Expansion of random wave phase in terms of eigenfunctions of phase correlation function

In numerical experiment the authors investigate a representation of the phase of random optical wave through the Karhunen-Loeve-Obukhov (KLO) functions obtained with the use of phase correlation function calculated from experimental data. For such KLO basis the averaged relative error of phase expansion is 5% for 10 basis functions in the expansion series, whereas for the KLO basis calculated with the Kolmogorov structure function of phase the error of phase expansion 5% has been obtained for 78 basis functions. When a propagation medium is close to Kolmogorov model it is possible to use this KLO basis obtained for a single section of distorted phase distribution for representation of whole phase distribution.