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SNR (Signal-to-Noise Ratio) の計算方法
本ガイドの対象者 :
SNRの計算方法を知りたい方
本ガイドの内容 :
SNRの計算式、計算に使用する要素について説明します。
SNRとは、全ての信号と全てのノイズの単純な比率のことです。科学計測用カメラの場合、以下の式で計算することができます。
- QE = Quantum efficiency (量子効率)
- S = Photons/pixel (光子/画素)
- Fn = Noise factor (ノイズファクター)
- Ib = Background (バックグラウンド)
- Nr = Readout noise (読み出しノイズ)
- M = EM gain (EMゲイン)
この式から、信号はカメラのQE (EM-CCDの場合は実効QE (eQE) ) に依存していることがわかります。QEとeQEについては、テクニカルガイド "カメラの仕様を理解する "で詳しく説明しています。
ノイズは、ノイズファクター、バックグラウンド、読み出しノイズ、EMゲインに依存します。
■シグナル、バックグラウンド (S、Ib)
センサに入射する光子は、平均的な光量の変動を持ちます。この光量の変動はポアソン分布に支配されるため、光子の数の平方根である標準偏差を持ちます (= 光ショットノイズ)。イメージングでは、光子 (と光ショットノイズ) の発生源として、シグナル（S）とバックグラウンドからの信号 (Ib) の2つが存在します。SNRの高い画像を得るためには、Ibの量を制限し、Sを増加させることが重要です。
■量子効率 (QE)
カメラのQEとは、光子が光電子に変換される確率のことです。QEはSNRの式で支配的な要素であるため、基本的に高いQEを持つセンサほど高いSNRを得ることができます。
■M (EMゲイン) 、Fn (増倍ゆらぎ) *EM-CCDのみ
EMゲイン (M) は印加電圧に依存して段階的に増加していき、その総量は印加電圧とEMレジスタのステップ数で決まります。EMゲインは統計的な分布を持ち、関連する分散はFnで説明されます。一般的なEM-CCDのゲインでは、Fn＝√2≒1.4である。EM-CCDのすべての信号は、この追加のノイズにさらされることになります。CCDとCMOSセンサはEMゲインを持たないので、これらのカメラではFn = 1となります。
■読み出しノイズ (Nr)
読み出しノイズ (e-) は、各画素の光電子信号をデジタル数値に変換する際の電子回路内でのばらつきを統計的に表現したものです。
■ダークノイズ (Nd; 上図には記載なし)
ダークノイズは、熱起因で発生した電子に由来するノイズで、露光時間やセンサの温度に依存します。Ndの値は非常に小さいことに加え、一般的にカメラの露光時間をそこまで長くすることはないため、ノイズの総量に大きな影響を与えません。そのため、ここでは計算式に含めていません。
■ノイズ要素を追加する場合
これらと相関の無いノイズは誤差伝搬の法則により加算することができます。つまり、各ノイズの項をまず2乗し、他の項と加算してから平方根をとって総ノイズを算出する必要があります。
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