Vol. 10, issue 08, article # 13

pdf Isaev Yu. N., Zakharova E. V. Representation of Karhunen-Loeve-Obukhov functions in the Walsh and Haar bases. // Atmospheric and oceanic optics. 1997. V. 10. No. 08. P. 598-603.
Copy the reference to clipboard

We have derived analytical relationships that enable one to make a transition from the Haar and Walsh bases in the expansions of the optical phase to a statistically optimal Karhunen–Loeve–Obukhov basis. The former bases are most convenient for use in compensating devices of the adaptive optics systems while the latter one is most correct and comprehensive when formulating criteria of an adaptive optics system closeness to an ideal diffraction-limited system. The relationships derived, if used in parallel with the algorithms of fast Walsh and Haar transforms, enable one to approach real time operation mode when reconstructing the wave fronts. Besides, the transform matrix obtained enables one to allow for the effect of the turbulence outer scale.