Reflectivity under the Kinematic Approximation

In the kinematic approximation the intensity of scattering, as discussed in Section 1.5.2, is given by 

The constants Cx and Cy are equal to 2nLx and 2ixLy, respectively, Lx and Ly being the dimensions of the illuminated surface (LxLy = A). 

For the sake of interested readers the demonstration that CxCy is equal to (2tc)2 A is given as follows. That CxCy should be proportional to LxLy can easily be rationalized from the fact that the intensity must be proportional to the illuminated area. The factors 2tt in Cx and Cy essentially arise from the use of q instead of s as the scattering vector. To see this, we make use of Parseval s theorem11 that states that 

Integrating (7.40) with respect to dQ to obtain the reflected beam energy e, we find s = J j(2jt)2LxLyS(qx)S(qy) f p(z) 2 g Qdqx dqy 

Using (B.18), which states that the Fourier transform of the derivative of a function is iq times the Fourier transform of the function, (7.46) can be written also as 

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