To improve spatial and energy acceptance of multi-reflecting time-of-flight, open traps, and electrostatic trap analyzers, a novel ion mirror is disclosed. Incorporation of immersion lens between ion mirrors allows reaching the fifth order time per energy focusing simultaneously with the third order time per spatial focusing including energy-spatial cross terms. Preferably the analyzer has hollow cylindrical geometry for extended flight path. The time-of-flight analyzer preferably incorporates spatially modulated ion mirror field for isochronous ion focusing in the tangential direction.