axis have been removed, then the image shown in fig. 19 results.
 Fig. 29.—The lens is spherically corrected for OO′, but the sine-condition is not fulfilled. Hence the different magnifications of a point O1 beyond the axis. |
The cones of rays issuing from a point situated only a little to the side, which traverse different zones of the objective, have a different magnification. The sine-condition can therefore also be understood as follows: that all objective zones must have the same magnification for the plane-element.
 Fig. 30.—O′ is the virtual image of O formed at a spherical surface of centre C and radius CS. |
According to Abbe, a system can only be regarded as aplanatic if it is spherically corrected for not only one axial point, but when it also fulfils the sine-condition and thus magnifies equally in all zones a surface-element situated vertically on the axis at this point.
A second method of correcting the spherical aberration depends on the notion of aplanatic points. If there are two transparent substances separated from one another by a spherical surface, then there are two points on the axis where they can be reproduced free from error by monochromatic light, and these are called “aplanatic points.” The first is the centre of the sphere. All rays issuing from this point pass unrefracted through the dividing surface; its image-point coincides with it. Besides this there is a second point on the axis, from which all issuing rays are so refracted at the surface of the sphere that, after the refraction, they appear to originate from one point—the image-point (see fig. 30). With this, the object-point O, and consequently the image-point O′ also, will be at a quite definite distance from the centre. If however the object-point does not lie in the medium with the index n, but before it, and the medium is, for example, like a front lens, still limited by a plane surface, just in front of which is the object-point, then in traversing the plane surface spherical aberrations of the under-corrected type again arise, and must be removed. By homogeneous immersion the object-point can readily be reduced to an aplanatic point. By experiment Abbe proved that old, good microscope objectives, which by mere testing had become so corrected that they produced usable images, were not only free from spherical aberrations, 'but also fulfilled the sine-condition, and were therefore really aplanatic systems.
The second aberration which must be removed from microscope objectives are the chromatic. To diminish these a collective lens of crown-glass is combined with a dispersing lens of flint; in such a system the red and the blue rays intersect at a point (see Aberration). In systems employed for visual observation (to which class the microscope belongs) the red and blue rays, which include the physiologically most active part of the spectrum, are combined; but rays other than the two selected are not united in one point. The transverse sections of these cones of rays diverge more or less from the transverse section of the chosen blue and red cones, and produce a secondary spectrum in the image, and the images still appear to have a slightly coloured edge, mostly greenish-yellow or purple; in other words, a chromatic difference of the spherical aberrations arises (see fig. 31). This refers to systems with small apertures, but still more so to systems with large ones; chromatic aberrations are exceptionally increased by large apertures.
 Fig. 31.—Showing a system with chromatic difference of spherical aberration. O′′＝image of O for red light; O′′′ for blue. The system is under-corrected for red, and over-corrected for blue rays. |
The new glasses produced at Schott’s glass works, Jena, possessed in part optical qualities which differed considerably from those of the older kinds of glass. In the old crown and flint glass a high refractive index was always connected with a strong dispersion and the reverse. Schott succeeded, however, in producing glasses which with a comparatively low refraction have a high dispersion, and with a high refraction a low dispersion. By using these glasses and employing minerals with special optical properties, it is possible to correct objectives so that three colours can be combined, leaving only a quite slight tertiary spectrum, and removing the spherical aberration for two colours. Abbe called such systems “apochromats.” Good apochromats often have as many as twelve lenses, whilst systems of simpler construction are only achromatic, and are therefore called “achromats.”
Even in apochromats it is not possible to entirely remove the chromatic difference of magnification, i.e. the images produced by the red rays are somewhat smaller than the images produced by the blue. A white object is represented with blue streaks and a black one with red streaks. This aberration can, however, be successfully controlled by a suitable eyepiece (see below).
A further aberration which can only be overcome with difficulty, and even then only partially, is the “curvature of the field,” i.e. the points situated in the middle and at the edge of the plane object can not be seen clearly at the same focusing.
Historical Development.—The first real improvement in the microscope objective dates from 1830 when V. and C. Chevalier, at first after the designs of Selligue, produced objectives, consisting of several achromatic systems arranged one above the other. The systems could be used separately or in any combination. A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used. Selligue had no particular comprehension of the problem, for his achromatic single systems were simply telescope objectives corrected for an infinitely distant point, and were placed so that the same. surface was turned towards the object in the microscope objective as in the telescope objective; although contrary to the telescope, the distance of the object in the microscope objective is small in proportion to the distance of the image. It would have been more correct to have employed these objectives in a reverse position.
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| Fig. 32. | Fig. 33. |
These circumstances were considered by Chevalier and Lister. Lister showed that a combination of lenses can be achromatic for only two points on the axis, and therefore that the single systems must be so arranged that the aplanatic (virtual) image-point O′ (fig. 32) of the first system coincides with the object-point of the next system. This system will always be aplanatic. These objectives permitted a much larger aperture than a simple achromatic system. Although such systems have been made recently for special purposes, this construction was abandoned, and a more complex one adopted which also made the production of better objectives possible; this is the principle of the compensation of the aberrations produced in the different parts of the objective. Even Lister, who proceeded on quite different lines,
hinted at the possibility of such a compensation. This method makes it specially possible to overcome the chromatic and spherical aberrations of higher orders and to fulfil the sine-condition, and the chief merit of this improvement belongs to Amici. He had recognized that the good operation of a microscope objective depended essentially upon the size of the aperture, and he therefore endeavoured to produce systems with wide aperture and good correction. He used chiefly a highly curved plano-convex front lens, which has since always been employed in strong systems. Even if the object-point on the axis cannot be reproduced quite free from aberration through such a lens, because aberrations of the type of an under-correction have been produced by the first plane outer limiting surface, yet the defects with the strong refraction are relatively small and can be well compensated by other systems. Amici chiefly employed cemented pairs of lenses consisting of a plano-convex flint lens and a biconvex crown lens (fig. 33), and constructed objectives with an aperture of 135°. He also showed the influence of the cover-slip on pencils of such wide aperture. The lower surface of the slip causes under-correction on being traversed by the pencil, with over-correction when it leaves it; and since the aberration of the surface lying farthest from the object, i.e. those caused by the upper surface preponderate, an over-corrected cone of rays enters the objective. The over-correction increases when the glass is thickened. In order to counteract this aberration the whole objective must be correspondingly under-corrected. Objectives with definite under-correction can however only produce really good images with glass covers of a specified thickness. With apertures of 0·90—0·95 differences of even 0·004—0·008 in. in the glass covers can be noticed by the deterioration of the image. In systems with smaller apertures variations of the thickness of the glass cover are not so
