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

Abstract

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. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Signal-to-noise ratio for photon counting after photometric corrections

“…The goal is to get a more accurate approximation to the desired SNR in Eq. (9). First, the application of Nemati's algorithm for photometric corrections to data is considered, and then the theoretical SNR, which effectively expresses the desired mean electron rate in terms of observable variates, is computed.…”

“…The Roman Telescope’s CGI will use photon counting and employ photometric corrections so the error budget requirements are met 7 . Methods of signal extraction from photon-counted observations have been studied in the literature 8 , 9 . Bijan Nemati 5 introduced an algorithm that estimates the mean number of electrons for a given detector pixel to within the requisite 0.5% accuracy with respect to the true mean.…”

“…7 Methods of signal extraction from photon-counted observations have been studied in the literature. 8,9 Bijan Nemati 5 introduced an algorithm that estimates the mean number of electrons for a given detector pixel to within the requisite 0.5% accuracy with respect to the true mean. The relationship between the mean electron rate and the number of counts out of the gain register is nonlinear, and an algorithm is required to correct for this nonlinearity.…”

Information-theoretical Limits of Recursive Estimation and Closed-loop Control in High-contrast Imaging

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