in which 



Furthermore, 



when 



( 



OBJECTS OF PERIODIC STRUCTURE .267 



'^--'i^-^-^-d£)- ^--) 





wherein N.A. is the numerical aperture of the objective and M is the 

 magnification ratio between the object and image planes. 



The amplitude and phase distribution of the light entering the image 

 plane may now be compared with the amplitude and phase distribution of 

 the light leaving the object plane. From Eq. 8.9 it will be seen that the 

 phase factor e"'"^"^^''/i?i, is not included in the function Fq{x, y, po,qo). 

 For purposes of direct comparison we therefore exclude this phase 

 factor from xU'o, Vo, Po, Qo) as given by Eq. 8.8 and write 



XoU-o, yo, Po, go) - e2.,:(poxo+<,o.o) j(,.^^ y^y (10.19) 



We call xo(^'o, Vo, Po, Qo) the composite object Junction. It may be inter- 

 preted as the amplitude and phase distribution of the coherent light 

 which leaves the object plane. g27ri{pua;u+go2/o) jg jj^ fg^^^ ^^ phase factor 

 which specifies the phase distribution induced upon the object plane by 

 the incidence of a wave front whose normal has the optical direction 

 cosines (po, <1q)- Hence the equations 



Xo(.ro, 2/0, Po, go) = e2-'-<^«-«+^«^«^ ^^ J.J^ (? +^°); (10.20) 



Foix, y, Po, go) = 



J^2 2^2^B.J,,,e ^^^' ^'^-^ (10.21) 



describe the amplitude and phase distributions which leave the object 

 plane and enter the image plane, respectively. Suppose that B^,^ = 1. 

 Since points Xq, yo of the object plane are imaged into points x, y of the 

 image plane such that x = Mxq, y — Myo, it follows that 



Xo = M^Fo (10.22) 



when 



5,.^ = 1. (10.23) 



