CONDITIONS FOR OPTOIUM BRIGHT CONTRAST 55 



13. CONDITIONS FOR OPTIMUM BRIGHT CONTRAST 



Thus far, our attention has been hmited to the conditions which h 

 and 5 must satisfy in order to cause the particle to appear in darkest 

 contrast. Whereas definite, unique conditions can be discovered for 

 darkest contrast, the same is not true with respect to the conditions for 

 optimum bright contrast. 



Returning to Eqs. 8.3 and 8.4, we see that 



G, = 0; (13.1) 



(?p = iH^e'^ - l|2 



= hi^a - 2^ cos A + r); (13.2) 



when h = 0. Since (1—2^ cos A + ^") is not eciual to zero unless 

 A = and ^ = 1 so that the particle is indistinguishable from its sur- 

 round in white light, Gp 9^ when Gg = 0. The Schlieren case, h = 0, 

 produces the greatest bright contrast, therefore, for the particle appears 

 bright against a theoretically black background. In the Schlieren 

 case, however, the quality of the image is deteriorated because the image 

 is formed by the deviated wave alone. We can expect that a more 

 favorable compromise between contrast and definition will be obtained 

 when the h value is chosen no smaller than the value required to equalize 

 the amplitudes of the undeviated and deviated waves. It has been 

 shown in Section 12 that this is precisely the value of h that is required 

 for obtaining darkest contrast in the image of the particle. We shall 

 accordingly define optimum bright contrast as the brightest contrast that 

 can be obtained by varying 5 with h fixed at its value for darkest con- 

 trast. The problem of discovering the maximizing value of 5 reduces 

 therefore to the task of finding the value of b for which dGp/d8 = 0, 

 where Gp is the total energy density over the geometrical image of the 

 particle as given by Eq. 8.8. 



SC 



— - = 2hi^h[— {h cos 8 -\- g cos A — 1) sin 5 + (h sin 5 + gf sin A) cos 5]; 

 d8 



= 2hi^h[(\ — g cos A) sin 5 + gr sin A cos 5]. 



Thus, BGp/db = 0, provided that 



— 9 sin A 



tan 5 = (13.3) 



I — g cos A 



Now Eq. 13.3 can also be obtained through division of Eqs. 9.3 

 and 9.4. If 8d denotes the value of 5 computed from Eqs. 9.3 and 9.4, it 

 follows that 8d is a solution of Eq. 13.3 where 5^ is the optical path 

 difference between the conjugate and complementary areas of the 



