## The aberrations of a quadrupole quadruplet projector |

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aberration integral method aberration terms analytic function antisymmetric quadruplet aperture aberrations aperture plane calculated charged particle chromatic aberrations CM rH composite field shape Computer Program derivatives determine the stigmatic Dhuicq discrepancy effective length electron microscope electron optical systems electron trajectory excitations exit plane experimental Fermat's principle focal lengths focal point position fringing fields Grivet Hawkes image plane individual quadrupoles inscribed radius ionally symmetric lens system magnetic quadrupoles magnification Measured Field octupole Optik order aberrations order geometrical aberrations outer doublet parameters paraxial equations plotted pole pieces power series method power series solution projector lens projector system properties quad quadru quadruplet system quadrupole system radial distortion range of focal ray tracing rectangular model refractive index Reisman rH rH rotation rotationally symmetric lens Runge-Kutta ruplet rupole Septier shown in Figure single quadrupoles st st stigmatic condition curve symmetric lenses symmetry planes third order geometrical