几何光学中近轴光学与高斯光学的区别

近轴光学

Paraxial means very close to, but not restricted to, the axis Thus, the paraxial region of an axially centered optical system can be viewed as a tiny channel surrounding the axis. Rays lying everywhere within this channel are called palax-ial lays. Palaxial ray heights and ray angles arevery small and approach zero in the limit.

it can be shown that all ray from an object point on the axis are perfectly located at an image point on the axis. There are no aberrations. For a paraxial off-axis object point and paraxial rays, a perfect point image is similarly achieved. there is no field curvature and distortion. Even off-axis, there are no abelrations.

A paraxial ray is really only a mathematical abstraction,for if the diaphragm of a real lens were stopped down to a very small aperture in an effort to isolate only paraxial rays, the depth of focus would become so great that no definite image could be located, although the theoretical image

position can be calculated as a mathematical limit.

这里认为近轴光学只是一种数学抽象，尽管在这种数学极限的情况下，可以从理论上计算出像面的位置，但是如果光学系统的孔径减小到满足近轴光学的情况时，系统的焦深将变很大，以至于不能成明确位置的像。

Paraxial optics is first-order optics and yields perfect geometrical imagnery. It is important to note that the palaxial description is a limiting case, not an approximation. It really happens.

近轴光学是一阶光学，可以产生完善的几何像，值得注意的是近轴描述是一种极限情况，并不是一种近似，它是真实存在情况。

高斯在他1840年的论文中只是考虑真实近轴光线，他并没有指出有限孔径和视场下光学系统的一些基本性质，

Furthelnrore, the sizes of images and pupils can be estimated by an exterision of the paraxial description to f inite tranverse distance, To accomrnodate finite apertures and fields, the pralaxial region around the optical axis is transvelsely scaled up by some extremely lalgre number so that all transverse infinitesimal distances becorne finite in size( (thele are ways to handle this mathematically). ). No changes are made to longitudinal positions and distance. Thus. along the axis, the locations of surface vertices and centers ofcurvature are uchangged.

All principal planes. cardinal points. and focal lengths are unchanged. And the locations, rnagnifications, and orientations of all paraxial objects, images, and pupils are unchanged. However, all curved optical surfaces become so stretched out that they resemble planes tangent to the vertices of the unstretched sulfaces. Nevertheless, these "planes" retain their optical power to foucs light rays to form images.

如果对角度做适当的处理，然后近轴光线追迹方程仍然适用，当追迹近轴光线时，角度的正弦值直接用角度的弧度代替，这个值是用无限小的光线高度除以有限的纵向成像距离,但是当进行高斯光学计算时，the corresporrding angle is measuled by the ratio of a finite transverse distance to a finite longitudinal distance. Thus, sines of angles are replaced by angles, and then both are replaced by tangents of angles. In other words, ray angles are replaced by ray slopes.

When lens designers speak of tracing paraxial fays through an optical system. it is actually this modifiecl filst-order configuration. free of infinitesimal,that is used.

The imaging properties of this stretched paraxial configuration were developed by Maxwell and Abbe and are ploperly called a collinear mapping. The lays traced are properly called collinear rays.

However', over the years, collinear optics has become widely known as Gaussian optics, even though Gauss hiruself never considered this case. Although it is histolically inaccurrate to speak of collinear optics as Ganssian, the terms Gaussian optics and Gaussian rays will be adopted

here as labels for these concepts to conform with common practice.

高斯光学与近轴光学的区别与联系

Because the Ganssian descliption is merely a huge transverse scaling of the first-order paraxial description, the Gaussian description also yields perfect geometrical images; that is, all of Maxwell's criteria are satisfied (neglecting diffraction). But the Gaussian description of an optical systern is cleally not physically correct. The real lens surfaces are not planes with power, and the real images are not geometrically perfect. Thus, the Gaussian description is an approximation, not a limiting case.

近轴光学和高斯光学都是几何光学完善成像的一阶描述，但是它们是不同的，近轴光学只是适用于无限小垂轴距离的内光线的光线的成像，是一个准确的极限情况，而高斯光学描述（双线性映射描述）是近轴光学的扩展，包括近轴描述，适用有限的横向光线高度，是一种近似模型。高斯光线追迹并非真实的近轴光线追迹，在实际中是不存在的。

In summary, both the paraxial and Gaussian descriptions are filst-older descriptions with perfect -geometrical imagery (no aberrations), but they are not identical. The paraxial descliption applies only to infinitesimal transverse distances from the axis and is an accurate limiting case. The Gaussian (collinear) description is an extension of the palaxial descliption, includes the paraxial descliption, uses finite transverse distances, and is an approximation. Gaussian ray tracing, not true paraxial ray tracing. is actLrally done in practice. People sometirnes incorrectly use the terms first older,paraxial, and Gaussian interchangeably. If you understand the two concepts. you can recognize whether the limiting case or the approximation is being consicleled.

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几何光学中近轴光学与高斯光学的区别

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