Imaging Signal-to-Noise Ratio
Pixel SNR with background, dark charge, read noise and binning; noise budget, and the frames or co-added scans needed for a target SNR.
Signal
3500.0 e⁻
Background 350.0 e⁻, dark 0.010 e⁻
Read Noise per Super-Pixel
1.50 e⁻
Charge binning: read once
Total Noise (one frame)
62.07 e⁻
Shot noise of the signal 59.16 e⁻
SNR (one frame)
56.391
SNR (1 frame averaged)
56.391
SNR·√N
Rose Criterion
Detectable
SNR ≥ 5 to see a feature reliably
Frames for SNR 100
4
⌈(SNR_target/SNR₁)²⌉, white noise
Dominant Noise (one frame)
Signal shot noise
90.9 % of the variance
Noise Budget (one frame)
| Source | σ (e⁻ rms) | Share of variance |
|---|---|---|
| Signal shot noise | 59.16 | 90.9 % |
| Background shot noise | 18.71 | 9.1 % |
| Dark-charge shot noise | 0.10 | 0.0 % |
| Read noise | 1.50 | 0.1 % |
Independent sources add in quadrature, so the largest share of the variance sets the SNR.
Averaging Frames or Co-adding Scans
The same √N law holds for co-added spectra. It assumes noise that is independent from frame to frame; drift, fixed-pattern noise and 1/f noise are correlated and set a floor that averaging can't lower.
S = QE·N_signal·B², S_bg = QE·N_bg·B², D = R_dark·t·B²
SNR = S / √(S + S_bg + D + σ_read,B²); σ_read,B = σ_read (charge) or B·σ_read (digital)
N averaged frames: SNR_N = √N·SNR; frames for a target: N = ⌈(SNR_target/SNR)²⌉; Rose criterion SNR ≥ 5
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
CCD equation: Poisson signal, background and dark charge plus Gaussian read noise per binned super-pixel; charge binning reads once, a digital sum b² times. Averaging N frames (or co-adding N spectra) gains √N only for noise that is independent between frames; drift, 1/f and fixed-pattern noise don't average down. EM gain, fixed-pattern noise and error in the subtracted background are left out.
- Janesick J. R. (2007). Photon Transfer: DN → λ. SPIE Press, ch. 5. Signal-to-noise ratio with read, dark and shot noise. doi:10.1117/3.725073
- Rose A. (1948). The sensitivity performance of the human eye on an absolute scale. J. Opt. Soc. Am. 38, 196. An SNR of about 5 to detect a feature. doi:10.1364/JOSA.38.000196