Polynomial Optics: A Construction Kit for Efficient Ray‐Tracing of Lens Systems
Polynomial Optics: A Construction Kit for Efficient Ray‐Tracing of Lens Systems
复制标题
多项式光学器件：用于镜头系统高效光线追踪的构建套件
DOI：
10.1111/j.1467-8659.2012.03132.x
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发表时间：
2012
影响因子：
2.5
通讯作者：
W. Heidrich
中科院分区：
文献类型：
--
作者：
M. Hullin;J. Hanika;W. Heidrich
通过透镜系统的光传输模拟在图形学中起着重要作用。虽然基本成像特性可以方便地从线性模型（如 ABCD 矩阵）导出，但这些近似无法描述实际光学中出现的非线性效应和像差。这种效果可以通过适当的光线追踪来计算，然而，为此找到合适的采样和过滤策略通常不是一件容易的事。受像差理论的启发，像差理论用波前畸变描述了线性光线传输的偏差，我们提出了一种非线性效应的光线空间公式。特别是，我们通过射线参数的泰勒展开来近似射线追踪问题的解析解。这种表示方式使得本着矩阵光学的精神能够采用构建套件方法来构建复杂的光学系统。它的评估也非常简单，可以在 CPU 和 GPU 上高效执行，包括计算任意阶的混合导数。我们评估多项式模型的保真度和性能，并展示在高质量离线渲染和交互式帧速率下的应用。
Simulation of light transport through lens systems plays an important role in graphics. While basic imaging properties can be conveniently derived from linear models (like ABCD matrices), these approximations fail to describe nonlinear effects and aberrations that arise in real optics. Such effects can be computed by proper ray tracing, for which, however, finding suitable sampling and filtering strategies is often not a trivial task. Inspired by aberration theory, which describes the deviation from the linear ray transfer in terms of wavefront distortions, we propose a ray‐space formulation for nonlinear effects. In particular, we approximate the analytical solution to the ray tracing problem by means of a Taylor expansion in the ray parameters. This representation enables a construction‐kit approach to complex optical systems in the spirit of matrix optics. It is also very simple to evaluate, which allows for efficient execution on CPU and GPU alike, including the computation of mixed derivatives of any order. We evaluate fidelity and performance of our polynomial model, and show applications in high‐quality offline rendering and at interactive frame rates.