PRINCIPLES OF COLOR PHASE CONTRAST 103 



point of intersection of the two dispersion curves which describe the 

 change in tii and n-z with wavelength. A number of pairs of materials 

 may satisfy Eqs. 2.20 and 2.21 and therefore Eq. 2.25, but each pair may 

 satisfy Eq. 2.22 for a different wa\'elength Xq. 



The combination consisting of Eqs. 2.20 and 2.22 or the combination 

 consisting of Eqs. 2.21 and 2.22 has a solution of the same form as 

 Eq. 2.17 or 2.19. Let 



ni = ns + ai; (2.26) 



W2 = ne + a2; (2.27) 



th = ns - as; (2.28) 



n^ = n,, - 04- (2.29) 



Then, if two materials are selected which have the same index of refrac- 

 tion for the wavelength Xq and if Eqs. 2.20 and 2.21 are also satisfied, 

 it follows that 



(a2-ai)=^, (2.30) 



and 



(a4-a3) = j^- (2.31) 



Equations 2.20, 2.21, and 2.22 together with Eqs. 2.26-2.29 also show 

 that (ai — a2) = (^i — ^2) < and that (03 — 04) = (ri4 — riz) < 

 in this particular design for a reversal color diffraction plate. In 

 general, it is not possible to satisfy Ecis. 2.20, 2.21, and 2.22 simul- 

 taneously for any three arbitrary, preselected values of Xi, X2, and Xq 

 unless it is possible to introduce, also arbitrarily, second-order effects 

 into the dispersion characteristics of at least one of the substances 

 forming the diffraction plate. 



The designs presented here for color phase microscopy represent the 

 simplest and most direct approach to the problem if a result is to be 

 obtained by making use of the different dispersions of materials. Theory 

 does not limit the choice of optical path difference between the conjugate 

 and complementary areas to }4 wavelength for Xi and Xq, for example, 

 and to no path difference for Xq. Schemes are also allowed in which the 

 optical path difference for Xi and X2 are higher multiples of J^ wave- 

 length and in which the optical path difference for Xq is 3^ wavelength 

 or a multiple of 3-9 wavelength. For best performance it is necessary 

 that the amplitude of the deviated light and that of the undeviated 

 light be balanced with a color diffraction plate as with the standard, 

 neutral diffraction plate. A neutral absorbing material may be in- 



