Stefan Kück, Friedhelm Brandt, and Mario Taddeo, "Gold-coated copper cone detector as a new standard detector for F2 laser radiation at 157 nm," Appl. Opt. 44, 2258-2265 (2005)
A new standard detector for high-accuracy measurements of F2 laser radiation at 157 nm is presented. This gold-coated copper cone detector permits the measurement of average powers up to 2 W with an uncertainty of ∼1%. To the best of our knowledge, this is the first highly accurate standard detector for F2 laser radiation for this power level. It is fully characterized according to Guide to the Expression of Uncertainty in Measurement of the International Organization for Standardization and is connected to the calibration chain for laser radiation established by the German National Metrology Institute.
Ping-Shine Shaw, Keith R. Lykke, Rajeev Gupta, Thomas R. O’Brian, Uwe Arp, Hunter H. White, Thomas B. Lucatorto, Joseph L. Dehmer, and Albert C. Parr Appl. Opt. 38(1) 18-28 (1999)
Mathias Richter, Udo Kroth, Alexander Gottwald, Christopher Gerth, Kai Tiedtke, Terubumi Saito, Ivan Tassy, and Klaus Vogler Appl. Opt. 41(34) 7167-7172 (2002)
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Parameters of Primary Standard Detector LM8 at 157 nma
λ
157 nm
Material of cone
Gold-coated copper
Aperture angle
45°
ϕbeam
8 mm
Atmosphere
Vacuum, N2, air
ϕmax
≥3.2 W (at 200 Hz)
Qmax
≥24 mJ
s0 (22 °C, 0 W)
(6.256 ± 0.060) mV/W (air)
(6.263 ± 0.060) mV/W (N2)
(6.720 ± 0.064) mV/W (vacuum)
α
0.995 ± 0.005
βT
(0.177 ± 0.003)%/K (air)
(0.171 ± 0.003)%/K (N2)
(0.216 ± 0.004)%/K (vacuum)
βϕ
(−0.046 ± 0.002)%/W (air)
(−0.044 ± 0.003)%/W (N2)
(−0.085 ± 0.003)%/W (vacuum)
ϕmax, Qmax, maximum applicable power and energy, respectively; s0, spectral responsivity; α, absorptance (calculated from optical constants); βT, βϕ, βυ, linear temperature, power, and signal coefficient (βυ = βϕ/s0), respectively.
Table 3
Spectral Responsivities of Detector LM8 for Three Atmospheresa
Atmosphere
p (mbars)
s0(157 nm) (mV/W)
σ(s0)
U(s0)
(mV/W)
(%)
(mV/W)
(%)
Air
∼1050
6.256
0.026
0.42
0.060
0.96
N2
∼1100
6.263
0.026
0.42
0.060
0.96
Vacuum
1−2 × 10−6
6.720
0.028
0.45
0.064
1.03
σ, standard deviation; U, expanded uncertainty; k, expansion factor. k in all cases is 2.3.
Table 4
Quantities Used in Equation (A1) for Determination of Absolute Spectral Responsivity s1 (157 nm) of Standard Detector LM8 at 157 nm
Quantity
Unit
Definition
sk
mV/W
Corrected responsivity of standard detector LM8
sPr
mV/W
Measured responsivity of LM8
Fs0
Correction factor for the normalized responsivity of standard detector LM4
FVN
Correction factor for the voltage of LM4
FAN
Correction factor for amplification of the voltage of LM4
FVPr
Correction factor for the voltage of LM8
fTPr
Correction factor for the temperature dependence of LM8
fSt
Correction factor for the stability of LM8
fHPr
Correction factor for the inhomogeneity of LM8
fβVPr
Correction factor for the power dependence of LM8
Fα
Correction factor for the absorptance of LM4
Fk
Correction factor for the correction factor of LM4
FH
Correction factor for the inhomogeneity of LM4
FS
Correction factor for stray light
FβT
Correction factor for the temperature dependence of LM4
FβV
Correction factor for the power dependence of LM4
T0
°C
Standard temperature, 22 °C
βT
%/°C
Temperature coefficient of LM4
βT1
%/°C
Constant with the value of the temperature coefficient of LM4
T
°C
Temperature of LM4 during calibration
T1
°C
Temperature of LM4 during calibration
TPr
°C
Temperature of LM8 during calibration
T1Pr
°C
Temperature of LM8 during calibration
βV
%/mV
Signal coefficient of LM4 (βV = βϕ/s0)
βV1
%/mV
Constant with value of the signal coefficient of LM4 (βV = βϕ/s0)
V
mV
Output signal (thermal voltage) of LM4
V1
mV
Constant with value of the output signal (thermal voltage) of LM4
VPr
mV
Output signal (thermal voltage) of LM8
βTPr
%/°C
Temperature coefficient of LM8
VPr1
mV
Constant with value of the output signal (thermal voltage) of LM8
βTPr1
%/°C
Constant with the value of the temperature coefficient of LM8
βVPr
%/mV
Signal coefficient of LM8 (βV = βϕ/s0)
βVPr1
%/mV
Constant with value of the signal coefficient of LM8 (βV = βϕ/s0)
Table 5
Uncertainty Budget for Determination of Absolute Spectral Responsivity s1 (157 nm) of Standard Detector LM8a
Quantity
Value
Standard Uncertainty
Degree of Freedom
Coefficient of Sensitivity
Uncertainty (mV/W)
Index (%)
sPr
6.2829 mV/W
0.0461 mV/W
6
1.0
0.046
85.8
Fs0
1.00000
1.37 × 10−3
1500
6.3
8.6 × 10−3
3.0
FVN
1.00000000
5.77 × 10−6
∞
6.3
36 × 10−6
0.0
FAN
1.00000000
6.00 × 10−6
10
6.3
38 × 10−6
0.0
FVPr
1.0000000
28.9 × 10−6
∞
6.3
180 × 10−6
0.0
fTPr
1.00000000
9.00 × 10−6
fSt
1.0
0.0
∞
0.0
0.0
0.0
fHPr
1.000000
577 × 10−6
∞
6.3
3.6 × 10−3
0.5
fβVPr
1.00000000
8.00 × 10−6
Fα
1.00000
1.44 × 10−3
∞
6.3
9.0 × 10−3
3.3
Fk
1.000000
501 × 10−6
270
6.3
3.1 × 10−3
0.4
FH
1.000000
577 × 10−6
∞
6.3
3.6 × 10−3
0.5
FS
1.000000
144 × 10−6
∞
6.3
900 × 10−6
0.0
FβT
1.0000000
18.0 × 10−6
FβV
1.00000000
9.00 × 10−6
T0
22.0 °C
βT
0.21200%/°C
6.00 × 10−3%/°C
9
−0.019
−110 × 10−6
0.0
βT1
0.212%/°C
T
22.3 °C
T1
22.3 °C
TPr
22.3 °C
T1Pr
22.3 °C
βV
0.09200%/mV
3.00 × 10−3%/mV
10
−0.019
−56 × 10−6
0.0
βV1
0.092%/mV
V
0.3 mV
V1
0.3 mV
VPr
0.8 mV
βTPr
0.17100%/°C
3.00 × 10−3%/°C
10
−0.019
−6 × 10−6
0.0
VPr1
0.8 mV
βTPr1
0.171%/°C
βVPr
−0.01300%/mV
1.00 × 10−3%/mV
10
−0.050
−50 × 10−6
0.0
βVPr1
−0.013%/mV
sk
6.252 mV/W
0.0495 mV/W
8
Result: s1 (157 nm) = sk = (6.2520 ± 0.0495) mV/W for k = 1. The expanded uncertainty for a depth of coverage of 95% is 0.12 mV/W, calculated with an expansion factor of 2.4 (derived from the degree of freedom and the Student distribution).
Tables (5)
Table 1
Results of Radiation Calibration of Detector LM8 at Several Wavelengths λi in an Air Atmospherea
Parameters of Primary Standard Detector LM8 at 157 nma
λ
157 nm
Material of cone
Gold-coated copper
Aperture angle
45°
ϕbeam
8 mm
Atmosphere
Vacuum, N2, air
ϕmax
≥3.2 W (at 200 Hz)
Qmax
≥24 mJ
s0 (22 °C, 0 W)
(6.256 ± 0.060) mV/W (air)
(6.263 ± 0.060) mV/W (N2)
(6.720 ± 0.064) mV/W (vacuum)
α
0.995 ± 0.005
βT
(0.177 ± 0.003)%/K (air)
(0.171 ± 0.003)%/K (N2)
(0.216 ± 0.004)%/K (vacuum)
βϕ
(−0.046 ± 0.002)%/W (air)
(−0.044 ± 0.003)%/W (N2)
(−0.085 ± 0.003)%/W (vacuum)
ϕmax, Qmax, maximum applicable power and energy, respectively; s0, spectral responsivity; α, absorptance (calculated from optical constants); βT, βϕ, βυ, linear temperature, power, and signal coefficient (βυ = βϕ/s0), respectively.
Table 3
Spectral Responsivities of Detector LM8 for Three Atmospheresa
Atmosphere
p (mbars)
s0(157 nm) (mV/W)
σ(s0)
U(s0)
(mV/W)
(%)
(mV/W)
(%)
Air
∼1050
6.256
0.026
0.42
0.060
0.96
N2
∼1100
6.263
0.026
0.42
0.060
0.96
Vacuum
1−2 × 10−6
6.720
0.028
0.45
0.064
1.03
σ, standard deviation; U, expanded uncertainty; k, expansion factor. k in all cases is 2.3.
Table 4
Quantities Used in Equation (A1) for Determination of Absolute Spectral Responsivity s1 (157 nm) of Standard Detector LM8 at 157 nm
Quantity
Unit
Definition
sk
mV/W
Corrected responsivity of standard detector LM8
sPr
mV/W
Measured responsivity of LM8
Fs0
Correction factor for the normalized responsivity of standard detector LM4
FVN
Correction factor for the voltage of LM4
FAN
Correction factor for amplification of the voltage of LM4
FVPr
Correction factor for the voltage of LM8
fTPr
Correction factor for the temperature dependence of LM8
fSt
Correction factor for the stability of LM8
fHPr
Correction factor for the inhomogeneity of LM8
fβVPr
Correction factor for the power dependence of LM8
Fα
Correction factor for the absorptance of LM4
Fk
Correction factor for the correction factor of LM4
FH
Correction factor for the inhomogeneity of LM4
FS
Correction factor for stray light
FβT
Correction factor for the temperature dependence of LM4
FβV
Correction factor for the power dependence of LM4
T0
°C
Standard temperature, 22 °C
βT
%/°C
Temperature coefficient of LM4
βT1
%/°C
Constant with the value of the temperature coefficient of LM4
T
°C
Temperature of LM4 during calibration
T1
°C
Temperature of LM4 during calibration
TPr
°C
Temperature of LM8 during calibration
T1Pr
°C
Temperature of LM8 during calibration
βV
%/mV
Signal coefficient of LM4 (βV = βϕ/s0)
βV1
%/mV
Constant with value of the signal coefficient of LM4 (βV = βϕ/s0)
V
mV
Output signal (thermal voltage) of LM4
V1
mV
Constant with value of the output signal (thermal voltage) of LM4
VPr
mV
Output signal (thermal voltage) of LM8
βTPr
%/°C
Temperature coefficient of LM8
VPr1
mV
Constant with value of the output signal (thermal voltage) of LM8
βTPr1
%/°C
Constant with the value of the temperature coefficient of LM8
βVPr
%/mV
Signal coefficient of LM8 (βV = βϕ/s0)
βVPr1
%/mV
Constant with value of the signal coefficient of LM8 (βV = βϕ/s0)
Table 5
Uncertainty Budget for Determination of Absolute Spectral Responsivity s1 (157 nm) of Standard Detector LM8a
Quantity
Value
Standard Uncertainty
Degree of Freedom
Coefficient of Sensitivity
Uncertainty (mV/W)
Index (%)
sPr
6.2829 mV/W
0.0461 mV/W
6
1.0
0.046
85.8
Fs0
1.00000
1.37 × 10−3
1500
6.3
8.6 × 10−3
3.0
FVN
1.00000000
5.77 × 10−6
∞
6.3
36 × 10−6
0.0
FAN
1.00000000
6.00 × 10−6
10
6.3
38 × 10−6
0.0
FVPr
1.0000000
28.9 × 10−6
∞
6.3
180 × 10−6
0.0
fTPr
1.00000000
9.00 × 10−6
fSt
1.0
0.0
∞
0.0
0.0
0.0
fHPr
1.000000
577 × 10−6
∞
6.3
3.6 × 10−3
0.5
fβVPr
1.00000000
8.00 × 10−6
Fα
1.00000
1.44 × 10−3
∞
6.3
9.0 × 10−3
3.3
Fk
1.000000
501 × 10−6
270
6.3
3.1 × 10−3
0.4
FH
1.000000
577 × 10−6
∞
6.3
3.6 × 10−3
0.5
FS
1.000000
144 × 10−6
∞
6.3
900 × 10−6
0.0
FβT
1.0000000
18.0 × 10−6
FβV
1.00000000
9.00 × 10−6
T0
22.0 °C
βT
0.21200%/°C
6.00 × 10−3%/°C
9
−0.019
−110 × 10−6
0.0
βT1
0.212%/°C
T
22.3 °C
T1
22.3 °C
TPr
22.3 °C
T1Pr
22.3 °C
βV
0.09200%/mV
3.00 × 10−3%/mV
10
−0.019
−56 × 10−6
0.0
βV1
0.092%/mV
V
0.3 mV
V1
0.3 mV
VPr
0.8 mV
βTPr
0.17100%/°C
3.00 × 10−3%/°C
10
−0.019
−6 × 10−6
0.0
VPr1
0.8 mV
βTPr1
0.171%/°C
βVPr
−0.01300%/mV
1.00 × 10−3%/mV
10
−0.050
−50 × 10−6
0.0
βVPr1
−0.013%/mV
sk
6.252 mV/W
0.0495 mV/W
8
Result: s1 (157 nm) = sk = (6.2520 ± 0.0495) mV/W for k = 1. The expanded uncertainty for a depth of coverage of 95% is 0.12 mV/W, calculated with an expansion factor of 2.4 (derived from the degree of freedom and the Student distribution).