MODIFIED UXDEVIATED AND DEVIATED WAVES 45 



spectively by the equations 



in which U and D are complex numbers which will be used henceforth 

 in referring to the undeviated and deviated waves, respectively. It 

 will be noted that the phase factor (^-'^^"'oynpo ^yhJch arises from the 

 inclination of the incident wave front is common to both the undeviated 

 and the deviated wave. 



7. REPRESENTATION OF THE MODIFIED UNDEVIATED AJ\D DEVIATED 

 WAVES 



The relative amplitude and phase of the undeviated and deviated 

 waves is given by Eqs. 6.7 and 6.8 as these waves emerge from the object 

 plane. In a standard, highly corrected microscope these waves are 

 transported to the conjugate image plane without further relative modi- 

 fication other than a loss of the more steeply inclined portion of the 

 deviated bundle of rays. Let the plate which supports the coating 

 material of the diffraction plate be regarded as a component part of a 

 fully corrected microscope objective, and let the optical path from the 

 object to the image plane be T^ radians. In the absence of any coating 

 material on the dift'raction plate, the undeviated and deviated waves 

 then arrive at the image plane with relative amplitude and phase given 

 by 



D = giV^-2^imyopo^ggiA _ ly (j 2) 



It has been seen in Section 3 that the undeviated and deviated waves 

 pass through the conjugate and complementary areas of the diffraction 

 plate, respectively. Let the amplitude and phase transmission of the 

 conjugate area and of the complementary area be represented by the 

 complex numbers hoe'^^ and /iie'^S respectively. In the presence of 

 coating materials on the diffraction plate the undeviated and deviated 

 waves will now arrive at the image plane with amplitude and phase 

 determined by the equations 



U ^ e^ V-"''^"'^o''%e''^0; (7.8) 



D = e'V-"':'^o^o'"'(^.e^^_- l)/iie^"\ (7.4) 



These equations are obtained by multiplying the right-hand members 

 of Eqs. 7.1 and 7.2 by /ioe'^° and /?ie'^', respectively. When ho = hi = 1 

 and 6o = 5i = 0, the conjugate and complementarj^ areas of the dif- 



