![](data:image/png;base64,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)
(1)式で表わされるレーリー散乱は分子、微粒子などが比較的まばらに存在する気 体中
においてのものである。分子の密度が格段に高い液体中においては、近隣に分子による散
乱光に波動的な位相関係が存在し、散乱光どうしが干渉により弱め合うと言う現象がおきる。
結晶性の件著な固体においては、結晶の規則正しい配列のため光の直進方向以外への
散乱光は打ち消し合い、観測されにくい(本連載第 2 回2節参照)。ところが、
分子分布の規則性を持たない、そして熱運動する液体においては、変動はランダムであり、結
晶固体、気体における両方の散乱の性質を持っている。この散乱の数学的記述は、密
度分布
が完全にランダムであるとの仮定の基、 統計力学( 光学) 的処理により、
Smoluchorwski、Einstein らによって行われ、光が単位長進む間に散乱によって失うエネル
ギーの割合を示す散乱係数hは、を誘電率、kをボルツマン定数、T を絶対温度として、
8
3
h
3n
4
1
2
2
3
nkT
-(2)
として表わされる。は熱力学における等温圧縮率であり、絶対温度 T の変化が無い場合
の体積と圧力の微小変化分、V,pにより、
1 V
V p -(3)
T 0
となる。
特に近年、液体における光の散乱が注目されているのは、ガラス、或いはプラスチックの
溶融液体の固体化の製造工程においては、微視的には液体の組成がそのまま残されて、こ
れらの物質の光散乱を考える際には液体中の光散乱特性を考える必要があるからである。
3. ミー散乱
上述の様に、波長の 1/10 程度以下の大きさの反射物体による散乱はレーリー散乱とな
る。また、mmオーダーから次第に反射物体が小さくなるのに従い回折の影響が大きくなる事
も述べた。この領域ではスカラー回折理論による解析手法が取られる。つまり、光線追跡に
より波面を求めそれを基に、ホイヘンスの原理から光の伝播の様子が求められる。
ところが、
この理論は反射物体が0.
2mm程度の大きさ以上の場合にのみ安心して適用
できる。すな
わち、物体が小さくなり過ぎ、一般的回折近似理論の誤差が大きくなり、また完全に回折に
対する物体の大きさを無視する事もできないので、レーリー散乱の理論も成立しない領域が
存在する。この領域における任意な材質、任意の大きさの球による散乱
計算を担う理論がミ
ー(
Mie)理論( 1908年)である。この理論により計算される散乱を便
宜的にミー散乱と呼ぶ。
ミー理論は多くの場合、物体の大きさが数m程度から 100nm 程度の大きさに及ぶ、大気中
の水滴、粒子などによる散乱の解析に用いられる。
ミー理論は任意の大きさの球に対して成立する理論である。レーリー散乱も大きさが無視で
きるものとして扱われてはいるが、導出の際には球による散乱として導かれているので、レーリ
ー散乱もミー理論の一部と考えることもできる。つまり、ミー散乱とは本質的には物理現象その
ものを表わすのではなく、上述の計算理論が空白の物体の大きさの範囲を埋めるべく利用さ
れる、実はより広い範囲に応用性のあるミー理論によって解析される散乱の、一つの呼び方で
ある。