GENERAL CONSIDERATIONS OF DESIGN 81 



optical path across the diffraction phite be greater than 90° as the optical 

 path difference between the particle and its surround increases when the 

 particle is to be viewed in optimum l)right contrast. It is also of great 

 interest to investigate the range of A for which good contrast is obtained 

 in the image of a transparent particle (the case g = \) when 5 is fixed 

 at —90° and h is assigned different values which may depart considerably 

 from the particular h values required for darkest possible contrast or for 

 optimum bright contrast. Let the fi.xed values 8 = —90°, g = \, and 

 /ii = 1 be substituted into Eqs. II. 8. 7 and II. 8. 8. It follows from 

 Eq. II. 8. 8 that the value of A = A„un for which the light intensity in 

 the image of the particle is a minimum is related to the assigned h value 

 by the equation 



tan A,„in = h. (1.1) 



Also 



(^p)„un = /r + 2[1 - (1 +Jry^], (1.2) 



in which Gp is proportional to the amount of light energy in the image 

 of the particle. Gg is similarly proportional to the amount of light 

 energy in the image of the surround and is given by 



Gs = Jr. (1.3) 



The data of Table III.l have l)een calculated from Ecjs. 1.1-1.3. This 

 table shows that, if the relative amplitude transmission h of the conju- 



Tahle III.l 



The niiiiimum enerjiy densities (Gp)min and the contrast 



vahies K as functions of AnUn and h when 



^ h S 0.7 in the case ^ = 1 and 5 = -90° 



h ^°min (G'p)min Gs K ^ {Gp — Gs)/Gs 







0.1 5.72 0.0000248 0.01 



0.2 11.32 0.0003«»2 0.04 



0.3 16.70 0.00104 0.09 



0.4 21.80 0.00593 0,16 



0.5 26.57 0.0139 0.25 



0.6 30.97 0.0276 0.36 



0.7 35.00 0.0487 0.49 



gate area is adjusted so that Gp = (Gp) nnn, then the contrast values K 

 depart only slightly from the limiting value K = —1 corresponding to 

 darkest possible contrast. The range in A includes the optical path 

 differences normally encountered in phase microscopy. It still holds 

 that, as A becomes very small, h must also become very small in oixler 

 to obtain good contrast. The energy densities Gs and Gp associated 



