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光子の数はどのように測定するのですか？
本ガイドの対象者 :
実験で光子の数を測定する方法について知りたい方
本ガイドの内容 :
光子数の測定法を順を追って説明します。
光子の数を測定することは高度な機器と複雑な測定が必要な難しい問題だと思われています。しかし、ある特定のピクセルにいくつの光子が入射したかは簡単な計算とすでに持っている機器を使うことで、かなり精度の良い値を推定することができます。
カメラは画像の輝度情報をグレースケールで出力します。文献では画像の輝度情報を「ADU」や「DN」で表現しているのを見かけることがあります。ここで重要なのは、グレースケールはカメラごとに設定された任意の値であるということです。しかしこの値を使うことで光子数を逆算することができます。その方法は以下の通りです。
- 任意の実験条件下でサンプルの画像を撮影する。
- カメラのオフセット値を決定する。一般的にデジタルカメラには、ノイズの影響で輝度がマイナス方向に振れた際もデジタル化する値が0以下になることを防ぐ目的で、オフセットという値が設定されています。オフセットの値は通常カメラの取扱説明書に記載されていますが、自身で測定することも可能です。その方法は、カメラに入るすべての光を遮断して画像を取得した後、その画像の空間平均を求めるという方法です。空間平均はすべての画素の平均強度を計算します。ここで求めた空間平均の値がカメラのオフセットに相当します。 ※例えば、カメラを顕微鏡に接続している場合、顕微鏡の光路を切り替えたとしてもわずかにカメラに迷光が入っている可能性があるため、厳密に測定を行うためには一度カメラを顕微鏡から取り外し、付属のキャップを装着して画像を取得します。
- このオフセットの値をサンプル画像の各画素から差し引きます※基本的にカメラの画像解析ソフトにはこれらの処理や計算を行うための機能が実装されています。
- 画像の各ピクセルを変換係数で割って、グレースケールの単位を電子数に変換します。※変換係数またはコンバージョンファクターと呼ばれる値はすべてのデジタルカメラに備わっており、浜松ホトニクスではすべてのカメラにこの数値が記載された資料が付属しています。もしお持ちのカメラの変換係数がわからない場合はメーカーに問い合わせる必要があります。
- 最後に、各画素の電子数を撮影時に使用した波長におけるカメラの量子効率の値で割って、電子数を光子数に変換します。量子効率の値はカメラのスペックシートを参照する必要があります。
これで各ピクセルの光子の数がわかります。
もちろん、フィルタやレンズ、反射など細かな変数があるためこの値は変動することがあります。ただし、この計算方法で算出される光子数の誤差は数パーセント以内に収まります。
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