Two-dimensional integral mirror suitable for collimation light source incidence and design method thereof

Abstract

The invention belongs to the technical field of light field regulation and control, and discloses a two-dimensional integral mirror suitable for collimation light source incidence and a design method thereof, a reflecting surface of the two-dimensional integral mirror is formed by splicing M * N sub curved surface patches, each sub curved surface patch is defined by a parameter equation, and the whole mirror surface is continuous and smooth. Incident light emitted by the collimation light source is segmented and reflected by the sub curved surfaces, and is superposed in a target area to obtain uniform light spots. According to the design method, by introducing the target overturning mapping strategy and the area conservation constraint, the degree of freedom of design is improved, the smoothness of the mirror surface is guaranteed, uniform shaping of light spots in any spatial position and any shape and size is achieved, and the machining feasibility and design flexibility of the mirror surface are remarkably improved. The integral mirror is suitable for laser processing scenes such as laser cladding, quenching, welding and the like with high requirements on light spot uniformity, and has good engineering practicability and customization capability.

Description

Technical Field

[0001] The present invention belongs to the technical field of light field control, and more specifically, relates to a two-dimensional integrator mirror suitable for incident collimated light sources and a design method thereof. Background Art

[0002] In high-energy laser processing applications such as laser cladding and laser hardening, the laser energy must be uniformly distributed across the material surface. However, the energy of the laser beam directly emitted is often non-uniform, resulting in inconsistent material processing within the processing area and severely impacting processing quality. As a commonly used light field manipulation element, an integrator mirror can shape the incident non-uniform beam into a uniformly distributed spot on the target surface.

[0003] However, in the existing technology, most integrating mirror designs can only achieve homogenization in one dimension. For example, if the integrating mirror is rotated based on the main line on a plane, the resulting integrating mirror can generally only achieve homogenization in one dimension. Although some studies have attempted to achieve homogenization in two dimensions, for example, the existing technology discloses a method of using spliced paraboloids to achieve two-dimensional homogenization, the resulting spot size is relatively small. There are also some methods that fix the coordinates of the sampling points x and y on the integrating mirror and design the value of z to obtain the required integrating mirror. Since the coordinates of x and y are fixed, the control dimension is limited, making it difficult to balance the smoothness of the mirror and the size of the spot. There are problems such as the mirror surface being rough and difficult to process, or the generated spot size being relatively small, and the practicality is limited. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a two-dimensional integrating mirror suitable for incident collimated light sources and a design method thereof. The purpose is to design a two-dimensional integrating mirror that can generate a uniform light spot of arbitrary size, shape and spatial position, while having good surface smoothness and processing feasibility.

[0005] To achieve the above-mentioned object, the present invention provides a design method for a two-dimensional integrator mirror suitable for incident collimated light sources, the two-dimensional integrator mirror comprising: a substrate and a reflective surface disposed on the substrate; the reflective surface is composed of M×N sub-surface pieces; the design method comprises:

[0006] S1. Initialize a plane P* covering the substrate as the initial surface of the two-dimensional integrator mirror, and divide the plane P* into M×N sub-surfaces; perform grid sampling on the plane P* to obtain the initial spatial coordinates P of each sampling point. * (x,y,z), expressed as parameter form P * (x(u,v), y(u,v), z(u,v)); (u,v) is used to represent the row and column order of grid sampling at each sampling point;

[0007] S2. Based on the expected spatial position, spot shape and energy distribution of the collimated light on the target surface after being reflected by each sub-surface, the target spot model Q corresponding to each sub-surface is constructed. i,j =Q i,j (x(u,v),y(u,v),z(u,v)), i∈[1,M], j∈[1,N]; among them, Q i,j Represents the point cloud position of the collimated light on the target surface after passing through each sampling point in the sub-surface (i, j); the target spot model Q corresponding to each sub-surface i,j Superimpose in sampling order to obtain the target spot model Q;

[0008] S3. Establish a constraint equation for the two-dimensional integrating mirror reflection surface based on the reflection law satisfied by the direction I of the incident collimated light, the direction R of the light reflected by the two-dimensional integrating mirror reflection surface, and the normal vector N at each sampling point on the two-dimensional integrating mirror reflection surface; wherein R=QP, and P is the spatial coordinate of each sampling point on the two-dimensional integrating mirror reflection surface;

[0009] S4. Construct area-preserving constraints: Wherein, (x, y) is the x, y coordinate of the sampling point (x, y, z) on the reflecting surface, σ is the infinitesimal area of the sampling point (x, y, z) on the xoy plane, the xoy plane is a plane perpendicular to the collimated light, and the coordinate zero point o is the center of the reflecting surface of the two-dimensional integrating mirror;

[0010] S5. Under the area constraint, P * (x(u,v),y(u,v),z(u,v)) is the initial solution. Solve the constraint equation of the two-dimensional integrating mirror reflection surface to obtain the spatial coordinates P of each sampling point on the two-dimensional integrating mirror reflection surface. Fit the spatial coordinates P to obtain the three-dimensional geometric shape of each sub-surface patch, and complete the design of the two-dimensional integrating mirror.

[0011] Furthermore, in S2, the target spot model Q corresponding to each sub-facet is constructed i,j =Q i,j (x(u,v),y(u,v),z(u,v)), including:

[0012] Select one sub-surface (i, j) from the M×N sub-surfaces as the reference surface; construct the target spot model Q corresponding to the reference surface based on the expected spatial position, spot shape and energy distribution of the collimated light after reflection from each sub-surface. i,j =Q i,j (x(u,v),y(u,v),z(u,v));

[0013] For sub-surface (i-1, j) and sub-surface (i+1, j), the corresponding target spot model Qi-1,j and Q i+1,j for:

[0014] Q i-1,j =Q i,j (flip(x(u,v),1),y(u,v),z(u,v))

[0015] Q i+1,j =Q i,j (flip(x(u,v),1),y(u,v),z(u,v))

[0016] For sub-surface (i, j-1) and sub-surface (i, j+1), the corresponding target spot model Q i,j-1 and Q i,j+1 for:

[0017] Q i,j-1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v))

[0018] Q i,j+1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v))

[0019] Among them, flip(x(u,v),1) means flipping x(u,v) along the dimension of u, and flip(y(u,v),2) means flipping y(u,v) along the dimension of v;

[0020] According to the above flip principle, the target spot model Q corresponding to each sub-face is obtained i,j .

[0021] Furthermore, in S3, the constraint equation of the two-dimensional integrating mirror reflection surface is:

[0022]

[0023] Wherein, |I| represents the vector modulus length of I, |R| represents the vector modulus length of R, and λ is the proportional coefficient.

[0024] Furthermore, in S5, a parametric spline surface or a non-uniform rational B-spline surface is used to fit the spatial coordinate P to obtain the three-dimensional geometric shape of each sub-surface patch.

[0025] The present invention also provides a two-dimensional integrator mirror suitable for incident collimated light sources, comprising a substrate and a reflective surface arranged on the substrate; the reflective surface is composed of M×N sub-curved surface pieces; the three-dimensional geometric shape of each sub-curved surface piece is designed using the design method described above.

[0026] The present invention also provides a two-dimensional integrator mirror design system suitable for incident collimated light sources, comprising a computer-readable storage medium and a processor;

[0027] The computer-readable storage medium is used to store executable instructions;

[0028] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute any of the above-mentioned design methods.

[0029] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements any of the above-described design methods.

[0030] The present invention also provides a computer program product, comprising a computer program, which enables the computer to execute any one of the above-mentioned design methods when the computer program is run on a computer.

[0031] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0032] (1) The present invention divides the reflective surface of the integrating mirror into M×N sub-surfaces in rows and columns, so that the integrating mirror can generate a two-dimensional uniform light spot of any size, shape and spatial position, while having good surface smoothness and processing feasibility. Specifically, by using parametric equations to describe both the integrating mirror and the target light spot, a mapping relationship between each sub-surface and the target light spot is established, so that the design process can flexibly adapt to any position and posture of the target light spot in three-dimensional space, thereby improving the adaptability and customization of the system. In the design process of the integrating mirror, an area-preserving mapping constraint is introduced. In this way, the x, y coordinates at the sampling point (x, y, z) of the integrating mirror are introduced into the design process, which increases the dimension of the variable, improves the geometric design freedom, and thus enhances the adaptability of the integrating mirror to different light spot sizes and shapes, while taking into account the smoothness of the mirror surface. Experiments have shown that the integrating mirror designed by the present invention can meet the beam shaping requirements of the target light spot located on an inclined plane, curved surface or non-coplanar area, and can generate a large-sized and highly uniform target light spot.

[0033] (2) As a preference, by constructing a mapping relationship between each sub-surface and the target light spot in a horizontal and vertical flipping manner, it can be ensured that the light at the boundary of adjacent sub-regions will be reflected to the same position of the target surface, ensuring a smooth transition between the sub-surface patches and having extremely high processing feasibility.

[0034] In summary, the two-dimensional integrating mirror designed in this invention can generate uniform light spots of arbitrary size, shape, and spatial position, while also exhibiting excellent surface smoothness and processability. During use, collimated laser light is incident on the integrating mirror surface. After being independently reflected and modulated by each sub-surface, it converges on the target surface to form a uniform light spot with controllable shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the operation of a two-dimensional integrating mirror in an embodiment of the present invention;

[0036] Figure 2 Schematic diagram of dividing a two-dimensional integrator mirror surface into sub-surface patches in an embodiment of the present invention;

[0037] Figure 3 Schematic diagram of grid sampling on a two-dimensional integrating mirror surface in an embodiment of the present invention;

[0038] Figure 4 Schematic diagram of the area-preserving constraint transformation effect of a two-dimensional integrating mirror in an embodiment of the present invention;

[0039] Figure 5 is a light path diagram of a two-dimensional integrating mirror in an embodiment of the present invention under one implementation mode;

[0040] Figure 6 yes Figure 5 The effect diagram of the two-dimensional integrating mirror shown;

[0041] Figure 7 is a light path diagram of the two-dimensional integrating mirror in an embodiment of the present invention under another implementation manner;

[0042] Figure 8 yes Figure 7 The effect diagram of the two-dimensional integrating mirror is shown.

[0043] Throughout the drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0044] 1- Collimated beam, 2- Two-dimensional integrator, 3- Target surface. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0046] Example 1

[0047] like Figure 1As shown, an embodiment of the present invention provides a two-dimensional integrator suitable for incident light from a collimated source. The two-dimensional integrator 2 includes a substrate and a reflective surface disposed on the substrate. The reflective surface is composed of M×N sub-surface pieces, which are spliced together to form a continuous, smooth surface. The three-dimensional geometric shape of each sub-surface piece of the two-dimensional integrator is determined as follows:

[0048] S1. Initialize a plane P* that completely covers the base of the two-dimensional integrator mirror to be designed as the initial integrator mirror surface shape, and divide the plane P* into M×N sub-surface patches, where M and N are positive integers, representing the number of segments of the plane P* in the horizontal and vertical directions, respectively, corresponding to the number of horizontal and vertical edges of the two-dimensional integrator mirror reflection surface. The horizontal and vertical edges are staggered to divide the reflection surface into M×N sub-surface patches; perform grid sampling on the plane P* to obtain the initial spatial coordinates P of each sampling point. * (x, y, z); and the initial spatial coordinates P of each sampling point * (x,y,z) is expressed as parameter form P * (x(u,v), y(u,v), z(u,v)); where (u,v) is used to represent the grid sampling order of each sampling point, u is the row number of the grid sampling on plane P*, and v is the column number of the grid sampling on plane P*. The sampling number is the global sampling number (the sampling number of the entire mirror), not the local sampling number on each sub-patch.

[0049] S2. Based on the expected spatial position, expected spot shape and spot energy distribution of the collimated light beam after being reflected by each sub-surface, the target spot model Q corresponding to each sub-surface is constructed. i,j =Q i,j (x(u,v),y(u,v),z(u,v)),i∈[1,M],j∈[1,N]; where the target spot model Q i,j It represents the intersection of the collimated light beam 1 on the target surface 3 after passing through each sampling point in the current sub-surface (i, j), that is, the spatial position of the point cloud on the target surface. i,j The target spot model Q is obtained by superimposing them in the sampling order.

[0050] S3. Based on the reflection law satisfied by the incident direction I of the collimated light beam, the direction R of the light reflected from the reflecting surface of the ideal integrating mirror, and the normal vector N at each sampling point of the ideal integrating mirror type, the constraint equation of the ideal integrating mirror surface is established; wherein, R=QP, P is the three-dimensional coordinate of each sampling point of the ideal integrating mirror type (the quantity to be solved), and the three-dimensional coordinate of the sampling point (x, y, z) on the ideal integrating mirror type can be expressed as P(x, y, z).

[0051] S4. Construct area preservation constraints: Where (x, y) is the x, y coordinate of the sampling point (x, y, z) on the ideal integrating mirror, (u, v) is the sampling number corresponding to (x, y), and σ is the infinitesimal area of the sampling point on the mirror surface of the ideal integrating mirror on the xoy plane. In this embodiment of the present invention, a three-dimensional rectangular coordinate system is constructed with the center of the integrating mirror's reflecting surface as the zero point of the coordinate system and the plane perpendicular to the collimated incident light as the xoy plane. The constructed area-preserving constraint ensures that the projected area of light reflected by each sub-surface of the ideal integrating mirror remains consistent on the target surface, thereby achieving uniform energy distribution at a larger spot size.

[0052] S5. Under the area constraint, the initial coordinates P of each sampling point are * (x(u,v),y(u,v),z(u,v)) is used as the initial solution to solve the constraint equations of the ideal integral mirror surface, and the three-dimensional coordinates P of each sampling point of the ideal integral mirror type are obtained in the computer; the three-dimensional coordinates P are used as the three-dimensional coordinates of each sampling point of the two-dimensional integral mirror type to be designed, and each sampling point is fitted to obtain the three-dimensional geometric shape of each sub-surface patch, and then the required two-dimensional integral mirror type is obtained, completing the overall design of the two-dimensional integral mirror.

[0053] In S1, the number of sub-areas into which the mirror surface is divided is set according to the physical size of the incident collimated light beam, the size of the substrate, and the processing accuracy, so as to ensure the uniformity of the light spot generated on the target surface after the incident collimated light beam passes through the reflecting surface of the integrator, while taking into account the design complexity and processing feasibility. Preferably, M and N are 7 or 9, that is, the reflecting surface is composed of 7×7, 7×9, 9×7 or 9×9 sub-surface pieces. The substrate is preferably a copper substrate. In an embodiment of the present invention, the target light spot is of any shape, preferably a rectangle, and it can be located on an inclined plane or a curved surface in three-dimensional space.

[0054] In S2, the target spot model is expressed as a parametric equation using parameters (u, v), which is consistent with the parameter definition of the integrating mirror reflection surface.

[0055] As a specific implementation method, in S2, the target spot model Q corresponding to each sub-face is constructed i,j =Q i,j (x(u,v),y(u,v),z(u,v)), including:

[0056] Select a sub-surface (i, j) from the M×N sub-surfaces as the reference surface, i∈[1, M], j∈[1, N]; obtain the target spot model Q corresponding to the reference surface i,j =Q i,j (x(u,v),y(u,v),z(u,v));

[0057] For sub-surface (i-1, j) and sub-surface (i+1, j), the corresponding target spot model Q i-1,j and Q i+1,j Both are:

[0058] Q i-1,i =Q i,j (flip(x(u,v),1),y(u,v),z(u,v))

[0059] Q i+1,j =Q i,j (flip(x(u,v),1),y(u,v),z(u,v))

[0060] For sub-surface (i, j-1) and sub-surface (i, j+1), the corresponding target spot model Q i,j-1 and Q i,j+1 Both are:

[0061] Q i,j-1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v))

[0062] Q i,j+1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v))

[0063] Among them, the function flip(A, dim) represents mirroring and flipping the order of elements in the matrix A along the dimension dim; in the embodiment of the present invention, flip(x(u, v), 1) represents flipping x(u, v) along the dimension u, that is, flipping the matrix composed of all x(u, v) values in the reference patch left and right to obtain the target spot model Q corresponding to the sub-patch (i-1, j) and the sub-patch (i+1, j) i-1,j and Q i+1,j The x(u,c) values, y(u,v), and z(u,c) in the image are the same as those in the reference patch. flip(y(u,v),2) means flipping y(u,v) along the dimension of v, that is, flipping the matrix composed of all y(u,v) values in the reference patch upside down to obtain the target spot model Q corresponding to the sub-patch (i,j-1) and the sub-patch (i,j+1). i,j-1 and Q i,j+1 The y(u,v) values, x(u,v) and z(u,v) in are the same as those of the reference patch.

[0064] According to the above flip principle, the target spot model Q corresponding to each sub-face is obtained i,j .

[0065] In the embodiment of the present invention, a mapping relationship between each sub-surface and the target light spot is constructed by flipping horizontally and vertically, which can ensure that the light at the boundary of adjacent sub-areas will be reflected to the same position of the target surface. For example, a collimated light beam is incident on a point a at the boundary of adjacent sub-areas, and point a belongs to two adjacent sub-areas. The target light spot model determined by the flipping horizontally and vertically in the present invention can ensure that after the light passes through point a belonging to the two adjacent sub-areas, it will be reflected at the same position of the target surface, so as to ensure the geometric continuity and smoothness of the mirror surface at the splicing point. At this time, the boundaries of adjacent sub-surfaces satisfy the normal vector continuity.

[0066] In the embodiment of the present invention, Figure 2 As shown, taking 5×5 sub-surface patches as an example, the sub-surface patch (i, j) is as follows Figure 2 As shown, 1≤i≤5, 1≤j≤5, Figure 2 Each grid in corresponds to an independent sub-surface patch. Each sub-surface patch is further meshed (grid sampling), and each sub-surface patch is divided into multiple sub-grids (sampling points). Each sampling point is represented by a parameter form (u, v). For example, for a 2×2 sub-surface, Figure 3 Each black dot in the figure shows a sampling point. Each sub-surface is further discretized into 4×4 sampling points. The two-dimensional parameters (u, v) of the entire mirror are represented by the row and column numbers (serial numbers) of the sampling points, where u∈[1,7], v∈[1,7] (the boundaries of each adjacent sub-surface share the same sampling points).

[0067] As a specific implementation, in S3, the reflection relationship satisfied by the incident direction I of the collimated light beam, the direction R of the light reflected from the reflective surface of the ideal integrating mirror, and the normal vector N at each sampling point of the ideal integrating mirror surface is:

[0068]

[0069] Among them, |I| means taking the vector modulus length of I, |R| means taking the vector modulus length of R, R is the proportional coefficient, which means Collinear with N.

[0070] In S4, an area-preserving constraint is introduced during the design process. This constraint ensures that the projected area of the light energy reflected by the sub-surface (i, j) in the initialized plane P* and the corresponding sub-surface (i, j) in the designed ideal integrating mirror are consistent on the target surface, thereby achieving uniform energy distribution at a larger spot size. Figure 4 As shown, the left side is the initialized plane P*, and the right side is the ideal integrating mirror obtained through calculation.

[0071] Preferably, in S5, a parametric spline surface or a non-uniform rational B-spline surface (NURBS) is used for fitting to obtain the three-dimensional geometric shape of each sub-surface patch.

[0072] The effects of the two-dimensional integrating mirror designed by the present invention are described below with two specific examples.

[0073] Example 1

[0074] Based on the above-mentioned integrator mirror design model, a specific design scheme for a two-dimensional integrator mirror is provided to achieve uniform shaping of a large rectangular light spot. The requirement is to generate a 100mm×100mm square uniform light spot at a working distance of 300mm between the integrator mirror and the target surface (i.e., the spatial position of the target surface) under the condition of incident collimated Gaussian beam with a diameter of 30mm. The incident optical axis of the collimated beam is perpendicular to the output optical axis, and the target surface is perpendicular to the output optical axis. The simulated optical path is as follows: Figure 5 shown.

[0075] Specifically, the integrator mirror to be designed uses a copper cylinder substrate with a diameter of 49.5 mm. Its reflective surface is divided into 7×7 subsurfaces, forming a mirror array consisting of 49 subsurfaces. To facilitate consistency with computer storage and calculation methods, the parameters (u, v) are directly taken as the serial numbers of the mirror sampling points. In other embodiments, they can be normalized representations of the serial numbers of the mirror sampling points. Each subsurface is further discretized uniformly into 101×101 sampling points. The two-dimensional parameters (u, v) of the entire mirror are represented by the sampling point numbers (serial numbers), where u∈[1,701] and v∈[1,701] (the boundaries of each adjacent subsurface share a sampling point).

[0076] In the selection of the coordinate system, the positive direction of the incident light is defined as the negative direction of the z-axis, that is, the light source is located in the positive direction of the z-axis. The center of the integrating mirror reflection surface is located at the zero point of the coordinate system, and the center of the target surface is set at 300mm in the positive direction of the x-axis, that is, the plane where the target surface is located is x = 300mm. In order to facilitate the unified expression of the target point position, a parameterized method is used to construct the coordinate function of the target spot area. Considering that the overall mirror surface is composed of multiple sub-surfaces, in order to uniformly describe the target areas corresponding to different sub-surfaces, it is necessary to combine the row and column numbers of the sub-surfaces in the mirror array for coordinate transformation. Let the sub-surface number be (i, j), i∈[1,7], j∈[1,7]. For a single sub-surface (i, j), the corresponding target surface area can be expressed as:

[0077]

[0078] Among them, Q i,jrepresents the target position coordinates on the target surface corresponding to each sampling point (u, v) after the collimated beam passes through each sampling point (u, v) within the sub-surface (i, j), in mm. This expression ensures that the target spot is uniformly distributed and covers an area of 100 mm × 100 mm.

[0079] In this example, the sub-surface with i=4 and j=4 is selected as the reference patch, and the point clouds of the target surfaces corresponding to the remaining sub-surfaces are obtained by flipping.

[0080] In a computer, different sub-surface point clouds can be connected in series and parallel (spliced) in a matrix to obtain a complete correspondence, that is, a complete target spot model Q. At the same time, to ensure the boundary continuity between adjacent sub-surfaces, adjacent sub-surfaces share a column or row of sampling point data at the boundary.

[0081] The above parameterization method establishes a spatial mapping relationship from mirror sampling points to the target spot area. In the specific calculation, a plane reflector is initialized based on the spatial position of the target area. Then, the constraint equations of the ideal integrating mirror surface and the area-preserving constraint equation are iteratively solved to obtain the distribution of discrete points on the specific mirror surface. Finally, a fitting is performed to obtain a mirror model that can be used for simulation and processing.

[0082] The simulation results of the target surface are as follows Figure 6 As shown in the figure, the design can achieve high uniformity shaping of large-sized rectangular spots under close working conditions, verifying the applicability and effectiveness of the method of the present invention under actual engineering conditions.

[0083] Example 2

[0084] Based on the above-mentioned integrator mirror design model, a specific design scheme for a two-dimensional integrator mirror is provided, which is used to generate a specific design method for a two-dimensional integrator mirror with a rectangular uniform spot on an inclined plane. The requirement is that under the condition of a 20mm diameter collimated Gaussian beam incident, the working distance between the integrator mirror and the target surface is A 10mm×10mm square uniform light spot is generated at the position of the laser beam. The angle between the incident light axis and the outgoing light axis of the reflected light beam after the light beam passes through the integrator is 45°, and the angle between the target surface and the yoz surface is 30°. The simulated light path is as follows: Figure 7 shown.

[0085] Specifically, the integrating mirror uses a copper cylinder substrate with a diameter of 34.5 mm. Its reflective surface is divided into 5×5 subsurfaces, forming a mirror array consisting of 25 subsurfaces. To facilitate consistency with computer storage and calculation methods, the parameters (u, v) are directly taken as the mirror sampling point sequence. Each subsurface is further discretized uniformly into 101×101 sampling points, and the sampling point number is represented by the two-dimensional parameters (u, v), where u∈[1,501] and v∈[1,501].

[0086] In the selection of the coordinate system, the positive direction of the incident light is defined as the negative direction of the z-axis, that is, the light source is located in the positive direction of the z-axis. The center of the integrating mirror is located at the zero point of the coordinate system, and the center of the target surface is set at the spatial coordinates (500mm, 0, 500mm). To facilitate the unified expression of the target point position, a parameterized method is used to construct the coordinate function of the target spot area. For a single sub-surface (i, j), its corresponding target surface area can be expressed as:

[0087]

[0088] Among them, Q i,j represents the target position coordinates of each sampling point (u,v) on the target surface after the collimated beam passes through each sampling point (u,v) within the sub-surface (i,j), in mm. This expression ensures a uniform distribution of the target spot, covering a 10mm × 10mm area, while also accounting for the specific spatial distribution of the tilted plane.

[0089] In this example, the sub-surface with i=3 and j=3 is selected as the reference surface patch, and the point clouds of the target surface corresponding to the remaining sub-surfaces are obtained by flipping. In a computer, different sub-surface point clouds can be connected in series and parallel (spliced) in a matrix to obtain a complete correspondence, that is, to obtain a complete target spot model Q.

[0090] The above parameterization method establishes a spatial mapping relationship from the mirror sampling point to the target spot area. In the specific calculation, a plane reflector is first initialized according to the spatial position of the target area. Then, the constraint equations of the ideal integrating mirror surface and the area-preserving constraint equation are iteratively solved to obtain the discrete point distribution of the specific mirror surface. Finally, fitting is performed to obtain a mirror model that can be used for simulation and processing.

[0091] The simulation results of the target surface are as follows Figure 8 This design can achieve high uniformity shaping of the rectangular light spot on an inclined plane that is not perpendicular to the output optical axis, verifying the applicability and effectiveness of the method of the present invention under actual engineering conditions.

[0092] Based on the two-dimensional integrating mirror designed by the present invention, during use, the collimated laser is incident on the integrating mirror surface, and after being independently reflected and modulated by each sub-surface, it converges on the target surface to form a uniform light spot with controllable shape.

[0093] Example 2

[0094] This embodiment of the present invention provides a method for designing a two-dimensional integrator mirror suitable for use with collimated light sources. The two-dimensional integrator mirror includes a substrate and a reflective surface disposed on the substrate; the reflective surface is composed of M×N sub-surface patches. The method for determining the three-dimensional geometric shape of each sub-surface patch is described in Example 1 above and will not be repeated here.

[0095] Example 3

[0096] An embodiment of the present invention provides a two-dimensional integrator mirror design system suitable for incident collimated light sources, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the design method in the above-mentioned embodiment 2 are implemented.

[0097] The relevant technical solutions are the same as above and will not be repeated here.

[0098] Example 4

[0099] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the design method in the above-mentioned embodiment 2 are implemented.

[0100] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0101] The relevant technical solutions are the same as above and will not be repeated here.

[0102] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A design method for a two-dimensional integrator mirror suitable for incident collimated light sources, characterized in that: The two-dimensional integrating mirror comprises a substrate and a reflecting surface arranged on the substrate; The reflective surface is composed of M×N sub-surface patches, and the design method includes: S1. Initialize a plane P* covering the substrate as the initial surface of the two-dimensional integrating mirror, and divide the plane P* into M×N sub-surfaces; perform grid sampling on the plane P* to obtain the initial spatial coordinates P of each sampling point. * (x,y,z), and expressed in parameter form P * (x(u,v),y(u,v),z(u,v)); (u,v) is used to represent the row and column order of grid sampling at each sampling point; S2. Based on the expected spatial position, spot shape and energy distribution of the collimated light on the target surface after being reflected by each sub-surface, the target spot model Q corresponding to each sub-surface is constructed. i,j =Q i,j (x(u,v),y(u,v),z(u,v)), i∈[1,M], j∈[1,N]; among them, Q i,j Represents the point cloud position of the collimated light on the target surface after passing through each sampling point in the sub-surface (i, j); the target spot model Q corresponding to each sub-surface i,j Superimpose in sampling order to obtain the target spot model Q; S3. Establish a constraint equation for the two-dimensional integrating mirror reflection surface based on the reflection law satisfied by the direction I of the incident collimated light, the direction R of the light reflected by the two-dimensional integrating mirror reflection surface, and the normal vector N at each sampling point on the two-dimensional integrating mirror reflection surface; wherein R=QP, and P is the spatial coordinate of each sampling point on the two-dimensional integrating mirror reflection surface; S4. Construct area preservation constraints: Wherein, (x, y) is the x, y coordinate of the sampling point (x, y, z) on the reflecting surface, σ is the infinitesimal area of the sampling point (x, y, z) on the xoy plane, the xoy plane is a plane perpendicular to the collimated light, and the coordinate zero point o is the center of the reflecting surface of the two-dimensional integrating mirror; S5. Under the area constraint, P * (x(u,v),y(u,v),z(u,v)) is the initial solution. Solve the constraint equation of the two-dimensional integrating mirror reflection surface to obtain the spatial coordinates P of each sampling point on the two-dimensional integrating mirror reflection surface. Fit the spatial coordinates P to obtain the three-dimensional geometric shape of each sub-surface patch, and complete the design of the two-dimensional integrating mirror.

2. The design method according to claim 1, characterized in that: In S2, the target spot model Q corresponding to each sub-face is constructed i,j =Q i,j (x(u,v),y(u,v),z(u,v)), including: Select one sub-surface (i, j) from the M×N sub-surfaces as the reference surface; construct the target spot model Q corresponding to the reference surface based on the expected spatial position, spot shape and energy distribution of the collimated light after reflection from each sub-surface. i,j =Q i,j (x(u,v),y(u,v),z(u,v)); For sub-surface (i-1, j) and sub-surface (i+1, j), the corresponding target spot model Q i-1,i and Q i+1,j for: Q i-1,j =Q i,j (flip(x(u,v),1),y(u,v),z(u,v)) Q i+1,j =Q i,j (flip(x(u,v),1),y(u,v),z(u,v)) For sub-surface (i, j-1) and sub-surface (i, j+1), the corresponding target spot model Q i,j-1 and Q i,j+1 for: Q i,j-1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v)) Q i,j+1 =Q i,j (x(u,v),flip(y(u,v),2),z(u,v)) Among them, flip(x(u,v),1) means flipping x(v,v) along the dimension of u, and flip(y(u,v),2) means flipping y(u,v) along the dimension of v; According to the above flip principle, the target spot model Q corresponding to each sub-face is obtained i,j .

3. The design method according to claim 1 or 2, characterized in that: In S3, the constraint equation of the two-dimensional integrating mirror reflection surface is: Wherein, |I| represents the vector modulus length of I, |R| represents the vector modulus length of R, and λ is the proportional coefficient.

4. The design method according to claim 3, characterized in that: In S5, a parametric spline surface or a non-uniform rational B-spline surface is used to fit the spatial coordinate P to obtain the three-dimensional geometric shape of each sub-surface patch.

5. A two-dimensional integrator suitable for incident collimated light source, characterized in that: It comprises a base and a reflecting surface arranged on the base; the reflecting surface is formed by splicing M×N sub-curved surface pieces; the three-dimensional geometric shape of each sub-curved surface piece is designed by the design method according to any one of claims 1 to 4.

6. A two-dimensional integrator mirror design system suitable for incident collimated light source, characterized in that: comprising a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the design method described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the design method according to any one of claims 1 to 4 is implemented.

8. A computer program product, characterized in that The invention comprises a computer program, which, when running on a computer, enables the computer to execute the design method according to any one of claims 1 to 4.

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