同轴柱面光学系统的象差

本文首先由柱面系统中描写光线所须的参数和对称性,确定了同轴柱面系统的独立象差数是八个,而对无限远物体而言则只有六个。而后由矢量代数方法证明空间光线在柱面系统中的折射光路与发生折射率改变后的子午截面内光路全同,由此得出柱面系统有别于球面系统的二种象差与色差相当。从而导出了校正柱面象差的条件并对柱面望远镜象差作了估值。结果表明,校正柱象差一般而言是很困难的,另一方面虽不加以校正影响也不算严重。最后讨论了柱面望远镜的高斯光学,结果表明,望远镜使一方向余弦按定比例缩小,而另一方向余弦不变时,它所成出的直线的象是弯曲的。

THE ABERRATIONS OF CYLINDRICAL OPTICAL SYSTEMS

This paper deals with the aberrations of optical systems consisting of cylindrical components with their axes, parallal and having a common axis of symmetry. By symmetry and by a proper choice of the parameters for describing an optical ray, it is found that for primary aberrations the independent aberration terms amount to eight. For a. telescopic system the number of terms reduces to six. By method of vector analysis, it is further proved that the skew rays passing through such a systems is equivalent to a ray-tracing passing through its principal section but with the respective refractive index of each medium changed from n to (n²-η²)^1/2, η being the direction cosine of the ray in the direction of cylindrical axes times n, an invariant throughout the system for a given ray. Thus the two term specifying "cylindrical" aberrations proper in a telescopic system (the other four terms being exactly the same as for spherical surfaces) can be treated in a similar way as longitudinal and transversal "chromatic" aberrations. However, the connection of such aberrations requires choice of optical materials difficult to comply with what is necessary for proper chromatic correction. On the otherhand, the serious effect of distortion usually found in cylindrical telescopic systems should be attributed as mainly intrinsic to Gaussian optics with which the practical requirement in imagery in such systems does not fully agree.