i.e. the focal length is still positive.

Astigmatism is closely related to the field of curvature. If the lens is not corrected for the astigmatism, the two paraboloidal image surfaces (tangential and sagittal) exist. At a given height the distance of the points on the Petzval surface and tangential surface is three times the distance between the points on petzval surface and sagittal surface.

Distortion

This lens aberration is due to the fact that the transverse magnification (lateral magnification) is function of the distance of object from the axis. The distortion arises areas of the lens have different focal lengths and different magnification. In the absence of any other aberration, ie. even if the all the image points are shjarply focused, the shape of the imahe distorts as shown in figure.