func_acf Module

Function that returns $\exp \left(\alpha \sqrt{\left(\frac{x}{\tau_1}\right)^2+ \left(\frac{y}{\tau_2}\right)^2} \right)$

Arguments

Return Value real(kind=r8)

Function that returns the acf of an array. $$\begin{align*} acf(i,j) &= (z \ast z)(i,j) = \sum_{k,l}^{n,n} z(k+1-i,l+1-j)z(k,l) \\ TF(acf) &= ACF = Z \cdot Z \\ acf &= TF^{-1}(ACF) = TF^{-1}(Z^2) \end{align*}$$

Arguments

Function that returns an apodized array.
To prevent gaps from appearing after FFT (because of non periodic waves), the surface must be transformed, but not too much. Here a modified Tukey window is determined. The starting surface is not modified below the “correlation lengths”. Above the correlation lengths, a smooth decrease is forced with a cosine squared.

Arguments

Function that returns the theoretical autocorrelation function in an array.
The autocorrelation function is supposed to be obtained from a real surface which must be periodic or nearly periodic (because of the use of FFTs). In addition, the surface is supposed to be 0 mean and normalized ($\sigma = 1$), therefore acf is zero-mean and normalized so that its max value is 1.

Arguments