著者

松居 吉哉

出版者

公益社団法人 応用物理学会

雑誌

応用物理 (ISSN:03698009)

巻号頁・発行日

vol.29, no.3, pp.184-194, 1960-03-10 (Released:2009-04-02)

参考文献数

6

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In the previous papers, new practical aberration coefficients are defined and various transformation formulas based on the general properties of coaxial optical system are considered. For actual calculations, however, formulas to compute the aberration coefficients by using constructional data of the optical system are needed. The object of this article is to develop computing formulas of the simplest and most reasonable form. For the present, the optical system is assumed to be composed merely of the spherical refractive surfaces.The relations between the intrinsic and the total aberration coefficients are already explained in the previous paper (I. General Theory, §11). Thus, the problem in hand is to derive the expressions of the intrinsic aberration coefficients. These expressions can be derived by starting from the special case in which the coefficients become zero and by applying the various transformation formulas (given in the previous paper) as was worked out by J. Focke (see reference 4). These can also be derived from the Focke's expressions by applying the two transformations as shown in the previous paper (I. General Theory, §4 and §5).In either case, the greatest difficulty is in arranging these expressions to develop computing formulas of the simplest form. One way to avoid confusion in the process is to express the intrinsic coefficients by independent variables and then develop the simplest forms by introducing the suitable dependent variables. Among the variables that have influence upon the intrinsic coefficients, three variables besides the constructional data are independent. Many sets of the three independent variables can be considered, but the most reasonable sets to express the intrinsic coefficients are the following two, viz.i) h, h, Q;ii) h, h, Q;here, h and h are the incident heights of paraxially traced object and pupil rays; Q and Q are the Abbe's invariants for these rays respectively. By using either set, the intrinsic coefficients can be expressed “uniquely”. Thus, two sets of “unique” expressions of the intrinsic aberration coefficients are derived. These expreseions may be regarded as the bases to develop the computing formulas.