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A selected set of points on the trajectories of charged particles traversing an electron‐optical system may be considered to be an object space, and another set an image space. Electron‐optical lenses are said to be ideally focused if the transformation of the points in object space to those in image space is one to one and continuous. A necessary condition for ideal focusing is used to prove that a number of electron‐optical systems require the presence of space charge in order to be ideally focused. Expressions for some ideally focused electron‐optical lenses are given, in particular those for cylindrical lenses without space charge derived from spherical lenses with space charge.