On the Mode of Vision with Wide Apertures. By Prof. Abbe. 23 



Fig. 5. 



This is of course perfectly defined by determining the delinea- 

 tion of the upper plane surface A B, and of the lower Ai Bj (fig. 5). 

 The result of the previous consideration must apply to both plane 

 surfaces successively, pro- 

 vided their distance along 

 the axis is sufficiently 

 small. For in this case, 

 an objective v^hich is 

 aplanatic for the conju- 

 gate points A and B v^ill 

 still be aplanatic for the 

 neighbouring pair of con- 

 jugate points Ai and Bj. 



Consequently the 

 whole pencils a and yS 

 from the surface A B will 

 yield a distinct image 

 A* B* at a certain plane, 

 and at the same time the 

 whole pencils a^, and /3i, 

 from the other surface 

 Ai Bi, will also project a 

 distinct image A* Bi* at 

 another (lower) plane. 



Suppose (1) that the 

 image is delineated by 

 means of narrow axial 

 pencils a a and /3 a, and 

 the ocular focused to the 

 exact level of the lower 

 layer Ai* Bi*. The points 

 A* and B* of the upper 

 layer will in this case ap- 

 pear as small dissipation 

 circles projected upon the 

 distinctly seen points Ai* 

 and Bi* of the lower layer, 

 the centres of these circles 

 coinciding with the latter. 



Suppose now (2) the 

 image to be delineated by 



A^ 



as projected by the objective to the field of the 

 ocular. 



The diagram shows the manner in which the 

 two successive layers A B and Aj Bj of the ob- 

 ject are delineated by means of the whole pencils 

 (full aperture pencils) a, j3 and a^, Bi, or by 

 means of the elementary pencils a a, ^ a, and 

 a-fl, fi^a, or am, ^m and ai-m, P^m, and indicates 

 the manner in which the image of the upper 

 layer is seen projected upon the image of the 

 lower layer. The thick lines indicate the dia- 

 meters of the circles of indistinctness which 

 represent the points A* and B* under various 

 circumstances at the plane of the lower layer (in 

 one case broad and in the other small) on the 

 assumption that this lower layer is exactly 

 focused and seen in perfect distinctness. 



the whole aperture, i. e. by the wide pencils a and y8, and the ocular 

 focused to the lower layer as before. The points of the upper image, 

 which is not exactly focused, will now give much broader dissipa- 

 tion circles projected on the sharply seen points Ai* Bi* but the 

 centres of the two sets of points will still coincide. 



