We perform experimental and theoretical study of the parallel-series arrays of Cold-Electron Bolometers (CEBs) integrated into a cross-slot antenna and composed with an immersion silicon lens. The purpose is to determine the absorption efficiency, the responsivity and the noise equivalent power (NEP) of the bolometers. The absorbed power has been found in two independent ways. The comparison of two approaches gives better understanding of the system and secures from misinterpretations. The first approach is fitting of the bolometer IV curves with solutions of heat-balance equations. The second approach is modeling of electromagnetic properties of the system, including an antenna, lens, optical can, band-pass filters and black body source. The difference between both methods does not exceed $30%$. The optimization of experimental setup is proposed to approach the photon limited detection mode.
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