Milgram 



Appendix B 

 EVALUATION OF LIFTING- LINE IMAGE INTEGRALS 



This section contains the evaluation of the set of integrals 



, cos n d4> 



Let 



Then, 



4h 



2 + — - (cos0+ cos 0) 

 b 



4h , , 



= 2 + — - cosi//> 1 

 b 



77- 



f COS n0 



I = ^d0 



" J Q - cos c^ 



(Bl) 



(B2) 



(B3) 



A difference equation for the i^'s will now be derived. 



TT 



COS (n+1) 4> + cos (n-l)0 



In+l + ^n-l 



Q - cos 



dcp 



This can be written as 



I 4.1 + I -1 



n+ 1 n 1 



2Q cos ik; 



2 cos na 



d0 



(B4) 



(B5) 



Q - cos 4> 



Since the integrated value of the second term of Eq. (B5) is zero, 



In.l + In-1 = 2 0I„ . (B6) 



The solution of Eq. (B6) contains two constants which can be determined by 

 equating the solution to i^ for two different values of n . Iq and l^ can be de- 

 termined by simple integration, giving 



" VQ^ - 1 



(B7) 



and 



1432 



