Lattice Line Discretization

The idea behind lattice line discretization is given in the figure below: a model function based on the physical measurement process is sought which describes as accurately as possible the measured intensities.

For a bandwidth limited, discretized function is real-space, the resulting Fourier space is sufficiently described by a finite number of (complex) coefficients S_n or . If we would already know these coefficients for a particular lattice line, then we could calculate the central-section intersection value F_hk at a particular z* by

Note that F_hk and S_n are complex numbers. What we really have is the intensity at each z*, i.e. I=|F|² :

This non-linear equation can be solved to obtain a set of (Re_n, Im_n ), from which the discretized intensities are easily obtained: I_n=[Re_n]² + [Im_n]².

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