一种基于共轭节面的图像畸变分析方法

无像差的光学相机的成像模型可由其共轭节面模型等效表示。针孔模型本身忽略了偏离该等效模型的误差，也无法表示平板玻璃的平移误差、光轴的安装误差以及实际相机光学系统的像差，这四个因素都会引起图像畸变。基于此利用共轭节面的性质建立了一种图像畸变几何模型，并与广泛采用的像差模型进行了对比，从理论上解释了像差模型各个系数的物理意义。对某实际针孔相机进行仿真分析，该几何模型给出的相对径向畸变、角度误差在设计参数的范围以内，并且可以模拟图像的非对称畸变。该几何模型需要辨识包含主面相关参数、光轴倾斜角和平板玻璃的轴向球差在内的4个参数，辨识参数较少，理论上可以作为一种新的图像畸变校正方法。

A Method of Analyzing Image Distortion Based on Conjugate Nodal Plane

The imaging model of an optical camera without aberration can be equivalently expressed by its conjugate nodal plane model. A pinhole camera model neglects aberration of corresponding equivalent model, and also fails to represent translation error of flat glass, tilt error of optical axis as well as aberration of an actual optical system. All of these four factors give rise to image distortion. Based on this, a geometry model of image distortion is proposed by utilizing the property of conjugate nodal plane. By comparing with commonly used aberration model, this model can theoretically interpret their physical significances. The simulation of an actual optical system indicates that the relative radial distortion and relevant angle error both calculated by this model appears in the range of rational design parameters. Meanwhile, the phenomenon of asymmetric image distortion is seen. In this model, four unknown parameters needed to be recognized are relevant parameters of principal plane, tilt angle of optical axis and axial spherical aberration of flat glass. Theoretically, this geometric model can be used to correct image distortion with less parameters to be identified.