Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which the focus changes from the center to the edge of the field of view.
In the presence of astigmatism, this problem is compounded because there are two separate astigmatic focal surfaces.
Field curvature varies with the square of field angle or the square of the image height. Therefore, by reducing the field angle by one-half, it is possible to reduce the blur from field curvature to a value of 0.25 of its original size.
Positive lens elements usually have inward curving fields, and negative lenses have outward curving fields. Field curvature can thus be corrected to some extent by combining positive and negative lens elements. Lenses with virtually no field curvature are called flat-field lenses.