DIFFRACTION PLATES FOR SMALL A AND g = 1 59 



complementary areas is 12%. The h~ values predicted by the simplified 

 theory are usually smaller than those employed in the phase microscope. 

 Thus, h- values in the range 15% to 25% have been preferred experi- 

 mentally for particles whose A value varies through a considerable 

 range about the point Ia| = X/18. 



The most pertinent properties of the curves of Fig. 11.14 for the 

 thesis of the present section are: 



1. The energy densities Gp and the contrast A' change only slightly 

 as 5 varies by ±10° about the points 8 = —80° and 100° for dark and 

 bright contrast, respectively. In fact, a range of ±20° in 5 can be 

 tolerated for many purposes. Since the tolerable range of variation in 5 

 amounts to almost 3^ wavelength, it is to be expected that the phase 

 differences between the conjugate and complementary areas in a series 

 of diffraction plates need be spaced no nearer than 3^ wavelength apart. 



2. Since the values 8 = ±90° = ±X/4 fall only 10° from the best 

 values of —80° and 100° for the case A = X/18, the particle discussed 

 in this section should appear in good to excellent contrast when viewed 

 with the aid of diffraction plates whose phase difference 8 is ±X/4 as 

 recommended by Zernike. 



3. Since the A' value at dark contrast varies only from —0.7 to —1 

 to —0.95 and since the A value at bright contrast varies only from 5.5 

 to 2.2 as h is varied from 0.2236 to 0.4472, a wide tolerance also on the 

 h value is admissible. 



It can therefore be expected on the one hand that in constructing a 

 diffraction plate for obtaining good contrast with a given object specimen 

 the required values of h and 8 are not critical and that on the other hand a 

 diffraction plate with a given pair of h and 5 values can be used with 

 excellent to moderate success for object specimens having a range of 

 optical path differences A. In order to illustrate more explicitly how a 

 single diffraction plate performs over a range of A values, the contrast 

 values A have been plotted as a function of A in Fig. 11.15 for the 

 indicated values of 8 and with h fixed at the value of 0.3473. The curve 

 of A applies to a diffraction plate selected for dark contrast; the curve 

 of B applies to a diffraction plate selected for bright contrast. A shows 

 that the indicated diffraction plate can be expected to produce good to 

 excellent contrast for A values in the range 8° < A < 32°. For A values 

 outside this range, for example with A = 3.6° = X/100, another diffrac- 

 tion plate should be selected. B shows that the indicated diffraction 

 plate can be expected to produce good to excellent bright contrast for 

 A values in the range 8° to 40° but that another diffraction plate should 

 be selected when A falls in or below the neighborhood of 3.6° = X 100, 



