Correlation function of lamellar structure

Instead of comparing the observed intensity with the one calculated on the basis of an assumed model, we may derive the correlation function from the observed intensity and then analyze it directly or compare it with the one calculated from the model. The potential advantage of such a correlation function approach has been stressed by some workers.36 37 From the observed one-dimensional intensity I (q), the one-dimensional correlation function Ti(x) can be obtained by 

If I q) is known only in arbitrary units, as is usually the case in practice, the normalized correlation function y (x) may instead be evaluated by 

The correlation function, on the other hand, can be calculated from the assumed structure by 

Certain features of the self-correlation triangle centered at the origin are of interest and can be interpreted directly in terms of the structural parameters. In view of the definition of the correlation function, Equation (5.159), we find the following  

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