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A two dimensional coma-corrected zoned mirror has been investigated by a rigorous integral equation formulation, for whose solution a procedure of successive approximation can be established. For computational convenience, the exact first order solution is again approximated. The error committed in this approximation is investigated. The higher order solutions due to couplings between zones are not significant so far as the image field is concerned. In the example studied, it is found that for a system with small -number and an illumination of small taper the coma aberration of this zoned mirror is practically eliminated for scan angles up to , in sharp contrast to a smooth parabola whose scanning characteristics are also presented for comparison. However, the chromatic aberration overshadows this advantage for a wide-band application; the total bandwidth of this example is only a few per cent.