On Projective Connection of Optically Conjugate Points of Static Mass Analyzers

The Barber rule, known in the theory of sector static mass analyzers and connecting geometrically the axial point of an object and its electron-optical image (Gaussian points) in the case of a uniform field of a magnetic sector with a normal incidence, is generalized to the case of arbitrary geometries and fields of magnetic and electrostatic sectors. It is proved that the Gaussian points of the optical axis of the mass analyzer are connected by a bipolar projection through two points – the poles of this projection, located on the straight lines passing through the optical foci of the mass analyzer parallel to the input and output arms of the optical axis. The distances of these poles from the foci adjacent to them are subject to the well-known optical invariant of Newton.