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Third‐order aberration theory of Wien filters for monochromators and aberration correctors
Author(s) -
TSUNO K.,
IOANOVICIU D.,
MARTÍNEZ G.
Publication year - 2005
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.2005.01443.x
Subject(s) - chromatic aberration , optics , physics , aperture (computer memory) , focus (optics) , spherical aberration , monochromator , quadrupole , diffraction , dipole , chromatic scale , lens (geology) , wavelength , atomic physics , quantum mechanics , acoustics
Summary 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: E 1 , B 1 ; quadrupole: E 2 , B 2 ; hexapole: E 3 , B 3 and octupole: E 4 , B 4 . The aberration coefficients are expressed under the second‐order geometrical aberration free conditions of E 2 = −( m + 2) E 1 /8R, B 2 = − mB 1 /8 R and E 3 R 2 / E 1 − B 3 R 2 / B 1 = m /16, where m is an arbitrary value common to all equations. Aberration figures under the conditions of zero x ‐ and y ‐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 when B 3 = 5 m 2 B 1 /144 R 2 and ( E 4 / E 1 − B 4 / B 1 ) R 3 = −29 m 2 /1152. In this special case, aberration figures contain only chromatic and aperture aberrations at the second focus. The chromatic aberrations become zero when m = 2 and aperture aberrations become zero when m = 1.101 and 10.899 at the second focus. Negative chromatic aberrations are obtained when m < 2 and negative aperture aberrations for m < 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.