Isoplanatism in a multiconjugate adaptive optics system

Turbulence correction in a large field of view by use of an adaptive optics imaging system with several deformable mirrors (DM's) conjugated to variou s heights is considered. The residual phase variance is computed for an opt imized linear algorithm in which a correction of each turbulent layer is ac hieved by applying a combination of suitably smoothed and scaled input phas e screens to all DM's. Finite turbulence outer scale and finite spatial res olution of the DM's are taken into account. A general expression for the is oplanatic angle BM of a system with M mirrors is derived in the limiting ca se of infinitely large apertures and Kolmogorov turbulence. Like Fried's is oplanatic angle theta(0), theta(M) is a function only of the turbulence ver tical profile, is scalable with wavelength, and is independent of the teles cope diameter. Use of angle BM permits the gain in the field of view due to the increased number of DM's to be quantified and their optimal conjugate heights to be found. Calculations with real turbulence profiles show that w ith three DM's a gain of 7-10x is possible, giving the typical and best iso planatic field-of-view radii of 16 and 30 arcseconds, respectively, at lamb da = 0.5 mu m. It is shown that in the actual systems the isoplanatic field will be somewhat larger than theta(M) owing to the combined effects of fin ite aperture diameter, finite outer scale, and optimized wave-front spatial filtering. However, this additional gain is not dramatic; it is less than 1.5x for large-aperture telescopes. (C) 2000 Optical Society of America [S0 740-3232(00)02010-X] OCIS codes: 010.0010, 010.1080, 010.1330.