Image forming methods are proposed to obtain large demagnification factors by a three element quadrupole lens system. The inlet element of the lens system with axial length 2 L acts as a quadrupole singlet. Middle and outlet elements, both of equal length L, act as a quadrupole doublet. Their paraxial focusing characteristics are calculated based on a rectangular field model.
A virtual image is formed by the diverging singlet within the singlet system and a real image of the virtual one can be formed outside of the lens system by the converging doublet. Magnification factors of the final image are about ten times smaller for the same object and image distances than those obtained by a symmetrical triplet having an equal total lens length to the above system. The accuracy is discussed, compared with those based on a modified bell-shaped model. The parameters of the model are determined from the potential distribution measured by an electrolytic tank method.