  Because exoplanets are extremely dim, an Electron Multiplying Charged Coupled
Device (EMCCD) operating in photon counting (PC) mode is necessary to reduce
the detector noise level and enable their detection. Typically, PC images are
added together as a co-added image before processing. We present here a signal
detection and estimation technique that works directly with individual PC
images. The method is based on the generalized likelihood ratio test (GLRT) and
uses a Bernoulli distribution between PC images. The Bernoulli distribution is
derived from a stochastic model for the detector, which accurately represents
its noise characteristics. We show that our technique outperforms a previously
used GLRT method that relies on co-added images under a Gaussian noise
assumption and two detection algorithms based on signal-to-noise ratio (SNR).
Furthermore, our method provides the maximum likelihood estimate of exoplanet
intensity and background intensity while doing detection. It can be applied
online, so it is possible to stop observations once a specified threshold is
reached, providing confidence for the existence (or absence) of planets. As a
result, the observation time is efficiently used. Besides the observation time,
the analysis of detection performance introduced in the paper also gives
quantitative guidance on the choice of imaging parameters, such as the
threshold. Lastly, though this work focuses on the example of detecting point
source, the framework is widely applicable.
