where formula_44 is the optical phase error introduced by atmospheric turbulence, r (k) is a two-dimensional square array of independent random complex numbers which have a gaussian distribution about zero and white noise spectrum, k (k) is the (real) fourier amplitude expected from the kolmogorov (or von karman) spectrum, re[] represents taking the real part, and ft[] represents a discrete fourier transform of the resulting two-dimensional square array (typically an fft).