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

Abstract

Direct imaging of exoplanets is challenging; the flux ratio between an Earth-like exoplanet and its Sun-like host star is around ${10}^{-10}$ in reflected light at visible wavelengths.¹ A starshade or internal coronagraph can suppress the starlight and leave only the planet’s light to be detected; however, the planets are extremely faint and detecting them is still a challenge. An Earth-like planet ranges from 28th to 30th magnitude or fainter. As a result, the signal can be smaller than the camera read noise. An electron multiplying charge-coupled device (EMCCD) can alleviate this problem by amplifying the signal in an electron-multiplication (EM) register, thus reducing the effective readout noise to less than 1 electron.² Unfortunately, at the same time, a new noise is introduced—the multiplicative noise from the amplification process. This can be overcome by operating in photon counting (PC) mode. PC mode reports a value of 1 or 0 in each pixel for each integration time by thresholding the value at the final stage. The value reported in the pixel is 1 if the number of electrons in a pixel is bigger than a chosen threshold and 0 otherwise. The binary value only indicates the existence of photons in the pixels during the integration time but does not reveal the exact number of those photons, so we need to choose the exposure time such that the expected photon count in any pixel is much less than 1.³ Examples of simulated PC images are shown in Fig. 1 (all the simulations mentioned in this work use a 1-s integration time) and details on the generation of simulated images can be found in Ref. 4.