We analyse the optimal conditions for operation of a time-dependent magnetic field lens recently proposed. The lens consists of an axially symmetric ellipsoidal coil producing a spatially homogeneous but time-pulsating magnetic field. This system is capable of focusing a beam of charged particles drifting parallel to the coil axis as well as forming images of an object emitting electrons. This lens has no spherical aberration and, consequently, opens the possibility of surpassing the resolving power of conventional round static field lenses. The cardinal elements of this lens are functions of time and thereby the image position, its magnification factor and orientation change in time. We show how by a suitable choice of the magnetic field pulse parameters and the introduction of screens with circular apertures, it is possible to render all the image characteristics stationary. The effect of diffraction is also discussed in the context of transfer function theory.