False Alarm Rate based Statistical Detection Limit for Astronomical Photon Detectors
Abstract
In ultra-fast astronomical observations featuring fast transients on sub-s time scales, the conventional Signal-to-Noise Ratio (SNR) threshold, often fixed at , becomes inadequate as observational window timescales shorten, leading to unsustainably high False Alarm Rates (FAR). We provide a basic statistical framework that captures the essential noise generation processes relevant to the analysis of time series data from photon-counting detectors. In particular, we establish a protocol of defining detection limits in astronomical photon-counting experiments, such that a FAR-based criterion is preferred over the traditional SNR-based threshold scheme. We developed statistical models that account for noise sources such as dark counts, sky background, and crosstalk, and establish a probabilistic detection criterion applicable to high-speed detectors. The model is testified against the on-site data obtained in the Single-Photon Imager for Nanosecond Astrophysics (SPINA) experiment and consistency is confirmed. We compare the performance of several detector technologies, including photon-counting CMOS/CCDs, SPADs, SiPMs, and PMTs, in detecting faint astronomical signals. These findings offer insights into optimizing detector choice for future ultra-fast astronomical instruments and suggest pathways for improving detection fidelity under rapid observational conditions.
Keywords
Cite
@article{arxiv.2409.15536,
title = {False Alarm Rate based Statistical Detection Limit for Astronomical Photon Detectors},
author = {Albert Wai Kit Lau and Leo W. H. Fung and George F. Smoot},
journal= {arXiv preprint arXiv:2409.15536},
year = {2025}
}