An inverse design of magnetic focussing coil for electrostatic and magnetic imaging is investigated in this paper. For the inverse problem of designing magnetic coil

a mathematical model has been developed

an optimization method called BFGS has been introduced and an universal programme using FORTRAN language has been drawn up in the paper. On the basis of computational results

a magnetic focussing coil with four variable magnifications and a prototype tube of electrostatic and magnetic imaging without image rotation have been made

the results show that the computational and measuring values of axial magnetic induction coincide with the theoretical ones. It fully proves that the theory of electrostatic and magnetic imaging without image rotation and the method of inverse design described here are correct.