Is there a method to compute an average amplitude for 2D sinusoids using the F.C.'s? I am working on FFT analysis AFM like the one shown below. I am currently at a point where I understand fairly well what an FFT does, and how to think about the information it gives. I currently have an $M\times N$ matrix of Fourier coefficients (FC) for a 2D-image like the one below. Choosing to look at the real and imaginary part of the FC's gives the amplitudes for sine and cosine terms in the Fourier expansion. I use the notation $X[k,l]$ to index the FC's. For some of my images the real and imaginary parts of the FFT look something like what is shown below. 

Sample Image:

 

Real part of FC's:



Imaginary part of FC's:



Note that the above FC plots are not for the image shown above. I am looking now to pull out the dominant functional forms. In general with these experiments it is expected that there will be 2 two-directions along which there are dominant sinusoids. 

Are there standard ways of computing an average amplitude for 2D-FFT's? I was thinking that there is probably a way to perform a weighted average using the magnitudes of the Fourier coefficients. References and suggestions appreciated.

Additional:

I am thinking something like this in order to compute the average amplitude:

$\langle X \rangle=\sum_{k=0}^{M-1}\sum_{l=0}^{M-1}\frac{X_R^2}{X_R^2+X_I^2}X_R(k,l)-\frac{X_I^2}{X_R^2+X_I^2}X_I(k,l)$

The terms in front of $X_R$ and $X_I$ are my crude way to weight the importance of each sinusoid to the total signal. I have no justification for my choice, which is something I would like clarified. Perhaps there is an accepted way to weight the amplitudes. Clearly, my average is bad because of when $X_R=X_I=0$ I get a 0/0. 

Cheers.
Easy thing first: You might want to look into spatial statistics 


A fast library to compute Spatial Statistics in Matlab using FFTs.
A good description of Spatial Statistics from a past student


Long Stuff:

The trouble with comparing materials science information (eg AFM) is that the piece of material was measured at a position in space and time.  It is difficult to quantitatively compare images in one place and an image in another place.  

When you take the Fourier transform, you are measuring the frequency of that material at a position in space and time.  

You can remove the spatial dependency by taking a convolution of the Fourier transform with itself.  This process is akin to Point Distribution Functions, N-Point Statistics, or Joint Probability Density Functions.  The Spatial Statistics Matlab library can be applied to most image data.