Mechanical Aberrations of a Magnetic Quadrupole Quadruplet Lens

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Abstract
The mechanical aberrations of a system of two or more magnetic quadrupoles have been studied. Displacement, rotation, and tilting of one quadrupole, and the effects of radial and rotational errors in alignment of one pole are considered as well as the inhomogeneity of the material used in the system. The changes in field distribution introduced by these errors are calculated and the corresponding aberration formulas are derived. As a particular case, the mechanical aberrations of a quadruplet projector, are computed. The construction tolerances are estimated for an allowable image defect (magnification error) of 3% in the radial and rotatinoal directions. The calculations indicate that the projector system can be used in an electron microscope without excessive image defects. The image is most sensitive to rotational misalignment with a required tolerance of ±2×10−3 rad.

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