When evaluating sensor performance, it’s useful to express all noise sources in terms of their equivalent number of input electrons: the physical signal that initiated the chain of image formation. This concept, known as input-referred noise, allows us to compare different sensors, modes, and ISOs on a consistent basis.
Image sensors measure light by converting incident photons into electrons in the pinned photodiode (PPD). These electrons are then:
- Transferred to a floating diffusion,
- Amplified (via source follower and PGA),
- Converted to digital representations (DN, or just counts) via ADC.
Noise can be introduced at any point downstream from the PPD. But to understand the true sensitivity and low-light performance of a sensor, we want to know: How many electrons’ worth of uncertainty does that noise represent?
The input-referred noise is the amount of signal (in electrons) at the PPD input that would account for the observed noise at the output.
Input-referred noise = Output noise (DN) ÷ Conversion gain (e⁻/DN)
This tells you how many electrons the downstream noise sources are “worth.”
The key to converting from digital numbers back to electrons is the conversion gain, often expressed in:
e⁻/DN (electrons per digital number), or its inverse: DN/e⁻
Conversion gain varies with analog gain, which is usually controlled by the ISO setting. At higher ISO, analog gain is increased before the ADC, so:
- The signal is amplified,
- Downstream (read) noise is amplified,
- But the number of electrons per DN decreases.
This means:
- At low ISO, 1 DN might represent 2–3 electrons.
- At high ISO, 1 DN might represent <1 electron.
So, when ISO changes, you must re-estimate conversion gain to properly refer the noise to the input.
How to Measure Input-Referred Noise
Step 1: Measure Output Noise (in DN)
Capture a dark frame or very low-exposure image and compute the standard deviation of pixel values in a flat region.
Step 2: Determine Conversion Gain
Use a photon transfer curve (PTC), or a flat-field pair method, to determine e⁻/DN at the ISO of interest.
Example: In the shot-noise-limited region of the PTC, the slope of variance vs. mean equals the inverse of the conversion gain:
CG = 1 / slope
Alternatively, some camera manufacturers publish CG values per ISO.
Step 3: Compute Input-Referred Noise
Divide the output noise by the conversion gain:
σ_input (e⁻) = σ_output (DN) × CG (e⁻/DN)
Let’s say at ISO 800, your measured read noise is 2.5 DN, and you’ve determined the conversion gain is 0.30 e⁻/DN:
σ_input = 2.5 DN × 0.30 e⁻/DN = 0.75 e⁻
That’s a clean readout: less than one electron’s worth of noise.
Now repeat the measurement at ISO 100, where CG might be 2.4 e⁻/DN. If the output noise is 1.2 DN:
σ_input = 1.2 DN × 2.4 e⁻/DN = 2.88 e⁻
So, although the digital read noise is lower at ISO 100, the input-referred noise is higher because the signal wasn’t amplified as much before digitization.
Why It’s Useful
- Sensor comparisons: Input-referred noise is intrinsic to the sensor — not affected by ADC bit depth or gain settings.
- ISO tuning: Helps determine which ISO setting gives the lowest effective read noise.
- System modeling: Allows unified noise budgets, since photon noise, read noise, and PRNU can all be expressed in electrons.
Input-referred noise connects the physical world of photons and electrons to the digital world of image files. It lets you answer the most meaningful question in sensor evaluation: How much uncertainty is there, in terms of the number of electrons, at the very beginning of the signal chain?
By combining dark frame measurements with conversion gain analysis, you can cut through ISO-related confusion and get to the true performance of your imaging system.
Leave a Reply