Abel Inversion Scheme for Marked Improvement of a Reflectron Time-of-Flight Mass Spectrometer

This letter describes a simple Abel inversion scheme for marked improvement of a reflectron time-of-flight (TOF) mass spectrometer having a reflecting electric potential U(X) along its central axis X. To maximize the resolving power, the inverse function X(U) was determined using the Abel inversion of the most-desirable TOF tau(E), which is a function of the total energy E. Based on the linear nature of the Abel transform, we could derive an additional condition necessary for the electrostatic realization of X(U). Our numerical results demonstrated the definite superiority of this approach compared with the conventional energy-focusing method.