UNIFORMLY ALTERED HIGHER ORDERS 271 



structure. For highest resohition the conjugate area should extend to 

 the edge of the clear aperture of the phase objective in viewing periodic 

 structure. On the other hand, the physical limit of resolution will be 

 approached more closely by the phase microscope than by the ordinary 

 microscope for those periodic structures which appear with poor con- 

 trast in the ordinary microscope. This statement follows from Eq. 

 10.20 because the left-hand member must exceed the right-hand member 

 by greater amounts for those systems of microscopy which reveal the 

 object in poorer contrast. Since the denominator of the right-hand 

 member of Eq. 10.26 is only slightly different with phase and ordinary 

 microscopes and since the physical limit can be approached more closely 

 by the phase microscope, there may exist periodic structures that are 

 resoh-ed better by the phase microscope than by the ordinary micro- 

 scope. Periodic structures whose troughs and elevations represent 

 slight optical path differences belong to this category of object specimens. 



n 



1 1 r 



f(x^) 



JJ 1 1 r 



X, 



I 



H 21- 



FiG. VII. 9. Simply periodic, pure phase gratings as object specimen. The grating 

 spacing is 21 along the Xq direction. The troughs and elevations are supposed to be 



equal in width. 



10.1. Phase gratings whose higher orders are altered uniformly 



A simple, pure phase grating is a simply periodic structure whose 

 troughs and elevations represent differences in optical path only. Let 

 the troughs and elevations be arranged across the Xq direction as in 

 Fig. MI. 9. The object function /(xq, ?/o) = fixo) is taken as unity 

 o\QV the troughs and as c'^ over the elevations. A is the optical path 

 difference between the elevations and the troughs and is considered 

 positi^'e when the optical path through the elevations exceeds that 

 through the troughs. This object function is expressed as the Fourier 

 series 



