Abstract

The errors caused by monochromator bandwidth in spectral responsivity measurements with a monochromator-based apparatus are discussed. Bandwidth effects are not negligible in high-accuracy cryogenic radiometer-based calibrations. A simple numerical method is used to calculate bandwidth effects for different types of detectors, monochromator slit scattering functions, and monochromator output spectral distributions. The method uses low-order Lagrange polynomials fitted segmentwise to measured spectral responsivity and monochromator spectral distribution data in order to make the calculations. It is shown that the shape of the slit function has only a small influence on the bandwidth errors, whereas the output spectral distribution of the monochromator can strongly affect bandwidth errors. It is also shown that in most cases the magnitude of bandwidth effects will vary as the square of the bandwidth. Bandwidth error calculations are presented for various types of detectors (silicon, silicon trap, germanium, InGaAs), for a V(λ) detector, and for a typical filter radiometer. A comparison is made between calculated and measured bandwidth effects to validate the method used. In general, calculations of bandwidth effects will be mostly useful for determining uncertainties associated with monochromator bandwidth in spectral responsivity measurements; however, in certain cases the calculations can be used to apply corrections for such effects.

© 2002 Optical Society of America

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References

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  1. E. F. Zalewski, C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867–2873 (1983).
    [CrossRef] [PubMed]
  2. J. L. Gardner, “Transmission trap detectors,” Appl. Opt. 33, 5914–5918 (1994).
    [CrossRef] [PubMed]
  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. K. D. Stock, H. Hofer, “PTB primary standard for optical radiant power: transfer-optimized facility in the clean-room centre,” Metrologia 32, 545–549 (1996).
    [CrossRef]
  5. L. P. Boivin, K. Gibb, “Monochromator-based cryogenic radiometry at the NRC,” Metrologia 32, 565–570 (1995/1996).
    [CrossRef]
  6. 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]
  7. R. Nemecek, P. Nemecek, “Spectral bandwidth correction by responsivity measurement,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovský, A. Štrba, W. Urbanczyk, eds., Proc. SPIE3820, 322–328 (1999).
    [CrossRef]
  8. A. Corrons, E. F. Zalewski, “Detector spectral response from 350 to 1200 nm using a monochromator based spectral comparator,” Natl. Bur. Stand. Tech. Note 988 (National Bureau of Standards, Gaithersburg, Md., 1978).

1998 (1)

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]

1996 (2)

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]

K. D. Stock, H. Hofer, “PTB primary standard for optical radiant power: transfer-optimized facility in the clean-room centre,” Metrologia 32, 545–549 (1996).
[CrossRef]

1994 (1)

1983 (1)

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]

Boivin, L. P.

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

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]

Corrons, A.

A. Corrons, E. F. Zalewski, “Detector spectral response from 350 to 1200 nm using a monochromator based spectral comparator,” Natl. Bur. Stand. Tech. Note 988 (National Bureau of Standards, Gaithersburg, Md., 1978).

Cromer, C. L.

Duda, C. R.

Gardner, J. L.

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]

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

Hardis, J. E.

Hofer, H.

K. D. Stock, H. Hofer, “PTB primary standard for optical radiant power: transfer-optimized facility in the clean-room centre,” Metrologia 32, 545–549 (1996).
[CrossRef]

Houston, J. M.

Nemecek, P.

R. Nemecek, P. Nemecek, “Spectral bandwidth correction by responsivity measurement,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovský, A. Štrba, W. Urbanczyk, eds., Proc. SPIE3820, 322–328 (1999).
[CrossRef]

Nemecek, R.

R. Nemecek, P. Nemecek, “Spectral bandwidth correction by responsivity measurement,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovský, A. Štrba, W. Urbanczyk, eds., Proc. SPIE3820, 322–328 (1999).
[CrossRef]

Parr, A. C.

Reijn, H.

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

Stock, K. D.

K. D. Stock, H. Hofer, “PTB primary standard for optical radiant power: transfer-optimized facility in the clean-room centre,” Metrologia 32, 545–549 (1996).
[CrossRef]

Zalewski, E. F.

E. F. Zalewski, C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867–2873 (1983).
[CrossRef] [PubMed]

A. Corrons, E. F. Zalewski, “Detector spectral response from 350 to 1200 nm using a monochromator based spectral comparator,” Natl. Bur. Stand. Tech. Note 988 (National Bureau of Standards, Gaithersburg, Md., 1978).

Appl. Opt. (3)

Metrologia (3)

K. D. Stock, H. Hofer, “PTB primary standard for optical radiant power: transfer-optimized facility in the clean-room centre,” Metrologia 32, 545–549 (1996).
[CrossRef]

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

Other (2)

R. Nemecek, P. Nemecek, “Spectral bandwidth correction by responsivity measurement,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovský, A. Štrba, W. Urbanczyk, eds., Proc. SPIE3820, 322–328 (1999).
[CrossRef]

A. Corrons, E. F. Zalewski, “Detector spectral response from 350 to 1200 nm using a monochromator based spectral comparator,” Natl. Bur. Stand. Tech. Note 988 (National Bureau of Standards, Gaithersburg, Md., 1978).

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Figures (9)

Fig. 1
Fig. 1

Comparison of the theoretical and measured slit scattering function for a monochromator having a slit entrance and round aperture exit configuration; also shown is the theoretical slit function for a monochromator having equal width entrance and exit slits.

Fig. 2
Fig. 2

Spectral distribution of the output radiation of a typical monochromator using a tungsten halogen or xenon-arc source.

Fig. 3
Fig. 3

Calculated bandwidth errors corresponding to a 10-nm bandwidth for a typical silicon photodiode and for monochromator output power distributions corresponding to tungsten or xenon sources, as shown in Fig. 2, and also for the ideal case of a spectrally uniform distribution.

Fig. 4
Fig. 4

Comparison of the calculated bandwidth errors corresponding to two types of monochromator slit scattering function: the ideal triangular function for equal entrance and exit slits and the theoretical Gaussian-like function corresponding to a slit entrance and round aperture exit (Fig. 1). Calculations were carried out for a bandwidth of 10 nm and a typical silicon diode.

Fig. 5
Fig. 5

Departure of the calculated bandwidth errors from a square-law variation for two different monochromator output power distributions; the distributions corresponding to the tungsten and xenon sources are the ones shown in Fig. 2. The bandwidth errors are calculated for a silicon photodiode, and differences are calculated relative to values for a 2-nm bandwidth.

Fig. 6
Fig. 6

Spectral responsivity curves of the detectors for which bandwidth errors are calculated in the paper.

Fig. 7
Fig. 7

Calculated bandwidth errors corresponding to a 10-nm bandwidth, for a typical silicon photodiode, for a trap detector using the same type of diode, and for a V(λ) detector.

Fig. 8
Fig. 8

Calculated bandwidth errors corresponding to a 10-nm bandwidth, for typical germanium and InGaAs detectors.

Fig. 9
Fig. 9

Comparison between calculated and measured bandwidth errors for a filtered silicon diode. The curves give the differences between the bandwidth errors corresponding to 10- and 3-nm bandwidths, for both calculated and measured values; the relative spectral responsivity of the filtered detector is shown as a heavy solid line.

Equations (10)

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Stestmλ0=Srefλ0λ0-Δλ0+Δ StestλPλIλdλλ0-Δλ0+Δ SrefλPλIλdλ,
Stestmλ0=λ0-Δλ0+Δ StestλPλIλdλλ0-Δλ0+Δ PλIλdλ.
δλ0=Stestmλ0-Stestλ0/Stestλ0.
δeff=λ0-Δλ0+Δ δλPλIλdλλ0-Δλ0+Δ PλIλdλ.
Spolyλ=k=0N StestλkLN,kλ,
LN,kλ=i=0ikNλ-λii=0ikNλk-λi.
Iλ=1-λ0Δ+λΔ for λ0-Δλλ0, Iλ=1+λ0Δ-λΔ for λ0λλ0+Δ.
Iλ=0.5-2π2|λ-λ0|Δ-1×|λ-λ0|Δ-λ-λ02Δ21/2-sin-12|λ-λ0|/Δ-1π
Smλ0=k=0Nakλ0k+21+Δλ0k+2+1-Δλ0k+2-2k+1k+2Δ2.
δ=Δ212k=0N akkk-1λ0k-2Sλ0.

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