Abstract

The combination of a cryogenic radiometer and synchrotron radiation enables detector scale realization in spectral regions that are otherwise difficult to access. Cryogenic radiometry is the most accurate primary detector-based standard available to date, and synchrotron radiation gives a unique broadband and continuous spectrum that extends from x ray to far IR. We describe a new cryogenic radiometer-based UV radiometry facility at the Synchrotron Ultraviolet Radiation Facility II at the National Institute of Standards and Technology. The facility is designed to perform a variety of detector and optical materials characterizations. The facility combines a high-throughput, normal incidence monochromator with an absolute cryogenic radiometer optimized for UV measurements to provide absolute radiometric measurements in the spectral range from 125 nm to approximately 320 nm. We discuss results on photodetector characterizations, including absolute spectroradiometric calibration, spatial responsivity mapping, spectroreflectance, and internal quantum efficiency. In addition, such characterizations are used to study UV radiation damage in photodetectors that can shed light on the mechanism of the damage process. Examples are also given for UV optical materials characterization.

© 1999 Optical Society of America

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  1. D. C. Ginnings, M. L. Reilly, “Calorimetric measurement of thermodynamic temperatures above 0 °C using total blackbody radiation,” in Temperature: Its Measurement and Control in Science and Industry, H. H. Plumb, ed. (Instrument Society of America, Pittsburgh, Pa., 1972), Vol. 4, Part I, pp. 339–348.
  2. C. R. Yokley, “Long wave infrared testing at NBS,” in Applications of Optical Metrology: Techniques and Measurements II, R. C. Harney, ed., Proc. SPIE416, 2–8 (1983).
  3. T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant,” in Precision Measurement and Fundamental Constants II, Natl. Bur. Stand. (U.S.) Spec. Publ.617, 291–297 (1984).
  4. T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant and thermodynamic temperature between -40 °C and +100 °C,” Philos. Trans. R. Soc. London Ser. A 316, 85–189 (1985).
    [CrossRef]
  5. J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
    [CrossRef]
  6. T. R. Gentile, J. M. Houston, C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392–4403 (1996).
    [CrossRef] [PubMed]
  7. 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]
  8. T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
    [CrossRef]
  9. T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).
  10. See, for example, G. Margaritondo, Introduction to Synchrotron Radiation (Oxford U. Press, New York, 1988), Chaps. 1 and 2.
  11. D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).
  12. M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
    [CrossRef]
  13. J. Schwinger, “On the classical radiation of accelerated electrons,” Phys. Rev. 75, 1912–1925 (1949).
    [CrossRef]
  14. B. Wende, “Radiometry with synchrotron radiation,” Metrologia 32, 419–423 (1996).
    [CrossRef]
  15. G. Ulm, B. Wende, “The radiometry laboratory of PTB at BESSY,” Rev. Sci. Instrum. 66, 2244–2247 (1995).
    [CrossRef]
  16. H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
    [CrossRef]
  17. L. R. Canfield, “New far UV detector calibration facility at the National Bureau of Standards,” Appl. Opt. 26, 3831–3837 (1987).
    [CrossRef] [PubMed]
  18. L. R. Canfield, N. Swanson, “Far ultraviolet detector standards,” J. Res. Natl. Bur. Stand. 92, 97–112 (1987).
    [CrossRef]
  19. R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
    [CrossRef]
  20. A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).
  21. H. Rabus, V. Persch, G. Ulm, “Synchrotron-radiation-operated cryogenic electric-substitution radiometer as the high-accuracy primary detector standard in the ultraviolet, vacuum-ultraviolet, and soft-x-ray spectral ranges,” Appl. Opt. 36, 5421–5440 (1997).
    [CrossRef] [PubMed]
  22. P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).
  23. J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
    [CrossRef] [PubMed]
  24. J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
    [CrossRef]
  25. D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
    [CrossRef]
  26. L. R. Hughey, “Improved resolution and flexibility of the SURF II high-throughput 2-m normal incidence monochromator,” Nucl. Instrum. Methods A 347, 294–298 (1994).
    [CrossRef]
  27. L. P. Boivin, K. Gibb, “Monochromator-based cryogenic radiometry at the NRC,” Metrologia 32, 565–570 (1995/1996).
  28. Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
  29. B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” , 2nd ed. (National Institute of Standards and Technology, Gaithersburg, Md., 1994).
  30. T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
    [CrossRef]
  31. R. Korde, J. Geist, “Quantum efficiency stability of silicon photodiodes,” Appl. Opt. 26, 5284–5290 (1987).
    [CrossRef] [PubMed]
  32. L. Fu, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia 30, 297–303 (1993).
    [CrossRef]
  33. C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).
  34. K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
    [CrossRef]
  35. T. R. O’Brian, “SURF III: the next generation radiometric storage ring facility at NIST,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation, R. E. Huffman, C. G. Stergis, eds., Proc. SPIE2831, 222–228 (1996).
    [CrossRef]

1998

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

1997

H. Rabus, V. Persch, G. Ulm, “Synchrotron-radiation-operated cryogenic electric-substitution radiometer as the high-accuracy primary detector standard in the ultraviolet, vacuum-ultraviolet, and soft-x-ray spectral ranges,” Appl. Opt. 36, 5421–5440 (1997).
[CrossRef] [PubMed]

T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).

1996

T. R. Gentile, J. M. Houston, C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392–4403 (1996).
[CrossRef] [PubMed]

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]

T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
[CrossRef]

B. Wende, “Radiometry with synchrotron radiation,” Metrologia 32, 419–423 (1996).
[CrossRef]

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

1995

G. Ulm, B. Wende, “The radiometry laboratory of PTB at BESSY,” Rev. Sci. Instrum. 66, 2244–2247 (1995).
[CrossRef]

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

1994

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

L. R. Hughey, “Improved resolution and flexibility of the SURF II high-throughput 2-m normal incidence monochromator,” Nucl. Instrum. Methods A 347, 294–298 (1994).
[CrossRef]

1993

L. Fu, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia 30, 297–303 (1993).
[CrossRef]

1992

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

1989

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

1987

1985

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant and thermodynamic temperature between -40 °C and +100 °C,” Philos. Trans. R. Soc. London Ser. A 316, 85–189 (1985).
[CrossRef]

J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

1980

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
[CrossRef] [PubMed]

D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
[CrossRef]

1975

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

1949

J. Schwinger, “On the classical radiation of accelerated electrons,” Phys. Rev. 75, 1912–1925 (1949).
[CrossRef]

Arp, U.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Boivin, L. P.

L. P. Boivin, K. Gibb, “Monochromator-based cryogenic radiometry at the NRC,” Metrologia 32, 565–570 (1995/1996).

Bruce, S. S.

T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).

T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
[CrossRef]

Canfield, L. R.

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

L. R. Canfield, “New far UV detector calibration facility at the National Bureau of Standards,” Appl. Opt. 26, 3831–3837 (1987).
[CrossRef] [PubMed]

L. R. Canfield, N. Swanson, “Far ultraviolet detector standards,” J. Res. Natl. Bur. Stand. 92, 97–112 (1987).
[CrossRef]

Chandler-Horowitz, D.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

Cole, B. E.

D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
[CrossRef]

Cromer, C. L.

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
[CrossRef]

T. R. Gentile, J. M. Houston, C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392–4403 (1996).
[CrossRef] [PubMed]

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]

Dehmer, J. L.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Ebner, S. C.

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

Ederer, D. L.

D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
[CrossRef]

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

Fischer, J.

L. Fu, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia 30, 297–303 (1993).
[CrossRef]

Fox, N. P.

J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Fu, L.

L. Fu, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia 30, 297–303 (1993).
[CrossRef]

Furst, M. L.

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

Geist, J.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

R. Korde, J. Geist, “Quantum efficiency stability of silicon photodiodes,” Appl. Opt. 26, 5284–5290 (1987).
[CrossRef] [PubMed]

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
[CrossRef] [PubMed]

Gentile, T. R.

Gibb, K.

L. P. Boivin, K. Gibb, “Monochromator-based cryogenic radiometry at the NRC,” Metrologia 32, 565–570 (1995/1996).

Ginnings, D. C.

D. C. Ginnings, M. L. Reilly, “Calorimetric measurement of thermodynamic temperatures above 0 °C using total blackbody radiation,” in Temperature: Its Measurement and Control in Science and Industry, H. H. Plumb, ed. (Instrument Society of America, Pittsburgh, Pa., 1972), Vol. 4, Part I, pp. 339–348.

Graves, R. M.

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

Gupta, R.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Hardis, J. E.

Houston, J. M.

Hughey, L. R.

L. R. Hughey, “Improved resolution and flexibility of the SURF II high-throughput 2-m normal incidence monochromator,” Nucl. Instrum. Methods A 347, 294–298 (1994).
[CrossRef]

James, C. R.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

Katori, K.

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

Key, P. G.

J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Korde, R.

Kroth, U.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

Kuschnerus, P.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” , 2nd ed. (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

Larason, T. C.

T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).

T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
[CrossRef]

Lau-Frambs, A.

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

Lucatorto, T. B.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

Lykke, K. R.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Madden, R. P.

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

Margaritondo, G.

See, for example, G. Margaritondo, Introduction to Synchrotron Radiation (Oxford U. Press, New York, 1988), Chaps. 1 and 2.

Martin, J. E.

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant and thermodynamic temperature between -40 °C and +100 °C,” Philos. Trans. R. Soc. London Ser. A 316, 85–189 (1985).
[CrossRef]

J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant,” in Precision Measurement and Fundamental Constants II, Natl. Bur. Stand. (U.S.) Spec. Publ.617, 291–297 (1984).

Melchior, H.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

Nishi, M.

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

O’Brian, T. R.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

T. R. O’Brian, “SURF III: the next generation radiometric storage ring facility at NIST,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation, R. E. Huffman, C. G. Stergis, eds., Proc. SPIE2831, 222–228 (1996).
[CrossRef]

Onuki, H.

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

Parr, A. C.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).

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]

Persch, V.

H. Rabus, V. Persch, G. Ulm, “Synchrotron-radiation-operated cryogenic electric-substitution radiometer as the high-accuracy primary detector standard in the ultraviolet, vacuum-ultraviolet, and soft-x-ray spectral ranges,” Appl. Opt. 36, 5421–5440 (1997).
[CrossRef] [PubMed]

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

Quinn, T. J.

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant and thermodynamic temperature between -40 °C and +100 °C,” Philos. Trans. R. Soc. London Ser. A 316, 85–189 (1985).
[CrossRef]

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant,” in Precision Measurement and Fundamental Constants II, Natl. Bur. Stand. (U.S.) Spec. Publ.617, 291–297 (1984).

Rabus, H.

H. Rabus, V. Persch, G. Ulm, “Synchrotron-radiation-operated cryogenic electric-substitution radiometer as the high-accuracy primary detector standard in the ultraviolet, vacuum-ultraviolet, and soft-x-ray spectral ranges,” Appl. Opt. 36, 5421–5440 (1997).
[CrossRef] [PubMed]

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

Reilly, M. L.

D. C. Ginnings, M. L. Reilly, “Calorimetric measurement of thermodynamic temperatures above 0 °C using total blackbody radiation,” in Temperature: Its Measurement and Control in Science and Industry, H. H. Plumb, ed. (Instrument Society of America, Pittsburgh, Pa., 1972), Vol. 4, Part I, pp. 339–348.

Richter, M.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

Robinson, A. M.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

Saito, T.

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

Saloman, E. B.

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

Schaefer, A. R.

Scholze, F.

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

Schwinger, J.

J. Schwinger, “On the classical radiation of accelerated electrons,” Phys. Rev. 75, 1912–1925 (1949).
[CrossRef]

Shaw, P. S.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Solt, K.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

Swanson, N.

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

L. R. Canfield, N. Swanson, “Far ultraviolet detector standards,” J. Res. Natl. Bur. Stand. 92, 97–112 (1987).
[CrossRef]

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” , 2nd ed. (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

Tegeler, E.

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

Thornagel, R.

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

Ulm, G.

H. Rabus, V. Persch, G. Ulm, “Synchrotron-radiation-operated cryogenic electric-substitution radiometer as the high-accuracy primary detector standard in the ultraviolet, vacuum-ultraviolet, and soft-x-ray spectral ranges,” Appl. Opt. 36, 5421–5440 (1997).
[CrossRef] [PubMed]

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

G. Ulm, B. Wende, “The radiometry laboratory of PTB at BESSY,” Rev. Sci. Instrum. 66, 2244–2247 (1995).
[CrossRef]

Vest, R. E.

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

Walhout, M.

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

Wende, B.

B. Wende, “Radiometry with synchrotron radiation,” Metrologia 32, 419–423 (1996).
[CrossRef]

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

G. Ulm, B. Wende, “The radiometry laboratory of PTB at BESSY,” Rev. Sci. Instrum. 66, 2244–2247 (1995).
[CrossRef]

West, J. B.

D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
[CrossRef]

White, H. H.

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

Yokley, C. R.

C. R. Yokley, “Long wave infrared testing at NBS,” in Applications of Optical Metrology: Techniques and Measurements II, R. C. Harney, ed., Proc. SPIE416, 2–8 (1983).

Zalewski, E. F.

Appl. Opt.

Appl. Phys. Lett.

K. Solt, H. Melchior, U. Kroth, P. Kuschnerus, V. Persch, H. Rabus, M. Richter, G. Ulm, “PtSi-n-Si Schottky-barrier photodetectors with stable spectral responsivity in the 120 nm to 250 nm spectral range,” Appl. Phys. Lett. 69, 3662–3664 (1996).
[CrossRef]

J. Res. Natl. Bur. Stand.

L. R. Canfield, N. Swanson, “Far ultraviolet detector standards,” J. Res. Natl. Bur. Stand. 92, 97–112 (1987).
[CrossRef]

J. Res. Natl. Inst. Stand.

T. C. Larason, S. S. Bruce, C. L. Cromer, “The NIST high accuracy scale for absolute spectral response from 406 nm to 920 nm,” J. Res. Natl. Inst. Stand. 101, 133–140 (1996).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol.

D. L. Ederer, E. B. Saloman, S. C. Ebner, R. P. Madden, “The use of synchrotron radiation as an absolute source of VUV radiation,” J. Res. Natl. Inst. Stand. Technol. 79 A761–774 (1975).

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1992).
[CrossRef]

Metrologia

P. S. Shaw, K. R. Lykke, R. Gupta, T. R. O’Brian, U. Arp, H. H. White, T. B. Lucatorto, J. L. Dehmer, A. C. Parr, “New UV radiometry beamline at the Synchrotron Ultraviolet Radiation Facility at NIST,” Metrologia 35 (1998).

L. P. Boivin, K. Gibb, “Monochromator-based cryogenic radiometry at the NRC,” Metrologia 32, 565–570 (1995/1996).

L. Fu, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia 30, 297–303 (1993).
[CrossRef]

A. Lau-Frambs, U. Kroth, H. Rabus, E. Tegeler, G. Ulm, B. Wende, “First results with the new PTB cryogenic radiometer for the vacuum ultraviolet spectral range,” Metrologia 32, 571–574 (1995/1996).

B. Wende, “Radiometry with synchrotron radiation,” Metrologia 32, 419–423 (1996).
[CrossRef]

J. E. Martin, N. P. Fox, P. G. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Natl. Inst. Stand. Technol. (U.S.) Spec. Publ.

T. C. Larason, S. S. Bruce, A. C. Parr, “NIST measurement services: spectroradiometric detector measurements: Parts I and II—ultraviolet and visible to near infrared detectors,” Natl. Inst. Stand. Technol. (U.S.) Spec. Publ. 250–41 (1997).

Nucl. Instrum. Methods

D. L. Ederer, B. E. Cole, J. B. West, “A high-throughput 2-m normal incidence monochromator for SURF II,” Nucl. Instrum. Methods 172, 185–190 (1980).
[CrossRef]

Nucl. Instrum. Methods A

L. R. Hughey, “Improved resolution and flexibility of the SURF II high-throughput 2-m normal incidence monochromator,” Nucl. Instrum. Methods A 347, 294–298 (1994).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. P. Madden, N. Swanson, “Dual grating monochromator for detector calibrations using synchrotron radiation as an absolute source at NIST,” Nucl. Instrum. Methods A 347, 291–294 (1994).
[CrossRef]

H. Rabus, F. Scholze, R. Thornagel, G. Ulm, “Detector calibration at the PTB radiometry laboratory at BESSY,” Nucl. Instrum. Methods A 377, 209–216 (1996).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant and thermodynamic temperature between -40 °C and +100 °C,” Philos. Trans. R. Soc. London Ser. A 316, 85–189 (1985).
[CrossRef]

Phys. Rev.

J. Schwinger, “On the classical radiation of accelerated electrons,” Phys. Rev. 75, 1912–1925 (1949).
[CrossRef]

Rev. Sci. Instrum.

G. Ulm, B. Wende, “The radiometry laboratory of PTB at BESSY,” Rev. Sci. Instrum. 66, 2244–2247 (1995).
[CrossRef]

M. L. Furst, R. M. Graves, L. R. Canfield, R. E. Vest, “Radiometry at the NIST SURF II storage ring facility,” Rev. Sci. Instrum. 66, 2257–2259 (1995).
[CrossRef]

T. Saito, K. Katori, M. Nishi, H. Onuki, “Spectral quantum efficiencies of semiconductor photodiodes in the far ultraviolet region,” Rev. Sci. Instrum. 60, 2303–2306 (1989).
[CrossRef]

Solid State Technol.

C. L. Cromer, T. B. Lucatorto, T. R. O’Brian, M. Walhout, “Improved dose metrology in optical lithography,” Solid State Technol. 39, 75 (1996).

Other

T. R. O’Brian, “SURF III: the next generation radiometric storage ring facility at NIST,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation, R. E. Huffman, C. G. Stergis, eds., Proc. SPIE2831, 222–228 (1996).
[CrossRef]

Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” , 2nd ed. (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

D. C. Ginnings, M. L. Reilly, “Calorimetric measurement of thermodynamic temperatures above 0 °C using total blackbody radiation,” in Temperature: Its Measurement and Control in Science and Industry, H. H. Plumb, ed. (Instrument Society of America, Pittsburgh, Pa., 1972), Vol. 4, Part I, pp. 339–348.

C. R. Yokley, “Long wave infrared testing at NBS,” in Applications of Optical Metrology: Techniques and Measurements II, R. C. Harney, ed., Proc. SPIE416, 2–8 (1983).

T. J. Quinn, J. E. Martin, “A radiometric determination of the Stefan–Boltzmann constant,” in Precision Measurement and Fundamental Constants II, Natl. Bur. Stand. (U.S.) Spec. Publ.617, 291–297 (1984).

See, for example, G. Margaritondo, Introduction to Synchrotron Radiation (Oxford U. Press, New York, 1988), Chaps. 1 and 2.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the ACR-based beamline for UV radiometry. NIM, normal incidence monochromator; DPC, differential pumping chamber.

Fig. 2
Fig. 2

Positioning of the test detector and the ACR to bring the test detector or the ACR to the focal position of the SR beam. The ACR measures the total power of radiation when the ACR is in the focal position, and the response of the test detector is measured when the test detector is positioned in the focal position.

Fig. 3
Fig. 3

Measured optical power output from the beamline monochromator with 90 mA of electron-beam current and a slit size of 3 × 3 mm2 (∼2-nm resolution). In this measurement a quartz window was inserted before the exit slit to suppress higher-order light when the wavelength setting of the monochromator was longer than 220 nm.

Fig. 4
Fig. 4

Measured spectral response of a photodiode in the air-filled detector box from 180 to 200 nm. The oxygen Schumann–Runge bands are used for wavelength calibration.

Fig. 5
Fig. 5

Time scan of the trap-detector response and the ACR power measurement with a He–Ne laser. The trap detector is a transfer standard that was precalibrated by HACR. The apparent background change for the ACR power measurement results from use of the ACR for viewing either the back of the trap detector (for measuring the trap detector response) or the proper background that views the beamline.

Fig. 6
Fig. 6

Data collection process for measuring the spectral responsivity of the detector. The measurement cycle for each wavelength is as follows: (1) Move the ACR to the focal position, close the shutter, and measure the ACR background. (2) Open the shutter, and measure the ACR power. (3) Move the detector to the focal position, and measure the signal of test detector from the current-to-voltage amplifier. (4) Move the ACR to the focal position, and measure ACR power. (5) With the shutter closed, measure the ACR background.

Fig. 7
Fig. 7

Measured spectral responsivity for UV photodetectors of silicon p-on-n (Hamamatsu 1337), nitrided silicon n-on-p (IRD UVG), silicon n-on-p with protective window (UDT UV100), Schottky-type PtSi-n-Si, GaN, GaP, GaAsP, and diamond photoconductive detector. A bias voltage of 90 V was used for diamond photoconductive detector measurement.

Fig. 8
Fig. 8

Measured spatial uniformity of a GaN photodiode at 180 nm.

Fig. 9
Fig. 9

Reflectance and internal quantum efficiency for PtSi, GaN, GaP, and GaAsP photodiodes.

Fig. 10
Fig. 10

Change of detector responsivity from 135-nm UV radiation for (a) Hamamatsu 1337, (b) Hamamatsu 5227, (c) International Radiation Detectors silicon, (d) PtSi photodiodes.

Fig. 11
Fig. 11

Measured change of absolute spectral responsivity and reflectance of a Hamamatsu Si 1337 photodiode. Diamonds are before and circles are after 135-nm UV radiation for a total dose of 16 mJ cm-2.

Fig. 12
Fig. 12

UV transmittance of two samples, calcium fluoride and fused silica, measured with the new radiometric beamline.

Tables (1)

Tables Icon

Table 1 Components of the Combined Relative Standard Uncertainty of Spectral Responsivitya

Equations (4)

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

VpλVrλ=PλSpλrλPλSrλ,
rλ=VrλSpλVpλSrλ.
Spλ=1-rλ-aλehν qintλ,
qintλ=hνeSpλ1-rλ.

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