Off-axis observations made with adaptive optics are severely limited by anisoplanatism errors. However, conjugating the deformable mirror to an optimal altitude can reduce these errors; it is then necessary to control, through extrapolation, actuators that are not measured by the wave-front sensor (unilluminated actuators). In this study various common extrapolation schemes are investigated, and an optimal method that achieves a significantly better performance is proposed. This extrapolation method involves a simple matrix multiplication and will be implemented in ALTAIR, the Gemini North Telescope adaptive optics system located on Mauna Kea, Hawaii. With this optimal method, the relative H-band Strehl reduction due to extrapolation errors is only 5%, 16%, and 30% when the angular distance between the guide source and the science target is 20, 40 and 60 arc sec, respectively. For a site such as Mauna Kea, these errors are largely outweighed by the increase in the size of the isoplanatic field.

© 2000 Optical Society of America

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