjust the control points until the facet coefficient deviations at the four corners of each control point are within 1%; adjust the optical spline surface based on the new control points.

[0008] Optimize in the Z-axis direction: Use the normal vector to adjust the control points until the Z value deviation between the surface normal vectors of adjacent control points and the target normal vector is within 1% under the same X and Y values, and adjust the optical spline surface according to the new control points.

[0009] Furthermore, when optimizing in the XY plane, the control point adjustment method includes the following steps:

[0010] S11: Set the iteration value for calculating the surface element coefficients around the control point.

[0011] S12: Calculate the panel coefficients at the four corners of the control point.

[0012] S13: If the deviation of the four bin coefficients is within 1%, proceed to step S17; if the deviation of the four bin coefficients is greater than 1%, proceed to step S14.

[0013] S14: Calculate the offset between the X value and the Y value of the new control point and the original control point according to the panel coefficient calculated in step S13.

[0014] S15: Calculate new control point coordinates according to the deviation.

[0015] S16: Execute step S12.

[0016] S17: The control point calculation is completed.

[0017] Furthermore, during the Z-axis optimization, the control point adjustment method includes the following steps:

[0018] S21: Determine a reference control point, calculate the surface normal vector between the reference control point and the adjacent control points, and calculate the target normal vector between the reference control point and the adjacent control points according to the law of refraction.

[0019] S22: Calculate the Z value corresponding to the surface normal vector and the target normal vector given the X value and Y value. If the deviation between the two is within 1%, proceed to step S25; if the deviation between the two is greater than 1%, proceed to step S23.

[0020] S23: adjusting the Z value of the control point adjacent to the reference control point according to the surface normal vector Z value calculated in step S22 to generate a new reference control point.

[0021] S24: Execute step S21.

[0022] S25: The control point calculation is completed.

[0023] Furthermore, the initial parameters include the surface order, the number of surface segments, the node vector, the incident light angle, the incident medium refractive index, the exit light angle, and the exit medium refractive index.

[0024] Furthermore, the calculation formula of the panel coefficient is:

[0025]

[0026] Wherein, (u, v) represents the surface element vector of the optical spline surface, and s represents the projection area of ​​the surface element of the optical spline surface on the XY plane.

[0027] Furthermore, the surface normal vector calculation formula of any point on the optical spline surface is:

[0028] n(u,v)=S′ u ×S′ v

[0029] Among them, S′ u and S′ v is the tangent vector of the optical spline surface at (u, v).

[0030] Furthermore, the new control point is offset from the original control point to a direction with a larger panel coefficient, and the offset is smaller than the iteration value.

[0031] Furthermore, the initial optical spline surface is a p-order B-spline curve, and the surface formula is:

[0032]

[0033] Among them, {P0=[x0, y0, z0]} is the coordinate of the initial control point, U and V are the node vectors in the u and v directions respectively, and the node vector U={0,…,0,a,…,a,b,…,b,1,…,1}, which contains p+1 0s, p a's, p b's and p+1 1s, 0<a<b<1.

[0034] Furthermore, the projection of the optical spline surface in the XY plane is a rectangular area, and the target light distribution is a cross-shaped area located in the rectangular area.

[0035] Furthermore, control points P0~P p , P p ~P2p , P 2p ~P 3p , P 3p ~P 4p They are linear distributions respectively.

[0036] The beneficial effects of the present invention are:

[0037] The present invention simplifies the calculation process of optical free-form surfaces, adjusts the free-form surface control points according to the calculation of local parameters around the control points, and describes the generated free-form surfaces using B-spline functions, thereby reducing process data, saving computer memory, improving calculation efficiency, and significantly reducing calculation time. The generated free-form surface format is universal and data is streamlined, and can be directly used for subsequent data stitching, cutting and other processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0039] Figure 1 It is a schematic diagram of the positional relationship between the coordinate system of the optical spline surface and the target light and the optical axis in the present invention;

[0040] Figure 2 It is a schematic diagram of the optical path of the unoptimized optical spline surface;

[0041] Figure 3 is the light intensity diagram of a rectangular light distribution;

[0042] Figure 4 It is the initial optical spline surface mesh diagram and the surface element coefficient and offset data diagram of each control point;

[0043] Figure 5 It is the optical spline surface mesh diagram after preliminary optimization and the surface element coefficient data diagram of each control point;

[0044] Figure 6 It is the surface normal vector, target normal vector and Z-axis offset data graph of the optical spline surface;

[0045] Figure 7 This is a schematic diagram of the optical path of the fully optimized optical spline surface;

[0046] Figure 8 It is a flowchart optimized in the XY plane;

[0047] Fig. 9 It is a flowchart optimized in the Z-axis direction.

[0048] In the figure, 1. optical spline surface, 2. target light, 3. incident light, 4. outgoing light, 5. rectangular light distribution, 6. invalid light distribution, 7. optical axis. DETAILED DESCRIPTION

[0049] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0050] The following example uses the solution of the refractive surface to describe in detail how to generate a rectangular optical spline surface and achieve a uniform cross-shaped output light distribution:

[0051] The setting conditions for this example are as follows:

[0052] 1. Unoptimized optical spline surface 1 Figure 2 As shown, the uv direction is all fourth-order and the segments are all three-segment, and the projection of the optical spline surface 1 in the XY plane is a rectangle.

[0053] 2. The distribution of target light 2 is Figure 3 The cross shape shown has a cross height of V=±8°, a cross width of H=±13°, a cross line width of ±3°, and a uniform distribution of light intensity within the cross area, while there is no constraint on the light intensity outside the cross area. Obviously, the lower the luminous flux outside the cross area, the higher the light efficiency of the optical spline surface 1.

[0054] 3. Light path Figure 2 As shown, the incident light 3 is a uniformly incident parallel light, the medium is polycarbonate (PC), and the refractive index n pc =1.586, the incident light 3 is refracted by the optical spline surface 1 to form the outgoing light 4, the medium of the outgoing light 4 is air, and the refractive index is 1.

[0055] The following is the emission effect formed by the unoptimized ordinary rectangular optical spline surface 1:

[0056] 1. The projection of the optical spline surface 1 in the XY plane is a rectangle. The four initial control points of the optical spline surface 1 are selected according to the size of the target light 2: S(0,0)=(-13,-8,0), S(1,0)=(13,-8,0), S(0,1)=(-13,8,0), S(1,1)=(13,8,0).

[0057] 2. Define the u-direction node vector of the optical spline surface 1 as {0, 0, 0, 0, 10 / 26, 10 / 26, 10 / 26, 10 / 26, 16 / 26, 16 / 26, 16 / 26, 16 / 26, 1, 1, 1, 1, 1}. The x-coordinate of the optical spline surface 1 is only related to u, and x(u) is linearly distributed in the interval [0, 1]. The optical spline surface 1 is segmented at x(10 / 26) = -3 and x(16 / 26) = 3. It can be seen that dx / du≡26, dx / dv≡0 of the optical spline surface 1; the v-direction node vector is {0, 0, 0, 0, 0, 5 / 16, 5 / 16, 5 / 16, 5 / 16, 11 / 16, 11 / 16, 11 / 16, 11 / 16, 1, 1, 1, 1}, the y coordinate of the optical spline surface 1 is only related to v, and y(v) is linearly distributed in the interval [0, 1], then the optical spline surface 1 is segmented at y(5 / 16) = -3 and y(11 / 16) = 3, it can be seen that dy / du≡h, dy / dv≡16 of the optical spline surface 1, so the surface element coefficient of the optical spline surface 1 is a constant 26mm×16mm=416mm in the interval u∈[0, 1], v∈[0, 1]. 2 .

[0058] 3. Define the horizontal angle H(u) of the outgoing light of the optical spline surface 1 to be linearly distributed between [0, 1], with H(0) = -13°, H(1) = +13°; define the vertical angle V(v) of the outgoing light to be linearly distributed between [h, 1], with V(0) = 8°, V(1) = -8°.

[0059] 4. The distribution of the emitted light from the optical spline surface 1 is: Figure 3 As shown in the uniform rectangular light distribution 5, since the target light 2 is distributed in a cross-shaped area, the four corners of the rectangular light distribution 5 are invalid light distributions 6, the area of ​​the rectangular light distribution 5 is 26×16=416, the area of ​​the invalid light distribution 6 is 10×5×4=200, and the light efficiency of the optical spline surface is (416-200) / 416≈52%.

[0060] Therefore, it is necessary to use the method of the present invention to optimize the optical spline surface to improve the light efficiency.

[0061] The initial parameters used in the optimization method of the present invention are as follows:

[0062] 1. The projection of the initial optical spline surface in the XY plane is a rectangle, and the four initial control points are: S(0,0)=(-12,-7,0), S(1,0)=(12,-7,0), S(0,1)=(-12,7,0), S(1,1)=(12,7,0).

[0063] 2. The u-direction node vector of the optical spline surface 1 is {0, 0, 0, 0, 10 / 26, 10 / 26, 10 / 26, 10 / 26, 16 / 26, 16 / 26, 16 / 26, 1, 1, 1, 1, 1}, and it is segmented at x(10 / 26) = -3 and x(16 / 26) = 3. The initial x coordinate of the optical spline surface 1 is only related to u and is linearly distributed in each segment; the v-direction node vector is {0, 0, 0, 0, 0, 5 / 16, 5 / 16, 5 / 16, 5 / 16, 11 / 16, 11 / 16, 11 / 16, 11 / 16, 1, 1, 1, 1}, and segmented at y(5 / 16) = -3 and y(11 / 16) = 3. The initial y coordinate of the optical spline surface 1 is only related to v, and y(v) is linearly distributed in each segment. Therefore, the rectangular area {(u, v)|u∈[10 / 26, 16 / 26] and v∈[5 / 16, 10 / 16]} is the initial projection area. In the initial case, the panel coefficient k of the optical spline surface 1 is s In the rectangular area {(u, v)|u∈[10 / 26,16 / 26] and v∈[5 / 16,10 / 16]}, it is a constant 26mm×16mm=416mm 2 .

[0064] The optimization objectives of the present invention are as follows:

[0065] 1. By adjusting the X and Y values ​​of the control points in the optical spline surface 1, the surface element coefficient is a constant of 416 mm in the cross-shaped area {(u, v)|u∈[10 / 26, 16 / 26] or v∈[5 / 16, 10 / 16]} of the target light 2. 2 , outside the cross-shaped area of ​​target light 2 is less than 416mm 2 constant, that is, the luminous flux in the area where the target light 2 is located is larger.

[0066] 2. By adjusting the Z value of the control point in the optical spline surface 1, the horizontal angle H(u) of the outgoing light is linearly distributed between [0, 1], and H(0) = -13°, H(1) = +13°; the vertical angle V(v) of the outgoing light is linearly distributed between [0, 1], and V(0) = 8°, H(1) = -8°.

[0067] 3. Goal 1 and Goal 2 ensure that in the uv space and in the cross region {(u, v)|u∈[10 / 26, 16 / 26] or v∈[5 / 16, 10 / 16]}, the area and luminous flux of the face element du·dv are uniformly distributed, and the HV angle of the emitted light is uniformly transitioned. Therefore, the emitted light in the cross region forms a uniform cross distribution. The optimized optical spline surface 1 is shown in Figure 7 shown.

[0068] The following are specific implementation methods to achieve the above goals.

[0069] A method for generating and optimizing an optical spline surface comprises the following steps:

[0070] The surface parallel to target light 2 is taken as the XY plane, the direction perpendicular to target light 2 is taken as the Z axis direction, the initial optical spline surface is established according to the initial parameters, and the initial control points are selected. Figure 1 , which is a schematic diagram of the positional relationship between the coordinate system of the optical spline surface 1 and the target light 2 and the optical axis 7.

[0071] The optical spline surface 1 is described by a B-spline function. The initial parameters include the surface order, the number of surface segments, the node vector, the incident light angle, the incident medium refractive index, the exit light angle, and the exit medium refractive index. The incident light angle, the incident medium refractive index, the exit light angle, and the exit medium refractive index can be used to calculate the target normal vector, the incident light angle includes the incident light horizontal angle and the incident light vertical angle, the exit light angle includes the exit light horizontal angle and the exit light vertical angle, and the target normal vector refers to the normal vector of the incident surface required to achieve the target exit light horizontal angle and the exit light vertical angle.

[0072] The initial optical spline surface in the present invention is a p-order B-spline curve. When the surface element is small, it can be assumed that the control points are linearly distributed in a part of the area. The control point P i If P is a linear distribution, i You can write:

[0073]

[0074] The surface formula is:

[0075]

[0076] That is, C(u) is a linear function of u, where {P h =[x h ,y h , z h ]} is the initial control point coordinate, U and V are the node vectors in the u direction and v direction respectively, the node vector U = {h, ​​..., 0, a, ..., a, b, ..., b, 1, ..., 1}, which contains p+1 0s, p a's, p b's and p+1 1's, 0<a<b<1. The present invention preferably assumes that the control point P h ~P p , P p ~P 2p , P 2p ~P 3p , P 3p ~P 4p If they are linearly distributed respectively, then C(u) is a linear function of u in the interval [h, a], [a, b]….

[0077] Optimization within the XY plane: This step is to determine the area range of the facet that can achieve the maximum luminous flux in the target light 2 area. Since the XY plane is parallel to the plane where the target light 2 is located, the luminous flux of the optical axis 7 reaching the target light 2 after refraction by the optical spline surface 1 is mainly related to the area range of the XY plane. The main method is to use the facet coefficient to adjust the control point until the facet coefficient deviation at the four vertex corners of each control point is within 1%; adjust the optical spline surface according to the new control point.

[0078] Optimization in the Z-axis direction: This step is to achieve the target specified horizontal angle and vertical angle of the emitted light, which can be achieved through normal vector comparison calculation. The main method is to use the normal vector to adjust the control point until the Z value deviation of the surface normal vector of the adjacent control point and the target normal vector is within 1% under the same X and Y values, and adjust the optical spline surface according to the new control point.

[0079] When optimizing in the XY plane, the control point adjustment method includes the following steps: Figure 8 As shown:

[0080] S11: setting an iteration value for calculating the bin coefficients around the control point, and determining the bin where the bin coefficients to be calculated are located according to the iteration value.

[0081] S12: Calculate the panel coefficients at the four corners of the control point. Here, multiple control points on the spline surface can be calculated simultaneously. The calculation formula of the panel coefficient is:

[0082]

[0083] Where (u, v) represents the surface element vector of the optical spline surface, and s represents the projection area of ​​the surface element of the optical spline surface on the XY plane. s Indicates the light intensity energy after the light of the current surface element is projected.

[0084] S13: If the deviation of the four facet coefficients is within 1%, it means that the energy of the facet is uniform and there is no need to adjust the optical spline surface here, so enter step S17; if the deviation of the four facet coefficients is greater than 1%, it means that the energy of the facet is uneven and it is necessary to adjust the control point to adjust the optical spline surface to the maximum luminous flux, so enter step S14.

[0085] S14: According to the bin coefficient calculated in step S13, calculate the offset of the new control point from the X value and Y value of the original control point. A larger bin coefficient indicates that the light projection efficiency of the area is higher, and the control point needs to be closer to the area. Therefore, the principle of selecting a new control point is to offset the original control point in the direction of the larger bin coefficient, and the offset is less than the iteration value, to ensure that the new control point is located in the bin area corresponding to the bin coefficient.

[0086] Figure 4 The figure shows the mesh diagram of the initial spline surface. The enlarged figure m on the right is the facet coefficient at the four corners of each control point, and the enlarged figure n is the offset of each control point. Figure 4 It can be seen that the facet coefficients at the four corners of control point p1 and control point p3 are equal and do not need to be offset. The facet coefficients on the right side of control point p2 and control point p4 are larger, so they are offset to the right by a value of 41.6. Figure 5 The figure shows the mesh diagram of the spline surface after preliminary optimization and the test diagram of the facet coefficients near its control points. From the enlarged diagram on the right, it can be seen that the deviation of the four facet coefficients near each control point is small, and the values ​​are all greater than 400, which is relatively Figure 4 The values ​​of most of the panel coefficients in are improved.

[0087] S15: Calculate new control point coordinates according to the deviation.

[0088] S16: Execute step S12.

[0089] S17: The control point calculation is completed.

[0090] When optimizing in the Z-axis direction, the control point adjustment method includes the following steps: Fig. 9 As shown:

[0091] S21: Determine the reference control point, calculate the surface normal vector between the reference control point and the adjacent control point, and calculate the target normal vector between the reference control point and the adjacent control point according to the law of refraction. Multiple reference control points can also be set, and the calculation is performed synchronously in different areas on the surface. The surface normal vector calculation formula for any point on the optical spline surface is:

[0092] n(u,v)=S′ u ×S′ v

[0093] Among them, S′ u and S′ v is the tangent vector of the optical spline surface at (u,v).

[0094] S22: Calculate the Z value corresponding to the surface normal vector and the target normal vector given the X value and the Y value. If the deviation between the two is within 1%, it means that the surface normal vector and the target normal vector tend to coincide, so go to step S25; if the deviation between the two is greater than 1%, it means that there is a large deviation between the surface normal vector and the target normal vector, and it is necessary to move closer to the target normal vector, so go to step S23.

[0095] Figure 6 The figure shows the Z value adjustment diagram of the optical spline surface 1 during the Z axis optimization. Figure 6Taking the control point p5 and the control point p6 in as an example, the three sets of data on the line segment connecting the control point p5 and the control point p6 are, from top to bottom: surface normal vector, target normal vector, and Z value adjustment amount of the control points p5 and p6.

[0096] S23: adjusting the Z value of the control point adjacent to the reference control point according to the surface normal vector Z value calculated in step S22 to generate a new reference control point.

[0097] S24: Execute step S21.

[0098] S25: The control point calculation is completed.

[0099] In this specification, the schematic representation of the terms does not necessarily refer to the same embodiment. Moreover, the specific features, structures, materials or characteristics described can be combined in any suitable manner in one or more embodiments.

[0100] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for generating and optimizing an optical spline surface, characterized in that: The following steps are involved: Taking the surface parallel to the target light as the XY plane and the direction perpendicular to the target light as the Z axis, the initial optical spline surface is established according to the initial parameters, and the initial control points are selected; Optimize in the XY plane: Use the facet coefficients to adjust the control points until the facet coefficients at the four corners of each control point are within 1%; adjust the optical spline surface based on the new control points; Optimize in the Z-axis direction: Use the normal vector to adjust the control points until the Z value deviation between the surface normal vectors of adjacent control points and the target normal vector is within 1% under the same X and Y values, and adjust the optical spline surface according to the new control points.

2. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: When optimizing in the XY plane, the control point adjustment method includes the following steps: S11: setting the iteration value for calculating the surface element coefficient around the control point; S12: Calculate the panel coefficients at the four corners of the control point; S13: If the deviation of the four bin coefficients is within 1%, proceed to step S17; if the deviation of the four bin coefficients is greater than 1%, proceed to step S14; S14: Calculate the offset between the X value and the Y value of the new control point and the original control point according to the panel coefficient calculated in step S13; S15: Calculate new control point coordinates according to the deviation; S16: Execute step S12; S17: The control point calculation is completed.

3. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: When optimizing in the Z-axis direction, the control point adjustment method includes the following steps: S21: Determine a reference control point, calculate the surface normal vector between the reference control point and the adjacent control points, and calculate the target normal vector between the reference control point and the adjacent control points according to the law of refraction; S22: Calculate the Z value corresponding to the surface normal vector and the target normal vector given the X value and Y value. If the deviation between the two is within 1%, proceed to step S25; if the deviation between the two is greater than 1%, proceed to step S23; S23: adjusting the Z value of the control point adjacent to the reference control point according to the surface normal vector Z value calculated in step S22 to generate a new reference control point; S24: Execute step S21; S25: The control point calculation is completed.

4. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: The initial parameters include the surface order, the number of surface segments, the node vector, the incident light angle, the incident medium refractive index, the exit light angle, and the exit medium refractive index.

5. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: The calculation formula of the panel coefficient is: Wherein, (u, v) represents the surface element vector of the optical spline surface, and s represents the projection area of ​​the surface element of the optical spline surface on the XY plane.

6. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: The calculation formula of the surface normal vector of any point on the optical spline surface is: n(u,v)=S′ u ×S′ v Among them, S′ u and S′ v is the tangent vector of the optical spline surface at (u, v).

7. The method for generating and optimizing an optical spline surface according to claim 2, characterized in that: The new control point is offset from the original control point in the direction of larger surface element coefficient, and the offset is less than the iteration value.

8. The method for generating and optimizing an optical spline surface according to claim 4, characterized in that: The initial optical spline surface is a p-order B-spline curve, and the surface formula is: Among them, {P0=[x0, y0, z0]} is the coordinate of the initial control point, U and V are the node vectors in the u and v directions respectively, and the node vector U={0,…,0,a,…,a,b,…,b,1,…,1}, which contains p+1 0s, p a's, p b's and p+1 1s, 0<a<b<1.

9. The method for generating and optimizing an optical spline surface according to claim 1, characterized in that: The projection of the optical spline surface in the XY plane is a rectangular area, and the target light distribution is a cross-shaped area located in the rectangular area.

10. The method for generating and optimizing an optical spline surface according to claim 8, characterized in that: Control points P0~P p , P p ~P 2p , P 2p ~P 3p , P 3p ~P 4p They are linear distributions respectively.

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