The Signal-to-Noise Ratio for Photon Counting After Photometric Corrections

TL;DR

This paper derives analytical expressions for the signal-to-noise ratio in photon counting with EMCCDs, considering photometric corrections, aiding the planning of astronomical observations with the Nancy Grace Roman Telescope.

Contribution

It provides the first explicit analytic formulas for SNR in photon counting with photometric corrections, enhancing observational planning accuracy.

Findings

Derived SNR expressions before and after photometric corrections.

Facilitates improved observation planning for the Nancy Grace Roman Telescope.

Clarifies the impact of photometric corrections on SNR calculations.

Abstract

Photon counting is a mode of processing astronomical observations of low-signal targets that have been observed using an electron-multiplying charge-coupled device (EMCCD). In photon counting, the EMCCD amplifies the signal, and a thresholding technique effectively selects for the signal electrons while drastically reducing relative noise sources. Photometric corrections have been developed which result in the extraction of a more accurate estimate of the signal of electrons, and the Nancy Grace Roman Telescope will utilize a theoretical expression for the signal-to-noise ratio (SNR) given these corrections based on well-calibrated noise parameters to plan observations taken by its coronagraph instrument. I derive here analytic expressions for the SNR for the method of photon counting, before and after these photometric corrections have been applied.