Read noise

Read noise is the uncertainty that the readout chain of an image sensor or integrating detector adds every time it converts a pixel's collected charge into a number. It is quoted in electrons rms referred to the pixel input, the same units as the photoelectron signal. Unlike shot noise and the noise from dark current, it does not grow with signal or exposure time: it is paid once per read. Scientific CMOS sensors reach about 1–2 e⁻ rms, slow-scan CCDs a few electrons, with values of 3–10 e⁻ common, and InGaAs arrays for the short-wave infrared typically tens of electrons, sometimes more (see CCD vs CMOS and SWIR camera).

Sources in the readout chain

Three contributions dominate. Resetting the sense node, a capacitance $C$, leaves a random charge set by thermal noise, the reset or kTC noise:

$$\sigma_\text{reset} = \frac{\sqrt{k_B T C}}{q}$$

For $C$ = 10 fF at 300 K this is 40 e⁻ rms, or 0.64 mV at the node's conversion gain of 16 µV per electron. The source-follower amplifier then adds white and 1/f noise, and the analog-to-digital converter adds quantization noise of one step divided by $\sqrt{12}$, 0.14 e⁻ for a gain of 0.5 e⁻ per digital number (DN).

Correlated double sampling (CDS) removes the reset term. The output is sampled once just after reset and once after the charge is transferred; both carry the same frozen reset level, so their difference contains only the signal, and slow amplifier drift is partly canceled as well. With CDS, a pixel whose reset noise is 40 e⁻ can be specified at 1.5 e⁻. What remains is mostly amplifier noise, which grows with readout bandwidth, so a CCD read quickly through one output is noisier than the same CCD read slowly.

Measurement

Read noise is measured from bias frames: exposures of zero length, or as short as the sensor allows, taken in the dark. The difference of two bias frames removes fixed-pattern offsets; its standard deviation divided by $\sqrt{2}$ gives the read noise in DN, and multiplying by the conversion gain, found from a photon transfer curve of variance against mean signal, gives electrons. A difference-image standard deviation of 3.0 DN at 0.5 e⁻/DN corresponds to 1.06 e⁻. In CMOS sensors each pixel has its own amplifier, so read noise is a distribution, and a quoted median is lower than the rms.

Effect on signal-to-noise ratio

With a signal $S$, dark charge $D$ and read noise $\sigma_r$, all in electrons, the signal-to-noise ratio of one pixel is

$$\mathrm{SNR} = \frac{S}{\sqrt{S + D + \sigma_r^2}}$$

as under integration time. Read noise matters when $\sigma_r^2$ is comparable with $S$. For $S$ = 20 e⁻ and negligible dark charge, the shot-noise limit is 4.47; a read noise of 1.5 e⁻ gives 4.24, and 8 e⁻ gives 2.18. The full-well capacity divided by the read noise sets the sensor's dynamic range: 86 dB for 30,000 e⁻ and 1.5 e⁻.

In the read-noise-limited regime, the remedies reduce the number of reads per detected electron:

• Longer integration. One read of a longer exposure carries one $\sigma_r$; summing many short frames carries one per frame.
• Binning. A CCD can sum the charge of neighboring pixels before the amplifier. Four pixels of 20 e⁻ binned 2 × 2 give 80 e⁻ with a single 8 e⁻ read, an SNR of 6.67; adding four separately read pixels gives 4.36. Digital binning in a CMOS sensor adds the read noise of each pixel, which costs little at 1.5 e⁻ (SNR 8.48 for the same 80 e⁻).
• Gain before readout. An electron-multiplying CCD (EMCCD) amplifies the charge in a gain register before the output amplifier, so an output noise of 50 e⁻ at a gain of 300 is 0.17 e⁻ referred to the input. The price is an excess noise factor of about 2 in noise power (√2 in amplitude), which doubles the shot-noise variance. At 20 e⁻ an EMCCD reaches an SNR of 3.16 against 4.24 for a 1.5 e⁻ sCMOS sensor; the two are equal at $S = \sigma_r^2$, 2.25 e⁻, and the EMCCD wins only below that.

Pitfalls

A read noise quoted in DN needs the conversion gain to be interpreted. A sensor's read noise changes with readout mode, pixel rate and gain mode, so the value in a datasheet applies to the mode in which it was measured. Cooling reduces dark current strongly but read noise only weakly.

Common questions

Does read noise depend on exposure time?

No. It is added once per readout, which is why the SNR grows in proportion to exposure time in the read-noise limit and as its square root in the shot-noise limit.

What is the difference between read noise and dark noise?

Dark noise is the shot noise of thermally generated charge, $\sqrt{D}$, which grows with exposure time and temperature. Read noise is fixed per frame.

What read noise counts as low?

For photon-starved imaging, about 2 e⁻ or less: shot noise then dominates once the signal exceeds $\sigma_r^2$, 4 e⁻. Read noise far below one electron allows individual photoelectrons to be resolved in a pixel value.

References: J. R. Janesick, Photon Transfer: DN → λ (SPIE Press, 2007); J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, 2001); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).