Sensor Noise: How to Measure the Invisible express

Original: "Valley-Peak Modulation in Phase Space: an Exposure-Invariant VPM and its Theta-Function Structure"
arXiv:2603.01199 · 2026-03-01 · CC BY 4.0 · 1 min
Scientists have found a way to measure the tiniest camera noise, independent of light brightness.

You are counting sand grains falling in an hourglass, but each time the wind adds or removes a few. In the most sensitive cameras, the task is similar: you need to figure out how many "sand grains" (electrons) the sensor itself added, and how many came from light. This inherent sensor noise is called readout noise, and it hinders seeing weak signals — for example, the light of a distant star.

Usually, readout noise is measured by varying light brightness, but that's like trying to catch the wind. The authors found a way to bypass this dependence. They noticed that if you look not at the signal values themselves but at how they "wrap around" after each integer number of electrons, you get a pattern that depends only on the sensor noise. This pattern resembles a repeating ornament on a clock face — the hand may point to different numbers, but the clock face itself is unchanged.

In the most sensitive sensors, readout noise is less than one electron, like a scale that could weigh a single sand grain but itself trembles slightly.

This approach resembles an old trick: to measure the trembling of a hand more accurately, you look not at its position but at how it passes the same divisions many times. The scientists derived a simple formula linking this pattern to readout noise and tested it on a computer model. Now cameras can be calibrated faster and more accurately, without adjusting for light brightness.

In the most sensitive CMOS sensors, readout noise can be less than one electron: that's like hearing a single sand grain fall in a noisy room.

R(\sigma) = \frac{\vartheta_4(q)}{\vartheta_3(q)}, \quad q = e^{-2\pi^2\sigma^2}
The ratio of Jacobi theta functions, where $\sigma$ is the readout noise in electrons; this quantity is independent of exposure and determines the sensor noise.
Scientists
David DeutschErwin SchrödingerJohn Stewart BellLouis de BroglieLov GroverPaul Benioff
Concepts
volt per metre volume optically detected magnetic resonance modulation frequency modulation valley phase noise