![](data:image/png;base64,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)
図5をご覧いただければ一目瞭然であるが、光の集中の傾向は確かに現れていて、かなり
エネルギーの集中の高そうな点も存在はしていても、どこに集まっているか?と考えれば
かなり混沌とした状態になっている。それぞれの光線は全て光軸方向に曲がってはいるが、
その方向はかなりバラバラである。本来はどこかの一つの場所に光が集まることが効率か
らすると理想である。また本来一点から出た光が再びフィルム上で一点に集光しようとす
る程度は写真などの画像の性質を考える上では大変重要に成る。この光線が一点に収束す
ることからのずれを収差と呼ぶ。結局、この収差を低減することがレンズ設計という仕事の
非常に大きな部分を占めている。
従って、こうした作業においては(或いは場合によってはレンズを使用するに際しても)、
この収差というものを定量化しなければならない。具体的には基準座標、基準位置を設けて
光線通過位置の、そこからのずれを知ることが必要になる。その基準位置となるものが理想
像点、というものである。
4.理想的な像点
図5を良く見ていただくと、光軸のそばを通過する光線は、境界面で僅かに屈折した後、
光軸上の殆ど同じあたりを横切っていることが、なんとなく分かる。光軸のそばにどんどん
近くなるように光線を発射させれば、ある位置に、この光軸と光線のクロス点は収束してい
く。これが理想的な像点である。軸に近いところ(近軸領域)の光線で定義されるので近軸
像点と称される。これが収差を計るための基準と成る。
実はこの近軸像点は(1)式を
2211
nn
(2)
として、光線の屈折を計算することによって簡単に定まる。なぜ、このような簡略化が可能
かといえば、sin は
!5!3
sin
53
(3)
と続く多項式に展開できる。右辺の無限の項まで考えてはじめて右辺と左辺が一致するわ
けであるが、θが極小さい場合には右辺第一項で事足りる。つまり
sin (4)
である。従って上記の近軸領域の場合には、(2)式が成立する。
さてこの(2)式で光線の屈折を考えるとどうなるであろうか?