Possibility of detection of Earth-like exo-planets and recognition of their surface areas with a hypertelescope

Abstract

A possible variant of the direct observation of Earth-like planets with the help of a hypertelescope containing circular and/or annular collecting mirrors is considered. Analytical expressions describing the imaging in the focal plane are presented. They give the opportunity to estimate the influence of the photodetector pixel exposure time and accuracy parameters of the mirror control/stabilization system on the quality of the image in the plane of the photodetector and to evaluate a signal-to-noise ratio (SNR) at its output. Numerical results obtained for the hypertelescope containing 126 (for detection) and 1164 (for recognition) identical annular mirrors of diameter 1 m illustrate an opportunity of detecting an Earth-like exo-planet moving around a Sun-like star at a distance of 1 au and recognizing its surface area at a distance of 1 pc on conditions that some technique blocking out the radiation from the exo-planet’s star is used. Some dependencies of the corresponding SNR values on the pixel exposure time and the accuracy parameters of the mirror stabilization system are shown. Several typical aperture configurations are investigated for the case of recognition and the most appropriate configuration is defined.