Improving the energy resolution of a hemispherical spectrograph using a paracentric entry at a non-zero potential

We demonstrate by ray tracing analysis that the focusing properties of a hemispherical spectrograph depend critically on the placement of the electron entrance position R0 and the value of the potential V0 at R0. Improvements over conventional spectrographs using R0=R̄, the mean radius and V0=0 are predicted for particular combinations of R0 and V0. A spectrograph with R̄=101.6 mm and an entrance at R0=82.55 mm using a zoom lens and a two-dimensional position sensitive detector (2D-PSD) with 40 mm multichannel plates and resistive anode encoder has been used to confirm the predicted qualitative behaviour. These results suggest that improvement in energy resolution may be attained without the use of fringing field correctors.