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Field curvature is an aberration (distortion) in the image of some optical instruments (such as some telescopes), in that it brings the image to focus at a curved surface-shape rather than a flat shape (i.e., plane). A flat sensor within a telescope that suffers from this can be placed so the sensor's center has the best focus, or can be placed so that a concentric ring around the center has the best focus. The rest of the image projected on the sensor will be fuzzier.
A Schmidt telescope has considerable field curvature, a choice in its design to gain other advantages. Its spherical mirror produces spherical aberration, and a lens (the Schmidt corrector plate) reduces the spherical aberration but leaves it with substantial field curvature. The design's advantage is an easier-to-manufacture mirror, and a good image despite a short focal length giving it a large field of view suitable for surveys. I believe special curved photographic plates were used with them, but the CCDs more-recently used are generally flat. I read that one current strategy is an additional lens which reduces the field curvature (a field flattener lens).