DIFFRACTION PLATES FOR SMALL A AND g = 1 57 



14. CHOICE OF DIFFRACTION PLATE WITH PARTICLES HAVING SMALL 

 OPTICAL PATH DIFFERENCES AND THE AMPLITUDE RATIO g ^ I. 



Darkest or optimum liright contrast in the image will not be obtained 

 except with suitably chosen object particles when the phase microscope 

 is provided with a single diffraction plate. As the number of different 

 diffraction plates is increased, the range of choice of object particle 

 increases. We shall see that the choice of diffraction plate is not at all 

 critical. Contrast in the image falls off slowly from its darkest or 

 optimum liright ^'alue as the amplitude ratio h and the phase difference 5 

 of the diffraction plate depart from the values required for darkest or 

 optimum bright contrast. The \-ariation in the contrast with h and 8 

 will now be described for the case in which A = +X '18 and (/ = 1. 

 This case applies, for example, to unstained biological specimens whose 

 optical path difference A is so small that contrast in the ordinary 

 microscope is poor. 



The energy densities Gs and Gp have been computed as fiuictions 

 of 5 at several fixed values of h and are plotted for comparison in Fig. 11.14 

 in which 5 is represented in degrees. The corresponding values of 5 

 in wavelengths can be obtained by dividing by 300. It will be noted 

 that the energy density Gp in the image of the particle is maximum in all 

 cases when 5 = 100° and minimum when 8 = —80°. Beginning with 

 the cur-\'es drawn for h = 0.1225, we see that Gp > Gs for all values of 8. 

 If we define the contrast K b}^ the equation 



K is a maximum of 13.7 at 5 = 100°. The maximum value of K de- 

 creases steadily with increasing h and is equal to 3 when h = 0.3473, the 

 value of h at which the amplitudes of the undeviated and deviated waves 

 are alike and at which the contrast is defined as optimum bright con- 

 trast. Since Gp — 4Gs at optimum bright contrast, K is always ec^ual to 

 3 at optimum bright contrast. When h = 0.1738, the curve Gp touches 

 the curve Gg at 5 = —80°. For larger values of h the curve Gp dips 

 below the curve for Gg in the neighborhood of 5 = —80°. Contrast 

 in the image may now be reversed by changing, for example, 5 from 

 100° to -80°. With h = 0.3473, Gp = and K = -1 at 5 = -80°, 

 the point of darkest possible contrast. As h is increased from 0.3473 

 to 0.50, the contrast value K at 8 = —80° increases slowly from K = —I 

 to K = —0.9 at h = 0.5. Both the dark and bright contrasts deteri- 

 orate steadily with h when h > 0.3473. Since h^ = 0.12 when 

 h = 0.3473, the energy transmission ratio between the conjugate and 



