Abstract

We have developed a facility for measuring the transmittance of optical filters at a wavelength of 1064 nm, using a Nd:YAG laser, a power stabilizer, and linear photodiode detectors. A direct measurement method was used for filters with optical densities (OD’s) less than or equal to 4, and a reference substitution technique was used for filters with OD’s as great as 10. The apparatus and data-acquisition system are described. Measurement results for a set of filters are presented. The expanded uncertainties for the measured OD and deduced absorption coefficient are determined through a detailed analysis of all the uncertainty components.

© 1997 Optical Society of America

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References

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  1. E. D. Palik, ed., Handbook of Otical Constants of Solids (Academic, Orlando, Fla., 1985), Chap. 2, pp. 11–24.
  2. K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).
  3. J. C. Zwinkels, D. S. Gignac, “Design and testing of a new high-accuracy ultraviolet-visible-near-infrared spectrophotometer,” Appl. Opt. 31, 1557–1567 (1992).
    [CrossRef] [PubMed]
  4. K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
    [CrossRef]
  5. G. Eppeldauer, J. E. Hardis, “Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature,” Appl. Opt. 30, 3091–3099 (1991).
    [CrossRef] [PubMed]
  6. A. L. Migdall, C. Winnewisser, “Linearity of a silicon photodiode at 30 MHz and its effect on heterodyne measurements,” J. Res. Natl. Inst. Stand. Technol. 96, 143–146 (1991).
    [CrossRef]
  7. A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
    [CrossRef]
  8. A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
    [CrossRef]
  9. T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.
  10. Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).
  11. Z. M. Zhang, “Optical properties of layered structures for partially coherent radiation,” in Heat Transfer 1994—Proceedings of the Tenth International Heat Transfer Conference, G. F. Hewitt, ed. (Institution of Chemical Engineers, Rugby, UK, 1994), Vol. 2, pp. 177–182.
  12. Z. M. Zhang, “Reexamination of the transmittance formulae of a lamina,” J. Heat Transfer 119, 643–647 (1997).
    [CrossRef]
  13. Catalog, Photodiodes (Hamamatsu Photonics K.K., Hamamatsu City, Japan, 1994), pp. 14–15. The use of trade and company names is for identification only and does not imply endorsement by the National Institute of Standards and Technology, nor does it imply that the material or product identified is necessarily the best available for the purpose.
  14. Catalog, Optical Glass Filters (Schott Glass Technologies, Inc., Duryea, Pa., 1984), p. 97.
  15. C. R. Bamford, Colour Generation and Control in Glass (Elsevier, New York, 1977), Chap. 1.
  16. M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
    [CrossRef]
  17. S. G. Kaplan, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication).
  18. A. A. Kaminskii, Laser Crystals (Springer-Verlag, New York, 1981), p. 332.
  19. J. Hecht, The Laser Handbook (McGraw-Hill, New York, 1992), Chap. 22.
  20. B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, D.C., 1994).

1997 (1)

Z. M. Zhang, “Reexamination of the transmittance formulae of a lamina,” J. Heat Transfer 119, 643–647 (1997).
[CrossRef]

1993 (2)

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
[CrossRef]

1992 (2)

J. C. Zwinkels, D. S. Gignac, “Design and testing of a new high-accuracy ultraviolet-visible-near-infrared spectrophotometer,” Appl. Opt. 31, 1557–1567 (1992).
[CrossRef] [PubMed]

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

1991 (3)

A. L. Migdall, C. Winnewisser, “Linearity of a silicon photodiode at 30 MHz and its effect on heterodyne measurements,” J. Res. Natl. Inst. Stand. Technol. 96, 143–146 (1991).
[CrossRef]

A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
[CrossRef]

G. Eppeldauer, J. E. Hardis, “Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature,” Appl. Opt. 30, 3091–3099 (1991).
[CrossRef] [PubMed]

Bamford, C. R.

C. R. Bamford, Colour Generation and Control in Glass (Elsevier, New York, 1977), Chap. 1.

Bastie, J.

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

Datla, R. U.

Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).

Eckerle, K. L.

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).

Eppeldauer, G.

Flik, M. I.

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

Frenkel, A.

A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
[CrossRef]

T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.

Gentile, T. R.

T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.

Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).

Gignac, D. S.

Hardis, J. E.

Hecht, J.

J. Hecht, The Laser Handbook (McGraw-Hill, New York, 1992), Chap. 22.

Hsia, J. J.

K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).

Kaminskii, A. A.

A. A. Kaminskii, Laser Crystals (Springer-Verlag, New York, 1981), p. 332.

Kaplan, S. G.

S. G. Kaplan, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication).

Kelleher, D. E.

A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
[CrossRef]

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, D.C., 1994).

Loop, B.

A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
[CrossRef]

Mielenz, K. D.

K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).

Migdall, A. L.

A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
[CrossRef]

A. L. Migdall, C. Winnewisser, “Linearity of a silicon photodiode at 30 MHz and its effect on heterodyne measurements,” J. Res. Natl. Inst. Stand. Technol. 96, 143–146 (1991).
[CrossRef]

A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
[CrossRef]

Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).

T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.

Saprisky, V.

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, D.C., 1994).

Ulyanov, A.

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

Weidner, V. R.

K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).

Winnewisser, C.

A. L. Migdall, C. Winnewisser, “Linearity of a silicon photodiode at 30 MHz and its effect on heterodyne measurements,” J. Res. Natl. Inst. Stand. Technol. 96, 143–146 (1991).
[CrossRef]

Xai, G. J.

A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
[CrossRef]

Zhang, Z. M.

Z. M. Zhang, “Reexamination of the transmittance formulae of a lamina,” J. Heat Transfer 119, 643–647 (1997).
[CrossRef]

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).

Z. M. Zhang, “Optical properties of layered structures for partially coherent radiation,” in Heat Transfer 1994—Proceedings of the Tenth International Heat Transfer Conference, G. F. Hewitt, ed. (Institution of Chemical Engineers, Rugby, UK, 1994), Vol. 2, pp. 177–182.

T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.

Zwinkels, J.

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

Zwinkels, J. C.

Appl. Opt. (2)

Color Res. Appl. (1)

K. L. Eckerle, J. Bastie, J. Zwinkels, V. Saprisky, A. Ulyanov, “Comparison of regular transmittance scales of four national standardizing laboratories,” Color Res. Appl. 18, 35–40 (Feb.1993).
[CrossRef]

J. Heat Transfer (1)

Z. M. Zhang, “Reexamination of the transmittance formulae of a lamina,” J. Heat Transfer 119, 643–647 (1997).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (2)

A. L. Migdall, C. Winnewisser, “Linearity of a silicon photodiode at 30 MHz and its effect on heterodyne measurements,” J. Res. Natl. Inst. Stand. Technol. 96, 143–146 (1991).
[CrossRef]

A. L. Migdall, A. Frenkel, D. E. Kelleher, “Filter transmittance measurements in the infrared,” J. Res. Natl. Inst. Stand. Technol. 98, 691–697 (1993).
[CrossRef]

Metrologia (1)

A. L. Migdall, B. Loop, G. J. Xai, “Measuring filter transmittance using heterodyne detection,” Metrologia 28, 217–220 (1991).
[CrossRef]

Other (12)

S. G. Kaplan, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication).

A. A. Kaminskii, Laser Crystals (Springer-Verlag, New York, 1981), p. 332.

J. Hecht, The Laser Handbook (McGraw-Hill, New York, 1992), Chap. 22.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, D.C., 1994).

E. D. Palik, ed., Handbook of Otical Constants of Solids (Academic, Orlando, Fla., 1985), Chap. 2, pp. 11–24.

K. L. Eckerle, J. J. Hsia, K. D. Mielenz, V. R. Weidner, “Regular spectral transmittance,” (U.S. GPO, Washington, D.C., July1987).

T. R. Gentile, A. Frenkel, A. L. Migdall, Z. M. Zhang, “Neutral density filter measurements at the National Institute of Standards and Technology,” in Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess, D. G. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 129–139.

Z. M. Zhang, T. R. Gentile, A. L. Migdall, R. U. Datla, “Transmission filters with measured optical density at 1064-nm wavelength—SRMS 2046, 2047, 2048, 2049, 2050, 2051,” (U.S. GPO, Washington, D.C., 1998).

Z. M. Zhang, “Optical properties of layered structures for partially coherent radiation,” in Heat Transfer 1994—Proceedings of the Tenth International Heat Transfer Conference, G. F. Hewitt, ed. (Institution of Chemical Engineers, Rugby, UK, 1994), Vol. 2, pp. 177–182.

Catalog, Photodiodes (Hamamatsu Photonics K.K., Hamamatsu City, Japan, 1994), pp. 14–15. The use of trade and company names is for identification only and does not imply endorsement by the National Institute of Standards and Technology, nor does it imply that the material or product identified is necessarily the best available for the purpose.

Catalog, Optical Glass Filters (Schott Glass Technologies, Inc., Duryea, Pa., 1984), p. 97.

C. R. Bamford, Colour Generation and Control in Glass (Elsevier, New York, 1977), Chap. 1.

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Figures (4)

Fig. 1
Fig. 1

Optical setup for transmittance measurements at 1064-nm wavelength: M, mirror; FD, feedback detector; MD, monitor detector; SD, signal detector.

Fig. 2
Fig. 2

Optical density OD of two filters measured at different laser powers: (a) nominal OD = 1; (b) nominal OD = 4.

Fig. 3
Fig. 3

Temperature dependence of the absorption coefficient.

Fig. 4
Fig. 4

Transmittance spectra measured with a Fourier transform infrared spectrometer.

Tables (2)

Tables Icon

Table 1 Uncertainty in OD for a Single Measurement at a Fixed Positiona

Tables Icon

Table 2 Measurement Results for a Set of Filters with OD’s from 1 to 10a

Equations (9)

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T=1-ρ2τ.
OD=-log10 T.
a=OD+2 log101-ρd log10e.
Trelative=Vs1-Vs0/VmsampleVs1-Vs0/Vmtreference,
Tsample=Trelative×Treference,
T=1-ρ2τ1+ρ2τ2-2ρτ cos4πnd/λ.
σcomb=σrepeat2+σreprod2+σnonlin2+σtemp2+σref21/2,
ΔOD=2×σcomb2+σspatial2+σinterf21/2.
Δa=aODΔOD2+aρρnΔn2+adΔd21/2.

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