Microlens array surface ray tracing method and system for tolerance analysis
By distinguishing the subunits of microlens arrays through indexing and integrating ray tracing, the microlens array simulation problem in the prior art is solved and the production success rate of optical systems is improved.
Patent Information
- Application Number
- CN202510295049.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-13
- Publication Date
- 2025-08-01
AI Technical Summary
Existing simulation software is difficult to achieve effective modeling and simulation of complex parameter microlens arrays, resulting in a degradation of optical system performance.
The index method is used to distinguish the sub-units of the microlens array, and the ray tracing interaction process between the ray and the microlens array list surface is realized through the index. It is integrated into the global ray tracing process, and the coordinate index and storage medium index are used to store and read ray parameters.
Optical simulation of microlens arrays containing processing errors is realized, the production success rate of microlens array optical system is improved, and the losses caused by processing technology are reduced.
Smart Images
Figure CN120408926A_ABST
Abstract
Description
Technical Field
[0001] The present invention is applicable to the field of optical system simulation involving microlens arrays, and particularly relates to a method and system for ray tracing on the surface of a microlens array for tolerance analysis. Background Art
[0002] With the continuous improvement of microlens array processing technology, microlens arrays are widely used in optical systems and play an important role in many fields such as light field cameras, non-imaging beam homogenization systems, wavefront sensing, and beam scanning. In an optical system involving a microlens array, due to the differences between the actual processing and the ideal design parameters of the microlens array, a large amount of stray light or beams deviating from the design values will be introduced into the optical path, thus seriously affecting the performance of the optical system. Therefore, achieving effective simulation and control of these beams is of great significance to optical system designers.
[0003] The errors between the processed physical object of the microlens array and the ideal design are reflected in many aspects, including the surface profile mutation at the connection of adjacent sub-units, the inconsistency of curvature between each sub-unit, and the randomness of the surface profile error of the sub-units. If the above factors are not fully considered in the propagation optical path, the physical effect of the system will deviate seriously from the design value. To fully consider these factors, effective optical simulation is required. In engineering practice, geometric ray tracing is usually used for stray light analysis of optical systems to achieve effective optical simulation, but it is difficult to model and simulate microlens arrays with complex parameters in existing simulation software. Therefore, if a modeling and simulation method for microlens arrays with processing errors can be realized, it has practical value for various microlens array optical systems. Summary of the Invention
[0004] The purpose of the present invention is to provide a method and system for ray tracing on the surface of a microlens array for tolerance analysis, and apply this method to the global ray tracing process of an optical system to achieve optical simulation of a microlens array with processing errors.
[0005] To achieve the purpose of the present invention, the technical solutions provided by the present invention are as follows:
[0006] In the first aspect
[0007] The present invention provides a method for ray tracing on the surface of a microlens array for tolerance analysis. The method is applied to the global ray tracing process of an optical system including a microlens array, and includes:
[0008] Distinguish each sub-unit of the microlens array by using indexing, and store and read the surface parameter information of the microlens array through indexing; and
[0009] Implement a ray tracing interaction process between light rays and the surface of a microlens array using index and microlens array surface parameter information, and integrate the ray tracing interaction process into the global ray tracing process.
[0010] Further, the index includes two index types, namely coordinate index and storage medium index. The coordinate index is an index that has a corresponding relationship with the reference plane coordinate system, and the storage medium index is an index that has a corresponding relationship with the medium storing the surface parameter information.
[0011] Further, the ray tracing interaction process includes the following operations:
[0012] Before the global ray tracing is executed, establish a coordinate index and a storage medium index for all sub-units on the surface of the microlens array. A conversion relationship is formed between the two indexes, and storage operations and initialization operations are performed on the surface parameters of all sub-units according to the indexes. After completing the surface parameter initialization operation, then execute the global ray tracing;
[0013] During the global ray tracing process, when the light ray propagates to the surface of the microlens array, first locate the light ray position vector on the reference plane, determine the coordinate index of the sub-unit where the light ray is located according to the coordinates on the reference plane, and then obtain the surface parameter according to the coordinate index and use the surface parameter in the process of iteratively finding the intersection point. In this process, if the light ray coordinates exceed the sub-unit area, mark the light ray as an incorrect index and do not participate in the subsequent iteration. After the iteration step of all light rays is less than the specified accuracy and the iteration exits, correct the index of the incorrect index light ray and re-find the intersection point. Loop this process until all light rays find the correct intersection points, and then use the index to obtain the surface parameter again to calculate the intersection point normal vector and the refraction and reflection azimuth vectors of the light ray. Finally, convert the position vector and azimuth vector of the light ray back to the global coordinate system to complete the subsequent surface tracing.
[0014] In the second aspect
[0015] Corresponding to the above method, the present invention also provides a microlens array surface ray tracing system for tolerance analysis. The system is applied to the global ray tracing process of an optical system including a microlens array, and includes: a storage and reading unit for surface parameter information and a ray tracing interaction process unit;
[0016] The storage and reading unit for surface parameter information is used to distinguish each sub-unit of the microlens array by using an index, and realize the storage and reading of the surface parameter information of the microlens array through the index;
[0017] The ray tracing interaction process unit is used to implement the ray tracing interaction process between light rays and the surface of the microlens array by using the index and the surface parameter information of the microlens array.
[0018] Further, the index includes two types of index, namely coordinate index and storage medium index. The coordinate index is an index corresponding to the reference plane coordinate system, and the storage medium index is an index corresponding to the medium storing surface parameter information.
[0019] Further, the ray tracing interaction process includes the following operations:
[0020] Before the global ray tracing is executed, coordinate indexes and storage medium indexes are established for all sub-units on the surface of the microlens array. A conversion relationship is formed between the two indexes, and storage operations and initialization operations are performed on the surface parameters of all sub-units according to the indexes. After the surface parameter initialization operation is completed, the global ray tracing is executed;
[0021] During the global ray tracing process, when the ray propagates to the surface of the microlens array, first position the ray position vector on the reference plane, determine the coordinate index of the sub-unit where the ray is located according to the coordinates on the reference plane, and then obtain the surface parameters according to the coordinate index and use the surface parameters in the process of iterative intersection calculation. In this process, if the ray coordinates exceed the sub-unit area, mark the ray as an incorrect index and do not participate in the subsequent iteration. After the iteration step of all rays is less than the specified precision and the iteration exits, correct the index of the incorrect index ray and re-calculate the intersection point. Loop this process until the correct intersection points of all rays are found, and then use the index to obtain the surface parameters again to calculate the intersection point normal vector and the refraction and reflection azimuth vectors of the ray. Finally, convert the position vector and azimuth vector of the ray back to the global coordinate system to complete the subsequent surface tracing.
[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0023] The method provided by the present invention can realize the ray tracing interaction of a microlens array with actual processing errors such as parameter inconsistency and randomness of height error on the sub-unit surface, complete the optical system simulation of the microlens array with processing errors, thereby effectively evaluate the error magnitude of the processing technology of the microlens array, and then improve the production success rate of the microlens array optical system, reduce the losses caused by the processing technology of the microlens array, and has important engineering significance for the optical system design containing the microlens array. Description of the Drawings
[0024] Figure 1 It is a schematic flow chart of the method for ray tracing on the surface of the microlens array provided by the embodiment of the present invention;
[0025] Figure 2 It is a schematic diagram of the local coordinate system and reference plane of the surface provided by the embodiment of the present invention;
[0026] Figure 3Schematic diagram of the index distribution of the square microlens array provided by the embodiments of the present invention. Detailed implementation manners
[0027] The following describes clearly and completely the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0028] It should be noted that a method and system for ray tracing on the surface of a microlens array for tolerance analysis provided by the present invention can be implemented only when the number of units, the unit shape, and the arrangement mode of the microlens array are known. Before performing global ray tracing, a matrix for storing surface parameters needs to be established according to the number of units of the microlens array. By numbering each sub-unit of the microlens array, each sub-unit has a unique index, and the surface parameters of any sub-unit can be obtained by using the index value and the surface parameter matrix. When performing global ray tracing, when a ray passes through the microlens array to be analyzed, in order to realize the ray tracing simulation of the microlens array with actual processing errors, the ray should be refracted or reflected according to its own propagation direction, starting point coordinates, and the surface parameter information of the microlens array, so as to complete the ray tracing task on the surface of the microlens array.
[0029] Among them, Figure 1 The overall working process of the implementation process of the method of the present invention is provided. It should be noted that this method needs to be used in combination with the global ray tracing process of the optical system. The global ray tracing mainly refers to the complete tracing process required for the optical system to realize system evaluation. The tracing method is based on geometric optics and is carried out in the global coordinate system. The global ray tracing process should be integrated into the tolerance analysis process. Each random experiment in the analysis requires random system parameters. Therefore, for each random experiment, these random system parameters should be determined before performing global ray tracing and evaluation, so as to realize the tolerance analysis of the microlens array system with processing errors.
[0030] The following Figure 1 The working process in is introduced, and then detailed explanations are given in combination with specific embodiments.
[0031] Before starting global ray tracing, the microlens array needs to be placed in the global coordinate system of the optical system. The defocus height expression of the microlens array should be defined in the local coordinate system. Index information for all sub-units also needs to be established based on information such as the shape of the sub-units of the microlens array, the number of units, and the arrangement method. Then, according to the index information, inconsistent surface parameter vectors are generated for each sub-unit, and a one-to-one correspondence is established between the index and the surface parameter vector. The surface parameters refer to the parameters used to form the surface profile of the sub-unit. Taking an even aspheric surface as an example, its surface parameters usually include the radius of curvature, the conic coefficient, and the high-order term coefficients. In addition, to express the random defocus error, a Zernike polynomial surface can be used, so the surface parameters can also include Zernike polynomial coefficients.
[0032] After completing the construction of the sub-unit index and surface parameter information, global ray tracing can be carried out. When the ray propagates to this microlens array surface during the global tracing process, the starting point and azimuth vector of the ray in the global coordinate system need to be converted to the local coordinate system of this surface. The X-Y plane where Z = 0 in the local coordinate system constitutes the reference plane.
[0033] Propagate the ray to the reference plane in the local coordinate system. Determine the index value of the sub-unit according to the intersection coordinates of the ray and the reference plane and the spatial region where each sub-unit of the microlens array is located, so that the surface parameter information of the sub-unit can be obtained according to the index value. Use this information and the iterative method to find the intersection point of the ray and the surface.
[0034] Each iteration needs to record the rays that exceed the sub-unit region, mark them as rays with incorrect landing points, and they will no longer participate in subsequent iterations. Because if the ray deviates from the sub-unit region during the iteration process, it means that the ray will eventually intersect with adjacent sub-units, so the current sub-unit index value and surface parameter information are incorrect and need to be corrected and the iterative method is used again to find the intersection point. Considering the vectorized architecture of the ray tracing algorithm, the rays with incorrect indices can be recorded during the iteration process. After the iteration step size of the remaining correct rays is lower than the specified accuracy, the iteration is exited, and then the indices of these rays with incorrect indices are corrected. The index correction process is to use the intersection coordinates obtained from the last iteration of the ray to determine the matrix index of the sub-unit, and then let the ray start from the reference plane again for a new iteration. Continuously repeat the index correction process until the correct index is found for all rays.
[0035] Next, use the iterated ray coordinates as the intersection coordinates, and obtain the surface parameter information according to the corrected index value. Use the surface parameter information to calculate the normal vector at the intersection point and calculate the refraction and reflection direction vectors of the ray. Finally, transform the intersection coordinates and azimuth vector in the local coordinate system of the ray to the global coordinate system, thereby completing the ray tracing interaction on the surface of the current micro-lens array to be analyzed, and continue the tracing interaction on the subsequent surfaces to complete the global ray tracing.
[0036] The following uses a square micro-lens array as an example for a detailed description.
[0037] Assume that the size of the sub-units of the square micro-lens array is 1×1 mm, the number of sub-units is 5×5, and the basic surface shape of the sub-units is an even aspheric surface.
[0038] Figure 2 The distribution schematic diagram of the local coordinate system on the surface of the micro-lens array and the reference plane is given. The expression of the height deviation of the micro-lens array is established in this local coordinate system, and the reference plane is the X-Y plane where Z = 0. The starting point of the ray is point P, and the coordinates of point P and the azimuth vector of the ray should be transformed from the global coordinate system to the local coordinate system. During the propagation of the ray, it intersects the reference plane at point Q, and then it is necessary to determine the intersection point of the ray and the surface of the micro-lens array according to the index information on the reference plane and the iterative method.
[0039] Figure 3 The local coordinate system on the reference plane and the index marking of each sub-unit are given. Suppose there are n surface parameters for the sub-units. In order to store the surface parameter information of all sub-units, it is necessary to define a three-dimensional tensor of 5×5×n, where the first dimension corresponds to the y coordinate, the second dimension corresponds to the x coordinate, and the third dimension corresponds to the surface parameters. Figure 3 The square brackets represent the two-dimensional matrix index formed by the first two dimensions in the three-dimensional tensor. The first value in the square brackets is the matrix row index, and the second value is the matrix column index; the round brackets are the index values determined according to the coordinates of the centroid of the sub-unit, called the coordinate index. (0,0) exactly corresponds to the matrix index [3,3]. The coordinate index should be an integer and ensure that each sub-unit has a different index. Note that the first index value in the round brackets is the y coordinate index, and the second index value is the x coordinate index.
[0040] According to the above definition method of the index, the corresponding relationship between the coordinate index and the matrix index can be obtained as follows:
[0041]
[0042] where, row represents the row index of the matrix, col represents the column index of the matrix, that is, [row, col], I y and I xRepresent the y and x coordinate indices in the parentheses, i.e., (I y , I x ). Actually, if the number of sub-units is l×m, the expression can be written as:
[0043]
[0044] where both l and m are odd numbers, l is the number in the y direction, and m is the number in the x direction. If the number of sub-units is even, the corresponding relationship needs to be set according to a certain rule, which will not be elaborated here.
[0045] After setting the corresponding relationship between the coordinate index and the matrix index, a three-dimensional tensor for storing surface parameters needs to be generated. During the process of generating surface parameters, in order to realize the random height error simulation of the microlens array, Zernike polynomials are introduced into the height. The expression is as follows:
[0046]
[0047] In the formula, q represents a total of q terms of Zernike polynomials, a i represents the coefficient of the i-th term, Z i (ρ,θ) is the Zernike polynomial in polar coordinate form. In actual use, it should be calculated in the local coordinate system established by the centroid of the sub-unit, and pay attention to the conversion between Cartesian coordinates and polar coordinates.
[0048] After introducing Zernike polynomials, the surface parameter information will consist of elements such as the radius of curvature, conic coefficient, high-order aspheric coefficient, and Zernike polynomial coefficient. These parameters are integrated into a vector, and then stored in the third dimension of the three-dimensional tensor according to the matrix index. In order to simulate the inconsistency of surface parameters during the tolerance analysis process, the surface parameters of each sub-unit should be randomly sampled within a certain range, and random surface parameters need to be generated for each random experiment.
[0049] After completing the storage of the surface parameter information of the microlens array, the global ray tracing can be started. When the traced ray propagates to the surface of the microlens array to be analyzed, the position vector and azimuth vector of the ray are converted from the global coordinate system to the local coordinate system of the microlens array surface. Then, the corresponding matrix index needs to be obtained according to the ray landing point, and further the surface parameters of the corresponding sub-unit are obtained. Now assume that the coordinate position of the ray on the reference plane of the local coordinate system is (x0, y0), then the coordinate index of the sub-unit corresponding to this position follows the following expression:
[0050]
[0051] In the formula, h x and h yDenote the half-width of the rectangular sub-unit in the x and y directions as w x and w y denote the full width or the gap (assuming the gap of the array is the same as the sub-unit width). denote floor function, denote ceiling function. Then, according to the correspondence between the coordinate index and the matrix index, the surface parameters at any ray coordinate position can be obtained. The above index definition method is only applicable to a rectangular microlens array with an odd number of sub-units.
[0052] After obtaining the surface parameters of the sub-unit based on the ray landing point, the Newton iteration method is then used to find the intersection point of the ray and the surface. During the iteration, the x and y coordinates of the ray position vector are in the local coordinate system established with the centroid of the sub-unit, rather than the local coordinate system of the reference plane. For the convenience of subsequent description, let the local coordinate system on the surface of the microlens array be {L}, and the local coordinate system of the sub-unit be {S}. Before starting the iteration, convert the coordinates (x0, y0) of the ray in {L} to {S}, and let the converted coordinates be (x s , y s ). Then, let the coordinates of the centroid of the sub-unit in {L} be (x c , y c ). Then, the above coordinates satisfy the following expressions:
[0053] x s = x0 - x c y s = y0 - y c
[0054] Perform Newton iteration on (x s , y s ) to find the intersection point. If it is found during the iteration that |x s | > h x or |y s | > h y , it means that the coordinates of the ray exceed the range of the square sub-unit. Then, these rays need to be marked as error indices and do not participate in the subsequent iteration. The rays that are not marked as error indices continue to iterate until the iteration step size is less than the specified accuracy and the iteration exits. Then, it is judged whether there are rays with error indices. If so, the error indices are corrected according to the following rules:
[0055] x i = x′ s + x c y i = y′ s + y c
[0056] where x′ s and y' sDenote the coordinates of the error index ray in {S} during the last iteration, x i and y i Denote the virtual coordinates in {L}, which are used to determine the new sub - unit index. After obtaining the new index, these error index rays need to be iteratively intersected again, and this process is repeated until there are no error index rays.
[0057] If all the error index rays are corrected, the intersection coordinates of all rays with the surface of the microlens array in the {L} coordinate system can be obtained. Then, according to the intersection coordinates of each ray, the index and surface parameter information of the sub - unit are determined. The normal vector at the intersection is calculated using the surface parameter information, and then the azimuth vector after refraction and reflection of the ray is obtained. Then, taking the ray intersection coordinates as the position vector, the position vector and azimuth vector of the ray are transformed into the global coordinate system, and then the subsequent surface tracking is carried out to complete all the tracking processes.
[0058] Next, the results of global ray tracing should be used to evaluate the optical system, so as to realize the tolerance simulation of a single random experiment. Then, the surface parameters of the microlens array are randomly reset again, and the next round of random experiment is carried out, and finally the overall tolerance analysis of the system is realized. This method only focuses on the local coordinate system of the surface of the microlens array. In fact, the eccentricity and tilt of the surface of the microlens array can also be operated on the surface in the global coordinate system, so as to realize the optical simulation of the surface of the microlens array with misalignment types such as eccentricity, tilt or rotation along the optical axis.
[0059] In other embodiments, correspondingly to the above - mentioned method, the present invention also provides a microlens array surface ray - tracing system for tolerance analysis, which is applied to the global ray - tracing process of an optical system including a microlens array, and includes: a storage and reading unit for surface parameter information and a ray - tracing interaction process unit;
[0060] The storage and reading unit for surface parameter information is used to distinguish each sub - unit of the microlens array by using an index, and to realize the storage and reading of the surface parameter information of the microlens array through the index;
[0061] The ray - tracing interaction process unit is used to realize the ray - tracing interaction process between the ray and the surface of the microlens array by using the index and the surface parameter information of the microlens array.
[0062] Further, the index includes two index types, namely coordinate index and storage medium index. The coordinate index is an index corresponding to the reference plane coordinate system, and the storage medium index is an index corresponding to the medium storing the surface parameter information.
[0063] Further, the ray - tracing interaction process includes the following operations:
[0064] Before the global ray tracing is performed, coordinate indexes and storage medium indexes are established for all sub-units on the surface of the microlens array. A conversion relationship is formed between the two indexes. According to the indexes, storage operations and initialization operations are performed on the surface parameters of all sub-units. After the surface parameter initialization operation is completed, the global ray tracing is executed;
[0065] During the global ray tracing process, when the ray propagates to the surface of the microlens array, first position the ray position vector on the reference plane. Determine the sub-unit coordinate index where the ray is located according to the coordinates on the reference plane. Then, obtain the surface parameters according to the coordinate index and use the surface parameters in the process of iteratively finding the intersection point. In this process, if the ray coordinates exceed the sub-unit area, mark the ray as an incorrect index and do not participate in the subsequent iteration. After the iteration step of all rays is less than the specified accuracy and the iteration exits, correct the index of the ray with the incorrect index and find the intersection point again. Loop this process until the correct intersection points of all rays are found. Then, use the index to obtain the surface parameters again to calculate the intersection point normal vector and the refraction and reflection azimuth vectors of the ray. Finally, convert the position vector and azimuth vector of the ray back to the global coordinate system to complete the subsequent surface tracing.
[0066] Finally, it should be noted that the above embodiments are only used for exemplifying and illustrating the present invention, and are not intended to limit the present invention to the scope of the described embodiments. In addition, those skilled in the art can understand that the present invention is not limited to the above embodiments, and more variations and modifications can be made according to the teachings of the present invention, and these variations and modifications all fall within the scope claimed by the present invention.
Claims
1. A method for ray tracing on the surface of a microlens array for tolerance analysis, characterized in that The method is applied to the global ray tracing process of an optical system with a microlens array, and includes: Distinguishing each subunit of the microlens array by using indexing, and storing and reading the surface parameter information of the microlens array through indexing; and Implementing the ray tracing interaction process between the ray and the surface of the microlens array by using indexing and the surface parameter information of the microlens array, and integrating the ray tracing interaction process into the global ray tracing process.
2. A method for ray tracing on the surface of a microlens array for tolerance analysis according to claim 1, characterized in that, The indexing includes two types of indexing, namely coordinate indexing and storage medium indexing. Coordinate indexing is an index that has a corresponding relationship with the reference plane coordinate system, and storage medium indexing is an index that has a corresponding relationship with the medium storing the surface parameter information.
3. A method for ray tracing on the surface of a microlens array for tolerance analysis according to claim 1, wherein The ray tracing interaction process includes the following operations: Before the global ray tracing is executed, establish coordinate indexing and storage medium indexing for all subunits on the surface of the microlens array, form a conversion relationship between the two indexes, perform storage operations and initialization operations on the surface parameters of all subunits according to the indexes, and then execute the global ray tracing after completing the surface parameter initialization operation; During the global ray tracing process, when the ray propagates to the surface of the microlens array, first locate the ray position vector on the reference plane, determine the coordinate index of the subunit where the ray is located according to the coordinates on the reference plane, and then obtain the surface parameter according to the coordinate index and use the surface parameter in the process of iteratively finding the intersection point. In this process, if the ray coordinates exceed the subunit area, mark the ray as an incorrect index and do not participate in the subsequent iteration. After the iteration step sizes of all rays are less than the specified accuracy and the iteration exits, correct the index of the incorrect index ray and find the intersection point again. Loop this process until the correct intersection points of all rays are found, and then use the index to obtain the surface parameter again to calculate the intersection point normal vector and the refraction and reflection azimuth vectors of the ray. Finally, convert the position vector and azimuth vector of the ray back to the global coordinate system to complete the subsequent surface tracing.
4. A surface ray tracing system for a microlens array used for tolerance analysis, characterized in that, The system is applied to the global ray tracing process of an optical system with a microlens array, and includes: a storage and reading unit for surface parameter information and a ray tracing interaction process unit; The storage and reading unit for surface parameter information is used to distinguish each subunit of the microlens array by using indexing, and store and read the surface parameter information of the microlens array through indexing; The ray tracing interaction process unit is used to implement the ray tracing interaction process between the ray and the surface of the microlens array by using indexing and the surface parameter information of the microlens array.
5. A system for ray tracing on the surface of a microlens array for tolerance analysis according to claim 4, characterized in that, The indexing includes two types of indexing, namely coordinate indexing and storage medium indexing. Coordinate indexing is an index that has a corresponding relationship with the reference plane coordinate system, and storage medium indexing is an index that has a corresponding relationship with the medium storing the surface parameter information.
6. A surface ray tracing system for a microlens array for tolerance analysis according to claim 4, wherein The ray tracing interaction process includes the following operations: Before the global ray tracing is executed, establish coordinate indexing and storage medium indexing for all subunits on the surface of the microlens array, form a conversion relationship between the two indexes, perform storage operations and initialization operations on the surface parameters of all subunits according to the indexes, and then execute the global ray tracing after completing the surface parameter initialization operation; During the global ray tracing process, when the ray propagates to the surface of the microlens array, first locate the ray position vector on the reference plane, determine the coordinate index of the sub-unit where the ray is located according to the coordinates on the reference plane, and then obtain the surface parameters according to the coordinate index and use the surface parameters in the process of iterative intersection calculation. In this process, if the ray coordinates exceed the sub-unit area, mark the ray as an incorrect index and do not participate in subsequent iterations. After the iteration step of all rays is less than the specified accuracy and the iteration exits, correct the index of the incorrect index rays and recalculate the intersection points. Loop this process until the correct intersection points of all rays are found. Then, use the index again to obtain the surface parameters to calculate the intersection normal vector and the refraction and reflection azimuth vectors of the rays. Finally, convert the position vector and azimuth vector of the rays back to the global coordinate system to complete the tracing of the subsequent surface.