TMA, or three mirror anastigmats, have already been used successfully for various space missions. In the frame of earth observation, ProbaV satellite uses 3 TMAs to cover a total 102.4° field-of-view; ground sampling distance is about 100m at the center of field-of view and 370m at the edge. For future earth observation missions, the goal would be to reach 100m spatial resolution all over the 102.4° FOV. This would require to up-scale optical specifications, thus increasing geometrical aberrations. FMA, or four mirror anastigmats, could thus be a good candidate for future missions, as a fourth mirror would allow better correction of optical aberrations. In this work, TMA and FMA have been optimized over different fields-of view. Performance limitations are then derived, which show that FMA seems promising for future missions. Radiometry aspects are discussed and preliminary tolerance analysis is carried out.