Theories of Microscojrical Vision. By A. E. Conrady. 549 



I purposely chose a pattern of small perforations ; with large 

 perforations we have the possibility of reversed phase in some of 

 the spectra — in fact, we may have perforations such that even some 

 of the innermost spectra will be reversed in phase. I must leave 

 these to be dealt with separately, merely pointing out now that it is 

 found that the phase -reversals again prove to be the agency through 

 which the finer peculiarities of the structure are brought out in the 

 image. Fig. 128 illustrates a possible case of this kind : the long 

 oblique perforations will be noted to be formed round the centres 

 of the small dots of fig. 125 ; they are, therefore, arranged in the 

 same configuration as fig. 125, and give diffraction-spectra arranged 

 in the manner of fig. 125a, but it is not difficult to see on reference 

 to my former paper that the spectra A x will be reversed in phase. 



We will next briefly study the image to be obtained of the 

 rccijyrocal grating corresponding to the one discussed above, i.e. a 

 black dot design of which fig. 125 would be an actual (positive) 

 representation. From what has been said concerning Babinet's 

 theorem, it will be clear that, referred to the lines connecting the 

 black dots, all the inner spectra will now be opposed in phase to^ 

 the direct light, i.e. the light of all these inner spectra will arrive 

 at the corresponding lines of the image in the phase opposite to 

 that in which the direct light reaches them, and there will, on the 

 other hand, be a tendency to form bright lines midway between the 

 lines a, b, c, etc., of fig. 125. In the cases represented in figs. 127a 

 and 127b we shall thus obtain intersecting bright lines midway 

 between the lines a and b respectively which leave dark spots 

 between them precisely corresponding to the real dots of the 

 object. Similarly, the combinations of spectra 3 and 4 shown in 

 figs. 127c, 127d, and 127e, now lead to the formation of bright dots 

 at? various points between the dark dots of the pattern, thus leading to 

 a more and more uniform filling with light of the spaces outside 

 the true images of the black dots, and to a corresponding improve- 

 ment in the verisimilitude of the image of the black dot pattern. 



The triangular pattern represented in fig. 126 may be similarly 

 discussed ; we again find first intersecting lines indicating fairly 

 accurately the position of the actual bright or black dot, and 

 next, as soon as more than two maxima are admitted by the object- 

 glass, the formation of bright dot images which are so distributed 

 as to improve the resemblance between object and image. The 

 only difference is that a very much smaller increase of aperture 

 leads to this latter result in the case of the triangular pattern than 

 in the more fully discussed case of a pattern arranged in perfect 

 squares, for the simple reason that a circle only slightly larger than 

 that required to enclose say the direct light and spectrum A x of 

 fig. 126a will suffice to embrace three adjacent maxima, such as 

 direct light and spectra A! and B^ 



On the other hand, it will be seen by reference to fig. 126a that 



