Petzval’s curvature, named after 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 exacerbated because there are two separate astigmatic focal surfaces.
The field curvature varies with the square of the field angle or the square of the image height. Therefore, by reducing the field angle by half, it is possible to reduce the blur caused by field curvature to a value of 0.25 of its original magnitude. Positive lens elements typically have inward curving fields, and negative lenses have outward curving fields. Field curvature can therefore be corrected to some extent by combining positive and negative lens elements. Lenses with virtually no field curvature are called flat-field lenses.