NOX-UNIFORMLY ALTERED HIGHER ORDERS 



279 



the diffraction plate consists of two spots which coincide with the in^ages 

 produced by the oppositely inclined zero orders. 



The object function is described by Eqs. 10.1.1 and 10.1.2. The 

 amplitude and phase distribution over the plane of the image is given 

 by Eq. 10.1.3 but with the pupil function subject to Eq. 10.3.1. Since 

 two narrow cones of light are incident upon the object plane, an argument 

 similar to that which leads to Eq. 10.1.7 shows that 



3 



G(-) = § 



EK" + 



-3 



.1/ 2J//, 



3 



/. 



JiirvxIMl) 





Let 



;-= -3 

 3 



M 



- + :T^Ue'^""^''') 



2il//. 





(10.3.2) 



(10.3.3) 



(10.3.4) 



I. = -3 



Let P = Po or Pi, according as the point p = {±po/M + v/2Ml) falls 

 in the conjugate or in the complementary area. Thus P — Fq when 



\M 2MlJ \ M 2Mh 



= Po; 



p^'^^±r] = p,^ 



/po 



+ 



\M 2MI 



= P 



M 2MI 

 ' -Po 3_ 



2ML 



0. 



These statements follow directly from the arrangement of the spectral 

 orders of Fig. VILll. Since /^ = /_^, we obtain 



TVX 



Si {x) = /oFo + 2Pifi cos — + Po/3,-'(3-/iv/» . (10.3.5) 



WX 



SoAx) = /oPo + 2Pi/i cos ^ + Pofse'^'-'''^"''\ 



(10.3.6) 



At the points x = 0, ±:n2Ml, in the centers of the troughs 



Si{±n2Mr) = S2{±7i2Ml) = /qPo + 2P1/1 + P0/3; (10.3.7) 

 n = 0, 1, 2, 3, etc. 



