NON-UNIFORMLY ALTERED HIGHER ORDERS 277 



the amplitude transmission of the elevations. As an example, suppose 

 that the grating spacing is chosen relative to the numerical aperture of 

 the objective such that tlii'ee of the higher spectral orders are trans- 

 mitted. Suppose that the energy transmission of the elevations 

 (Fig. VII. 10) is 81% of the energy transmission of the troughs. Then 

 A^" = 3 and g = (0.81)' = 0.9. Such a grating will be seen in fair to 

 poor contrast in the ordinary mici'oscope. From Eq. 10.2.7 6 = t 

 radians or 0.5 wavelength. From Eq. 10.2.8 



3 



/i = - — y^ - sin — = 0.05808; h^ = 0.0034. 



j' = i 



Hence an 0.0034Azb0.5X diffraction plate will cause the centers of the 

 troughs to appear black. On the other hand, an 0.0034A±0.0X diffrac- 

 tion plate will cause the centers of the elevations to appear black. 



An examination of Eq. 10.2.8 shows that the choice of B-type diffrac- 

 tion plates is hardly to be expected with gratings of the present section 

 since h will usually be less than unity. However, B-type diffraction 

 plates are required theoretically with other types of object specimens. 

 Equation 10.2.7 shows that the optimum 8 value of a diffraction plate 

 is either or X/2 for observing equally spaced, purely absorbing struc- 

 tures, all of whose higher spectral orders pass through the complementary 

 area. 



10.3. Phase gratings whose zero order is altered non-unifornily 

 with respect to the higher orders 



It was seen in Section 10.1 that the optimum 8 values of the diffraction 

 plate are ±7r/2 radians when all the higher spectral orders pass through 

 the complementary area. It will be the thesis of this section to demon- 

 strate that the optimum 8 values are not necessarily ±7r '2 radians with 

 pure phase gratings when some of the higher spectral orders pass through 

 the conjugate area. This conclusion is of sufficient importance to phase 

 microscopy that a general demonstration of its truth would be appropri- 

 ate. Up to the present time a general demonstration does not appear 

 to have been published. The conclusion has, however, been demon- 

 strated in a number of special cases. Let us consider the special case 

 in which the pure phase grating is arranged as in Fig. VII. 9 and in 

 which the grating spacing 21 has been chosen so that the complete first 

 order passes through the objective and so that only one branch of the 

 third spectral order passes through the diffraction plate. We suppose 

 that the first order passes through the complementary area but that the 

 transmitted branch of the third order passes through the conjugate area. 



