By adjusting the position of P to give a sharp focus for the intermediate zone cd, the central and marginal (ab) parts of the image can be considered nearly sharp. The useful field of the lens is then limited to the angle AOB.
the image of a square AAAA centred on the axis by a meniscus lens will be either a pin cushion shape BBBB (Fig. 30 or) barrel shaped CCCC, according to the position of the stop relatively to the lens. The deformation is greater the greater the angle the square subtends at the lens. Fig. 31 explains in a simple manner the mechanism of this phenomenon. According to the position of the stop, different portions of an oblique beam possessing aberration are used for forming the image, so that the concentration of light occurs at different distances from the axis, whilst for a pencil parallel to the axis the position of the image is independent of the position of the diaphragm. The more or less blurred images BBBB and CCCC result from the selection by the diaphragm of certain rays which, in its absence, would give an extremely blurred image combining these two partial images.' The distortion is reversed if the stop is placed behind instead of in front, from which the simple conclusion was arrived at that by placing the stop in the plane of symmetry of an objective formed The curvature of the field of anastigmats is always very much less than that of ordinary objectives. In the least favourable cases the radius of curvature of the field is at least four times the focal length.' 52. Distortion. It has long been known that of symmetrical elements the distortion would be zero. Although, in fact, distortion is reduced under these conditions, it will only be zero if such an objective (said to be rectilinear) is used symmetrically, i.e. when producing an image of a plane surface the same size. In fact, a symmetrical lens, when used with an angular field of 90° in the photography of distant objects, gives quite distinct pincushion distortion.
Actually, distortion is a very general pheno menon, being present (although to only a small extent) in lenses corrected for astigmatism and curvature of the field, and arises from spherical aberration of the nodal points, i.e. from a slight
variation in the position of these points accord ing to the obliquity of the axes considered. Fig. 32, where the nodal point aberration is considerably exaggerated, shows that in these circumstances the images abed of equidistant points ABCD cannot themselves be equidistant, the scale of the image (ratio of the object to the image) varying progressively from the centre to the edge. With pincushion distortion the scale increases from centre to edges, and the distortion is said to be with barrel dis tortion (negative) the scale decreases from the centre to the edge.
Aberration of the nodal points, like all manifestations of spherical aberration, is reduced by using smaller stops, which at the same time reduce the distortion.
With an unsymmetrical objective, the optician can remove distortion completely by a proper choice of the constructive elements at his dis posal,' for a given scale of image, chosen at will, or, what amounts to the same thing, for a definite object distance (e.g. for an infinitely distant object in lenses designed for aerial photography or landscape work ; object distance of several yards for portrait lenses ; scale approximately unity for process lenses). For every other distance or scale, distortion will be present (the more so with large-aperture lenses), although it may remain so small as only to be detected by laboratory Distortion, like the other aberrations, can be represented graphically. In Figs. 33A and 33B, drawn respectively for a symmetrical and an unsymmetrical lens respectively (both by the same maker, of equal excellence, and of the same aperture), the divisions of the vertical scale correspond to the angles made by the secondary axes with the principal axis, while the horizontal scale indicates percentage variation of scale, positive (+) or negative H. Two curves are shown for each lens, one for objects at infinity 00) and the other for an object photographed at a reduction of one-tenth (from E. Wander sleb).