尽管这篇文章简短，但翻译它还是比较费力的。
初学者读起来可能会有些迷糊，但只要时间多一点，经验多一点，就容易理解了:)
近轴并非理想
小结
平面物体经过理想透镜所成的像清晰,没有畸变。初学者常常认为一个理想透镜的行为应该遵守近轴光线追迹法则。事实并非如此。尽管由近轴光线的计算可以得像面位置和放大率,但是实际上,除了在极靠近光轴的区域以外,近轴光线所走的路径并不遵守费马原理。理想透镜仅可以在一对共轭位置上成理想像,而且此时光线的路径不遵守近轴光线追迹公式。
我们还有比近轴模型更为精确的理想透镜模型，而且还用这一模型并没带来太多不必要的计算复杂度。OSLO采用aplanatic model（等光程模型）来描述理想透镜。在等光程模型物空间和像空间的轴光束光锥（半）角的正弦之比为常数，而在在近轴模型物空间和像空间的轴光束光锥（半）角的正切之比为常数。如果遵循这一定义来绘制光路图，当物空间光线和像空间光线投射到单个面上相交时，结果就显得有些奇怪。光线的轨迹看起来在这个面上中断了！这种事情在现实中不可能发生。等光程模型并不是错误的，这只是说明并不存在理想的“薄”透镜这种东西。
讨论
近轴近似仅严格适用于无限靠近光轴的光线。这种光线才可以称为近轴光线。而现在光学设计的日常工作中，近轴的概念和术语已经被用于那些远离光轴的光线。例如，用近轴F/#（焦距与孔径之比）来描述孔径已经达到F/2的镜头。经过孔径边缘的光线已经很明显不满足近轴条件了。但是，如果以折射面（反射面）的切平面来代替折射面（反射面）本身，那些本来仅适用于真正的近轴光线的追迹公式，也可以用于有较大倾角的光线。同时由于内在的几何关系，此时的光线追迹公式可以推导出理想像面的位置，如下图所示。这一运算中的有较大倾角的光线可以称为形式上的近轴光线（formal paraxial rays）。
真正的问题在于，现实世界中，光线从来就不会走这种路线。有些情况下，实际光线和近轴光线的轨迹差异很小，可以忽略。而在有些情况下（如上图所示）差异很大。在包含有场镜（field lenses）的系统中，光瞳像差和系统像差的综合作用，使系统无法校至理想状态。此时，采用近轴透镜模型就会带来相当的误差。事实上，形式上的近轴光线的追迹路径是不遵守费马定律（Fermat's principle）的[1]。
170年前，我们已经意识到理想透镜仅仅可以在一对共轭位置上成完美像。这也就是Herschel条件陈述的内容。Herschel条件的命名来源于它的发现者William Herschel，他是一个杰出的天文学家（就是他发现了天王星）和音乐家（擅长双簧管吹奏和作曲）。Herschel条件的发现比广为人知的Abbe正弦条件要早50年，但却没有Abbe正弦条件那么有名气。Herschel条件的推演和讨论参见Walther [2]的第六章，或者Born Wolf [3]的4.5小节.
给定了焦距和放大率（也就是共轭位置），OSLO就可以正确地定义理想透镜。另外一些光学设计软件中就没有这样做。OSLO Optical Reference中提供了一个理想透镜的例子可供参考。
1. A. Walther, "Teaching the theory of real lenses", Am. J. Phys. 64 (9), 1161-1165 (1996).
2. A. Walther, "The Ray and Wave Theory of Lenses", Cambridge University Press 1995, ISBN 0-521-45.
3. Max Born and Emil Wolf, "Principles of Optics", Pergamon Press, ISBN 0-08-018018 3.
原文
Paraxial is not Perfect
Summary
A perfect lens forms a sharp, undistorted image of a planar object. Newcomers to optics sometimes think that a perfect lens should obey the rules for paraxial ray tracing. This is not true. Although paraxial rays can be used to predict the location and magnification of images, paraxial ray trajectories do not obey Fermat's principle, except in a region near the optical axis. A perfect lens can't form a perfect image at more than one magnification, and the trajectories of rays through it cannot be found using paraxial ray tracing.Fortunately, it is possible to use a perfect lens model that is more accurate than the paraxial model, without undue computational complexity. The aplanatic model used in OSLO considers that for a perfect lens, the ratio of the sines of axial ray angles in object and image space is constant. This leads to curious pictures showing that if rays in object and image space are projected on a single surface, the trajectories appear to be discontinuous. The fact that this obviously can't occur means that there is no such thing as a perfect thin lens, not that the aplanatic model is incorrect.
Discussion
The paraxial approximation applies strictly to rays that are infinitesimally displaced from the optical axis of a system. Such rays may be called true paraxial rays. In everyday optical design, however, paraxial concepts and terminology are used to describe rays that are far removed from the optical axis. For example, it is common to describe a lens by its paraxial f-number, defined to be the ratio of the focal length to the diameter, even when this ratio is quite small, e.g. f/2. The rays through the edge of the lens obviously don't satisfy the paraxial requirement. However, if surfaces are replaced by their tangent planes, the equations for true paraxial rays can be applied to rays having large slopes in a self consistent geometry that predicts perfect imagery, as shown below. These rays can be called formal paraxial rays.
The problem is that in the real world, light doesn't travel along those paths. Sometimes the discrepancy between the real ray trajectories and the paraxial trajectories is minimal; sometimes (as in the drawing in the note) it is quite large. In systems containing field lenses, the tradeoffs between pupil aberrations and image aberrations often make it impossible to correct the system to perfection, and the use of paraxial lenses can be quite misleading. In fact, it can be shown that formal paraxial ray trajectories do not obey Fermat's principle [1].
It has been known for about 170 years that a perfect lens can only be perfect at a single magnification. This is a consequence of the Herschel condition, named for its discoverer William Herschel, a brilliant astronomer (who discovered Uranus) and musician (oboist and composer). Curiously, the Herschel condition predates the better-known Abbe sine condition by more than 50 years. For a derivation and discussion of the Herschel condition, see chapter 6 of Walther [2] or section 4.5 of Born Wolf [3].
OSLO defines perfect lenses correctly, requiring the specification of both the focal length and magnification (this is not the case in some other programs). An example of a perfect lens is provided in the OSLO User's Guide.
1. A. Walther, "Teaching the theory of real lenses", Am. J. Phys. 64 (9), 1161-1165 (1996).
2. A. Walther, "The Ray and Wave Theory of Lenses", Cambridge University Press 1995, ISBN 0-521-45.
3. Max Born and Emil Wolf, "Principles of Optics", Pergamon Press, ISBN 0-08-018018 3.
>没看明白中心意思，郁闷啊～</P>
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