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A recent study by Angel (1994) using simplified analytical models indicated the feasibility of imaging extrasolar planets from the ground, making use of adaptive optics correction of a large telescope. We have performed detailed simulations of the method using computer codes that model propagation through atmospheric turbulence, adaptive correction, and broadband imaging. We confirm that high-resolution correction at the limit of photon noise errors reduces the halo intensity to 10 Ϫ6 of the peak star flux. Our work shows how to avoid systematic errors. Thus, we find that time delays between sensing the wave front and its detection lead to persistent structure in the stellar halo, which uncorrected would prevent rapid averaging of the residual halo speckle structure. A local wave front reconstructor that extrapolates ahead in time has been devised to remove this problem. We find the chromatic differences in wave front structure are small enough that the signal-to-noise ratio can be improved by wave front sensing and imaging in separate adjacent bands. We verify that correction of amplitude scintillation is needed and the optimum level of clipping is derived. A simulated image of a twin of the solar system at 8 pc is presented for the new 6.5 m telescope and the measured turbulence at the Multiple Mirror Telescope site. The Jupiter twin shows up at the 5 level in a 5 hr integration.