Figure 1: Generic adaptive optics schematic, introducing the chief components that must be incorporated into a first-order simulation of the system: the reference beacon ("guide star''), atmospheric turbulence, the telescope, wavefront sensor, deformable mirrors and a real-time control computer. | |
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Figure 2: Upper left - Fried geometry of WFS sub-apertures and DM actuators; upper right - the natural numbering of the actuators. Lower left - heuristic model for a Fried geometry interaction; numbers indicate the x- and y-component of the gradient registered in respective sub-aperture as a result of poking the central actuator. Lower right - numerical weights for the discrete definition C of the Laplacian curvature operator, for an internal, edge and corner point of the mesh. | |
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Figure 3: Modulus of G^{T}G+C^{T}C for n=69 and n=877. | |
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Figure 4: Required computing time as a function of the order of the system for explicit (pluses) matrix-vector multiplication and sparse (diamonds) PCG wavefront reconstruction algorithms. Slopes extrapolated from the last two data points are indicated next to each data set, where the two values for the PCG, 1.56 and 1.18, correspond to relative error tolerances of 10^{-6} and 10^{-2}. | |
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Figure 5: Flow diagram of the hybrid numerical simulation. | |
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Figure 6: Residual phase variance and number of PCG iterations versus the PCG relative error tolerance, for the Shack-Hartmann test configuration in conventional AO (dotted lines) and MCAO (dashed lines) mode. In the top field, a field-weighted average (pluses), an unweighted average (diamonds) and the on-axis value (asterisks) are plotted for comparison. | |
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Figure 7: Comparison between simulation results (phase variance - solid; Strehl ratio - dotted) for the hybrid simulation of the current study (diamonds) and a more accurate wave optical simulation with well-sampled turbulence (pluses). Dashed curves show for comparison the hybrid simulation result without fitting and aliasing compensation. | |
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Figure 8: On-axis residual phase variance versus telescope diameter D for LGS AO, for a range of outer scales L_{0}. Low- and high-order AO systems with d=0.8 m (solid) and d=0.5 m (dashed) are both shown for comparison. | |
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Figure 9: Same data as in Fig. 8 re-plotted on logarithmic axes to show the differing slopes. | |
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