D. G. Sandler, J. R. P. Angel, M. Lloyd-Hart, S. Stahl, and D. McCarthy, "Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes," J. Opt. Soc. Am. A 11, 925-945 (1994)
When equipped with adaptive optics, the coming generation of large 6–10-m telescopes can combine huge light grasp with very sharp images. We describe a specific design concept for recovery of diffraction-limited images in the 1.6- and the 2.2-μm atmospheric windows, yielding 0.05-arcsec resolution for an 8-m telescope. Our goal has been to achieve this performance routinely by not requiring above-average atmospheric conditions or the use of unusually bright nearby stars. Atmospheric blurring is sensed with a sodium laser beacon of a few watts. Image motion is sensed by starlight, with a quadrant detector that is sensitive to the broad infrared band in which photon flux is typically largest and the field star has been sharpened by laser-beacon correction that is shared with the science target. A detailed performance analysis shows that for typical conditions Strehl ratios of >25% are expected at 2.2 μm, with the probability of finding a sufficiently bright field star exceeding 50%.
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Atmospheric Parameters for the MK and the MMK Turbulence Models at λ = 0.5, λ = 1.6, λ = 2.2 μm
Parameter
MK
MMK
λ = 0.5 μm
λ = 1.6 μm
λ = 2.2 μm
λ = 0.5 μm
λ = 1.6 μm
λ = 2.2 μm
r0 (m)
0.18
0.72
1.06
0.15
0.61
0.89
θ0 (arcsec)
3.0
12.0
17.7
1.3
5.2
7.7
t0 (ms)
3.6
14.4
21.2
1.8
7.2
10.6
Table 2
Tilt Errors from the Combined Effects of Temporal Decorrelation and Measurement Noisea
Parameter
Star Flux [(photons/m2)/s]
400
1000
2500
Image width (arcsec)
0.05
0.12
0.05
0.12
0.05
0.12
Integration time (ms)
10.0
16.1
6.6
10.8
4.4
7.4
Rms centroid error (arcsec)
0.0103
0.0167
0.0068
0.0112
0.0046
0.0077
Corrected wave band
H
K
H
K
H
K
H
K
H
K
H
K
Strehl ratio (%)
75
85
54
69
87
93
72
83
94
97
85
91
The table gives the integration length that is necessary to balance decorrelation and measurement noise. The corresponding combined error, equal to [(σθnoise)2 + (σθtime)2]1/2, is expressed in rms motion (arcsec), and the corresponding Strehl ratio is computed from Eq. (9) with D = 8 m. The calculation is for different star flux levels, assuming a constant background sky flux of 9000 [(photon/s)/m2]/arcsec2 incident at the telescope. The quad-cell pixel size is 0.15 arcsec with readout noise of 5 electrons rms, and the overall system quantum efficiency is 40%.
Table 3
Error Sources for Correcting the High-Order Wave-Front across an 8-m Telescope at λ = 1.6 μm and λ = 2.2 μma
Parameter
MK
MMK
λ = 1.6 μm
λ = 2.2 μm
λ = 1.6 μm
λ = 2.2 μm
(σϕcone)2
0.28
0.15
0.77
0.41
(σϕrec)2
0.10
0.10
0.10
0.10
(σϕtime)2
0.073
0.038
0.23
0.12
(σϕfit)2
0.50
0.26
0.66
0.35
σϕ2
0.95
0.55
1.76
0.98
Sϕ
0.39
0.58
0.17
0.37
The value of σϕrec assumes a 1.5-W sodium laser for λ = 2.2 μm and a 3-W laser for λ = 1.6 μm.
Table 4
Contributions to the Total Strehl Ratio for the H (λ = 1.6 μm) and the K (λ = 2.2 μm) Wave Bandsa
Parameter
MK
MMK
λ = 1.6 μm
λ = 2.2 μm
λ = 1.6 μm
λ = 2.2 μm
Sϕ
0.39
0.58
0.17
0.37
Sθ
0.5
0.8
0.5
0.8
0.5
0.8
0.5
0.8
S
0.20
0.31
0.29
0.46
0.09
0.14
0.19
0.30
Ppole
33%
75%
8%
25%
P30°
65%
97%
19%
50%
The high-order Strehl ratios Sϕ, are taken from Table 3. The tilt Strehl ratios Sθ are appropriate if one is using a field star (50%) or a faint star that is coincident with the laser beacon (80%) as analyzed in Section 5. The total Strehl ratios are given by S = SθSϕ. The probabilities for finding at least one sufficiently bright field star within the required angle to give a 50% tilt Strehil ratio are given for the galactic pole (Ppole) and for 30° galactic latitude (P30°).
Tables (4)
Table 1
Atmospheric Parameters for the MK and the MMK Turbulence Models at λ = 0.5, λ = 1.6, λ = 2.2 μm
Parameter
MK
MMK
λ = 0.5 μm
λ = 1.6 μm
λ = 2.2 μm
λ = 0.5 μm
λ = 1.6 μm
λ = 2.2 μm
r0 (m)
0.18
0.72
1.06
0.15
0.61
0.89
θ0 (arcsec)
3.0
12.0
17.7
1.3
5.2
7.7
t0 (ms)
3.6
14.4
21.2
1.8
7.2
10.6
Table 2
Tilt Errors from the Combined Effects of Temporal Decorrelation and Measurement Noisea
Parameter
Star Flux [(photons/m2)/s]
400
1000
2500
Image width (arcsec)
0.05
0.12
0.05
0.12
0.05
0.12
Integration time (ms)
10.0
16.1
6.6
10.8
4.4
7.4
Rms centroid error (arcsec)
0.0103
0.0167
0.0068
0.0112
0.0046
0.0077
Corrected wave band
H
K
H
K
H
K
H
K
H
K
H
K
Strehl ratio (%)
75
85
54
69
87
93
72
83
94
97
85
91
The table gives the integration length that is necessary to balance decorrelation and measurement noise. The corresponding combined error, equal to [(σθnoise)2 + (σθtime)2]1/2, is expressed in rms motion (arcsec), and the corresponding Strehl ratio is computed from Eq. (9) with D = 8 m. The calculation is for different star flux levels, assuming a constant background sky flux of 9000 [(photon/s)/m2]/arcsec2 incident at the telescope. The quad-cell pixel size is 0.15 arcsec with readout noise of 5 electrons rms, and the overall system quantum efficiency is 40%.
Table 3
Error Sources for Correcting the High-Order Wave-Front across an 8-m Telescope at λ = 1.6 μm and λ = 2.2 μma
Parameter
MK
MMK
λ = 1.6 μm
λ = 2.2 μm
λ = 1.6 μm
λ = 2.2 μm
(σϕcone)2
0.28
0.15
0.77
0.41
(σϕrec)2
0.10
0.10
0.10
0.10
(σϕtime)2
0.073
0.038
0.23
0.12
(σϕfit)2
0.50
0.26
0.66
0.35
σϕ2
0.95
0.55
1.76
0.98
Sϕ
0.39
0.58
0.17
0.37
The value of σϕrec assumes a 1.5-W sodium laser for λ = 2.2 μm and a 3-W laser for λ = 1.6 μm.
Table 4
Contributions to the Total Strehl Ratio for the H (λ = 1.6 μm) and the K (λ = 2.2 μm) Wave Bandsa
Parameter
MK
MMK
λ = 1.6 μm
λ = 2.2 μm
λ = 1.6 μm
λ = 2.2 μm
Sϕ
0.39
0.58
0.17
0.37
Sθ
0.5
0.8
0.5
0.8
0.5
0.8
0.5
0.8
S
0.20
0.31
0.29
0.46
0.09
0.14
0.19
0.30
Ppole
33%
75%
8%
25%
P30°
65%
97%
19%
50%
The high-order Strehl ratios Sϕ, are taken from Table 3. The tilt Strehl ratios Sθ are appropriate if one is using a field star (50%) or a faint star that is coincident with the laser beacon (80%) as analyzed in Section 5. The total Strehl ratios are given by S = SθSϕ. The probabilities for finding at least one sufficiently bright field star within the required angle to give a 50% tilt Strehil ratio are given for the galactic pole (Ppole) and for 30° galactic latitude (P30°).
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