Abstract
It is shown that a concave axially symmetric electrostatic mirror can be found with a high enough ratio of chromatic aberration to spherical aberration to allow it to be used as an electron spectrometer. The potential field is given in terms of a finite Fourier-Bessel series. Using only three nonzero Fourier coefficients, a field can be specified that allows—in the case of a point source located within the mirror field—an energy resolution of 0.003% [full width at half maximum (FWHM)] and a transmission of 0.6% of 2π steradians to be obtained. This field can be used as a starting point in an optimizing procedure reported earlier by the author, to increase the transmission or adapt the spectrometer for use with sources of finite dimensions.
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