-532 Transactions of the Society. 



XI. — On the Influence on Images of Gratings of Phase-Differences 

 amongst their Spectra. 



By J. Rheinberg. 



{Read June 20th, 1906.) 



Some interesting points in regard to the above subject are brought 

 forward by Dr. Karl Strehl, of Erlangen, in the " Zeitschrift fur 

 wissenschaftliche Mikroskopie " of last September. 



In his booklet on the " Theory of Microscopic Vision," pub- 

 lished in 1900,* Dr. Strehl has referred to phase-differences occurring 

 in the diffraction spectra of complementary structures. He there 

 applies Babinet's principle, reasoning that, since the transparent 

 portions of the two complementary structures together make up a 

 surface of even illumination, the diffraction spectra of the two 

 complementary structures must together be equivalent to the 

 diffraction spectrum which the evenly illuminated surface would 

 give, viz. a single undiffracted maximum. From which it follows 

 that, whilst the zero maximum in the two sets of spectra would be 

 in the same phase, all the other maxima would have to cancel out, 

 and would, therefore, be opposed to each other in phase. 



He now shows how this fits in with the experiments and results 

 forming the subject of my two notes to this Journal,f which he 

 reviews. 



To follow matters more clearly, it may be useful to briefly 

 re-state to what differences in phase are due, as they arise from 

 two distinct and different causes, viz. : — 



1. The phase- differences in the diffraction spectra of gratings 

 which arise from the position of the grating on the stage of the 

 Microscope, and which were, I believe, first pointed out by R. T. 

 Glazebrook. 



Given a grating, so placed that one of its slits is on the optic 

 axis of the Microscope. If illuminated by plane waves, diffraction 

 spectra will, of course, be formed in the back focal plane of the 

 objective. Shift the grating in the stage through half a grating 

 interval, so that one of its bars is on the optic axis. Whilst the 

 grating is shifted, and its image in the view plane is shifted, the 

 diffraction spectra retain their position unaltered ; the movement of 

 the image in the view plane is accounted for by the changes of 

 phase which occur in the spectra. 



Professor Everett showed that, whilst the grating moves through 



* The Blaesings Universitats-Buchhandlung Erlangen. 

 t 1904, pp. 388-390 ; 1905, pp. 152-155. 



