Multi-object adaptive optics (MOAO) has been demonstrated by the CANARY instrument on the William Herschel Telescope. However, for proposed MOAO systems on the next generation Extremely Large Telescopes, such as EAGLE, many challenges remain. Here we investigate requirements that MOAO operation places on deformable mirrors (DMs) using a full end-to-end Monte-Carlo AO simulation code. By taking into consideration a prior global ground-layer (GL) correction, we show that actuator density for the MOAO DMs can be reduced with little performance loss. We note that this reduction is only possible with the addition of a GL DM, whose order is greater than or equal to that of the original MOAO mirrors. The addition of a GL DM of lesser order does not affect system performance (if tip/tilt star sharpening is ignored). We also quantify the maximum mechanical DM stroke requirements (3.5 $mu$m desired) and provide tolerances for the DM alignment accuracy, both lateral (to within an eighth of a sub-aperture) and rotational (to within 0.2$^circ$). By presenting results over a range of laser guide star asterism diameters, we ensure that these results are equally applicable for laser tomographic AO systems. We provide the opportunity for significant cost savings to be made in the implementation of MOAO systems, resulting from the lower requirement for DM actuator density.
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