Third-order aberration theory of Wien filters for monochromators and aberration correctors.

Third-order aberrations at the first and the second focus planes of double focus Wien filters are derived in terms of the following electric and magnetic field components– dipole:E₁,B₁; quadrupole:E₂,B₂; hexapole:E₃,B₃ and octupole:E₄,B₄. The aberration coefficients are expressed under the second-order geometrical aberration free conditions ofE₂ = −(m + 2)E₁/8R,B₂ = − mB₁/8RandE₃ R²/E₁ −  B₃ R²/B₁ =  m/16, wheremis an arbitrary value common to all equations. Aberration figures under the conditions of zerox- andy-axes values show very small probe size and similar patterns to those obtained using a previous numerical simulation[G. Martínez&K. Tsuno (2004)Ultramicroscopy,100, 105–114]. Round beam conditions are obtained whenB₃ = 5m² B₁/144R² and (E₄/E₁ −  B₄/B₁)R³ = −29m²/1152. In this special case, aberration figures contain only chromatic and aperture aberrations at the second focus. The chromatic aberrations become zero whenm = 2 and aperture aberrations become zero whenm = 1.101 and 10.899 at the second focus. Negative chromatic aberrations are obtained whenm<2 and negative aperture aberrations form< 1.101. The Wien filter functions not only as a monochromator but also as a corrector of both chromatic and aperture aberrations. There are two advantages in using a Wien filter aberration corrector. First, there is the simplicity that derives from it being a single component aberration correction system. Secondly, the aberration in the off-axis region varies very little from the on-axis figures. These characteristics make the corrector very easy to operate. [ABSTRACT FROM AUTHOR]