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We present experimental studies of terahertz radiation detection by InP double heterojunction based transistors. We analyze the relation between their static characteristics and the experimentally determined voltage and current responsivities, showing importance of internal device parasitic capacitances and the external circuit loading effects. Finally, we demonstrate the use of these transistors for terahertz radiation computed tomography leading to 3D visualization of concealed objects. Our results pave the way towards wide use of heterojunction based transistors for terahertz imaging.