Grazing incidence toroidal mirror pairs in imaging and spectroscopic applications

The optical performance of pairs of toroidal mirrors in grazing incidence has been studied analytically and numerically. Two types of toroidal surface are possible: football and bicycle tire. In grazing incidence and for configurations that compensate up to second-order aberrations, there are significant differences in performance between the two types. For football-type tori the best configuration appears to be Z-shaped with tangential and sagittal foci at the middle point between the mirrors. For bicycle tire-type tori the best configuration is U-shaped with the tangential focus at the middle point and the sagittal at infinity.