Improvement of a second-order focusing toroidal spectrometer by use of a pre-collimating lens

This paper presents a method for improving the performance of a second-order focusing toroidal spectrometer using a pre-collimating lens. Simulation results predict that the degree to which the energy resolution can be improved depends on the relative size of the lens. For a pre-collimating lens having a radius 180 times smaller than the spectrometer radius, the relative energy resolution is predicted to improve by an order of magnitude. The simulated relative energy resolution of the spectrometer with such a pre-collimating lens is 0.021% for an entrance aperture angular spread of ±6°, and 0.088% for an entrance angular spread of ±10°.