Temporal Noise

1/f noise from a corner frequency, white read noise and dark shot noise, versus frequency and integration time.

White Read Noise over B (e⁻ rms)Dark Current (e⁻/pix/s)Exposure Time (s)1/f Corner Frequency (Hz)Read-out Bandwidth B (Hz)Lower Band Edge f_L (Hz)Conversion Gain (μV/e⁻)

Read noise (white) = 5.0 e⁻

Dark shot noise = 0.03 e⁻

1/f noise from f_L to B = 0.50 e⁻

Total noise (with 1/f) = 5.02 e⁻ = 10.05 μV rms at the sense node

σ_1/f = σ_read·√((f_c/B)·ln(B/f_L)) | σ_dark = √(I_dark·t) | σ_total = √(σ²_read + σ²_dark + σ²_1/f)

f_L is set by how long the pixel is observed (of order 1/t for a time t; correlated double sampling raises it). The result depends on it only through the logarithm. Sharp band edges stand in for the real sampling filter.

Model and references

Illustrative. A simplified model that shows trends and orders of magnitude. Don't use its numbers for design. About the tiers

A white read noise with a 1/f corner, integrated between sharp band edges f_L and B, plus Poisson dark noise. The real correlated-double-sampling filter and the choice of f_L change the 1/f term.

Motchenbacher C. D., Connelly J. A. (1993). Low-Noise Electronic System Design. Wiley. Noise of a white floor with a 1/f corner: f_c·ln(f_H/f_L) + (f_H − f_L).
Janesick J. R. (2007). Photon Transfer. SPIE Press. Read-noise, shot-noise and dark-noise regimes; total noise as the quadrature sum. doi:10.1117/3.725073

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