False alarm rate-based statistical detection limit for astronomical photon detectors

Lau A.W.K. Fung L.W.H. Fung L.W.H. Smoot G.F.
1 April 2025 SPIE

Journal of Astronomical Telescopes, Instruments, and Systems
2025 #11 Issue 2

In ultra-fast astronomical observations featuring fast transients on sub-μs time scales, the conventional signal-to-noise ratio (SNR) threshold, often fixed at 5σ, 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 established a probabilistic detection criterion applicable to high-speed detectors. The model is tested 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.

photon detectors , statistics , ultra-fast astronomy

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University of Toronto, Dunlap Institute for Astronomy and Astrophysics, Toronto, ON, Canada
Hong Kong University of Science and Technology, Jockey Club Institute for Advanced Study, Kowloon, Hong Kong
Durham University, Institute for Computational Cosmology, Centre for Extragalactic Astronomy, Durham, United Kingdom
Hong Kong University of Science and Technology, Jockey Club Institute for Advanced Study, Clear Water Bay, Kowloon, Hong Kong
Nazarbayev University, Energetic Cosmos Laboratory, Astana, Kazakhstan
University of California, Berkeley, Department of Physics, Berkeley, CA, United States
Université Sorbonne Paris Cité, Université Paris Diderot, Laboratoire APC-PCCP, Paris, France
Université de Paris, Laboratoire Astroparticule et Cosmologie, Paris, France
University of the Basque Country UPV/EHU, Donostia International Physics Center, San Sebastian, Spain

University of Toronto
Hong Kong University of Science and Technology
Durham University
Hong Kong University of Science and Technology
Nazarbayev University
University of California
Université Sorbonne Paris Cité
Université de Paris
University of the Basque Country UPV/EHU

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