Abstract

The scanning-beam technique for measuring the response of a detector to an irradiance is analyzed. With this method the irradiance responsivity is determined by integration of the spatial responsivity. Since in practice the integration is approximated by a summation over steps with a finite step size, errors are introduced. It is shown both theoretically and experimentally that the error vanishes when the reciprocal step size lies beyond the diffraction limit. Furthermore, comparison shows that experiment and theory are in good agreement.

© 2000 Optical Society of America

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References

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  1. N. P. Fox, “Radiometry with cryogenic radiometers and semiconductor photodiodes,” Metrologia 32, 535–543 (1995/1996).
  2. K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
    [CrossRef]
  3. T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
    [CrossRef] [PubMed]
  4. C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
    [CrossRef]
  5. N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
    [CrossRef]
  6. C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
    [CrossRef]
  7. S. Castelletto, M. L. Rastello, “Luminous and photon standards by trap detectors,” IEEE Trans. Instrum. Meas. 47, 900–906 (1998).
    [CrossRef]
  8. A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
    [CrossRef]
  9. E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
    [CrossRef]
  10. P. Toivanen, F. Manoochehri, P. Kärhä, E. Ikonen, A. Lassila, “Method for characterization of filter radiometers,” Appl. Opt. 38, 1709–1713 (1999).
    [CrossRef]
  11. C. A. Schrama, H. Reijn, “Novel calibration method for filter radiometers,” Metrologia 36, 179–182 (1999).
    [CrossRef]
  12. T. B. A. Senior, Mathematical Methods in Electrical Engineering (Cambridge U Press, Cambridge, 1986), p. 250.
  13. J. D. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic, Orlando, Fla., 1984), p. 144.
  14. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1970), p. 11.
  15. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 480–490.
  16. E. F. Zalewski, C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867–2873 (1983).
    [CrossRef] [PubMed]

1999 (2)

1998 (4)

E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
[CrossRef]

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

S. Castelletto, M. L. Rastello, “Luminous and photon standards by trap detectors,” IEEE Trans. Instrum. Meas. 47, 900–906 (1998).
[CrossRef]

1997 (1)

A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
[CrossRef]

1996 (2)

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

1991 (1)

N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
[CrossRef]

1983 (1)

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1970), p. 11.

Bloembergen, P.

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 480–490.

Bosma, R.

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

Castelletto, S.

S. Castelletto, M. L. Rastello, “Luminous and photon standards by trap detectors,” IEEE Trans. Instrum. Meas. 47, 900–906 (1998).
[CrossRef]

Cromer, C. L.

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Davis, J. D.

J. D. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic, Orlando, Fla., 1984), p. 144.

Duda, C. R.

Eppeldauer, G.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Fox, N. P.

N. P. Fox, “Radiometry with cryogenic radiometers and semiconductor photodiodes,” Metrologia 32, 535–543 (1995/1996).

N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
[CrossRef]

Gentile, T. R.

Gibb, K.

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

Hardis, J. E.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

Hofer, H.

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

Houston, J. M.

Ikonen, E.

P. Toivanen, F. Manoochehri, P. Kärhä, E. Ikonen, A. Lassila, “Method for characterization of filter radiometers,” Appl. Opt. 38, 1709–1713 (1999).
[CrossRef]

E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
[CrossRef]

A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
[CrossRef]

Kärhä, P.

Larason, T. C.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Lassila, A.

P. Toivanen, F. Manoochehri, P. Kärhä, E. Ikonen, A. Lassila, “Method for characterization of filter radiometers,” Appl. Opt. 38, 1709–1713 (1999).
[CrossRef]

E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
[CrossRef]

A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
[CrossRef]

Manoochehri, F.

Martin, J. E.

N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
[CrossRef]

Metzdorf, J.

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

Nettleton, D. H.

N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
[CrossRef]

Ohna, Y.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Parr, A. C.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

Pawlak, M.

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

Rabinowitz, P.

J. D. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic, Orlando, Fla., 1984), p. 144.

Rastello, M. L.

S. Castelletto, M. L. Rastello, “Luminous and photon standards by trap detectors,” IEEE Trans. Instrum. Meas. 47, 900–906 (1998).
[CrossRef]

Reijn, H.

C. A. Schrama, H. Reijn, “Novel calibration method for filter radiometers,” Metrologia 36, 179–182 (1999).
[CrossRef]

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

Schrama, C. A.

C. A. Schrama, H. Reijn, “Novel calibration method for filter radiometers,” Metrologia 36, 179–182 (1999).
[CrossRef]

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

Senior, T. B. A.

T. B. A. Senior, Mathematical Methods in Electrical Engineering (Cambridge U Press, Cambridge, 1986), p. 250.

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1970), p. 11.

Stock, K. D.

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

Toivanen, P.

P. Toivanen, F. Manoochehri, P. Kärhä, E. Ikonen, A. Lassila, “Method for characterization of filter radiometers,” Appl. Opt. 38, 1709–1713 (1999).
[CrossRef]

E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
[CrossRef]

A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 480–490.

Zalewski, E. F.

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (1)

S. Castelletto, M. L. Rastello, “Luminous and photon standards by trap detectors,” IEEE Trans. Instrum. Meas. 47, 900–906 (1998).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (1)

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohna, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Meas. Sci. Technol. (1)

A. Lassila, P. Toivanen, E. Ikonen, “An optical method for direct determination of the radiometric aperture area at high accuracy,” Meas. Sci. Technol. 8, 973–977 (1997).
[CrossRef]

Metrologia (6)

E. Ikonen, P. Toivanen, A. Lassila, “A new optical method for high-accuracy determination of aperture area,” Metrologia 35, 369–372 (1998).
[CrossRef]

C. A. Schrama, H. Reijn, “Novel calibration method for filter radiometers,” Metrologia 36, 179–182 (1999).
[CrossRef]

C. A. Schrama, R. Bosma, K. Gibb, H. Reijn, P. Bloembergen, “Comparison of monochromator-based and laser-based cryogenic radiometry,” Metrologia 35, 431–435 (1998).
[CrossRef]

N. P. Fox, J. E. Martin, D. H. Nettleton, “Absolute spectral radiometric determination of the thermodynamic temperatures of the melting/freezing points of gold, silver and aluminium,” Metrologia 28, 357–374 (1991).
[CrossRef]

N. P. Fox, “Radiometry with cryogenic radiometers and semiconductor photodiodes,” Metrologia 32, 535–543 (1995/1996).

K. D. Stock, H. Hofer, M. Pawlak, J. Metzdorf, “Improvements to the German national primary standard of radiant power above 200 nm,” Metrologia 35, 279–282 (1998).
[CrossRef]

Other (4)

T. B. A. Senior, Mathematical Methods in Electrical Engineering (Cambridge U Press, Cambridge, 1986), p. 250.

J. D. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic, Orlando, Fla., 1984), p. 144.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1970), p. 11.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 480–490.

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Figures (3)

Fig. 1
Fig. 1

Position of the detector with responsivity R relative to irradiance distribution E.

Fig. 2
Fig. 2

Measurement data (●) and numerical simulation (○) of Ref. 8 as function of step size relative to the aperture diameter. The dashed curve is the leading term of Eq. (12), with η = 2.2, and the solid curve represents the first five terms. The inset is a magnification of the range between 0.1 and 0.7 mm; the solid curve has been omitted for clarity.

Fig. 3
Fig. 3

Error related to the relative irradiance responsivity measurements as function of step size. The measurements are normalized to the data points obtained between 1.5 and 2.5 mm. The error bars indicate the 1σ standard deviation of five measurements. The solid curve is a least-squares fit to the first-order term of Eq. (12). The inset is a magnification between 1.5 and 6 mm. The vertical dotted–dashed curve indicates the diffraction limit in this experimental set up.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

jy=R * Ey d2x RxEy-x,
S= d2x Rx.
Seh=h2xn Rxn,
Δh=Seh/S-1,
h2xn δx-xn=kmexpikm·x,
Δh=km\0 km,
k=d2x Rxexpik·xd2x Rx.
Δh=km\0 kmkm,
|Δh|km\0|km|.
h<λF.
k=exp- w|k|28,
k=2 J1|k|a|k|a,
Δhr=4 m1=0m2=1hrπm J12πmhrexp- 12πmhrη2,

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