Table 1: Computational requirements for various orders of adaptive optics systems. D and d are the telescope diameter and the inter-actuator distance given in meters, $N_{\rm DM}$ and $N_{\rm WFS}$ are the number of DMs and WFSs (>1 implies MCAO), n is the total number of actuators, the column " $\vec{c}=E\vec{ s}$ '' gives the required real-time processing power in Gflops for the matrix-vector multiplication, the column "comp. E'' gives the required number of floating point operations $\times 10^9$ for computing the reconstructor, and the last column gives the required storage space for E in Gb. A Shack-Hartmann type WFS with a Fried geometry of actuators was adopted for the calculations, so that the total number of measurements is $m\approx 2n$ , and the wavefront reconstruction rate was set to 1 kHz. An inter-actuator distance of one meter corresponds roughly to r₀ at 2.2 $\mu$ m, and d=0.25 approximately to r₀ at 0.7 $\mu$ m.
D (m) d (m) $N_{\rm DM}$ $N_{\rm WFS}$ n $\vec{c}=E\vec{ s}$ comp. E storage (Gb)

50 1 1 1 2000 8 8 0.03

50 1 2 5 4000 77 61 0.3

100 1 1 1 8000 123 484 0.5

100 1 2 5 16 000 1234 3876 5

50 0.25 1 1 32 000 1974 31 006 8

50 0.25 2 5 63 000 19 739 248 050 80

100 0.25 1 1 126 000 315 83 $2\times 10^6$ 126

100 0.25 2 5 252 000 315 827 $16\times 10^6$ 1263

**Table 1:** Computational requirements for various orders of adaptive optics systems. D and d are the telescope diameter and the inter-actuator distance given in meters, $N_{\rm DM}$ and $N_{\rm WFS}$ are the number of DMs and WFSs (>1 implies MCAO), n is the total number of actuators, the column " $\vec{c}=E\vec{ s}$ '' gives the required real-time processing power in Gflops for the matrix-vector multiplication, the column "comp. E'' gives the required number of floating point operations $\times 10^9$ for computing the reconstructor, and the last column gives the required storage space for E in Gb. A Shack-Hartmann type WFS with a Fried geometry of actuators was adopted for the calculations, so that the total number of measurements is $m\approx 2n$ , and the wavefront reconstruction rate was set to 1 kHz. An inter-actuator distance of one meter corresponds roughly to r₀ at 2.2 $\mu$ m, and d=0.25 approximately to r₀ at 0.7 $\mu$ m.
D (m)	d (m)	$N_{\rm DM}$	$N_{\rm WFS}$	n	$\vec{c}=E\vec{ s}$	comp. E	storage (Gb)
50	1	1	1	2000	8	8	0.03
50	1	2	5	4000	77	61	0.3
100	1	1	1	8000	123	484	0.5
100	1	2	5	16 000	1234	3876	5
50	0.25	1	1	32 000	1974	31 006	8
50	0.25	2	5	63 000	19 739	248 050	80
100	0.25	1	1	126 000	315 83	$2\times 10^6$	126
100	0.25	2	5	252 000	315 827	$16\times 10^6$	1263

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