III-78 



n = -1 



iJ_,(2kYh) + i-^A^J_^[kh(Yi + Y)]+A_^J„|kh(Y., +y)\ 



00 



+ V i^-"^A J rkh(Y^ + Y)l-0 (III-76C) 



m=-«> 



Then La Casce and Tamarkin assume that kh is so small that Bessel functions 

 of order greater than one (instead of zero as before) can be neglected. Further- 

 more, they assume that Ai is also very small. Then, from (III-76c) and (III- 

 76a) one obtains the approximations 



kh(Y^ +Y) 

 \--h <2khY) 1 



(III-77) 

 A.^« - i J^ (2khY) 



These expressions for A and A_ indicate an interaction between the specu- 

 larly reflected and higher order components. For frequencies so low that y^ 

 is complex, A is given only by 



- J (2khY) • (in-78) 



i.e. , there is a cutoff frequency below which the specular magnitude is given 

 simply by the Rayleigh approximation. 



Heaps has determined values of the Aj^ under the assumption that 

 Ajj = for n such that Yn is imaginary. This is equivalent to assuming that 

 all the reflected radiation is in plane undamped waves . For any particular 

 surface. Equation III- 72 becomes a finite set of linear equations for the Aj^, 

 which may be solved by ,the usual methods . 



arthur H.littlcJnir. 



S-7001-0307 



