On the Mode of Vision with Wide Ajpertures. By Prof. Abbe. 21 



incidence of the pencils, and on the basis of this view the natural 

 conclusion of course is that as a wide aperture admits pencils of 

 very different obliquities at the same time, the resulting image must 

 embrace as many different perspectives of the solid object, depicting 

 them to the observer's eye at the same time, just as if many narrow- 

 angled objectives (or eyes) A, K, Z, &c. (fig. 3) were arranged 

 around the object and their images united. 



According to the point of view adopted, or to the private taste 

 of the writer, this, as I have said, is 

 considered either as an advantage of wide- ^^<^- ^^ 



angle vision, or as a drawback. (^^^\ 



The fact is, however, that neither the 

 one nor the other of these views is correct, /C? S^ 



because no delineation of the objects takes \/ I I v 



place in the manner supposed. This is j | 



shown by the following consideration, 



which also shows at the same time the error of the view that the 

 resultant image of an objective of wide aperture is composed of 

 dissimilar images projected by rays of different inclinations, for 

 this is based on the same hypothesis essentially as the others just 

 referred to. 



First consider the case of a plane object. The course of the 

 rays through a wide-angled objective is shown in fig. 4, the 

 object being at A B. If we suppose the objective to be well 

 corrected (or aplanatic) all rays emanating from the axial point A 

 (i..e. the whole pencil a) will be collected at one point A*, and the 

 same is true not only for an axial point, but for an eccentric point 

 B also (up to a certain moderate distance from the axis at least).t 

 Consequently the whole pencil /3 from the point B will be collected 

 also to one distinct point B* of the image. 



Now it is an evident inference that the plane A B must be 

 delineated exactly in the same manner (as the same plane A* B* 

 of the image) whether it is delineated by the two axial pencils a a 

 and j3 a, or by any two oblique pencils a m and jB m, whatever be 

 their inclination to the plane of the object. For if all rays from 

 B are collected to the same point B*, the two partial pencils /S a 

 and /3 m, which are parts of the whole pencil /3, cannot be collected 

 to different points. 



t This idea of a well-corrected system has been considered formerly as quite 

 unconditional. It has been supposed that whenever the rays from the axial 

 point A are collected to a sharp focus, the rays from escentrical points B would 

 always be collected to sharp foci by themselves. I showed in 1873 that the 

 latter is not a necessary consequence of the former, and that a particular condition 

 must be fulfilled in order to have the same collection of rays from excentrical 

 points as is obtained from an axial one when the spherical aberration is corrected. 

 This condition is the law of aplanatic convergence — proportionality of the sines of 

 the angles at the foci A and A*. 



