The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e.
If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture - there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g.
Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.
Two " astigmatic image surfaces " correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second.
Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.