Off-axis parabolic elements have found application in Tera-Hertz imaging and new application in two-photon microscopy scan engines. Both these applications demand spatial and temporal precision in photon location. This modelling work examines how close off-axis parabolic elements are to the perfect image relay by calculating the geometrical performance metrics of spot diagrams, point spread functions and wavefront distortion for different arrangements of off-axis parabolas and a parabolic torus when compared to a close-coupled two mirror scan engine. Results identify the off-axis parabolic elements as a superior scan engine particularly in wide-field scan instruments. When within the optimum beam size versus parabola focus length ratio, the imaging of these systems is superb.
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