Achromatic and apochromatic lenses are not usually corrected for infra-red. When photo graphing with infra-red emulsions it is therefore necessary to rectify the focussing, this correc tion being made once and for all by methodical trial and error for each lens. As a rule the exten sion of the camera must be increased, after visual focussing, by o-3 to 0-4 per cent of its value.
For the study of other aberrations we shall suppose that chromatic aberration is eliminated by means of a colour filter.
47. Spherical Aberra tion. Among the aberra tions due to the spherical curvature of the lens surface, the name spher ical aberration is usually confined to that shown by light-rays at small inclinations to the axis.
If we suppose a lens divided into zones con centric to the optical axis, which can easily be realized in practice by means of diaphragms with annular apertures (Fig. 20) centred on the axis, the focal length of a convergent lens is found to diminish progressively from the central zone to the edge. For any posi tion of the screen or photographic plate between the extreme foci F and F" (Fig. 21), the image of a luminous point will be a circle, the bright ness of which diminishes from the centre to the This aberration can be diminished by limiting the surface of the lens to a single narrow zone (in practice, the central zone) by using a diaphragm, but it is obvious that the position of the sharpest focus will depend on the aperture of this diaphragm. The spherical aberration can also be diminished by suitable choice of curva tures of the lens. As a rule, spherical aberration is corrected by making the images produced by two zones of the lens coincide, generally the central zone and the extreme (marginal) zone, or one close to it. This correction, obtained by the employment of a more or less complex system in place of the single lens, is never absolute. In order to show the importance of residual aberrations a curve is drawn in the principal section, of which each point is defined (Fig. 22) by the intersection of the incident ray with a line drawn perpendicular to the axis through the corresponding focus (Fig. 22 indicates the aberration considerably exaggerated. It is usual to magnify the aberra tions, which in this case are those of a 4 in. lens, by 20).
An optical system rigorously corrected for this aberration is said to be (Greek free from error). As a matter of fact, no
photographic lens is rigorously aplanatic. It is possible to correct spherical aberration only for certain object distances, which are selected as being those at which the lens will most frequently be used, according to the purpose for which it is designed. In practice, the correction is sufficient for most requirements at intermediate distances. We shall see, however, that the residuals of this the rays of the meridian section converge, is then farther from the lens than the point C, to which the rays in the sagittal section converge.
If a screen (white paper, ground glass, etc.) is held perpendicular to the optical axis and gradually moved away from the lens, the beam emerging from the lens and originating in a aberration determine the distortion of the image.
48. Astigmatism. Astigmatism (Greek absence of point) is an aberration which is seen. in oblique pencils, and arises from the assyrn metry of the refraction in different sections of the beam ; the most obvious effect is the con. centration of light into two distinct foci.
To explain this effect, at least diagrammatic ally, consider the section of the lens made by a plane containing the secondary axis AilieB of an oblique pencil (Fig. 23A), and also the sequence of sections of the lens and of the pencil by planes perpendicular to the first plane and containing successive elements of the secondary axis, the different sections being projected on to the middle plane containing the interior portion A'B' of the secondary axis (Fig. 23B). In the first case (meridian section), the curvatures of the lens are less pronounced than in the second case (sagittal section). The point B, to which single point source will describe on the screen successively the following shapes : a circle (when the screen is in contact with the lens) ; ellipses becoming flatter and flatter with their long axes in the meridian plane, which degenerate to a. short straight line in that plane ; ellipses orient ated as before but becoming more and more circular ; a circle ; ellipses getting flatter and flatter, with their long axes in the sagittal plane ; a short straight line in the sagittal plane ; ellipses again. Fig. 24 represents this succession of " images " of a point source of light, consider ably exaggerated.