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図1 レンズ、ミラー面を表現する座標系
x
軸(光軸)についての回転対称な光学系の光軸を含む断面図。
z
軸は
x,y
軸
に直交している
(40-7)式におけるεは円錐係数(conic term)と呼ばれ、内容については
前回、前々回ですでに触れた。これらの式が回転対称高次非球面を表現する場
合の基本部となり、円錐曲面式とも呼ばれる1)。この式に、より高次の図 1に
おける
x
の量のズレ量を加えて、より複雑な形状を表すことになる。(40-8)
式を考慮した表現をして、一般的には以下の如くに表される1)。
x =
+++++ (1)
Aで表される各高次非球面係数により具体的な面形状が表現されて行くわけで
あるが、勿論、Aが全て 0の場合には、(40-7)式の円錐曲面となる。どんど
ん高次の項を付加していくことが可能である。(1)式は(40-8)式の通り
y、zのプラスマイナスの符号の違いに影響されないので
x
軸について回転対称
である。
ここで、実際に(1)式を用いて、実際の面形状を計算してみよう。まず、基
準としてε=1の球面の場合を計算してみると、前回図 2と同じ条件で以下の
通りである。