![](data:image/png;base64,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)
光学設計ノーツ 18(ver.1.0)
ストローベルの定理と輝度不変則
前回は共役関係にある物・像、S,S’についての輝度不変則を導きそこから
正弦条件を求めた。今回は共役関係に無い光斑 S,S’(途中に光学系が存在し
ていても良い)についてもこの輝度不変則が成立する事を示す。必ずしも共役
関係にある訳ではない、光源、被照明面の関係を扱う事の多い、一般的な照明
系の取り扱いにおいてはこちらの考え方のほうがより重宝であろう。そのため
にはまず、ストローベルの定理を導かねばならない。
1. ストローベルの定理の導出と輝度不変則
光路中にレンズなどの光学系が存在する場合の、光学系を透過した輝度に
ついて考えよう。
図 1 にある様に、平面上の微小な面積
dS
を持つ光源 S からの光束が形成するある平面
上の幾何光学的な光斑 S’の微小な面積を
dS’
と置く。ここでは
dS
と
dS’
は共役関係に無い一
般的な状態を想定する。また、光線 A、A’を定め、簡潔のために、この光線と光軸の定める
メリディオナル断面内に微小平面 S,S’の法線が含まれるとする。
さらにこの断面内においては S,S’はそれぞれ微小な長さ
dr、dr’
で表わされることにな
るが、光源面上、点 A から微小な距離
dr
離れた位置にある点 B を設ける。この B から光線
AA’と平行に射出し、被照明面上において点 A’から微小な距離 dr’離れた位置にある点 B’に至
る光線を考える。
そして平面 S の法線と光線 AA’のなす角度を、平面 S’の法線と光線 AA’のなす角度を’
としよう。物界、像界の屈折率はともに一様であり、それぞれ
n,n’
とする。さらに、B から
光線 AA’への垂線の交点を C とする。さらに光線 AA’に沿った光路長[CA’]と[BC’]が等しくな
るように光線 BB’上に点 C’を置く。従って
BCCBACACBBAA
(4)
BCACBBAA