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tion at right angles to A B through the oblique pencil is known as the secondary or equatorial section C D of the same oblique pencil. Proceeding now to follow the course of the rays after the oblique pencil has been refracted by the lens, we note that the rays of the equatorial section C D come to a focus at I in the form of a line, which radiates from the axis, while the rays of the meridian section A B, come to a focus further back at II as a horizontal line which is at right angles to the radial line at I, or, more strictly, it is tangential with respect to the circular image field. At the position I, therefore, we have vertical, or radial elements of the object in focus and horizontal details blurred beyond recognition, while at II we have horizontal, or tangential, object elements sharply delineated but the vertical elements hopelessly out of focus. Somewhere between I and II is a position of minimum indistinctness which is known as the circle of least confusion, and would represent the best marginal definition attainable with the uncorrected lens.
Fig. I
The converging of oblique pencils to two focal-lines is not the only consequence of oblique refraction, however, for the respective radial and tangential lines are located on two very curved surfaces, as the diagram shows, and these curved image-surfaces only coincide at the axis of the lens. The difference between the curvatures of the I and II astigmatic image-surfaces is known as the astigmatic difference, which increases with increasing angles of obliquity of the incident rays. This deformation of the image-surfaces, i. e., their departure from the flatness of an ideal focal-plane is known as curvature of the image-field, and it is found desirable when correcting an objective for the removal of astigmatism to abolish the astigmatism and the curvature of the field simultaneously.
By suitable design and choice of the glasses, an objective may be made which brings the I and II image-surfaces into contact, whereupon the lens is free from astigmatism and renders a sharp image, but this single anastigmatic image-field may still be a very considerably curved surface. It is therefore the aim of the optical computer to render the field flat and perpendicular to the axis at the theoretical focalplane simultaneously with the bringing together of the I and II image