For an autostereoscopic 3D TV display seen directly on Braun tube without glasses, it is desirable that Braun tube having curved face plate could be used, because there are established technologies which enable deflection and focusing of an electron beam with higher precision. But, little are known about the structure of observer's space supplied with such a shaped lenticular sheet fitting over a curved face plate of Braun tube. Recently, experimental observations have been done by using a high resolution beam-index Braun tube having a composite lens-plate which is shaped along the curved surface of the tube. This paper explains the conditions which are required for the display space to be suitable for autostereoscopic 3D images. Using a mathematical model of the composite lens-plate and approximate values of parameters of the experimental lens-plate and Braun tube, characteristics of the space are numerically investigated. Preliminary results reveal that the space having an equivalent projection lens array behind the face of the composite lens-plate can be obtained, as was experimentally observed. The influences of lenslet defocusing and lenslet aberrations are numerically explained.