Page 83 - Modern Optical Engineering The Design of Optical Systems

66 Chapter Four

Figure 4.6 (a) The Scheimpflug condition can be used to
determine the tilt of the image surface when the object sur-
face is tilted away from the normal to the optical axis. The
magnification under these conditions will vary across the
field, producing “keystone” distortion. As diagramed here,
the magnification of the top of the object is larger than that
of the bottom. (Compare the ratio of image distance to object
distance for the rays from the top and bottom of the object.)
(b) Keystoning can be avoided if the object and image planes
are parallel. The figure shows how the “projection axis” can be
tilted upward without producing keystone distortion.

Note that in general a tilted object or image plane will cause what is
called keystone distortion, because the magnification varies across the
field. This results from the variation of object and image distances
from top to bottom of the field. This distortion is often seen in overhead
projectors when the top mirror is tilted to raise the image projected
on the screen. This is equivalent to tilting the screen. As shown in
Fig. 4.6b, keystone distortion can be prevented by keeping the plane of