Abstract

Spectrally invariant detectors are commonly used to interpolate or extrapolate the responsivity of InGaAs detectors in the infrared from absolute calibrations at a few wavelengths. The random noise in such detectors limits the accuracy that can be achieved in a narrowband, double-monochromator setup. We propose the application of a dedicated digital filter, which reduces the uncertainty by 30%, and combine it by calibrating a group of three detectors. The uncertainties are propagated from the observed variance in the relative measurement to the combined uncertainty of 0.4% (2σ) in the responsivity values of the InGaAs detectors in the range of 1010–1640 nm.

© 2005 Optical Society of America

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References

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  1. N. P. Fox, “Improved near-infrared detectors,” Metrologia 30, 321–325 (1993).
    [CrossRef]
  2. D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
    [CrossRef]
  3. N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
    [CrossRef]
  4. L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
    [CrossRef]
  5. P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
    [CrossRef]
  6. I. W. Selesnick, C. S. Burrus, “Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands,” IEEE Trans. Circuits Syst. II 43, 671–675 (1996).
    [CrossRef]
  7. International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” (ISO, Geneva, 1993), Eq. H.9 in matrix form, p. 72.
  8. J. L. Gardner, “Correlations in primary spectral standards,” Metrologia 40, S167–S171 (2003).
    [CrossRef]
  9. J. Gran, A. S. Sudbø, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204–212 (2004).
    [CrossRef]

2004

J. Gran, A. S. Sudbø, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204–212 (2004).
[CrossRef]

2003

J. L. Gardner, “Correlations in primary spectral standards,” Metrologia 40, S167–S171 (2003).
[CrossRef]

2000

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

1998

N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[CrossRef]

1996

I. W. Selesnick, C. S. Burrus, “Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands,” IEEE Trans. Circuits Syst. II 43, 671–675 (1996).
[CrossRef]

1993

N. P. Fox, “Improved near-infrared detectors,” Metrologia 30, 321–325 (1993).
[CrossRef]

D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
[CrossRef]

Brown, S. W.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Burrus, C. S.

I. W. Selesnick, C. S. Burrus, “Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands,” IEEE Trans. Circuits Syst. II 43, 671–675 (1996).
[CrossRef]

Fox, N. P.

N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[CrossRef]

N. P. Fox, “Improved near-infrared detectors,” Metrologia 30, 321–325 (1993).
[CrossRef]

Friedrich, R.

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

Gardner, J. L.

J. L. Gardner, “Correlations in primary spectral standards,” Metrologia 40, S167–S171 (2003).
[CrossRef]

Gran, J.

J. Gran, A. S. Sudbø, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204–212 (2004).
[CrossRef]

Gupta, R.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Johannsen, U.

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

Larason, T. C.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Lykke, K. R.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Nettleton, D. H.

D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
[CrossRef]

Prior, T. R.

D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
[CrossRef]

Selesnick, I. W.

I. W. Selesnick, C. S. Burrus, “Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands,” IEEE Trans. Circuits Syst. II 43, 671–675 (1996).
[CrossRef]

Shaw, P. S.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Steiger, A.

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

Sudbø, A. S.

J. Gran, A. S. Sudbø, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204–212 (2004).
[CrossRef]

Theocharous, E.

N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[CrossRef]

Ward, T. H.

N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[CrossRef]

D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
[CrossRef]

Werner, L.

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

IEEE Trans. Circuits Syst. II

I. W. Selesnick, C. S. Burrus, “Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands,” IEEE Trans. Circuits Syst. II 43, 671–675 (1996).
[CrossRef]

J. Res. Natl. Stand. Technol.

P. S. Shaw, T. C. Larason, R. Gupta, S. W. Brown, K. R. Lykke, “Improved near-infrared spectral responsivity scale,” J. Res. Natl. Stand. Technol. 105, 689–700 (2000).
[CrossRef]

Metrologia

J. L. Gardner, “Correlations in primary spectral standards,” Metrologia 40, S167–S171 (2003).
[CrossRef]

J. Gran, A. S. Sudbø, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204–212 (2004).
[CrossRef]

N. P. Fox, “Improved near-infrared detectors,” Metrologia 30, 321–325 (1993).
[CrossRef]

D. H. Nettleton, T. R. Prior, T. H. Ward, “Improved spectral responsivity scales at the NPL, 400 nm to 20 µm,” Metrologia 30, 425–432 (1993).
[CrossRef]

N. P. Fox, E. Theocharous, T. H. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[CrossRef]

L. Werner, R. Friedrich, U. Johannsen, A. Steiger, “Precise scale of spectral responsivity for InGaAs detectors based on a cryogenic radiometer and several laser sources,” Metrologia 37, 523–526 (2000).
[CrossRef]

Other

International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” (ISO, Geneva, 1993), Eq. H.9 in matrix form, p. 72.

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Figures (10)

Fig. 1
Fig. 1

Relative spectral response measured against a CPD and the corresponding standard deviation for one of the three InGaAs detectors.

Fig. 2
Fig. 2

Spectral responsivity ratios between the three InGaAs detectors.

Fig. 3
Fig. 3

Ratios of the relative spectral response of the three InGaAs detectors, each measured against the CPD, for one randomly chosen series.

Fig. 4
Fig. 4

Frequency response of the digital filter in terms of sampling frequency shown in a linear scale. The frequency is given between 0 and fb, where fb is half of the sampling frequency (fs/2).

Fig. 5
Fig. 5

Weights of the digital filter. The wavelengths are given as the relative position to the sample point filtered with a sampling interval of 10 nm.

Fig. 6
Fig. 6

Flow diagram showing the principles in the realization of the spectral response scale.

Fig. 7
Fig. 7

Calculated correlation matrix for the responsivity values at different wavelengths. The ridge along the diagonal appears from the filter, and the broad spectral correlation coefficient is caused by the uncertainty in the scaling constant.

Fig. 8
Fig. 8

Estimated spectral dependence of the CPD for four different sets of reflectance data of UV-enhanced aluminum. The black curves are for the case in which the radiation undergoes two reflections on the aluminum-coated hemisphere, whereas the gray curves are calculated for the case in which the radiation undergoes one reflection at the hemisphere.

Fig. 9
Fig. 9

Spectral dependent uncertainty components for each of the measurement series in the establishment of a spectral response scale in the infrared, in addition to the combined uncertainty of all components. The uncertainties are given with a 1σ level of confidence.

Fig. 10
Fig. 10

Comparison of the propagated type A uncertainty and the observed standard deviation in the calculated responsivity values over the spectral range where the type A uncertainty is the dominating uncertainty component. The uncertainties are given with a 1σ level of confidence.

Tables (1)

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Table 1 Accounted Uncertainty Components in the Estimated Responsivity

Equations (8)

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y ¯ ( m ) = Wy ( m ) ,
u ( y ¯ ) ( m ) = W u ( y ) ( m ) W T ,
a ( m ) = 1 ( N n + 1 ) i = n N F ( 1 , m ) i r ( 1 , m ) i ,
Y ( 1 ) i = 1 3 [ y ( 1 ) i + 1 a ( 2 ) y ( 2 ) i F ( 1 , 2 ) i + 1 a ( 3 ) y ( 3 ) i F ( 1 , 3 ) i ] .
R ( 1 ) = K WY ( 1 ) .
K = 1 ( M n + 1 ) i = n M A ( 1 ) i [ W Y ( 1 ) ] i ,
u ( K ) = Ψ W u ( Y ) W T Ψ T + a u ( A ) α T ,
u ( R ) = K 2 W u ( Y ) W T + [ WY ( 1 ) ] u ( K ) [ WY ( 1 ) ] T ,

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