False Alarm Rate based Statistical Detection Limit for Astronomical Photon Detectors

TL;DR

This paper introduces a statistical detection limit framework based on false alarm rates for ultra-fast astronomical photon detectors, addressing limitations of traditional SNR thresholds in high-speed observations.

Contribution

It develops a probabilistic detection criterion that accounts for various noise sources and demonstrates its application to different detector technologies in ultra-fast astronomy.

Findings

The model accurately predicts detection limits under various noise conditions.

Comparison of detector technologies reveals their relative performance in high-speed detection.

The framework improves detection fidelity in ultra-fast astronomical observations.

Abstract

In ultra-fast astronomical observations featuring fast transients on sub-$\mu$s time scales, the conventional Signal-to-Noise Ratio (SNR) threshold, often fixed at $5\sigma$, 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.