  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.
