Curvature of Field
The image of an extended plane object due to a single lens is not a flat one but will be a curved surface. The central portion of the image nearer the axis is in focus but the outer regions of the image away from the axis are blurred. This defect is called the curvature of the field. This defect is due to the fact that the paraxial focal length is greater than the marginal focal length. This aberration is present even if the aperture of the lens is reduced by a suitable stop, usually employed to reduce spherical aberration, coma and astigmatism. Fig illustrates the presence of curvature of the field in the image formed by a convex lens. A real image formed by a convex lens curves towards the lens and a virtual image curves away from the lens. Fig. 3 represents the curvature of the field present in the image formed by a concave lens.
For a system of thin lenses the curvature of the final image can, theoretically, be given by the expression
where R is the radius of curvature of the final image, 
and ƒn are the refractive index and focal length of the nth lens. For the image to be flat, R must be infinity.
Correspondingly, the condition for two lenses placed in air, reduces to
This is known as Petzwal’s condition for no curvature. This condition holds good whether the lenses are separated by a distance or placed in contact. As the refractive indices 
and 
are positive, the above condition will be satisfied if the lenses are of opposite sign. If one of the lenses is convex, the other must be concave.
Astigmatism and coma are completely eliminated if the primary and secondary image surfaces are coincident and plane. In this case, the surface of best focus will also be a plane one. But this cannot be achieved with a single lens. Astigmatism or curvature of the field can be minimized by introducing suitable stops on the lens axis. If the primary and the secondary image surfaces are made to have equal and opposite curvatures the surface of best focus will be plane and midway between them. Astigmatism will, however, be present. Astigmatism can be eliminated by having the same curvature for the primary and the secondary image surfaces. In this case curvature of the field will be present. Correction for coma is more important than astigmatism for object points having comparatively small angular distances from the axis. Hence, telescope objectives, whose field of view is small are corrected for coma rather than for astigmatism. On the other hand a camera lens of wide field has to be necessarily corrected for astigmatism.
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