Curvature of the Field

Even if the deformation of image due to Spherical aberration, COMA and astigmatism are corrected, the image still suffers deformation due to the curvature of the field., ie. The image of a planer object normal to the axis of the lens is not planer in the image space. Only in the paraxial region, the image is planer and normal to the axis. Away from this region, the image plane is a curved surface.

Consider a curved object O as shown in figure, whose image I is also curved, both coaxial with the axis of the lens. Now, if the curved object is flattened as O', ie the points away from the axis of the lens are moved away from the center of lens (you may assume that object distance u is increasing for these point), the corresponding image points will move towards the lens (equivalently, the image distance v decreases) . The loci of all the image points thus forms a paraboloidal surface, known as Petzval Surface P. The aberration is known as Petzval field curvature. For a concave lens (negative focal length), the paraboloidal surface is reversed.

The displacement of an image point at a height on the petzval surface from the paraxial plane is given as