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)/8R 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. Martinez & K. Tsuno (2004) Ultramicroscopy, 100, 105-114]. Round beam conditions are obtained when B(3) = 5m(2)B(1)/144R(2) and (E(4)/E(1) - B(4)/B(1))R(3) = -29m(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.
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