Exposure-Referred Signal-to-Noise Ratio for Digital Image Sensors

The signal-to-noise ratio (SNR) is a fundamental tool to measure the performance of an image sensor. However, confusions sometimes arise between the two types of SNRs. The first one is the output-referred SNR which measures the ratio between the signal and the noise seen at the sensor's output. This SNR is easy to compute, and it is linear in the log-log scale for most image sensors. The second SNR is the exposure-referred SNR, also known as the input-referred SNR. This SNR considers the noise at the input by including a derivative term to the output-referred SNR. The two SNRs have similar behaviors for sensors with a large full-well capacity. However, for sensors with a small full-well capacity, the exposure-referred SNR can capture some behaviors that the output-referred SNR cannot. While the exposure-referred SNR has been known and used by the industry for a long time, a theoretically rigorous derivation from a signal processing perspective is lacking. In particular, while various equations can be found in different sources of the literature, there is currently no paper that attempts to assemble, derive, and organize these equations in one place. This paper aims to fill the gap by answering four questions: (1) How is the exposure-referred SNR derived from first principles? (2) Is the output-referred SNR a special case of the exposure-referred SNR, or are they completely different? (3) How to compute the SNR efficiently? (4) What utilities can the SNR bring to solving imaging tasks? New theoretical results are derived for image sensors of any bit-depth and full-well capacity.