RECONSTRUCTIVE CORRECTION OF ABERRATIONS IN NUCLEAR-PARTICLE SPECTROGRAPHS

A method is presented that allows the reconstruction of trajectories in particle spectrographs and the reconstructive correction of residual aberrations that otherwise limit the resolution. Using a computed or fitted high order transfer map that describes the uncorrected aberrations of the spectrograph, it is possible to calculate a map via an analytic recursion relation that allows the computation of the corrected data of interest such as reaction energy and scattering angle as well as the reconstructed trajectories in terms of position measurements in two planes near the focal plane. The technique is only limited by the accuracy of the position measurements, the incoherent spot sizes, and the accuracy of the transfer map. In practice the method can be expressed as an inversion of a nonlinear map and implemented in the differential algebraic framework. The method is applied to correct residual aberrations in the S800 spectrograph which is under construction at the National Superconducting Cyclotron Laboratory at Michigan State University and to two other high resolution spectrographs.