CN116243479A - Compact panoramic annular belt head unit design method and system based on ray tracing - Google Patents
Compact panoramic annular belt head unit design method and system based on ray tracingDownload PDFInfo
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Abstract
Translated fromChinese
Description
Translated fromChinese技术领域Technical Field
本发明属于光学系统技术领域，具体涉及基于光线跟踪的紧凑型全景环带头部单元设计方法。The invention belongs to the technical field of optical systems, and in particular relates to a design method for a compact panoramic ring-band head unit based on ray tracing.
背景技术Background Art
全景环带是一种折反射全景系统，主要由头部的全景环形透镜以及中继镜组构成。其原理是通过平面圆柱投影法，将三维空间的像成在一个环形区域内，使得360度成像成为了现实。作为全景环带的头部单元，全景环形透镜是实现全景成像的关键元件。The panoramic ring belt is a catadioptric panoramic system, mainly composed of a panoramic ring lens on the head and a relay lens group. Its principle is to use the plane cylindrical projection method to form a three-dimensional image in an annular area, making 360-degree imaging a reality. As the head unit of the panoramic ring belt, the panoramic ring lens is the key component to achieve panoramic imaging.
然而，全景环形透镜为了实现360度成像，利用了折射和反射原理，使得入射光线在透镜内部与光轴产生大角度，从而使全景环带的头部口径要远大于中继镜组的口径，进而会造成全景环带整体结构上不紧凑的问题。However, in order to achieve 360-degree imaging, the panoramic annular lens utilizes the principles of refraction and reflection, which causes the incident light to form a large angle with the optical axis inside the lens, thereby making the head aperture of the panoramic annular belt much larger than the aperture of the relay lens group, which in turn causes the overall structure of the panoramic annular belt to be not compact.
发明内容Summary of the invention
本方案采用多参数的梯度下降算法，能够确定使全景环带头部单元紧凑度值最低的紧凑度指标组合，并结合光线追踪模型进行指标验证，从而能够解决上述技术问题。This solution adopts a multi-parameter gradient descent algorithm to determine the compactness index combination that minimizes the compactness value of the panoramic ring head unit, and combines it with a ray tracing model to verify the index, thereby solving the above technical problems.
本发明具体的技术方案如下：The specific technical solutions of the present invention are as follows:
第一方面，本发明提供了基于光线跟踪的紧凑型全景环带头部单元设计方法，包括以下步骤：In a first aspect, the present invention provides a method for designing a compact panoramic ring band head unit based on ray tracing, comprising the following steps:
S1：根据已有的全景环带系统参数，获取全景环带系统的紧凑度指标；S1: Obtaining a compactness index of the panoramic ring belt system according to the existing panoramic ring belt system parameters;
S2：将已获取的多组紧凑度指标作为特征值，构建代价函数并利用多元梯度下降算法循环至收敛，采集多组不同梯度的特征值；S2: Using the obtained multiple sets of compactness indicators as eigenvalues, constructing a cost function and using the multivariate gradient descent algorithm to loop until convergence, collecting multiple sets of eigenvalues with different gradients;
S3：根据全景环带头部单元的结构以及入射光线的分布，构建光线跟踪模型；S3: Construct a ray tracing model based on the structure of the panoramic ring head unit and the distribution of incident light;
S4：将S2中采集到的多组特征值输入光线跟踪模型，选取能够满足入射光线的分布特征值组，并计算选取的每一组特征值所对应的紧凑度，将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。S4: Input the multiple groups of eigenvalues collected in S2 into the ray tracing model, select the distribution eigenvalue group that can satisfy the incident light, and calculate the compactness corresponding to each selected group of eigenvalues, and take the eigenvalue group with the lowest compactness as the optimal panoramic ring head unit design scheme.
在一些实施例中，所述步骤S1包括：In some embodiments, step S1 includes:
S11：根据全景环带头部单元结构，定义全景环带系统的紧凑度计算公式：S11: Based on the panoramic ring belt head unit structure, the compactness calculation formula of the panoramic ring belt system is defined as:
其中，K表示全景环带系统的紧凑度，D表示全景环带头部单元的最大口径，L表示像面的对角线长度；Among them, K represents the compactness of the panoramic ring belt system, D represents the maximum aperture of the panoramic ring belt head unit, and L represents the diagonal length of the image plane;
S12：根据紧凑度计算公式，获取全景环带系统的紧凑度指标，包括：第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度。S12: According to a compactness calculation formula, a compactness index of the panoramic ring belt system is obtained, including: a first transmission surface curvature radius, a first reflection surface curvature radius, and a lens thickness.
在一些实施例中，所述S2包括：In some embodiments, the S2 includes:
S21：将多组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值作为特征值，构建目标函数：S21: Taking multiple sets of first transmission surface curvature radii, first reflection surface curvature radii and lens thickness values as characteristic values, construct an objective function:
hθ(x)＝θ0x0+θ1x1+θ2x2+θ3x3；hθ (x)＝θ0 x0 +θ1 x1 +θ2 x2 +θ3 x3 ;
其中，hθ(x)表示目标函数，x0＝1，x1、x2、x3分别表示每一组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值的向量表示，θ0-θ3表示回归系数；Wherein, hθ (x) represents the objective function, x0 =1, x1 , x2 , x3 represent the vector representation of each set of the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness value, and θ0 -θ3 represent the regression coefficients;
S22：结合每一组特征值所对应的紧凑度，构建代价函数：S22: Combine the compactness corresponding to each set of eigenvalues to construct a cost function:
其中，Jθ0，θ1，θ1，θ3)表示代价函数，m表示样本个数，xi表示第i组样本的所有特征值，yi表示第i组样本所对应的紧凑度；Wherein, Jθ0 ,θ1 ,θ1 ,θ3 ) represents the cost function, m represents the number of samples,xi represents all eigenvalues of the i-th group of samples, andyi represents the compactness corresponding to the i-th group of samples;
S23：采用多元梯度下降算法进行收敛：S23: Use multivariate gradient descent algorithm to converge:
其中，
在一些实施例中，所述S3包括：In some embodiments, the S3 includes:
S31：对全景环带头部单元的结构进行数学建模，确定光轴、第一透射表面、第二透射表面、第一反射表面以及第二反射表面的位置；S31: mathematically modeling the structure of the panoramic ring belt head unit to determine the positions of the optical axis, the first transmission surface, the second transmission surface, the first reflection surface, and the second reflection surface;
S32：设置光源，使光源从第一透射表面发生折射，通过透镜传播到第一反射表面，经第一反射表面反射至第二反射表面，然后通过第二反射表面反射至第二投射表面，并记录光线传播路径；S32: Setting a light source so that the light source is refracted from the first transmission surface, propagated to the first reflection surface through the lens, reflected to the second reflection surface through the first reflection surface, and then reflected to the second projection surface through the second reflection surface, and recording the light propagation path;
S33：根据光线传播路径计算反射和折射，包括：法线、反射方向以及折射方向。S33: Calculate reflection and refraction according to the light propagation path, including: normal, reflection direction, and refraction direction.
在一些实施例中，所述S5包括：In some embodiments, the S5 includes:
S51：将S2中采集到的多组不同梯度的特征值输入光线跟踪模型，并验证每一组输入的特征值是否符合光线传播路径，若不符合，则剔除不符合的特征值，若符合，则跳转步骤S52；S51: Input the multiple groups of feature values with different gradients collected in S2 into the ray tracing model, and verify whether each group of input feature values conforms to the light propagation path. If not, remove the feature values that do not conform. If conform, jump to step S52;
S52：对于符合光线跟踪模型中光线传播路径的特征值组，计算每一组特征值所对应的紧凑度，并将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。S52: For the eigenvalue groups that conform to the light propagation path in the ray tracing model, the compactness corresponding to each group of eigenvalues is calculated, and the eigenvalue group with the lowest compactness is used as the optimal panoramic ring band head unit design solution.
第二方面，本发明提供了基于光线跟踪的紧凑型全景环带头部单元设计系统，包括：In a second aspect, the present invention provides a compact panoramic ring head unit design system based on ray tracing, comprising:
参数获取模块，用于根据已有的全景环带系统参数，获取全景环带系统的紧凑度指标；A parameter acquisition module, used to obtain a compactness index of the panoramic ring belt system according to existing panoramic ring belt system parameters;
循环收敛模块，用于将已获取的多组紧凑度指标作为特征值，构建代价函数并利用多元梯度下降算法循环至收敛，采集多组不同梯度的特征值；A loop convergence module is used to use the obtained multiple sets of compactness indicators as eigenvalues, construct a cost function and use a multivariate gradient descent algorithm to loop until convergence, and collect multiple sets of eigenvalues with different gradients;
光线跟踪模型构建模块，用于根据全景环带头部单元的结构以及入射光线的分布，构建光线跟踪模型；A ray tracing model building module is used to build a ray tracing model according to the structure of the panoramic ring belt head unit and the distribution of incident light;
特征值验证模块，用于将循环收敛模块中采集到的多组特征值输入光线跟踪模型，选取能够满足入射光线的分布特征值组，并计算选取的每一组特征值所对应的紧凑度，将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。The eigenvalue verification module is used to input multiple groups of eigenvalues collected in the loop convergence module into the ray tracing model, select the distribution eigenvalue group that can satisfy the incident light, and calculate the compactness corresponding to each selected group of eigenvalues, and take the eigenvalue group with the lowest compactness as the best panoramic ring head unit design scheme.
在一些实施例中，所述紧凑度指标获取模块包括：In some embodiments, the compactness index acquisition module includes:
紧凑度定义子模块，用于根据全景环带头部单元结构，定义全景环带系统的紧凑度计算公式：The compactness definition submodule is used to define the compactness calculation formula of the panoramic ring belt system according to the panoramic ring belt head unit structure:
其中，K表示全景环带系统的紧凑度，D表示全景环带头部单元的最大口径，L表示像面的对角线长度；Among them, K represents the compactness of the panoramic ring belt system, D represents the maximum aperture of the panoramic ring belt head unit, and L represents the diagonal length of the image plane;
紧凑度指标获取子模块，用于根据紧凑度计算公式，获取全景环带系统的紧凑度指标，包括：第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度。The compactness index acquisition submodule is used to obtain the compactness index of the panoramic ring belt system according to the compactness calculation formula, including: the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness.
在一些实施例中，所述循环收敛模块包括：In some embodiments, the loop convergence module includes:
目标函数构建子模块，用于将多组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值作为特征值，构建目标函数：The objective function construction submodule is used to construct the objective function by taking multiple sets of first transmission surface curvature radius, first reflection surface curvature radius and lens thickness values as characteristic values:
hθ(x)＝θ0x0+θ1x1+θ2x2+θ3x3；hθ (x)＝θ0 x0 +θ1 x1 +θ2 x2 +θ3 x3 ;
其中，hθ(x)表示目标函数，x0＝1，x1、x1、x3分别表示每一组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值的向量表示，θ0-θ3表示回归系数；Wherein, hθ (x) represents the objective function, x0 =1, x1 , x1 , x3 represent the vector representation of each set of the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness value, and θ0 -θ3 represent the regression coefficients;
代价函数构建子模块，用于结合每一组特征值所对应的紧凑度，构建代价函数：The cost function construction submodule is used to construct the cost function by combining the compactness corresponding to each set of eigenvalues:
其中，Jθ0，θ1，θ2，θ3)表示代价函数，m表示样本个数，xi表示第i组样本的所有特征值，yi表示第i组样本所对应的紧凑度；Wherein, Jθ0 ,θ1 ,θ2 ,θ3 ) represents the cost function, m represents the number of samples,xi represents all eigenvalues of the i-th group of samples, andyi represents the compactness corresponding to the i-th group of samples;
多元梯度下降子模块，用于采用多元梯度下降算法进行收敛：Multivariate gradient descent submodule, used to converge using the multivariate gradient descent algorithm:
其中，
在一些实施例中，所述光线跟踪模型构建模块包括：In some embodiments, the ray tracing model building module includes:
头部单元模型构建子模块，用于对全景环带头部单元的结构进行数学建模，确定光轴、第一透射表面、第二透射表面、第一反射表面以及第二反射表面的位置；A head unit model building submodule is used to mathematically model the structure of the panoramic ring band head unit and determine the positions of the optical axis, the first transmission surface, the second transmission surface, the first reflection surface and the second reflection surface;
光线路径设置子模块，用于设置光源，使光源从第一透射表面发生折射，通过透镜传播到第一反射表面，经第一反射表面反射至第二反射表面，然后通过第二反射表面反射至第二投射表面，并记录光线传播路径；A light path setting submodule is used to set the light source so that the light source is refracted from the first transmission surface, propagated to the first reflection surface through the lens, reflected from the first reflection surface to the second reflection surface, and then reflected from the second reflection surface to the second projection surface, and record the light propagation path;
反射折射计算子模块，用于根据光线传播路径计算反射和折射，包括：法线、反射方向以及折射方向。The reflection and refraction calculation submodule is used to calculate reflection and refraction according to the light propagation path, including: normal, reflection direction and refraction direction.
在一些实施例中，所述方案确定模块包括：In some embodiments, the solution determination module includes:
特征值验证子模块，用于将循环收敛模块中采集到的多组不同梯度的特征值输入光线跟踪模型，并验证每一组输入的特征值是否符合光线传播路径，若不符合，则剔除不符合的特征值，若符合，则跳转步骤S42；The eigenvalue verification submodule is used to input multiple groups of eigenvalues with different gradients collected in the loop convergence module into the ray tracing model, and verify whether each group of input eigenvalues conforms to the light propagation path. If not, the eigenvalues that do not conform are eliminated. If they conform, the process jumps to step S42.
紧凑度比较子模块，用于对符合光线跟踪模型中光线传播路径的特征值组，计算每一组特征值所对应的紧凑度，并将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。The compactness comparison submodule is used to calculate the compactness corresponding to each set of eigenvalues that conform to the light propagation path in the ray tracing model, and take the eigenvalue group with the lowest compactness as the best panoramic ring head unit design solution.
本申请的有益效果是：The beneficial effects of this application are:
本申请提供的基于光线跟踪的紧凑型全景环带头部单元设计方法及方法，能够根据多元梯度下降算法，获取特征值组，使全景环带头部单元达到需要的紧凑度，同时，还能够利用光线追踪模型，对特征值组进行验证，从而保证了该特征值组参数能够达到全景环带光线传播的要求，为紧凑型全景环带头部单元的设计提供了新的思路。The compact panoramic ring-band head unit design method and method based on ray tracing provided in the present application can obtain an eigenvalue group according to a multivariate gradient descent algorithm, so that the panoramic ring-band head unit reaches the required compactness. At the same time, the ray tracing model can be used to verify the eigenvalue group, thereby ensuring that the eigenvalue group parameters can meet the requirements of panoramic ring-band light propagation, providing a new idea for the design of a compact panoramic ring-band head unit.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本申请基于光线跟踪的紧凑型全景环带头部单元设计方法流程图；FIG1 is a flow chart of a design method for a compact panoramic ring band head unit based on ray tracing of the present application;
图2为本申请步骤S1的子流程图；FIG2 is a sub-flow chart of step S1 of the present application;
图3为本申请步骤S2的子流程图；FIG3 is a sub-flow chart of step S2 of the present application;
图4为本申请步骤S3的子流程图；FIG4 is a sub-flow chart of step S3 of the present application;
图5为本申请步骤S4的子流程图。FIG5 is a sub-flow chart of step S4 of the present application.
具体实施方式DETAILED DESCRIPTION
以下结合附图对本发明的原理和特征进行描述，所举实例只用于解释本发明，并非用于限定本发明的范围。The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.
为了能够更清楚地理解本申请的上述目的、特征和优点，下面结合附图和实施例对本公开作进一步的详细说明。可以理解的是，所描述的实施例是本公开的一部分实施例，而不是全部的实施例。此处所描述的具体实施例仅仅用于解释本公开，而非对本申请的限定。基于所描述的本申请的实施例，本领域普通技术人员所获得的所有其他实施例，都属于本申请保护的范围。In order to more clearly understand the above-mentioned purpose, features and advantages of the present application, the present disclosure is further described in detail below in conjunction with the accompanying drawings and examples. It is to be understood that the described embodiments are part of the embodiments of the present disclosure, rather than all of the embodiments. The specific embodiments described herein are merely used to explain the present disclosure, rather than to limit the present application. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.
需要说明的是，在本文中，诸如“第一”和“第二”等之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来，而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。It should be noted that, in this document, relational terms such as “first” and “second” are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations.
图1为本申请基于光线跟踪的紧凑型全景环带头部单元设计方法流程图。FIG1 is a flow chart of a method for designing a compact panoramic ring band head unit based on ray tracing of the present application.
基于光线跟踪的紧凑型全景环带头部单元设计方法，结合图1，包括以下步骤：The design method of the compact panoramic ring belt head unit based on ray tracing, combined with Figure 1, includes the following steps:
S1：根据已有的全景环带系统参数，获取全景环带系统的紧凑度指标；S1: Obtaining a compactness index of the panoramic ring belt system according to the existing panoramic ring belt system parameters;
在一些实施例中，结合图2即本申请步骤S1的子流程图，所述步骤S1包括：In some embodiments, in conjunction with FIG. 2 , which is a sub-flow chart of step S1 of the present application, step S1 includes:
S11：根据全景环带头部单元结构，定义全景环带系统的紧凑度计算公式：S11: Based on the panoramic ring belt head unit structure, the compactness calculation formula of the panoramic ring belt system is defined as:
其中，K表示全景环带系统的紧凑度，D表示全景环带头部单元的最大口径，L表示像面的对角线长度；Among them, K represents the compactness of the panoramic ring belt system, D represents the maximum aperture of the panoramic ring belt head unit, and L represents the diagonal length of the image plane;
S12：根据紧凑度计算公式，获取全景环带系统的紧凑度指标，包括：第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度。S12: According to a compactness calculation formula, a compactness index of the panoramic ring belt system is obtained, including: a first transmission surface curvature radius, a first reflection surface curvature radius, and a lens thickness.
具体的，影响全景环带系统紧凑性的主要部位在于全景环带系统的头部单元，因此，为了设计紧凑型的全景环带系统，首先需要对全景环带系统的头部单元进行分析，从而获取全景环带系统的紧凑度指标。对此，定义全景环带系统的紧凑度计算公式为：Specifically, the main part that affects the compactness of the panoramic belt system is the head unit of the panoramic belt system. Therefore, in order to design a compact panoramic belt system, it is necessary to first analyze the head unit of the panoramic belt system to obtain the compactness index of the panoramic belt system. In this regard, the calculation formula for the compactness of the panoramic belt system is defined as:
其中，K表示全景环带系统的紧凑度，D表示全景环带头部单元的最大口径，L表示像面的对角线长度，而根据全景环带头部单元即全景环形透镜的结构而言，影响全景环带头部单元最大口径的主要参数即为：全景环形透镜的第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度，因此，将这三种参数作为全景环带系统的紧凑度指标，该紧凑度指标越大，则表示该全景环形系统整体结构越不紧凑，反之，该紧凑度指标越小，则表示该全景环形系统整体结构越紧凑，这也是本申请想要达到的目的。Among them, K represents the compactness of the panoramic ring belt system, D represents the maximum aperture of the panoramic ring belt head unit, L represents the diagonal length of the image plane, and according to the structure of the panoramic ring belt head unit, that is, the panoramic annular lens, the main parameters affecting the maximum aperture of the panoramic ring belt head unit are: the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness of the panoramic annular lens. Therefore, these three parameters are used as compactness indicators of the panoramic ring belt system. The larger the compactness index is, the less compact the overall structure of the panoramic annular system is. Conversely, the smaller the compactness index is, the more compact the overall structure of the panoramic annular system is. This is also the purpose that this application wants to achieve.
SS2：将已获取的多组紧凑度指标作为特征值，构建代价函数并利用多元梯度下降算法循环至收敛，采集多组不同梯度的特征值；SS2: Use the obtained multiple sets of compactness indicators as eigenvalues, construct the cost function and use the multivariate gradient descent algorithm to loop until convergence, and collect multiple sets of eigenvalues with different gradients;
在一些实施例中，结合图3即本申请步骤S2的子流程图，所述S2包括：In some embodiments, in conjunction with FIG. 3 , which is a sub-flow chart of step S2 of the present application, S2 includes:
S21：将多组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值作为特征值，构建目标函数：S21: Taking multiple sets of first transmission surface curvature radii, first reflection surface curvature radii and lens thickness values as characteristic values, construct an objective function:
hθ(x)＝θ0x0+θ1x1+θ2x2+θ3x3；hθ (x)＝θ0 x0 +θ1 x1 +θ2 x2 +θ3 x3 ;
其中，hθ(x)表示目标函数，x0＝1，x1、x2、x3分别表示每一组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值的向量表示，θ0-θ3表示回归系数；Wherein, hθ (x) represents the objective function, x0 =1, x1 , x2 , x3 represent the vector representation of each set of the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness value, and θ0 -θ3 represent the regression coefficients;
S22：结合每一组特征值所对应的紧凑度，构建代价函数：S22: Combine the compactness corresponding to each set of eigenvalues to construct a cost function:
其中，Jθ0，θ1，θ2，θ3)表示代价函数，m表示样本个数，xi表示第i组样本的所有特征值，yi表示第i组样本所对应的紧凑度；Wherein, Jθ0 ,θ1 ,θ2 ,θ3 ) represents the cost function, m represents the number of samples,xi represents all eigenvalues of the i-th group of samples, andyi represents the compactness corresponding to the i-th group of samples;
S23：采用多元梯度下降算法进行收敛：S23: Use multivariate gradient descent algorithm to converge:
其中，
具体的，对于步骤S11-S12中获取到的全景环带系统的紧凑度指标，由于第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度均与全景环带头部单元的最大口径呈现了相关性，如第一透射表面曲率半径以及透镜厚度与全景环带头部单元的最大口径呈现正相关，第一反射表面曲率半径与第一反射表面曲率半径呈现负相关，因此，可以将这三种参数作为特征值，并采用多元梯度下降算法进行循环收敛，从而采集不同梯度的特征值组。多元梯度下降算法的主要过程为：首先需要根据特征值组确定目标函数：Specifically, for the compactness index of the panoramic ring belt system obtained in steps S11-S12, since the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness are all correlated with the maximum aperture of the panoramic ring belt head unit, such as the first transmission surface curvature radius and the lens thickness are positively correlated with the maximum aperture of the panoramic ring belt head unit, and the first reflection surface curvature radius is negatively correlated with the first reflection surface curvature radius, therefore, these three parameters can be used as eigenvalues, and the multivariate gradient descent algorithm is used for cyclic convergence, so as to collect eigenvalue groups with different gradients. The main process of the multivariate gradient descent algorithm is: first, the objective function needs to be determined according to the eigenvalue group:
hθ(x)＝θ0x0+θ1x1+θ2x2+θ3x3；hθ (x)＝θ0 x0 +θ1 x1 +θ2 x2 +θ3 x3 ;
其中，hθ(x)表示目标函数，x0＝1，x1、x2、x3分别表示每一组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值的向量表示，θ0-θ3表示回归系数；Wherein, hθ (x) represents the objective function, x0 =1, x1 , x2 , x3 represent the vector representation of each set of the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness value, and θ0 -θ3 represent the regression coefficients;
进而结合每一组特征值所对应的紧凑度，构建代价函数：Then, combined with the compactness corresponding to each set of eigenvalues, the cost function is constructed:
其中，Jθ0，θ1，θ2，θ3)表示代价函数，m表示样本个数，xi表示第i组样本的所有特征值，yi表示第i组样本所对应的紧凑度；Wherein, Jθ0 ,θ1 ,θ2 ,θ3 ) represents the cost function, m represents the number of samples,xi represents all eigenvalues of the i-th group of samples, andyi represents the compactness corresponding to the i-th group of samples;
进而采用多元梯度下降算法进行收敛：Then the multivariate gradient descent algorithm is used for convergence:
其中，
S3：根据全景环带头部单元的结构以及入射光线的分布，构建光线跟踪模型S3: Construct a ray tracing model based on the structure of the panoramic ring head unit and the distribution of incident light
在一些实施例中，结合图4即本申请步骤S3的子流程图，所述S3包括：In some embodiments, in conjunction with FIG. 4 , which is a sub-flow chart of step S3 of the present application, S3 includes:
S31：对全景环带头部单元的结构进行数学建模，确定光轴、第一透射表面、第二透射表面、第一反射表面以及第二反射表面的位置；S31: mathematically modeling the structure of the panoramic ring belt head unit to determine the positions of the optical axis, the first transmission surface, the second transmission surface, the first reflection surface, and the second reflection surface;
S32：设置光源，使光源从第一透射表面发生折射，通过透镜传播到第一反射表面，经第一反射表面反射至第二反射表面，然后通过第二反射表面反射至第二投射表面，并记录光线传播路径；S32: Setting a light source so that the light source is refracted from the first transmission surface, propagated to the first reflection surface through the lens, reflected to the second reflection surface through the first reflection surface, and then reflected to the second projection surface through the second reflection surface, and recording the light propagation path;
S33：根据光线传播路径计算反射和折射，包括：法线、反射方向以及折射方向。S33: Calculate reflection and refraction according to the light propagation path, including: normal, reflection direction, and refraction direction.
具体的，本方案在步骤S2-S23后虽然能够确定一组特征值，使得全景环带的紧凑度指标达到最低，但是在本方案中仍旧存在一个问题，那就是对于一个θ值，即使能够使代价函数最小化，即其对应梯度的特征值组能够使全景环带的紧凑度指标达到最低，也不一定能够满足全景环带的光学性能要求，那么这组特征值数据也就不能作为紧凑型全景环带头部单元的设计方案。因此，我们需要在步骤S2-S23中获取多组不同梯度的特征值组，并对多组特征值组进行光学验证，而最有效的验证方法是建立一个光线追踪模型。对于全景环带头部单元，一般是采用全景环形透镜，其包括第一透射表面、第二透射表面、第一反射表面以及第二反射表面，因此，根据全景环形透镜的结构，确定了光轴、第一透射表面、第二透射表面、第一反射表面以及第二反射表面的位置之后，可以设置一个光源，并根据光学原理计算出在透射表面的折射角度以及在反射表面的反射角度，从而能够确定光线的传播路径以及传播范围。Specifically, although this scheme can determine a set of eigenvalues after steps S2-S23 so that the compactness index of the panoramic annular belt reaches the minimum, there is still a problem in this scheme, that is, for a θ value, even if the cost function can be minimized, that is, the eigenvalue group of its corresponding gradient can make the compactness index of the panoramic annular belt reach the minimum, it may not be able to meet the optical performance requirements of the panoramic annular belt, so this set of eigenvalue data cannot be used as a design scheme for a compact panoramic annular belt head unit. Therefore, we need to obtain multiple sets of eigenvalue groups with different gradients in steps S2-S23, and perform optical verification on the multiple sets of eigenvalue groups, and the most effective verification method is to establish a ray tracing model. For the panoramic annular belt head unit, a panoramic annular lens is generally used, which includes a first transmission surface, a second transmission surface, a first reflection surface and a second reflection surface. Therefore, according to the structure of the panoramic annular lens, after determining the positions of the optical axis, the first transmission surface, the second transmission surface, the first reflection surface and the second reflection surface, a light source can be set, and the refraction angle on the transmission surface and the reflection angle on the reflection surface are calculated according to the optical principle, so that the propagation path and propagation range of the light can be determined.
S4：将S2中采集到的多组特征值输入光线跟踪模型，选取能够满足入射光线的分布特征值组，并计算选取的每一组特征值所对应的紧凑度，将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。S4: Input the multiple groups of eigenvalues collected in S2 into the ray tracing model, select the distribution eigenvalue group that can satisfy the incident light, and calculate the compactness corresponding to each selected group of eigenvalues, and take the eigenvalue group with the lowest compactness as the optimal panoramic ring head unit design scheme.
在一些实施例中，结合图5及本方案S4的子流程图，所述S4包括：In some embodiments, in combination with FIG. 5 and the sub-flow chart of S4 of this solution, S4 includes:
S41：将S2中采集到的多组不同梯度的特征值输入光线跟踪模型，并验证每一组输入的特征值是否符合光线传播路径，若不符合，则剔除不符合的特征值，若符合，则跳转步骤S42；S41: Input the multiple groups of feature values with different gradients collected in S2 into the ray tracing model, and verify whether each group of input feature values conforms to the light propagation path. If not, remove the feature values that do not conform. If conform, jump to step S42;
S42：对于符合光线跟踪模型中光线传播路径的特征值组，计算每一组特征值所对应的紧凑度，并将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。S42: For the eigenvalue groups that conform to the light propagation path in the ray tracing model, the compactness corresponding to each group of eigenvalues is calculated, and the eigenvalue group with the lowest compactness is used as the optimal panoramic ring band head unit design solution.
具体的，当获取了多组不同梯度的特征值数据，以及建立好光线追踪模型之后，可以将多组不同梯度的特征值数据输入到光线追踪模型，从而验证在这些不同梯度的的特征值所形成的全景环带头部单元的结构下，光线的传播路径是否符合要求，对于光线传播路径不符合要求的特征值组，需要将其剔除掉。对于剩下的符合光线传播路径的特征值组，还需要进一步验证，由于本方案的目的在于设计出紧凑型的全景环带头部单元，所以只需要对符合光线传播路径的特征值组所对应的紧凑度进行比较，并选取其中所对应的紧凑度值最低的特征值组，那么这个特征值组就可以作为全景环带头部单元的主要设计参数，Specifically, after obtaining multiple sets of eigenvalue data with different gradients and establishing a ray tracing model, the multiple sets of eigenvalue data with different gradients can be input into the ray tracing model to verify whether the light propagation path meets the requirements under the structure of the panoramic ring-band head unit formed by these eigenvalues with different gradients. The eigenvalue groups whose light propagation paths do not meet the requirements need to be eliminated. The remaining eigenvalue groups that meet the light propagation paths still need further verification. Since the purpose of this solution is to design a compact panoramic ring-band head unit, it is only necessary to compare the compactness corresponding to the eigenvalue groups that meet the light propagation paths and select the eigenvalue group with the lowest corresponding compactness value. This eigenvalue group can be used as the main design parameter of the panoramic ring-band head unit.
本发明第二方面还提供了基于光线跟踪的紧凑型全景环带头部单元设计系统，该系统包括：参数获取模块，用于根据已有的全景环带系统参数，获取全景环带系统的紧凑度指标；The second aspect of the present invention also provides a compact panoramic ring belt head unit design system based on ray tracing, the system comprising: a parameter acquisition module, for acquiring a compactness index of the panoramic ring belt system according to existing panoramic ring belt system parameters;
循环收敛模块，用于将已获取的多组紧凑度指标作为特征值，构建代价函数并利用多元梯度下降算法循环至收敛，采集多组不同梯度的特征值；A loop convergence module is used to use the obtained multiple sets of compactness indicators as eigenvalues, construct a cost function and use a multivariate gradient descent algorithm to loop until convergence, and collect multiple sets of eigenvalues with different gradients;
光线跟踪模型构建模块，用于根据全景环带头部单元的结构以及入射光线的分布，构建光线跟踪模型；A ray tracing model building module is used to build a ray tracing model according to the structure of the panoramic ring belt head unit and the distribution of incident light;
特征值验证模块，用于将循环收敛模块中采集到的多组特征值输入光线跟踪模型，选取能够满足入射光线的分布特征值组，并计算选取的每一组特征值所对应的紧凑度，将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。The eigenvalue verification module is used to input multiple groups of eigenvalues collected in the loop convergence module into the ray tracing model, select the distribution eigenvalue group that can satisfy the incident light, and calculate the compactness corresponding to each selected group of eigenvalues, and take the eigenvalue group with the lowest compactness as the best panoramic ring head unit design scheme.
在一些实施例中，所述紧凑度指标获取模块包括：In some embodiments, the compactness index acquisition module includes:
紧凑度定义子模块，用于根据全景环带头部单元结构，定义全景环带系统的紧凑度计算公式：The compactness definition submodule is used to define the compactness calculation formula of the panoramic ring belt system according to the panoramic ring belt head unit structure:
其中，K表示全景环带系统的紧凑度，D表示全景环带头部单元的最大口径，L表示像面的对角线长度；Among them, K represents the compactness of the panoramic ring belt system, D represents the maximum aperture of the panoramic ring belt head unit, and L represents the diagonal length of the image plane;
紧凑度指标获取子模块，用于根据紧凑度计算公式，获取全景环带系统的紧凑度指标，包括：第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度。The compactness index acquisition submodule is used to obtain the compactness index of the panoramic ring belt system according to the compactness calculation formula, including: the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness.
在一些实施例中，所述循环收敛模块包括：In some embodiments, the loop convergence module includes:
目标函数构建子模块，用于将多组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值作为特征值，构建目标函数：The objective function construction submodule is used to construct the objective function by taking multiple sets of first transmission surface curvature radius, first reflection surface curvature radius and lens thickness values as characteristic values:
hθ(x)＝θ0x0+θ1x1+θ2x2+θ3x3；hθ (x)＝θ0 x0 +θ1 x1 +θ2 x2 +θ3 x3 ;
其中，hθ(x)表示目标函数，x0＝1，x1、x2、x3分别表示每一组第一透射表面曲率半径、第一反射表面曲率半径以及透镜厚度值的向量表示，θ0-θ3表示回归系数；Wherein, hθ (x) represents the objective function, x0 =1, x1 , x2 , x3 represent the vector representation of each set of the first transmission surface curvature radius, the first reflection surface curvature radius and the lens thickness value, and θ0 -θ3 represent the regression coefficients;
代价函数构建子模块，用于结合每一组特征值所对应的紧凑度，构建代价函数：The cost function construction submodule is used to construct the cost function by combining the compactness corresponding to each set of eigenvalues:
其中，Jθ0，θ1，θ2，θ3)表示代价函数，m表示样本个数，xi表示第i组样本的所有特征值，yi表示第i组样本所对应的紧凑度；Wherein, Jθ0 ,θ1 ,θ2 ,θ3 ) represents the cost function, m represents the number of samples,xi represents all eigenvalues of the i-th group of samples, andyi represents the compactness corresponding to the i-th group of samples;
多元梯度下降子模块，用于采用多元梯度下降算法进行收敛：Multivariate gradient descent submodule, used to converge using the multivariate gradient descent algorithm:
其中，
在一些实施例中，所述光线跟踪模型构建模块包括：In some embodiments, the ray tracing model building module includes:
头部单元模型构建子模块，用于对全景环带头部单元的结构进行数学建模，确定光轴、第一透射表面、第二透射表面、第一反射表面以及第二反射表面的位置；A head unit model building submodule is used to mathematically model the structure of the panoramic ring band head unit and determine the positions of the optical axis, the first transmission surface, the second transmission surface, the first reflection surface and the second reflection surface;
光线路径设置子模块，用于设置光源，使光源从第一透射表面发生折射，通过透镜传播到第一反射表面，经第一反射表面反射至第二反射表面，然后通过第二反射表面反射至第二投射表面，并记录光线传播路径；A light path setting submodule is used to set the light source so that the light source is refracted from the first transmission surface, propagated to the first reflection surface through the lens, reflected from the first reflection surface to the second reflection surface, and then reflected from the second reflection surface to the second projection surface, and record the light propagation path;
反射折射计算子模块，用于根据光线传播路径计算反射和折射，包括：法线、反射方向以及折射方向。The reflection and refraction calculation submodule is used to calculate reflection and refraction according to the light propagation path, including: normal, reflection direction and refraction direction.
在一些实施例中，所述方案确定模块包括：In some embodiments, the solution determination module includes:
特征值验证子模块，用于将循环收敛模块中采集到的多组不同梯度的特征值输入光线跟踪模型，并验证每一组输入的特征值是否符合光线传播路径，若不符合，则剔除不符合的特征值，若符合，则跳转步骤S52；The eigenvalue verification submodule is used to input multiple groups of eigenvalues with different gradients collected in the loop convergence module into the ray tracing model, and verify whether each group of input eigenvalues conforms to the light propagation path. If not, the eigenvalues that do not conform are eliminated. If they conform, the process jumps to step S52.
紧凑度比较子模块，用于对符合光线跟踪模型中光线传播路径的特征值组，计算每一组特征值所对应的紧凑度，并将紧凑度最低的特征值组作为最佳的全景环带头部单元设计方案。The compactness comparison submodule is used to calculate the compactness corresponding to each set of eigenvalues that conform to the light propagation path in the ray tracing model, and take the eigenvalue group with the lowest compactness as the best panoramic ring head unit design solution.
本领域的技术人员能够理解，尽管在此所述的一些实施例包括其它实施例中所包括的某些特征而不是其它特征，但是不同实施例的特征的组合意味着处于本申请的范围之内并且形成不同的实施例。Those skilled in the art will appreciate that although some embodiments described herein include certain features included in other embodiments but not other features, the combination of features from different embodiments is meant to be within the scope of the present application and to form different embodiments.
本领域的技术人员能够理解，对各个实施例的描述都各有侧重，某个实施例中没有详述的部分，可以参见其他实施例的相关描述。Those skilled in the art will appreciate that the description of each embodiment has its own emphasis, and for parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.
虽然结合附图描述了本申请的实施方式，但是本领域技术人员可以在不脱离本申请的精神和范围的情况下做出各种修改和变型，这样的修改和变型均落入由所附权利要求所限定的范围之内以上，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到各种等效的修改或替换，这些修改或替换都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以权利要求的保护范围为准。Although the embodiments of the present application are described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present application, and such modifications and variations all fall within the scope defined by the attached claims. The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
以上，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到各种等效的修改或替换，这些修改或替换都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以权利要求的保护范围为准。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.
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