Design of an omega filter for a 200 kV electron microscope

Abstract

An omega (Ω) filter has been designed to satisfy the following four constraints: (1) the dispersion at 200 kV is larger than 1 μm/eV, (2) the principal second-order aberration coefficients Aγγγ, Bγδδ are less than 1000 mm, (3) all of the inclination angles of the entrance and the exit faces of the sector magnets are within 0–45° (positive), and (4) the drift length between the first and the second magnet (or between the third and the fourth magnet) is less than the radius of the largest magnet. The latter two are practical requirements and are important for the experimental adjustment of the optical axis. The optimization of filter dimensions was made using a numerical electron trajectory method as follows: (1) The optical axis was found by calculating the central electron trajectories using a table of the fringing field distribution and a constant field strength inside the magnet. (2) The stigmatic focus condition was found by changing the inclination angles of the faces of the magnets. (3) The 18 secondary aberration coefficients [H. Rose, Optik 51, 15 (1978)] were numerically calculated. A three-dimensional trajectory calculation was made for the selected filter shape. A filter with a 1.3 μm/eV dispersion at 200 kV has been designed.