高级象差理论

本文的主要目的在以近似方法讨论高级象差特性。首先由对称性讨论了二级象差的独立象差数,近似讨论了象差的几何意义,再由坐标变换的观点导出了光栏移动时象差变化的规律。由Fermat原理和同一光线可看作是各不同点发出的观点导出了物体移动时象差变化的规律。由于运用Fermat原理,所得的结果实际上是略去初级象差影响后的近似结果,因此表示式相当简单。然后我们把象差产生的原因分为二类。其一称作是本徵的,是入射光束无象差时必然产生的象差,用象差看作球差的观点导出了它们的表示式,结果表明,高级球差和本徵轴外球差是象差产生的原因,并导出了各种象差同时产生的状况。象差的另一类称作是衍生的,它们是由入射光线原有象差引起的初级象差差异,由初级象差理论即可得出它们的表示式。这一些高级象差的规律和近似表示可作为评断象差产生原因的半定量依据。最后,用Fermat原理讨论了高级色差问题,并说明Fermat原理之所以可在高级象差理论中应用的理由及不致误差过大的应用范围。

THEORY OF HIGH ORDER ABERRATIONS

This paper is to discuss the properties of high order aberrations taking advantage of as much as possible of using the methods of approximation. The number of independent terms of secondary aberrations is first accessed and its geometrical significance ascertained. By a coordinate transformation the effects of the change of stop position on aberration coefficients are determined. The relations between the position of the object and its aberration coefficients are found on the basis of Fermat principle, by regarding each ray as emitting from different object points lying along this ray.The high order aberrations can be regarded as coming from two sources. The first is of "intrinsic" origin caused by the refracting surface proper, the incident beam being regarded free from abberations. All aberrations of this origin can be represented in terms of high order spherical aberration and off-axis spherical aberration introduced by the respective surface. The other is of sequential character, introduced on account of the presence of primary aberration of the incident beam introduced by the preceeding refracting surfaces.The derivations so arrived may not accord exactly with theory but they are close enough for practical purposes so as to access the origin of various aberrations as well as to give a quantitative estimation of them.The application of Fermat principle to the question of high order chromatic aberration with advantage takes into account of the fact that the method is true only because all other aberrations are already nearly corrected in a given optical system.