CONTINUOUSLY VARIABLE AMPLITUDE RATIOS 161 



9.4. Polanret systems having conlinuously variable amplitude 

 ratios 



Systems of variable phase microscopy in which the ampHtude ratio h 

 is variable but the value of the phase difference remains fixed, for 

 example 8 = X/4, are likely to become important because of their utility 

 and feasibility. Experience has shown that it is more important to be 

 able to vary the amplitude ratio than the phase difference. 



One class of systems is obtained by omitting the fiuarter-wave plate 

 from the micoid disk shown in Fig. III. 14. The undeviated and 

 deviated waves which emerge from the conjugate and complementary 

 areas are polarized at right angles. Consequently, the amplitude 

 ratio h may be varied by rotating the analyzer. If the zonal polarizers 

 of the micoid disk are formed of polarizing sheets, the iniiform polarizer 

 can be omitted. This polarizer is necessary, however, when the zonal 

 polarizers consist of two left- and right-handed elements of quartz 

 which rotate the plane of polarization 45° or when the zonal polarizers 

 consist of two suitably oriented half-wave retarding plates. The fixed 

 phase difference d can be obtained by making one of the zonal polarizers 

 slightly thicker than the other or by depositing a material such as 

 magnesium fluoride upon one of the zonal polarizers or upon the conju- 

 gate or complementary area of one of the plates between which the zonal 

 polarizers are cemented. 



Suppose that 8 = +X/4 so that the greater optical path belongs to the 

 conjugate area. If the analyzer is rotated in the neutral quadrant, the 

 equivalent of an infinite, continuous series of !rA4-X/4 or 7'B + X/4 

 diffraction plates is obtained. On the other hand, the equivalent of a 

 continuous set of TA — X/4 and TB— X 4 diffraction plates is obtained by 

 rotating the analyzer in the anti-neutral quadrant. T is continuously 

 variable since T = Ir and since h can be varied practically from zero to 

 infinity. The limits zero and infinity will not be reached because 

 perfectly polarizing materials do not exist. More generally, if the phase 

 difference between the undeviated and deviated waves is 8i when these 

 waves emerge from the zonal polarizers, the apparent phase difference 

 between them is 5i when the analyzer is rotated in the neutral quadrant 

 and is 6i ± X/ 2 when the analyzer is rotated in the anti-neutral quadrant. 

 The values 5i + X/'2 and 5i — X/2 are equivalent in the practice of phase 

 microscopy. 



A method belonging to this class of polanret systems was discovered 

 independently and described by Taylor (1947). In Taylor's system the 

 zonal polarizers consist of left- and right-handed elements of quartz 

 which rotate the plane of polarization 45°. The light incident upon the 

 zonal polarizers was polarized linearly. A fixed phase difference of 



