GENERAL CONSIDERATIONS OF DESIGN 83 



tion plate can be expected to produce good contrast for all values of 

 A in the interval Ai ^ A ^ Ao. Such pairs of Ai and A2 have been 

 computed from Eqs. 1.4 and 1.5 and are listed in Table III. 2 as functions 

 of /). The simple theory predicts therefore that the general-purpose 

 diffraction plate (0.5 ^h^ 0.632; 8 = -90° = -X/4) will result in 

 good dark contrast for values of A lying between 12° and 47° and that the 

 particle will be visible against its surround for an even greater range of 

 values of A. 



Table ITI.2 



The interval Aj ^ A ^ Aj for which the contra.st K lies 

 hetMeeii the limits — l^K^ — ^^asa function of 

 h when 0.1 ^ h ^ 0.1 in the case g = 1 and 5 = —90° 



h Ai° A2° 



The specifications for a general-purpose diffraction plate for obtaining 

 bright contrast with transparent particles whose optical path exceeds 

 that of the surround are again 0.5 ^ h ^ 0.632, but 5 = +90° instead of 

 -90°. Let the fixed values 5 = +90°, g = I, and /ii = 1 be substituted 

 into Eqs. II.8.7 and II.8.8. Then 



Gp = /i^ + 2 - 2 cos A + 2/1 sin A. (1.6) 



The contrast values K = ((7,, - GJ 'Gs of Table III.3 have been com- 

 puted with the aid of Eqs. 1.6 for values of A in the first quadrant (i.e., 

 for the interval ^ A ^ 90°) and for values of h in the range ^ h ^ 

 0.7. Table III. 3 shows that, when h is fixed at any value, K is an in- 

 creasing function of A throughout the first quadrant. The behavior 

 of the bright-contrast values A' > for particles with A values which lie 

 in the first ciuadrant differs in two notable respects from the behavior 

 of the dark-contrast values /v < which result from setting 5 = —90° 

 instead of +90°. First, at fixed ^'alues of h the bright-contrast values 

 A' do not reach either a maximum or a minimum for any point A which 

 falls within the first quadrant. Second, since the contrast values of 

 Table III.3 are all positive, reversal of contrast does not occur at any 

 value of h or A listed in the table. Table III. 3 shows also that optimum 



