PHOTOGRAPHIC LENSES
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of equal or unequal focal length. This is a simple case where the principle of symmetry applies, a principle of which great use is made in connection with other aberrations. It will be considered in more detail later.
It should be evident that little importance attaches to equality in the sizes of images of different colours when they occupy different planes. Accordingly, the chief attention should be given to the positions in which the images of various wave-lengths are formed, and if some latitude is necessary it may be given in a slight variation of magnification with the wave-length. Owing to the properties of the transparent materials available for the construction of lenses it will, as a rule, only be possible to secure exact agreement of focussing plane for two wave-lengths. The two regions it has been found most satisfactory to bring into agreement are the neighbourhood of the D lines of sodium and the G' line of hydrogen, the former being not far from the dominant wave-length for visual observation, and the latter near the wave-length to which the photographic emulsions are most sensitive. This method of correcting enables a view to be correctly focussed for photographic recording by visual examination of the image.
(ii.) Spherical Aberrations.1—The remaining defects are of the type known to the optician as the spherical errors. The amount of these will also depend on the wave-length. They should usually be corrected for a wave-length in the neighbourhood of G' rather than for D. If this is done the photographic record will present a better appearance than the visible image, and it may be a matter of importance to concentrate attention almost entirely o i the portion of the image in the neighbourhood of the lens axis when judging the best position of focus visually, If the correction were made in the alternative way the visible image would appear very pleasing and the photographic record distinctly disappointing. In lenses for special purposes this consideration may not apply.
(a) Distortion. — In consequence of the spherical errors the image of a point in the object formed by light of a given wave-length will not on a ray theory be a point, or in one case its position, if a point, will be displaced from that which it should occupy were the image an exact projection bf the object. This particular defect is known as distortion, and the displacement is necessarily directly towards or away from the point in which the image plane is met by the lens axis. Tho displacement may be represented mathematically by a series of odd powers of the distance the point would be from the axis
1 For a discussion of the expressions given helow for the various aberrations see " Lens Systems Aberrations of." '
were the defect absent. Thus, if y, z be the co-ordinates of a point in the image plane and we take the axis of y parallel to the direction in question, so that y represents that distance,
The coefficients alt a2, as . . . may be used as measures of the extent to which the defect is present, and are named the coefficients of distortion of the first, second, third . . orders. If the defect is serious it becomes obvious that lines in the image which correspond to straight lines in the object are appreciably curved. This want of straight-ness, as the above equation shows, gradually makes its appearance as the shortest distance between the line and the point of the image plane on the lens axis increases.
(b) Spherical Aberration. — Another aberration of a very simple kind is central spherical aberration, the " central " referring to the distinctive 'property that, though equally present in other parts of the field of view, it is only aberrations of this group which appear in images on the axis itself. This aberration consists essentially in the rays from narrow zones of the aperture, bounded by nearly equal circles centered on the axis, coming to foci on the axis which vary gradually from one zone to another. Tho rays which in an ideal lens should pass through a single point of the axis, in a lans suffering from this defect, will touch a caustic surface which has two branches, one being a surface of revolution about the axis and tho other a length of the axis itself. If y, if are the co-ordinatos of the point in which the ray meets tho stop, tho intersection of the ray with tho imago piano will bo displaced from its ideal position given by y, z, by a distance whoso rectangular oo-ordinatos 8y, 02 satisfy
where rz=i>)z + £z. As before, blt bz, ba . , . are aberration coefficients of the first, second, third . . . orders. In telescope objectives, the removal of this aberration is of outstanding importance, but it is common to find appreciable amounts of central spherical aberration present in good photographic lenses, the reason being that up to a certain point this defect is less harmful than some other aberrations which cannot in the particular design be removed simultaneously with this central aberration.
(c) Curvature and Oomatic Aberrations. — Between tho two simple aberrations considered in (a) and (6), there He a series of others whose number and character depends upon tho order of the aberration. Several of these have received names suggested by the shape of their trace in the image plane or by some othernsists of two similar components whether