Stefan Kück, Friedhelm Brandt, and Mario Taddeo, "Gold-coated copper cone detector as a new standard detector for F_{2} laser radiation at 157 nm," Appl. Opt. 44, 2258-2265 (2005)

A new standard detector for high-accuracy measurements of F_{2} 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 F_{2} 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)

References

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Parameters of Primary Standard Detector LM8 at 157 nm^{a}

λ

157 nm

Material of cone

Gold-coated copper

Aperture angle

45°

ϕ_{beam}

8 mm

Atmosphere

Vacuum, N_{2}, air

ϕ_{max}

≥3.2 W (at 200 Hz)

Q_{max}

≥24 mJ

s_{0} (22 °C, 0 W)

(6.256 ± 0.060) mV/W (air)

(6.263 ± 0.060) mV/W (N_{2})

(6.720 ± 0.064) mV/W (vacuum)

α

0.995 ± 0.005

β_{T}

(0.177 ± 0.003)%/K (air)

(0.171 ± 0.003)%/K (N_{2})

(0.216 ± 0.004)%/K (vacuum)

β_{ϕ}

(−0.046 ± 0.002)%/W (air)

(−0.044 ± 0.003)%/W (N_{2})

(−0.085 ± 0.003)%/W (vacuum)

ϕ_{max}, Q_{max}, maximum applicable power and energy, respectively; s_{0}, spectral responsivity; α, absorptance (calculated from optical constants); β_{T}, β_{ϕ}, β_{υ}, linear temperature, power, and signal coefficient (β_{υ} = β_{ϕ}/s_{0}), respectively.

Table 3

Spectral Responsivities of Detector LM8 for Three Atmospheres^{a}

Atmosphere

p (mbars)

s_{0}(157 nm) (mV/W)

σ(s_{0})

U(s_{0})

(mV/W)

(%)

(mV/W)

(%)

Air

∼1050

6.256

0.026

0.42

0.060

0.96

N_{2}

∼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 s_{1} (157 nm) of Standard Detector LM8 at 157 nm

Quantity

Unit

Definition

s_{k}

mV/W

Corrected responsivity of standard detector LM8

s_{Pr}

mV/W

Measured responsivity of LM8

F_{s}_{0}

Correction factor for the normalized responsivity of standard detector LM4

F_{VN}

Correction factor for the voltage of LM4

F_{AN}

Correction factor for amplification of the voltage of LM4

F_{VPr}

Correction factor for the voltage of LM8

f_{TPr}

Correction factor for the temperature dependence of LM8

f_{St}

Correction factor for the stability of LM8

f_{HPr}

Correction factor for the inhomogeneity of LM8

f_{β}_{VPr}

Correction factor for the power dependence of LM8

F_{α}

Correction factor for the absorptance of LM4

F_{k}

Correction factor for the correction factor of LM4

F_{H}

Correction factor for the inhomogeneity of LM4

F_{S}

Correction factor for stray light

F_{β}_{T}

Correction factor for the temperature dependence of LM4

F_{β}_{V}

Correction factor for the power dependence of LM4

T_{0}

°C

Standard temperature, 22 °C

β_{T}

%/°C

Temperature coefficient of LM4

β_{T}_{1}

%/°C

Constant with the value of the temperature coefficient of LM4

T

°C

Temperature of LM4 during calibration

T_{1}

°C

Temperature of LM4 during calibration

T_{Pr}

°C

Temperature of LM8 during calibration

T_{1}_{Pr}

°C

Temperature of LM8 during calibration

β_{V}

%/mV

Signal coefficient of LM4 (β_{V} = β_{ϕ}/s_{0})

β_{V}_{1}

%/mV

Constant with value of the signal coefficient of LM4 (β_{V} = β_{ϕ}/s_{0})

V

mV

Output signal (thermal voltage) of LM4

V_{1}

mV

Constant with value of the output signal (thermal voltage) of LM4

V_{Pr}

mV

Output signal (thermal voltage) of LM8

β_{TPr}

%/°C

Temperature coefficient of LM8

V_{Pr}_{1}

mV

Constant with value of the output signal (thermal voltage) of LM8

β_{TPr}_{1}

%/°C

Constant with the value of the temperature coefficient of LM8

β_{VPr}

%/mV

Signal coefficient of LM8 (β_{V} = β_{ϕ}/s_{0})

β_{VPr}_{1}

%/mV

Constant with value of the signal coefficient of LM8 (β_{V} = β_{ϕ}/s_{0})

Table 5

Uncertainty Budget for Determination of Absolute Spectral Responsivity s_{1} (157 nm) of Standard Detector LM8^{a}

Quantity

Value

Standard Uncertainty

Degree of Freedom

Coefficient of Sensitivity

Uncertainty (mV/W)

Index (%)

s_{Pr}

6.2829 mV/W

0.0461 mV/W

6

1.0

0.046

85.8

F_{s}_{0}

1.00000

1.37 × 10^{−3}

1500

6.3

8.6 × 10^{−3}

3.0

F_{VN}

1.00000000

5.77 × 10^{−6}

∞

6.3

36 × 10^{−6}

0.0

F_{AN}

1.00000000

6.00 × 10^{−6}

10

6.3

38 × 10^{−6}

0.0

F_{VPr}

1.0000000

28.9 × 10^{−6}

∞

6.3

180 × 10^{−6}

0.0

f_{TPr}

1.00000000

9.00 × 10^{−6}

f_{St}

1.0

0.0

∞

0.0

0.0

0.0

f_{HPr}

1.000000

577 × 10^{−6}

∞

6.3

3.6 × 10^{−3}

0.5

f_{β}_{VPr}

1.00000000

8.00 × 10^{−6}

F_{α}

1.00000

1.44 × 10^{−3}

∞

6.3

9.0 × 10^{−3}

3.3

F_{k}

1.000000

501 × 10^{−6}

270

6.3

3.1 × 10^{−3}

0.4

F_{H}

1.000000

577 × 10^{−6}

∞

6.3

3.6 × 10^{−3}

0.5

F_{S}

1.000000

144 × 10^{−6}

∞

6.3

900 × 10^{−6}

0.0

F_{β}_{T}

1.0000000

18.0 × 10^{−6}

F_{β}_{V}

1.00000000

9.00 × 10^{−6}

T_{0}

22.0 °C

β_{T}

0.21200%/°C

6.00 × 10^{−3}%/°C

9

−0.019

−110 × 10^{−6}

0.0

β_{T}_{1}

0.212%/°C

T

22.3 °C

T_{1}

22.3 °C

T_{Pr}

22.3 °C

T_{1}_{Pr}

22.3 °C

β_{V}

0.09200%/mV

3.00 × 10^{−3}%/mV

10

−0.019

−56 × 10^{−6}

0.0

β_{V}_{1}

0.092%/mV

V

0.3 mV

V_{1}

0.3 mV

V_{Pr}

0.8 mV

β_{TPr}

0.17100%/°C

3.00 × 10^{−3}%/°C

10

−0.019

−6 × 10^{−6}

0.0

V_{Pr}_{1}

0.8 mV

β_{TPr}_{1}

0.171%/°C

β_{VPr}

−0.01300%/mV

1.00 × 10^{−3}%/mV

10

−0.050

−50 × 10^{−6}

0.0

β_{VPr}_{1}

−0.013%/mV

s_{k}

6.252 mV/W

0.0495 mV/W

8

Result: s_{1} (157 nm) = s_{k} = (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 λ_{i} in an Air Atmosphere^{a}

Parameters of Primary Standard Detector LM8 at 157 nm^{a}

λ

157 nm

Material of cone

Gold-coated copper

Aperture angle

45°

ϕ_{beam}

8 mm

Atmosphere

Vacuum, N_{2}, air

ϕ_{max}

≥3.2 W (at 200 Hz)

Q_{max}

≥24 mJ

s_{0} (22 °C, 0 W)

(6.256 ± 0.060) mV/W (air)

(6.263 ± 0.060) mV/W (N_{2})

(6.720 ± 0.064) mV/W (vacuum)

α

0.995 ± 0.005

β_{T}

(0.177 ± 0.003)%/K (air)

(0.171 ± 0.003)%/K (N_{2})

(0.216 ± 0.004)%/K (vacuum)

β_{ϕ}

(−0.046 ± 0.002)%/W (air)

(−0.044 ± 0.003)%/W (N_{2})

(−0.085 ± 0.003)%/W (vacuum)

ϕ_{max}, Q_{max}, maximum applicable power and energy, respectively; s_{0}, spectral responsivity; α, absorptance (calculated from optical constants); β_{T}, β_{ϕ}, β_{υ}, linear temperature, power, and signal coefficient (β_{υ} = β_{ϕ}/s_{0}), respectively.

Table 3

Spectral Responsivities of Detector LM8 for Three Atmospheres^{a}

Atmosphere

p (mbars)

s_{0}(157 nm) (mV/W)

σ(s_{0})

U(s_{0})

(mV/W)

(%)

(mV/W)

(%)

Air

∼1050

6.256

0.026

0.42

0.060

0.96

N_{2}

∼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 s_{1} (157 nm) of Standard Detector LM8 at 157 nm

Quantity

Unit

Definition

s_{k}

mV/W

Corrected responsivity of standard detector LM8

s_{Pr}

mV/W

Measured responsivity of LM8

F_{s}_{0}

Correction factor for the normalized responsivity of standard detector LM4

F_{VN}

Correction factor for the voltage of LM4

F_{AN}

Correction factor for amplification of the voltage of LM4

F_{VPr}

Correction factor for the voltage of LM8

f_{TPr}

Correction factor for the temperature dependence of LM8

f_{St}

Correction factor for the stability of LM8

f_{HPr}

Correction factor for the inhomogeneity of LM8

f_{β}_{VPr}

Correction factor for the power dependence of LM8

F_{α}

Correction factor for the absorptance of LM4

F_{k}

Correction factor for the correction factor of LM4

F_{H}

Correction factor for the inhomogeneity of LM4

F_{S}

Correction factor for stray light

F_{β}_{T}

Correction factor for the temperature dependence of LM4

F_{β}_{V}

Correction factor for the power dependence of LM4

T_{0}

°C

Standard temperature, 22 °C

β_{T}

%/°C

Temperature coefficient of LM4

β_{T}_{1}

%/°C

Constant with the value of the temperature coefficient of LM4

T

°C

Temperature of LM4 during calibration

T_{1}

°C

Temperature of LM4 during calibration

T_{Pr}

°C

Temperature of LM8 during calibration

T_{1}_{Pr}

°C

Temperature of LM8 during calibration

β_{V}

%/mV

Signal coefficient of LM4 (β_{V} = β_{ϕ}/s_{0})

β_{V}_{1}

%/mV

Constant with value of the signal coefficient of LM4 (β_{V} = β_{ϕ}/s_{0})

V

mV

Output signal (thermal voltage) of LM4

V_{1}

mV

Constant with value of the output signal (thermal voltage) of LM4

V_{Pr}

mV

Output signal (thermal voltage) of LM8

β_{TPr}

%/°C

Temperature coefficient of LM8

V_{Pr}_{1}

mV

Constant with value of the output signal (thermal voltage) of LM8

β_{TPr}_{1}

%/°C

Constant with the value of the temperature coefficient of LM8

β_{VPr}

%/mV

Signal coefficient of LM8 (β_{V} = β_{ϕ}/s_{0})

β_{VPr}_{1}

%/mV

Constant with value of the signal coefficient of LM8 (β_{V} = β_{ϕ}/s_{0})

Table 5

Uncertainty Budget for Determination of Absolute Spectral Responsivity s_{1} (157 nm) of Standard Detector LM8^{a}

Quantity

Value

Standard Uncertainty

Degree of Freedom

Coefficient of Sensitivity

Uncertainty (mV/W)

Index (%)

s_{Pr}

6.2829 mV/W

0.0461 mV/W

6

1.0

0.046

85.8

F_{s}_{0}

1.00000

1.37 × 10^{−3}

1500

6.3

8.6 × 10^{−3}

3.0

F_{VN}

1.00000000

5.77 × 10^{−6}

∞

6.3

36 × 10^{−6}

0.0

F_{AN}

1.00000000

6.00 × 10^{−6}

10

6.3

38 × 10^{−6}

0.0

F_{VPr}

1.0000000

28.9 × 10^{−6}

∞

6.3

180 × 10^{−6}

0.0

f_{TPr}

1.00000000

9.00 × 10^{−6}

f_{St}

1.0

0.0

∞

0.0

0.0

0.0

f_{HPr}

1.000000

577 × 10^{−6}

∞

6.3

3.6 × 10^{−3}

0.5

f_{β}_{VPr}

1.00000000

8.00 × 10^{−6}

F_{α}

1.00000

1.44 × 10^{−3}

∞

6.3

9.0 × 10^{−3}

3.3

F_{k}

1.000000

501 × 10^{−6}

270

6.3

3.1 × 10^{−3}

0.4

F_{H}

1.000000

577 × 10^{−6}

∞

6.3

3.6 × 10^{−3}

0.5

F_{S}

1.000000

144 × 10^{−6}

∞

6.3

900 × 10^{−6}

0.0

F_{β}_{T}

1.0000000

18.0 × 10^{−6}

F_{β}_{V}

1.00000000

9.00 × 10^{−6}

T_{0}

22.0 °C

β_{T}

0.21200%/°C

6.00 × 10^{−3}%/°C

9

−0.019

−110 × 10^{−6}

0.0

β_{T}_{1}

0.212%/°C

T

22.3 °C

T_{1}

22.3 °C

T_{Pr}

22.3 °C

T_{1}_{Pr}

22.3 °C

β_{V}

0.09200%/mV

3.00 × 10^{−3}%/mV

10

−0.019

−56 × 10^{−6}

0.0

β_{V}_{1}

0.092%/mV

V

0.3 mV

V_{1}

0.3 mV

V_{Pr}

0.8 mV

β_{TPr}

0.17100%/°C

3.00 × 10^{−3}%/°C

10

−0.019

−6 × 10^{−6}

0.0

V_{Pr}_{1}

0.8 mV

β_{TPr}_{1}

0.171%/°C

β_{VPr}

−0.01300%/mV

1.00 × 10^{−3}%/mV

10

−0.050

−50 × 10^{−6}

0.0

β_{VPr}_{1}

−0.013%/mV

s_{k}

6.252 mV/W

0.0495 mV/W

8

Result: s_{1} (157 nm) = s_{k} = (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).