OBJECTS OF PERIODIC STRUCTURE 



265 



where Fo(x, y, po, Qo) is the amplitude and phase distribution produced 

 over the image plane XY by the incidence upon the object plane of a 



Xn Yn (object plane) 



(image plane) XY i 



Normal 



-Coherent, incident wave front 

 Fig. VII. 8. Object specimens of periodic structure. 



wave front whose normals have the optical direction cosines po, Qq. 

 Introduce into Eq. 10.3 the change of variable 



Xi = X - ilf.ro; 2/1=2/- Myo; (10.4) 



then 



M'Foix, y, vo, qo) = e '' ZJl^ ^"^^'•'^ ' ^^^"^^ 



B 



U — x %J — 



-*■" ^ {.m + 5) + ^' (i^ + %')] 



V{x\. 2/1, ) ^xx dyx. 

 (10.6) 



Equations 10.3, 10.5, and 10.6 contain the assumption that the field of 

 view extends over a great number of wavelengths and over a large 

 number of the grating spacings. The limits — oo to + =0 in the integra- 

 tion with respect to dx^ dyo or to dxi dy\ now comprise an excellent ap- 

 proximation to the truth. 



The coefficients By^y, can be stated more simply from the following 

 considerations. Since 



U{x,, 2/1) =ffP(P' 9)^2"^^^^+^^^^ dpdq, 



(10.7) 



