Correlation of single-mode fiber radiation response and fabrication parameters
E. Joseph Friebele, Charles G. Askins, Cathy M. Shaw, Michael E. Gingerich, Calvin C. Harrington, David L. Griscom, Tsung-Ein Tsai, Un-Chul Paek, and William H. Schmidt
E. Joseph Friebele,5
Charles G. Askins,5
Cathy M. Shaw,4
Michael E. Gingerich,5
Calvin C. Harrington,4
David L. Griscom,5
Tsung-Ein Tsai,3
Un-Chul Paek,1
and William H. Schmidt2
1When this work was done, U. C. Paek was with AT&T Bell Laboratories (ERC), Princeton, New Jersey 08540. He is now with Korea Academy of Industrial Technology, Seoul, Korea.
2Michigan State University, East Lansing, Michigan 48824
3GeoCenters, Inc., Fort Washington, Maryland 20375
4SFA, Inc., Landover, Maryland 20785
5The other authors are with U.S. Naval Research Laboratory, Washington, DC 20375-5000.
E. Joseph Friebele, Charles G. Askins, Cathy M. Shaw, Michael E. Gingerich, Calvin C. Harrington, David L. Griscom, Tsung-Ein Tsai, Un-Chul Paek, and William H. Schmidt, "Correlation of single-mode fiber radiation response and fabrication parameters," Appl. Opt. 30, 1944-1957 (1991)
Statistically significant correlations have been established between certain fabrication parameters of matched clad, single-mode optical fiber waveguides and their response to an ionizing radiation dose of 2000 rad. The recovery data measured at −35°C following exposure have been fit to nth-order kinetic behavior where the adjustable parameters are the initial and permanent incremental losses (Ao and Af, respectively), the half-life of attenuation τ, and the order of kinetics n. The set of fibers chosen for analysis had Ge-doped silica cores. In fibers with Ge-F-doped silica clads, Ao correlates with the concentration of Ge-doped into the fiber core; Af correlates with the ratio of oxygen to reagents used during core deposition; and τ and n correlate with a two-way interaction of core oxygen and fiber draw speed. In P-F-doped clad fibers, the P concentration has been found to correlate with the order of the kinetics of recovery.
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Confounding of One-Way Contrasts with Higher-Order Interactions in the Phase 1 Experimental Designa
A1–3
A2–3
DE
FB
(5)
B1–3
(4)
B2–3
FA
(3,4)
C1–2
(4,6)
D1–2
AE
(3,4)
E1–3
(4)
E2–3
DA
(3,4)
F1–2
AB
(3,4)
CF
(3,4,6)
Numbers in parentheses indicate order of interactions.
Table IV
Analyzed Fiber Compositions (wt%), Oxygen-to-Reagent Ratio (O/R) Used During Deposition, Draw Tension (g), Draw Speed (m/s), and Radiation Recovery Parametersa
Core
Clad
Draw
Recovery Parameters
N
Ge
F
0/R
Ge
P
F
0/R
Tens
Spd
n
τ
A0
Af
1
7.5
0.07
5
0.0
0.0
0.00
5
6.6
0.5
1.8
12
420.0
10.0
2
9.4
0.06
15
0.0
0.0
0.00
10
7.3
4.0
2.0
15
260.0
10.0
3
7.4
0.10
15
2.5
0.0
0.55
10
3.5
4.0
4.0
70
12.2
0.3
4
10.3
0.20
5
2.4
0.0
0.50
5
4.0
0.5
3.0
100
1.9
1.5
5
10.2
0.10
5
0.0
0.0
0.00
5
5.0
4.0
2.0
20
60.0
7.0
6
6.2
0.04
15
0.0
0.0
0.00
10
5.3
0.5
2.3
22
243.0
0.0
7
11.4
0.24
15
2.5
0.0
0.51
10
7.7
0.5
4.0
25
7.0
0.0
8
6.2
0.14
5
2.3
0.0
0.53
5
6.6
4.0
4.0
350
9.1
6.9
9
12.0
0.18
15
2.5
0.0
0.49
5
4.7
0.5
4.0
75
4.9
0.1
10
15.2
0.26
5
2.4
0.0
0.54
10
5.9
4.0
10.0
60000
4.8
0.0
11
9.8
0.26
5
3.8
0.0
0.87
10
2.1
4.0
4.0
20000
5.7
2.6
12
15.4
0.27
15
3.9
0.0
0.84
5
2.2
0.5
4.0
80
4.0
0.6
13
16.0
0.19
15
2.4
0.0
0.53
5
2.4
4.0
4.0
70
4.5
0.0
14
8.6
0.16
5
2.4
0.0
0.50
10
1.8
0.5
4.0
2000
11.4
7.2
15
15.0
0.28
5
3.9
0.0
0.83
10
4.8
0.5
4.0
100
5.1
4.7
16
11.8
0.26
15
4.0
0.0
0.82
5
3.7
4.0
3.5
15
3.7
0.0
17
7.5
0.02
5
0.0
0.0
0.00
5
6.6
0.5
1.8
12
420.0
10.0
18
7.4
0.03
5
0.0
0.0
0.00
10
1.6
4.0
2.3
28
237.0
0.5
19
7.5
0.12
5
0.0
0.4
0.17
5
6.4
4.0
4.0
300
8.0
1.0
20
8.0
0.01
5
0.0
0.5
0.17
10
1.6
0.5
4.0
50
4.3
2.8
21
6.5
0.02
5
0.0
1.2
0.25
5
1.5
0.5
4.0
60
5.6
2.6
22
7.4
0.11
5
0.0
1.5
0.25
10
6.4
4.0
3.0
20
7.5
4.5
23
7.3
0.05
5
0.0
1.9
0.34
5
1.4
4.0
3.0
25
5.2
3.7
24
6.6
0.01
5
0.0
2.2
0.32
10
6.6
0.5
2.0
25
6.5
2.8
Initial and final losses Ao and Af in dB/km; half–life τ in seconds.
Table V
Correlation Matrix for Radiation Response Parameters of Phase 1—All Cases
n
τ
Ao
Af
n
1.00
τ
0.95
1.00
Ao
0.04
0.27
1.00
Af
−0.64
−0.74
−0.07
1.00
Table VI
Probabilities of Individual Null Effects and Interactions for the Phase 1 Design—All Fibers
n
τ
Ao
Af
A
0.17
0.43
0.40
0.88
B
0.93
0.78
0.01
0.14
C
0.42
0.24
0.94
0.41
E
0.45
0.75
0.35
0.07
F
0.31
0.27
0.27
0.81
CA
0.27
0.39
0.25
0.63
CB
0.53
0.74
0.99
0.99
CD
0.27
0.39
0.25
0.63
CE
0.27
0.39
0.25
0.63
CF
0.22
0.27
0.22
0.18
Table VII
Correlation Matrix for Radiation Response Parameters of Phase 1 for Reduced Design of Ge-F-Doped Silica Clad Fibers
n
τ
Ao
Af
n
1.00
τ
0.95
1.00
Ao
0.14
−0.16
1.00
Af
−0.22
−0.50
0.92
1.00
Table VIII
Probabilities for Individual Null Effects of Phase 1 Design for Reduced Design of Ge-F-Doped Clad Fibers
n
τ
Ao
Af
A
0.31
0.39
0.12
0.44
B
0.54
0.72
0.21
0.90
C
0.66
0.43
0.57
0.09
D
0.33
0.29
0.09
0.55
E
0.80
0.80
0.42
0.50
F
0.39
0.31
0.49
0.65
CF
0.21
0.12
0.73
0.52
Table IX
Probabilities for Individual Null Effects and Selected Estimated Effects for Reduced Phase 1 Design of Doped Silica Clads
Probabilities
Estimated Effects
Contrast
n
τ
Ao
Af
Ao
Af
A1–A3
0.19
0.21
0.05
0.25
7.3
4.0
A2–A3
0.23
0.45
0.45
0.77
1.2
0.5
B2–B3
0.36
0.50
0.47
0.67
C1–C2
0.66
0.42
0.57
0.09
3.8
D1–D2
0.42
0.43
0.08
0.85
E1–E3
0.61
0.78
0.32
0.79
E2–E3
0.44
0.54
0.19
0.31
F1–F2
0.29
0.19
0.50
0.34
Table X
Probabilities for Null Effect of P and Estimated Effect for Reduced Phase 2 Design of P-Doped Silica Clads
Probabilities
Estimated Effect
Contrast
n
τ
A0
Af
n
Linear
0.08
0.24
0.88
0.32
−1.1
Higher Order
0.65
0.55
0.74
0.39
−0.2
A (omnibus)
0.16
0.40
0.93
0.41
Table XI
Comparison of Af (dB/km) of the Phase 2 Fibers Determined Experimentally with that Predicted by Eq. (1)
N
[P]eff
Af (pred)
Af(meas)
19
0.09
0.9
1.0
20
0.14
1.2
2.8
21
0.44
3.0
2.6
22
0.39
2.7
4.5
23
0.53
3.5
3.7
24
0.66
4.3
2.8
Table XII
Equations Deriving the Significance of Each Factor In the Phase 1 Experiment from the Orthogonal Matrix Analysis
Confounding of One-Way Contrasts with Higher-Order Interactions in the Phase 1 Experimental Designa
A1–3
A2–3
DE
FB
(5)
B1–3
(4)
B2–3
FA
(3,4)
C1–2
(4,6)
D1–2
AE
(3,4)
E1–3
(4)
E2–3
DA
(3,4)
F1–2
AB
(3,4)
CF
(3,4,6)
Numbers in parentheses indicate order of interactions.
Table IV
Analyzed Fiber Compositions (wt%), Oxygen-to-Reagent Ratio (O/R) Used During Deposition, Draw Tension (g), Draw Speed (m/s), and Radiation Recovery Parametersa
Core
Clad
Draw
Recovery Parameters
N
Ge
F
0/R
Ge
P
F
0/R
Tens
Spd
n
τ
A0
Af
1
7.5
0.07
5
0.0
0.0
0.00
5
6.6
0.5
1.8
12
420.0
10.0
2
9.4
0.06
15
0.0
0.0
0.00
10
7.3
4.0
2.0
15
260.0
10.0
3
7.4
0.10
15
2.5
0.0
0.55
10
3.5
4.0
4.0
70
12.2
0.3
4
10.3
0.20
5
2.4
0.0
0.50
5
4.0
0.5
3.0
100
1.9
1.5
5
10.2
0.10
5
0.0
0.0
0.00
5
5.0
4.0
2.0
20
60.0
7.0
6
6.2
0.04
15
0.0
0.0
0.00
10
5.3
0.5
2.3
22
243.0
0.0
7
11.4
0.24
15
2.5
0.0
0.51
10
7.7
0.5
4.0
25
7.0
0.0
8
6.2
0.14
5
2.3
0.0
0.53
5
6.6
4.0
4.0
350
9.1
6.9
9
12.0
0.18
15
2.5
0.0
0.49
5
4.7
0.5
4.0
75
4.9
0.1
10
15.2
0.26
5
2.4
0.0
0.54
10
5.9
4.0
10.0
60000
4.8
0.0
11
9.8
0.26
5
3.8
0.0
0.87
10
2.1
4.0
4.0
20000
5.7
2.6
12
15.4
0.27
15
3.9
0.0
0.84
5
2.2
0.5
4.0
80
4.0
0.6
13
16.0
0.19
15
2.4
0.0
0.53
5
2.4
4.0
4.0
70
4.5
0.0
14
8.6
0.16
5
2.4
0.0
0.50
10
1.8
0.5
4.0
2000
11.4
7.2
15
15.0
0.28
5
3.9
0.0
0.83
10
4.8
0.5
4.0
100
5.1
4.7
16
11.8
0.26
15
4.0
0.0
0.82
5
3.7
4.0
3.5
15
3.7
0.0
17
7.5
0.02
5
0.0
0.0
0.00
5
6.6
0.5
1.8
12
420.0
10.0
18
7.4
0.03
5
0.0
0.0
0.00
10
1.6
4.0
2.3
28
237.0
0.5
19
7.5
0.12
5
0.0
0.4
0.17
5
6.4
4.0
4.0
300
8.0
1.0
20
8.0
0.01
5
0.0
0.5
0.17
10
1.6
0.5
4.0
50
4.3
2.8
21
6.5
0.02
5
0.0
1.2
0.25
5
1.5
0.5
4.0
60
5.6
2.6
22
7.4
0.11
5
0.0
1.5
0.25
10
6.4
4.0
3.0
20
7.5
4.5
23
7.3
0.05
5
0.0
1.9
0.34
5
1.4
4.0
3.0
25
5.2
3.7
24
6.6
0.01
5
0.0
2.2
0.32
10
6.6
0.5
2.0
25
6.5
2.8
Initial and final losses Ao and Af in dB/km; half–life τ in seconds.
Table V
Correlation Matrix for Radiation Response Parameters of Phase 1—All Cases
n
τ
Ao
Af
n
1.00
τ
0.95
1.00
Ao
0.04
0.27
1.00
Af
−0.64
−0.74
−0.07
1.00
Table VI
Probabilities of Individual Null Effects and Interactions for the Phase 1 Design—All Fibers
n
τ
Ao
Af
A
0.17
0.43
0.40
0.88
B
0.93
0.78
0.01
0.14
C
0.42
0.24
0.94
0.41
E
0.45
0.75
0.35
0.07
F
0.31
0.27
0.27
0.81
CA
0.27
0.39
0.25
0.63
CB
0.53
0.74
0.99
0.99
CD
0.27
0.39
0.25
0.63
CE
0.27
0.39
0.25
0.63
CF
0.22
0.27
0.22
0.18
Table VII
Correlation Matrix for Radiation Response Parameters of Phase 1 for Reduced Design of Ge-F-Doped Silica Clad Fibers
n
τ
Ao
Af
n
1.00
τ
0.95
1.00
Ao
0.14
−0.16
1.00
Af
−0.22
−0.50
0.92
1.00
Table VIII
Probabilities for Individual Null Effects of Phase 1 Design for Reduced Design of Ge-F-Doped Clad Fibers
n
τ
Ao
Af
A
0.31
0.39
0.12
0.44
B
0.54
0.72
0.21
0.90
C
0.66
0.43
0.57
0.09
D
0.33
0.29
0.09
0.55
E
0.80
0.80
0.42
0.50
F
0.39
0.31
0.49
0.65
CF
0.21
0.12
0.73
0.52
Table IX
Probabilities for Individual Null Effects and Selected Estimated Effects for Reduced Phase 1 Design of Doped Silica Clads
Probabilities
Estimated Effects
Contrast
n
τ
Ao
Af
Ao
Af
A1–A3
0.19
0.21
0.05
0.25
7.3
4.0
A2–A3
0.23
0.45
0.45
0.77
1.2
0.5
B2–B3
0.36
0.50
0.47
0.67
C1–C2
0.66
0.42
0.57
0.09
3.8
D1–D2
0.42
0.43
0.08
0.85
E1–E3
0.61
0.78
0.32
0.79
E2–E3
0.44
0.54
0.19
0.31
F1–F2
0.29
0.19
0.50
0.34
Table X
Probabilities for Null Effect of P and Estimated Effect for Reduced Phase 2 Design of P-Doped Silica Clads
Probabilities
Estimated Effect
Contrast
n
τ
A0
Af
n
Linear
0.08
0.24
0.88
0.32
−1.1
Higher Order
0.65
0.55
0.74
0.39
−0.2
A (omnibus)
0.16
0.40
0.93
0.41
Table XI
Comparison of Af (dB/km) of the Phase 2 Fibers Determined Experimentally with that Predicted by Eq. (1)
N
[P]eff
Af (pred)
Af(meas)
19
0.09
0.9
1.0
20
0.14
1.2
2.8
21
0.44
3.0
2.6
22
0.39
2.7
4.5
23
0.53
3.5
3.7
24
0.66
4.3
2.8
Table XII
Equations Deriving the Significance of Each Factor In the Phase 1 Experiment from the Orthogonal Matrix Analysis
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