Distortion of The Image

If now the image is sufficiently sharp, inasmuch as the rays proceeding from every object point meet in an image point of satisfactory exactitude, it may happen that the image is distorted, i.e. not sufficiently like the object.

This error consists in the different parts of the object being reproduced with different magnifications; for instance, the inner parts may differ in greater magnification than the outer (barrel-shaped distortion), or conversely (cushion-shaped distortion). This effect is called lens distortion or image distortion, and there are algorithms to correct it.

Systems free of distortion are called orthoscopic (orthos, right, skopein to look) or rectilinear (straight lines).

This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure.

If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g. a focusing screen, intersects the ray passing through the middle of the stop.

This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished; in practice, this generally occurs.

This ray, named by Abbe a principal ray (not to be confused with the principal rays of the Gaussian theory), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field.

Referring to fig. 8, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the scale or magnification of the image.

For N to be constant for all values of w, a' tan w'/a tan w must also be constant. If the ratio a'/a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i.e. tan w'/ tan w= a constant.

This simple relation is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named symmetrical or holosymmetrical objectives), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w' / tan w = 1.