This section is from the book "Complete Self-Instructing Library Of Practical Photography", by J. B. Schriever. Also available from Amazon: Complete Self-Instructing Library Of Practical Photography.
The Field Of The Lens. The field of a lens may be defined as the surface (imaginary) on which the image is formed. This must not be confounded with the surface (sensitive or otherwise) on which we intercept the image. A surface in geometry is considered to be made up of innumerable points. The image-bearing rays emanating from innumerable points on the object, form correspondingly innumerable image points, and we can imagine a surface made up of those image points. Now let us suppose that we point our lens at right angles to a flat object. The surface of this object we consider to consist of innumerable, infinitely small points from each one of which a set of rays enters the lens. Their course is so controlled that each set of rays is conveyed to one point, and all the points together constitute the surface which we term the field of the lens. As each point is an image point, we also say that the image is formed on that surface. If all the points are in one plane, that is, if they form a flat (plane) surface, we say that the field of the lens is flat, and the image is flat. In other words, a lens has a flat field when it is capable of producing a flat image of a flat object. Perfect flatness over the whole field of a lens has not yet been attained, the field of all lenses being more or less curved, concave towards the lens; but the best modern lenses come very near perfection.
Curvature Of The Field. After what has just been said, the term curvature of the field will hardly require any explanation. Fig. 8 shows a curved image of a straight object. If the object were a flat surface, it is evident that the image would be saucer like in shape. This defect is to a very great extent inherent in lenses of the old type, as flattening of the field in those lenses can be effected only to a very limited extent without causing too much astigmatism.
594. The disadvantage of a curved field is apparent from Fig. 9. The surface on which we project the image being flat, it would evidently be impossible to find a position for it where the different portions of the image would be rendered equally sharp, or even nearly so. In the plane of "c" the center only would be in focus; in the plane of "a" the margin only; and intermediate positions, as "b" for instance, would give us only intermediate portions of the image sharp. Reducing the aperture of the lens (stopping down) and thus gaining depth of focus, we might find an intermediate position where the whole image would be fairly well rendered; but as reduced aperture means reduced speed of the lens, the effort of the lens maker has been directed towards giving the lens as flat a field as possible without impairing its perfection in other respects. The flatter the field the larger is the area over which it will coincide with the flat surface on which the image is projected, consequently the greater is the covering power of the lens, providing it is at the same time capable of giving critical definition, over that area.