SNRideal

SNRideal is a concept used in imaging, astronomy, and related fields to denote the theoretical maximum signal-to-noise ratio achievable by a system under ideal conditions. It represents the photon-shot-noise-limited limit, where the only source of uncertainty is the inherent randomness of photon arrival.

Under Poisson statistics, the number of detected photons from a source in a given exposure is N. The signal is N, and the noise is the standard deviation sqrt(N). Therefore, the ideal SNR is SNRideal = N / sqrt(N) = sqrt(N). If expressed in electrons, assuming unit quantum efficiency, SNRideal = sqrt(N_electrons). In practice, N reflects the combination of source flux, exposure time, telescope or instrument throughput, and quantum efficiency.

In real systems, several non-ideal factors reduce the observed SNR below SNRideal. Detector readout noise, dark current, sky or background light, flat-fielding errors, and calibration uncertainties all contribute additional noise terms. Instrumental stability and atmospheric or environmental variations can further degrade the actual SNR. Consequently, SNRactual ≤ SNRideal, with the gap growing as background or instrumental noise dominates.

SNRideal serves as a reference for exposure planning and performance evaluation. It helps researchers estimate the maximum achievable precision for a given source brightness and exposure time and to compare different detectors or observing strategies. However, it should be interpreted with the caveat that real-world conditions rarely achieve the photon-limited, noise-free ideal.