3次収差係数を中間パラメーターとするレンズの自動補正
1964 年 33 巻 10 号 p. 707-714
詳細
1964 年 33 巻 10 号 p. 707-714
It is generally shown that residual aberrations ƒi (i=1……, m) of a lens system calculated from ray trace data can be regarded as a linear function of corresponding third-order aberration coefficients si (i=1 …… m) provided that range of variation of the system parameters xj (j=1, ……, n) is sufficiently small.
This paper discusses one method of automatic lens correction in which third-order aberration coefficients are used as intermediate parameters between residual aberrations and lens parameters of the system.
The correcting method used is made up of iterative procedures, each of which is composed of the following three steps. First, at the with iteration, residual aberrations (ƒi)v and third-order aberration coefficients (si)v of a system (xj)v are calculated. Then, target values of third-order aberration coefficients (si)v+1* are derived such that residual aberrations (ƒi)v become equal to prescribed values (ƒi)*, assuming linearity between small variations of ƒi and those of si.
Finally, new lens system (xj)v+1 in which third-order aberration coefficients are corrected to the target values (si)v+1* is obtained by minimizing the following third-order merit function
Φs=_??_ρsi{si-(si)v*}2
where ρsi (i=1, ……, m) are a set of positive weighting factors.
After the repeated applications of this procedure, one can obtain a sequence of lens systems {(xj)1, (xj)2, …(xj)v…} (j=1, ……, n) which converges to a solution.
The operation of a computer program to carry out the procedure is presented, together with the results of a four-components lens design as a numerical example. It is generally shown that four or five iterations are sufficient to obtain a well-corrected system and that computing time is considerably decreased compared with the ordinary least square method.
