Valerii Voitsekhovich,
Leonardo Sanchez,
Valeri Orlov,
and Salvador Cuevas
The authors are with the Instituto de Astronomia, Observatorio Astronomico Nacional, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-264, Cd. Universitaria, Mexico 04510, D.F., Mexico.
Valerii Voitsekhovich, Leonardo Sanchez, Valeri Orlov, and Salvador Cuevas, "Efficiency of the Hartmann test with different subpupil forms for the measurement of turbulence-induced phase distortions," Appl. Opt. 40, 1299-1304 (2001)
The reconstruction quality of turbulence-induced phase distortions
from Hartmann data is calculated for masks with different subpupil
forms by means of computer simulations. Four subpupil forms are
considered: the circle, the square, the hexagon, and the polar
segment. We show that, for the case of a circular aperture, the
mask with polar segment subpupils provides the best reconstruction
quality.
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Comparison of the Theoretical and the Simulated
Statistical Errors for Mask (c) in Fig. 1
Mode
Relative Statistical Errors (%)
Mode
Relative Statistical Errors (%)
Simulation
Theory
Simulation
Theory
2
0.25
0.25
12
10.24
10.34
3
0.25
0.25
13
10.25
10.34
4
0.89
0.89
14
8.41
8.45
5
0.81
0.82
15
8.46
8.45
6
0.81
0.82
16
15.80
15.89
7
3.27
3.27
17
15.92
15.89
8
3.26
3.27
18
6.71
6.74
9
1.96
1.96
19
6.87
6.89
10
1.20
1.21
20
9.91
9.91
11
15.82
15.84
21
9.94
9.91
Table 2
Statistical Errors Associated with Five Masks (Noiseless
Case)a
Mode
Relative Statistical Errors (%)
(a)
(b)
(c)
(d)
(e)
2
0.26
0.17
0.25
0.21
0.11
3
0.26
0.17
0.25
0.21
0.10
4
0.55
0.60
0.89
0.81
0.41
5
0.64
0.69
0.81
0.77
0.25
6
1.08
0.87
0.81
0.77
0.25
7
3.44
4.76
3.27
3.37
2.18
8
3.51
4.79
3.26
3.39
2.19
9
2.08
3.24
1.96
1.92
0.89
10
2.09
3.29
1.21
1.41
0.89
11
9.02
5.48
15.82
13.26
7.77
12
8.09
4.28
10.24
8.03
9.83
13
6.91
3.45
10.25
8.01
9.69
14
6.08
4.59
8.41
6.31
12.46
15
12.04
5.09
8.46
6.23
12.28
16
16.17
13.24
15.80
13.48
10.36
17
16.12
13.24
15.92
13.37
10.33
18
8.32
8.39
6.71
4.81
6.15
19
8.29
8.36
6.87
5.09
6.15
20
11.51
10.36
9.91
7.65
11.07
21
11.55
10.19
9.94
7.67
11.02
Total error
0.99
0.79
1.00
0.86
0.64
The masks are shown in Fig. 1. For
each mode the minimum error is shown in boldface, while the maximum
error is shown in italic. The last row shows the normalized total
errors. The normalization factor is equal to the absolute total
error associated with mask (c) in noiseless conditions.
Table 3
Statistical Errors Associated with Five Masks (Noise,
20%)a
Mode
Relative Statistical Errors (%)
(a)
(b)
(c)
(d)
(e)
2
0.47
0.36
0.47
0.43
0.30
3
0.47
0.37
0.46
0.42
0.30
4
1.15
1.17
1.49
1.41
1.06
5
1.78
1.81
1.88
1.82
1.33
6
2.21
1.97
1.87
1.81
1.31
7
4.97
6.18
4.84
4.89
3.58
8
5.00
6.22
4.90
4.93
3.58
9
4.44
5.75
4.08
4.07
2.89
10
4.29
5.69
3.26
3.50
2.93
11
11.22
8.03
17.85
15.63
9.62
12
10.08
6.63
12.14
9.97
11.31
13
9.05
5.89
12.14
9.99
11.46
14
9.84
9.14
11.81
9.77
15.47
15
15.72
9.68
11.77
9.82
15.16
16
20.42
19.06
20.01
17.86
14.62
17
20.68
19.14
19.92
17.79
14.36
18
11.64
13.04
9.74
8.12
8.97
19
11.70
12.85
9.53
7.92
8.75
20
18.12
18.63
15.28
13.45
15.69
21
17.85
18.56
15.40
13.58
15.75
Total error
1.65
1.47
1.66
1.51
1.24
The masks are shown in Fig. 1. For
each mode the minimum error is shown in boldface, while the maximum
error is shown in italic. The normalization factor is equal to the
absolute total error associated with mask (c) in noiseless
conditions.
Tables (3)
Table 1
Comparison of the Theoretical and the Simulated
Statistical Errors for Mask (c) in Fig. 1
Mode
Relative Statistical Errors (%)
Mode
Relative Statistical Errors (%)
Simulation
Theory
Simulation
Theory
2
0.25
0.25
12
10.24
10.34
3
0.25
0.25
13
10.25
10.34
4
0.89
0.89
14
8.41
8.45
5
0.81
0.82
15
8.46
8.45
6
0.81
0.82
16
15.80
15.89
7
3.27
3.27
17
15.92
15.89
8
3.26
3.27
18
6.71
6.74
9
1.96
1.96
19
6.87
6.89
10
1.20
1.21
20
9.91
9.91
11
15.82
15.84
21
9.94
9.91
Table 2
Statistical Errors Associated with Five Masks (Noiseless
Case)a
Mode
Relative Statistical Errors (%)
(a)
(b)
(c)
(d)
(e)
2
0.26
0.17
0.25
0.21
0.11
3
0.26
0.17
0.25
0.21
0.10
4
0.55
0.60
0.89
0.81
0.41
5
0.64
0.69
0.81
0.77
0.25
6
1.08
0.87
0.81
0.77
0.25
7
3.44
4.76
3.27
3.37
2.18
8
3.51
4.79
3.26
3.39
2.19
9
2.08
3.24
1.96
1.92
0.89
10
2.09
3.29
1.21
1.41
0.89
11
9.02
5.48
15.82
13.26
7.77
12
8.09
4.28
10.24
8.03
9.83
13
6.91
3.45
10.25
8.01
9.69
14
6.08
4.59
8.41
6.31
12.46
15
12.04
5.09
8.46
6.23
12.28
16
16.17
13.24
15.80
13.48
10.36
17
16.12
13.24
15.92
13.37
10.33
18
8.32
8.39
6.71
4.81
6.15
19
8.29
8.36
6.87
5.09
6.15
20
11.51
10.36
9.91
7.65
11.07
21
11.55
10.19
9.94
7.67
11.02
Total error
0.99
0.79
1.00
0.86
0.64
The masks are shown in Fig. 1. For
each mode the minimum error is shown in boldface, while the maximum
error is shown in italic. The last row shows the normalized total
errors. The normalization factor is equal to the absolute total
error associated with mask (c) in noiseless conditions.
Table 3
Statistical Errors Associated with Five Masks (Noise,
20%)a
Mode
Relative Statistical Errors (%)
(a)
(b)
(c)
(d)
(e)
2
0.47
0.36
0.47
0.43
0.30
3
0.47
0.37
0.46
0.42
0.30
4
1.15
1.17
1.49
1.41
1.06
5
1.78
1.81
1.88
1.82
1.33
6
2.21
1.97
1.87
1.81
1.31
7
4.97
6.18
4.84
4.89
3.58
8
5.00
6.22
4.90
4.93
3.58
9
4.44
5.75
4.08
4.07
2.89
10
4.29
5.69
3.26
3.50
2.93
11
11.22
8.03
17.85
15.63
9.62
12
10.08
6.63
12.14
9.97
11.31
13
9.05
5.89
12.14
9.99
11.46
14
9.84
9.14
11.81
9.77
15.47
15
15.72
9.68
11.77
9.82
15.16
16
20.42
19.06
20.01
17.86
14.62
17
20.68
19.14
19.92
17.79
14.36
18
11.64
13.04
9.74
8.12
8.97
19
11.70
12.85
9.53
7.92
8.75
20
18.12
18.63
15.28
13.45
15.69
21
17.85
18.56
15.40
13.58
15.75
Total error
1.65
1.47
1.66
1.51
1.24
The masks are shown in Fig. 1. For
each mode the minimum error is shown in boldface, while the maximum
error is shown in italic. The normalization factor is equal to the
absolute total error associated with mask (c) in noiseless
conditions.