This paper proposes a new method to measure the 2-D beam transverse phase space with computerized tomography (CT) technique and Cerenkov radiation "double imaging method". The usual method with CT technique entirely depends on the quadrupole-scanning and can not get a full pi Radon rotation angle, which is essential to the Radon transform, the mathematic, fundamental of CT technique. Therefore, it has to prior assume a certain kind of phase space distribution to extrapolate the vacancy of Radon rotation angle, which makes the reconstructed image imperfect and yields errors especially when the phase space distributions practically are not ideal. In this paper, by means of Cerenkov radiation double image method and mathematical analysis, we obtain a full rotation angle of the beam phase space precisely from 0 to pi. Hence we can measure the actual 2-D transverse-phase-space density without making any prior assumptions about phase space distributions. The simulation results show that this new method is feasible and with much higher precision.
