According to the assumption stated above, the function tp(x,y,z) varies 

 very slowly in the x-direction. In order to facilitate the analysis, we 

 take the Fourier transform of <{>_ such as 



OO 00 



I , ikx , iut I . 

 ij) e dx = e i/j e 



ix(k-K) dx 



= e ±a)t ?(k-K,y,z) (214) 



where \\) is the Fourier transform of ty. The diffraction potential satisfies 

 the Laplace equation 



2 2 2 



3 <j> 3 <j> 3 <J> 



—^ + —^ + —£■ = (215) 



3x 3y 3z 



and its Fourier transform is 



-k 2 * D+ -^ + - 1 £-0 (216) 



dy dz 



Substituting the above mentioned expression for the diffraction potential, 

 Equation (214), shifting the first term of Equation (216) to the right- 

 hand side and putting k - K = k' , we obtain 



■L| + A-|= (k'+K) 2 ? (217) 



3y 3z 



The basic assumption of the slow variation of ip suggests that, if ty = 0(1) 

 then TJT(k',y,z) = 0(l/k'). Therefore, k' must be 0(1) if ^T = 0(1). Since 



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