B. T. LOWNB ON INTERFERENCE PHENOMENA. 367 



parts of the objective as those rays which give the spectra, and 

 you cannot, th ere fore, block out the spectra without also destroy- 

 ing the diffraction image. 



Let us now see what diffraction and interference have to do with 

 the formation of an image. 



Professor Abbe says the image consists of a dioptric image with 

 numerous partial positive diffraction images superimposed upon it. 

 The image is a true image of structure wherever all the partial 

 diffraction images which can be formed by the object are exactly 

 superimposed upon each other, without any displacement due to 

 spherical or chromatic aberration. He further says the image can- 

 not be depended on unless all the rays which have any sensible 

 illuminating power are collected by the objective. 



First, the dioptric image depends upon the well-known optical 

 law — that a perfect system of aplanatic achromatic lenses brings 

 all the rays which come from a point in the object to a correspond- 

 ing point in the image. The more nearly these points in the image, 

 become mathematical points the sharper the picture. 



With ordinary illumination, Professor Abbe assumes that the 

 centre only of a wide angle object-glass is concerned in forming the 

 dioptric picture. His "ordinary illumination " means a very small 

 pencil of light from the condenser. 



The pencils of diffracted light which come from points in the 

 object are also subject to exactly the same dioptric law. They are 

 also brought to exact focal points, corresponding point for point 

 with the corresponding points in the object. 



In physical optics, a focus is defined as a point at which the 

 vibrations arrive at the same time, and in the same phase. There 

 can, therefore, be no interference within the limits of the diffrac- 

 tion pencil. 



Now, suppose we take the case in which we have a diffracted 

 pencil and a dioptric pencil ; the simplest case, according to Pro- 

 fessor Abbe, in which we can have delineation (" abbildung ") of 

 details in the image. What happens to produce these details ? 



The dioptric beam gives the illumination of the field by super- 

 imposed diffusion circles, its foci being those of the source of light. 

 These interfere with the foci of the diffracted pencil, and whenever 

 the light waves are in different phases a negative or dark image is 

 formed. This is the diffraction image. If the focal points of the 

 diffraction pencils correspond point for point with those of the 

 object, the black image in that plane represents the object exactly, 



