Now if the cardinal points of the optical system are assigned, the image-relief corre sponding to a 3-dimensional object may be con structed, as has been explained. This image relief (as was stated above) is almost invari.: ably received on a surface or screen of some kind, which may here be assumed to be a plane surface coincident with the so-called screen-plane. In the diagram (Fig. 62 the point M' conjugate to the axial object-point M is represented as sharply focused on the screen. Evidently, the system cannot be in focus for all the different points of the object relief at the same time, because the screen plane is conjugate to only one transversal plane of the object-space, namely, the focus-plane perpendicular to the optical axis at M. Thus, for example, the reproduction of a solid ob ject, such as the image of a landscape cast on the ground-glass plate of a photographic camera, is not an image at all in the strict sense of the word, inasmuch as it is not conjugate to the entire object point by point Only such points of the object as happen to lie in the focus-plane will be reproduced by sharp point images in the screen-plane; whereas object points situated on one side or the other of the focus-plane will be depicted by small luminons areas which are sections cut out by the screen plane from the cones of image-rays emanating originally from these points. These little patches of light, which are more or less ellipti cal in contour and whose dimensions depend on obvious geometrical factors, are the so-called in consequence whereof details of the image as projected on the screen are im paired to a greater or less degree or are, as we say, "out of focus.' The object-figure in the focus-plane which is optically conjugate to this configuration of image-points and blur-circles cast on the screen may be easily constructed by projecting the points of the object on to the focus-plane by cones of rays which have the entrance-pupil as their common basis. This "vicarious" object to which the image on the screen is optically conjugate is sometimes called the "projected copy of the object-relief' It hardly needs to be said that the blur circles which are incident to this mode of projecting the optical image of a solid object on a surface are due to no faults of the optical system itself, but are inherent in the method of representation and really have their origin in the object-space itself. The only possible way i of diminishing or eliminating the indistinctness or lack of detail consists in reducing the diameter of the aperture-stop or, as we say, "stopping down' the instrument'; until, finally, when the stop-opening is contracted more and more to the dimensions of a pin-hole, the pupils likewise will tend to become mere points at their centres 0, 0', and the blur-circles in both the focus-plane and the screen-plane will dimin ish in area paripassu, and ultimately collapse also into the points where the so-called chief rap, which intersect at the pupil-centres, cross this pair of conjugate planes. Under such cir cumstances, the pupil-centres 0, 0' are to be regarded as the centres of perspective of the object-space and image-space, respectively.
The extent of the field of view in the object space is determined by that one of the stops or stop-images which subtends the smallest angle at the centre 0 of the entrance-pupil. It is called the Similarly, the field of view in the image-space is limited by the so-called which is the stop or stop i;nage on that side of the instrument which sub tends the smallest angle at•the centre 0' of the exit-pupil. Just as the exit-pupil is the image of the entrance-pupil, so also the exit-port is the image of the entrance-port produced by the optical system.
Aberrations.—As a matter of fact, actual
optical images which are necessarily formed by ray-bundles of finite apertures are, in gen eral, more or less faulty, so that the theory of optical instruments is greatly complicated by numerous practical and well-nigh insurmount able difficulties. These faults — which are called sometimes escape unnoticed merely because they are too slight for the eye to perceive, but usually the image will be seriously impaired unless they are corrected as far as possible. This is a subject which cannot be adequately treated here, and we can merely say that there are two principal kinds of aberra tion, namely, (1) the chromatic aberrations or color-faults of the image in consequence of the different ref rangibilities of light of , different colors, whereby the image is affected with residual color-effects which are not apparent in the object, and (2) the so-called spherical aberrations caused by the imperfect convergence of rays of light of the same color. A problem of the greatest difficulty in the design and con struction of optical instruments is to determine the various factors (indices of refraction, radii of the surfaces, lens thicknesses and distances etc.) so that these defects will be at least comparatively negligible.
Newton erroneously concluded from his prism-experiments and investigations of dis persion of light that it was impossible to pro duce an achromatic image by refraction, and, despairing therefore of being able to improve refracting telescopes, he turned his attention to reflectors, as is well known. But in 1757 Dollond, a London optician, was able to con struct an object-glass, which was achromatic for red and blue light, and which consisted of a combination of a 'crown glass' lens with a "flint glass' lens, of which the former was the weaker in respect to both refraction and dis persion. For many years to come this re mained the high-water mark of practical achievement in the construction of optical in struments, and indeed no further progress was possible on account of the lack of suitable varieties of optical glass. Fraunhofer dearly perceived the difficulty in the way of advance ment in the manufacture of optical instruments, but it was not until the time of Abbe and the establishment in 1886 of the Glastechnisches Laboratorium of Schott and Genossen, where the now world-famous Jena glass is produced, that this obstacle was triumphantly overcome; and by the aid of the new kinds of optical glass it was possible to take another step in the cor rection of the chromatic aberrations by abolish ing also the so-called 'secondary spectrum' in the image.
In the older types of optical instruments (telescope and microscope), the first attempts at correcting the spherical aberrations were confined almost entirely to the improvement of the image of an object-point situated on the axis. With the development of the photo graphic lens and instruments with an extended field of view, it became more and more essential to take into account the other kinds of spherical aberrations as well as that along the axis. Among these may be mentioned astigmatism and gcoma" which are concerned especially with lack of detail in the image, curvature of the image, which is fundamentally Involved when the image has to be focussed on a receiving screen, and distortion due to the unequal mag nification of the parts of the image which are at different distances from the axis. How these difficulties and defects have been practically surmounted in the best types of modern optical instruments is a record of painstaking achieve ment which Cannot be described within the space allotted to this article.
James P. C. SOUTHALL, Associate Professor of Physics, Columbia University.