In most cases, when you design an optical system such as a camera lens, you require that the lens form an image of a scene on a flat surface. For example, Fig. 8.1 shows the imaging of an object at infinity onto a flat paraxial image plane by a perfect lens, i.e., one with no aberrations. However, the image surface for a real lens is not a plane but a curved surface whose z-axis departure from a flat paraxial image plane represents an image surface error for the lens called Petzval curvature. If the image plane is a curved surface (consider the shape of your retina), Petzval curvature may not cause any problem. However, because the majority of modern sensors are flat, not curved, Petzval curvature must be managed when designing a lens.

This chapter explores Petzval curvature and a second image-surface aberration, distortion, in more detail. Distortion is an image-surface error that does not blur the image but causes errors in the chief ray locations in the x-y plane, resulting in a change in magnification with image height. This results in a stretched (or compressed) image of the object.

8.1 Field Curves

As was shown in the previous chapter, an aplanatic lens exhibits little spherical aberration or coma, and the focal images reside on curved surfaces. Restore the OSDaplanat and trace three transverse ray fans YAN 0 7 10; VIE; FAN 9; GO. Figure 8.2 shows that the image points for the off-axis object points focus in front of the paraxial image plane defined by the on-axis ray fan. Although we could trace additional fans at other angles to get a better of picture of the image surface error, they won't add much to what is already demonstrated in Fig. 8.2. This same information was presented in a different manner by the transverse ray curves for the lens shown in Fig. 7.8. In those curves, the slope of the tangential curves increases with an increasing field. This indicates that the lens focuses farther away from the paraxial image plane with increasing angles. The same is true for the sagittal image surface, although the changes are less.