Bernoulli generalized likelihood ratio test for signal detection from photon counting images

Because exoplanets are extremely dim, an electron multiplying charge-coupled device 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 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. 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. In addition to 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 our work focuses on the example of detecting point source, the framework is widely applicable.