Matrix algebra applied to the calculation of fifth-order aberrations in optical systems.

Thesis (M.A.)--Boston UniversityThis paper is an extension of the work originally done by Dr. Willem Brouwer for his doctoral thesis at Delft University, Delft, Holland. He took the relationships governing:(l) the direction of a light ray before and after refraction at a surface; (2) the coordinates, with respect to the axis, of this light ray at two successive surfaces of an optical system; and set them into matrix form. He was then able to produce a matrix for one surface to obtain image plane coordinates from those in the object plane, when given an initial ray direction, by multiplying in proper syquence two translation and one refraction matrices. He also constructed another objeqt to image matrix which used paraxial magnifications from an object and reference plane, plus unknown coefficients for the higher powers of these two object plane coordinates (i.e. a general series expansion). He modified this basic matrix with another, and its inverse, which contained only powers of the paraxial magnifications. The modification allowed a series of the basic matrices to be multiplied (combining surfaces for a lens system) while causing the coefficients to be only additive for the third-order terms. The conclusions indicate that even preliminary study of the final expression for fifth-order spherical aberration showed that useful information could be derived from examining it in the final form presented