Reflectance matrix approach to absolute photoluminescence measurements with integrating spheres

Luke J. Sandilands; Joanne C. Zwinkels

doi:10.1364/OE.27.000423

Reflectance matrix approach to absolute photoluminescence measurements with integrating spheres

Luke J. Sandilands and Joanne C. Zwinkels

Optics Express
Vol. 27,
Issue 2,
pp. 423-435
(2019)
•https://doi.org/10.1364/OE.27.000423

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Luke J. Sandilands and Joanne C. Zwinkels, "Reflectance matrix approach to absolute photoluminescence measurements with integrating spheres," Opt. Express 27, 423-435 (2019)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Optical Sensors
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: November 12, 2018
- Revised Manuscript: December 13, 2018
- Manuscript Accepted: December 14, 2018
- Published: January 7, 2019

Accessible

Open Access

Abstract

Absolute measurements of photoluminescence are commonly performed using an integrating sphere setup, as this allows the collection of all emitted photons independent of the spatial characteristics of the emission. However, such measurements are plagued by multiple reflection effects occurring within the integrating sphere that make the sample illumination and sphere throughput sample dependent. To address this problem, we developed a matrix theory for integrating spheres with photoluminescent surfaces. In conjunction with a bispectral luminescence data set, this model allows for multiple reflection effects to be fully accounted for. The bispectral data is obtained by mounting both the sample and a non-luminescent reference on the sphere and permuting their positions in order to compare direct and diffuse sample illumination conditions. Experimental measurements of a photoluminescent standard confirm the validity of the method.

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References

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|
Author
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Publication

J. C. Zwinkels, “Metrology of photoluminescent materials,” Metrologia 47, S182 (2010).
[Crossref]
H. Zhu, C. C. Lin, W. Luo, S. Shu, Z. Liu, Y. Liu, J. Kong, E. Ma, Y. Cao, R.-S. Liu, and X. Chen, “Highly efficient non-rare-earth red emitting phosphor for warm white light-emitting diodes,” Nature Communications 5, 4312 (2014).
[Crossref] [PubMed]
T. Shakespeare and J. Shakespeare, “Problems in colour measurement of fluorescent paper grades,” Analytica Chimica Acta 380, 227–242 (1999).
[Crossref]
J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]
T.-S. Ahn, R. O. Al-Kaysi, A. M. Müller, K. M. Wentz, and C. J. Bardeen, “Self-absorption correction for solid-state photoluminescence quantum yields obtained from integrating sphere measurements,” Review of Scientific Instruments 78, 086105 (2007).
[Crossref] [PubMed]
D. H. Alman and F. W. Billmeyer Jr, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Research & Application 1, 141–145 (1976).
D. Gundlach and H. Terstiege, “Problems in measurement of fluorescent materials,” Color Research & Application 19, 427–436 (1994).
[Crossref]
N. Greenham, I. Samuel, G. Hayes, R. Phillips, Y. Kessener, S. Moratti, A. Holmes, and R. Friend, “Measurement of absolute photoluminescence quantum efficiencies in conjugated polymers,” Chemical Physics Letters 241, 89–96 (1995).
[Crossref]
K. Suzuki, A. Kobayashi, S. Kaneko, K. Takehira, T. Yoshihara, H. Ishida, Y. Shiina, S. Oishi, and S. Tobita, “Reevaluation of absolute luminescence quantum yields of standard solutions using a spectrometer with an integrating sphere and a back-thinned ccd detector,” Physical Chemistry Chemical Physics 11, 9850–9860 (2009).
[Crossref] [PubMed]
L. Wilson and B. Richards, “Measurement method for photoluminescent quantum yields of fluorescent organic dyes in polymethyl methacrylate for luminescent solar concentrators,” Applied Optics 48, 212–220 (2009).
[Crossref] [PubMed]
C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Comparison of methods and achievable uncertainties for the relative and absolute measurement of photoluminescence quantum yields,” Analytical Chemistry 83, 3431–3439 (2011).
[Crossref] [PubMed]
C. Würth, J. Pauli, C. Lochmann, M. Spieles, and U. Resch-Genger, “Integrating sphere setup for the traceable measurement of absolute photoluminescence quantum yields in the near infrared,” Analytical Chemistry 84, 1345–1352 (2012).
[Crossref] [PubMed]
C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nature Protocols 8, 1535 (2013).
[Crossref] [PubMed]
J. Valenta, “Determination of absolute quantum yields of luminescing nanomaterials over a broad spectral range: from the integrating sphere theory to the correct methodology,” Nanoscience Methods 3, 11–27 (2014).
[Crossref]
C.-H. Hung and C.-H. Tien, “Phosphor-converted LED modeling by bidirectional photometric data,” Optics Express 18, A261–A271 (2010).
[Crossref] [PubMed]
D. Timmerman, J. Valenta, K. Dohnalová, W. De Boer, and T. Gregorkiewicz, “Step-like enhancement of luminescence quantum yield of silicon nanocrystals,” Nature Nanotechnology 6, 710 (2011).
[Crossref] [PubMed]
R. Donaldson, “Spectrophotometry of fluorescent pigments,” British Journal of Applied Physics 5, 210 (1954).
[Crossref]
T. A. Germer, J. C. Zwinkels, and B. K. Tsai, Spectrophotometry: Accurate measurement of optical properties of materials, vol. 46 (Elsevier, 2014).
J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the National Research Council of Canada for high-accuracy fluorescence measurements,” Analytica Chimica Acta 380, 193–209 (1999).
[Crossref]
H. Minato, M. Nanjo, and Y. Nayatani, “Colorimetry and its accuracy in the measurement of fluorescent materials by the two-monochromator method,” Color Research & Application 10, 84–91 (1985).
[Crossref]
W. Budde and C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Die Farbe 19, 94–102 (1970).
R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Applied Optics 15, 827–828 (1976).
[Crossref] [PubMed]
P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]
P.-S. Shaw and Z. Li, “On the fluorescence from integrating spheres,” Applied Optics 47, 3962–3967 (2008).
[Crossref] [PubMed]
J. Valenta, “Photoluminescence of the integrating sphere walls, its influence on the absolute quantum yield measurements and correction methods,” AIP Advances 8, 105123 (2018).
[Crossref]
Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, “Simple spectral stray light correction method for array spectroradiometers,” Applied Optics 45, 1111–1119 (2006).
[Crossref] [PubMed]
J. Zwinkels, W. Neil, and M. Noël, “Characterization of a versatile reference instrument for traceable fluorescence measurements using different illumination and viewing geometries specified in practical colorimetry - part 1: bidirectional geometry (45: 0),” Metrologia 53, 1215 (2016).
[Crossref]
J. Zwinkels, W. Neil, M. Noël, and E. Côté, “Characterization of a versatile reference instrument for traceable fluorescence measurements using different illumination and viewing geometries specified in practical colorimetry - part 2: sphere geometry (8: d),” Metrologia 54, 129 (2017).
[Crossref]
P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]
P. C. DeRose, E. A. Early, and G. W. Kramer, “Qualification of a fluorescence spectrometer for measuring true fluorescence spectra,” Review of Scientific Instruments 78, 033107 (2007).
[Crossref] [PubMed]
T. L. Chow, Mathematical Methods for Physicists: A concise introduction(Cambridge University, 2000).
[Crossref]

2018 (1)

J. Valenta, “Photoluminescence of the integrating sphere walls, its influence on the absolute quantum yield measurements and correction methods,” AIP Advances 8, 105123 (2018).
[Crossref]

2017 (1)

J. Zwinkels, W. Neil, M. Noël, and E. Côté, “Characterization of a versatile reference instrument for traceable fluorescence measurements using different illumination and viewing geometries specified in practical colorimetry - part 2: sphere geometry (8: d),” Metrologia 54, 129 (2017).
[Crossref]

2016 (2)

P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]

J. Zwinkels, W. Neil, and M. Noël, “Characterization of a versatile reference instrument for traceable fluorescence measurements using different illumination and viewing geometries specified in practical colorimetry - part 1: bidirectional geometry (45: 0),” Metrologia 53, 1215 (2016).
[Crossref]

2014 (2)

H. Zhu, C. C. Lin, W. Luo, S. Shu, Z. Liu, Y. Liu, J. Kong, E. Ma, Y. Cao, R.-S. Liu, and X. Chen, “Highly efficient non-rare-earth red emitting phosphor for warm white light-emitting diodes,” Nature Communications 5, 4312 (2014).
[Crossref] [PubMed]

J. Valenta, “Determination of absolute quantum yields of luminescing nanomaterials over a broad spectral range: from the integrating sphere theory to the correct methodology,” Nanoscience Methods 3, 11–27 (2014).
[Crossref]

2013 (1)

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Relative and absolute determination of fluorescence quantum yields of transparent samples,” Nature Protocols 8, 1535 (2013).
[Crossref] [PubMed]

2012 (1)

C. Würth, J. Pauli, C. Lochmann, M. Spieles, and U. Resch-Genger, “Integrating sphere setup for the traceable measurement of absolute photoluminescence quantum yields in the near infrared,” Analytical Chemistry 84, 1345–1352 (2012).
[Crossref] [PubMed]

2011 (2)

C. Würth, M. Grabolle, J. Pauli, M. Spieles, and U. Resch-Genger, “Comparison of methods and achievable uncertainties for the relative and absolute measurement of photoluminescence quantum yields,” Analytical Chemistry 83, 3431–3439 (2011).
[Crossref] [PubMed]

D. Timmerman, J. Valenta, K. Dohnalová, W. De Boer, and T. Gregorkiewicz, “Step-like enhancement of luminescence quantum yield of silicon nanocrystals,” Nature Nanotechnology 6, 710 (2011).
[Crossref] [PubMed]

2010 (2)

C.-H. Hung and C.-H. Tien, “Phosphor-converted LED modeling by bidirectional photometric data,” Optics Express 18, A261–A271 (2010).
[Crossref] [PubMed]

J. C. Zwinkels, “Metrology of photoluminescent materials,” Metrologia 47, S182 (2010).
[Crossref]

2009 (2)

K. Suzuki, A. Kobayashi, S. Kaneko, K. Takehira, T. Yoshihara, H. Ishida, Y. Shiina, S. Oishi, and S. Tobita, “Reevaluation of absolute luminescence quantum yields of standard solutions using a spectrometer with an integrating sphere and a back-thinned ccd detector,” Physical Chemistry Chemical Physics 11, 9850–9860 (2009).
[Crossref] [PubMed]

L. Wilson and B. Richards, “Measurement method for photoluminescent quantum yields of fluorescent organic dyes in polymethyl methacrylate for luminescent solar concentrators,” Applied Optics 48, 212–220 (2009).
[Crossref] [PubMed]

2008 (1)

P.-S. Shaw and Z. Li, “On the fluorescence from integrating spheres,” Applied Optics 47, 3962–3967 (2008).
[Crossref] [PubMed]

2007 (3)

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

P. C. DeRose, E. A. Early, and G. W. Kramer, “Qualification of a fluorescence spectrometer for measuring true fluorescence spectra,” Review of Scientific Instruments 78, 033107 (2007).
[Crossref] [PubMed]

T.-S. Ahn, R. O. Al-Kaysi, A. M. Müller, K. M. Wentz, and C. J. Bardeen, “Self-absorption correction for solid-state photoluminescence quantum yields obtained from integrating sphere measurements,” Review of Scientific Instruments 78, 086105 (2007).
[Crossref] [PubMed]

2006 (1)

Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, “Simple spectral stray light correction method for array spectroradiometers,” Applied Optics 45, 1111–1119 (2006).
[Crossref] [PubMed]

1999 (2)

J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the National Research Council of Canada for high-accuracy fluorescence measurements,” Analytica Chimica Acta 380, 193–209 (1999).
[Crossref]

T. Shakespeare and J. Shakespeare, “Problems in colour measurement of fluorescent paper grades,” Analytica Chimica Acta 380, 227–242 (1999).
[Crossref]

1997 (1)

J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]

1995 (1)

N. Greenham, I. Samuel, G. Hayes, R. Phillips, Y. Kessener, S. Moratti, A. Holmes, and R. Friend, “Measurement of absolute photoluminescence quantum efficiencies in conjugated polymers,” Chemical Physics Letters 241, 89–96 (1995).
[Crossref]

1994 (1)

D. Gundlach and H. Terstiege, “Problems in measurement of fluorescent materials,” Color Research & Application 19, 427–436 (1994).
[Crossref]

1985 (1)

H. Minato, M. Nanjo, and Y. Nayatani, “Colorimetry and its accuracy in the measurement of fluorescent materials by the two-monochromator method,” Color Research & Application 10, 84–91 (1985).
[Crossref]

1976 (2)

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Applied Optics 15, 827–828 (1976).
[Crossref] [PubMed]

D. H. Alman and F. W. Billmeyer Jr, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Research & Application 1, 141–145 (1976).

1970 (1)

W. Budde and C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Die Farbe 19, 94–102 (1970).

1954 (1)

R. Donaldson, “Spectrophotometry of fluorescent pigments,” British Journal of Applied Physics 5, 210 (1954).
[Crossref]

Ahn, T.-S.

Al-Kaysi, R. O.

Alman, D. H.

D. H. Alman and F. W. Billmeyer Jr, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Research & Application 1, 141–145 (1976).

Arp, U.

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

Bardeen, C. J.

Billmeyer Jr, F. W.

D. H. Alman and F. W. Billmeyer Jr, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Research & Application 1, 141–145 (1976).

Boer, W. De

Brown, S. W.

Budde, W.

W. Budde and C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Die Farbe 19, 94–102 (1970).

Cao, Y.

Chen, X.

Chow, T. L.

T. L. Chow, Mathematical Methods for Physicists: A concise introduction(Cambridge University, 2000).
[Crossref]

Côté, E.

de Mello, J. C.

J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]

DeRose, P. C.

Dodd, C. X.

W. Budde and C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Die Farbe 19, 94–102 (1970).

Dohnalová, K.

Donaldson, R.

R. Donaldson, “Spectrophotometry of fluorescent pigments,” British Journal of Applied Physics 5, 210 (1954).
[Crossref]

Early, E. A.

Friend, R.

Friend, R. H.

J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]

Gauthier, F.

Germer, T. A.

T. A. Germer, J. C. Zwinkels, and B. K. Tsai, Spectrophotometry: Accurate measurement of optical properties of materials, vol. 46 (Elsevier, 2014).

Grabolle, M.

Greenham, N.

Gregorkiewicz, T.

Gundlach, D.

D. Gundlach and H. Terstiege, “Problems in measurement of fluorescent materials,” Color Research & Application 19, 427–436 (1994).
[Crossref]

Hayes, G.

Holmes, A.

Hung, C.-H.

C.-H. Hung and C.-H. Tien, “Phosphor-converted LED modeling by bidirectional photometric data,” Optics Express 18, A261–A271 (2010).
[Crossref] [PubMed]

Ikonen, E.

P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]

Ishida, H.

Jaanson, P.

P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]

Johnson, B. C.

Kaneko, S.

Kessener, Y.

Kobayashi, A.

Kong, J.

Kramer, G. W.

Li, Z.

P.-S. Shaw and Z. Li, “On the fluorescence from integrating spheres,” Applied Optics 47, 3962–3967 (2008).
[Crossref] [PubMed]

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

Lin, C. C.

Liu, R.-S.

Liu, Y.

Liu, Z.

Lochmann, C.

Luo, W.

Lykke, K. R.

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

Ma, E.

Manoocheri, F.

P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]

Minato, H.

Moratti, S.

Müller, A. M.

Nanjo, M.

Nayatani, Y.

Neil, W.

Noël, M.

Ohno, Y.

Oishi, S.

Ott, W. R.

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Applied Optics 15, 827–828 (1976).
[Crossref] [PubMed]

Pauli, J.

Phillips, R.

Resch-Genger, U.

Richards, B.

Samuel, I.

Saunders, R. D.

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Applied Optics 15, 827–828 (1976).
[Crossref] [PubMed]

Shakespeare, J.

T. Shakespeare and J. Shakespeare, “Problems in colour measurement of fluorescent paper grades,” Analytica Chimica Acta 380, 227–242 (1999).
[Crossref]

Shakespeare, T.

T. Shakespeare and J. Shakespeare, “Problems in colour measurement of fluorescent paper grades,” Analytica Chimica Acta 380, 227–242 (1999).
[Crossref]

Shaw, P.-S.

P.-S. Shaw and Z. Li, “On the fluorescence from integrating spheres,” Applied Optics 47, 3962–3967 (2008).
[Crossref] [PubMed]

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

Shiina, Y.

Shu, S.

Spieles, M.

Suzuki, K.

Takehira, K.

Terstiege, H.

D. Gundlach and H. Terstiege, “Problems in measurement of fluorescent materials,” Color Research & Application 19, 427–436 (1994).
[Crossref]

Tien, C.-H.

C.-H. Hung and C.-H. Tien, “Phosphor-converted LED modeling by bidirectional photometric data,” Optics Express 18, A261–A271 (2010).
[Crossref] [PubMed]

Timmerman, D.

Tobita, S.

Tsai, B. K.

T. A. Germer, J. C. Zwinkels, and B. K. Tsai, Spectrophotometry: Accurate measurement of optical properties of materials, vol. 46 (Elsevier, 2014).

Valenta, J.

J. Valenta, “Photoluminescence of the integrating sphere walls, its influence on the absolute quantum yield measurements and correction methods,” AIP Advances 8, 105123 (2018).
[Crossref]

Wentz, K. M.

Wilson, L.

Wittmann, H. F.

J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]

Würth, C.

Yoshihara, T.

Zhu, H.

Zong, Y.

Zwinkels, J.

Zwinkels, J. C.

J. C. Zwinkels, “Metrology of photoluminescent materials,” Metrologia 47, S182 (2010).
[Crossref]

T. A. Germer, J. C. Zwinkels, and B. K. Tsai, Spectrophotometry: Accurate measurement of optical properties of materials, vol. 46 (Elsevier, 2014).

Advanced Materials (1)

J. C. de Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photoluminescence quantum efficiency,” Advanced Materials 9, 230–232 (1997).
[Crossref]

AIP Advances (1)

J. Valenta, “Photoluminescence of the integrating sphere walls, its influence on the absolute quantum yield measurements and correction methods,” AIP Advances 8, 105123 (2018).
[Crossref]

Analytica Chimica Acta (2)

T. Shakespeare and J. Shakespeare, “Problems in colour measurement of fluorescent paper grades,” Analytica Chimica Acta 380, 227–242 (1999).
[Crossref]

Analytical Chemistry (2)

Applied Optics (5)

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Applied Optics 15, 827–828 (1976).
[Crossref] [PubMed]

P.-S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Applied Optics 46, 5119–5128 (2007).
[Crossref] [PubMed]

P.-S. Shaw and Z. Li, “On the fluorescence from integrating spheres,” Applied Optics 47, 3962–3967 (2008).
[Crossref] [PubMed]

British Journal of Applied Physics (1)

R. Donaldson, “Spectrophotometry of fluorescent pigments,” British Journal of Applied Physics 5, 210 (1954).
[Crossref]

Chemical Physics Letters (1)

Color Research & Application (3)

D. H. Alman and F. W. Billmeyer Jr, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Research & Application 1, 141–145 (1976).

D. Gundlach and H. Terstiege, “Problems in measurement of fluorescent materials,” Color Research & Application 19, 427–436 (1994).
[Crossref]

Die Farbe (1)

W. Budde and C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Die Farbe 19, 94–102 (1970).

Measurement Science and Technology (1)

P. Jaanson, F. Manoocheri, and E. Ikonen, “Goniometrical measurements of fluorescence quantum efficiency,” Measurement Science and Technology 27, 025204 (2016).
[Crossref]

Metrologia (3)

J. C. Zwinkels, “Metrology of photoluminescent materials,” Metrologia 47, S182 (2010).
[Crossref]

Nanoscience Methods (1)

Nature Communications (1)

Nature Nanotechnology (1)

Nature Protocols (1)

Optics Express (1)

C.-H. Hung and C.-H. Tien, “Phosphor-converted LED modeling by bidirectional photometric data,” Optics Express 18, A261–A271 (2010).
[Crossref] [PubMed]

Physical Chemistry Chemical Physics (1)

Review of Scientific Instruments (2)

Other (2)

T. L. Chow, Mathematical Methods for Physicists: A concise introduction(Cambridge University, 2000).
[Crossref]

T. A. Germer, J. C. Zwinkels, and B. K. Tsai, Spectrophotometry: Accurate measurement of optical properties of materials, vol. 46 (Elsevier, 2014).

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Fig. 1 Multiple reflection effects occurring in an integrating sphere with photoluminescent sample.

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Fig. 2 Two-monochromator configuration with integrating sphere for measuring the D_s matrix of a photoluminescent sample.

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Fig. 3 (a)-(c) Matrices V_s, V_r, and D_s measured with the 20 cm sphere. (d)-(f) Matrices V_s, V_r, and D_s measured with the 30 cm sphere. V_s and V_r have been normalized to their maximum values. (g) Normalized slit scattering function NSSF(λ) measured at 410 nm. (h) Diagonal elements

ϕ_{o} (μ)

of the spectral excitation matrix Φ_o. (i)Sample spectral reflectance

ρ_{s} (μ)

, corresponding to diagonal elements of matrix D_s measured in the 20 cm sphere.

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Fig. 4 (a) Emission profile

D_{s} (λ)

under μ = 350 nm excitation for the 20 and 30 cm data sets. (b) Spectral quantum yield QY(μ) for the 20 and 30 cm data sets. (c) Difference between the spectral QY derived from the 20 and 30 cm data sets compared with the experimental reproducibility. Inset to (b): Sample absorption

1 - ρ_{s} (μ)

measured in the 30 cm sphere.

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Fig. 5 (a) Emission profiles

D_{s} (λ)

under μ = 350 nm excitation and (b) spectral quantum yields QY(μ) from the full matrix method for the 20 cm sphere compared with the results of the partial matrix method for the 20 and 30 cm spheres.

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Tables (1)

Table 1 Dimensions of the two integrating spheres.

View Table

Equations (21)

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

ϕ_{r} (λ) = ρ (λ) ϕ_{e} (λ) + \int_{0}^{\infty} β (λ, μ) ϕ_{e} (μ) d μ .

ϕ_{r} (λ_{i}) = ρ (λ_{i}) ϕ_{e} (λ_{i}) + Δ μ \sum_{j = 0}^{m} β (λ_{i}, μ_{j}) ϕ_{e} (μ_{j}) .

ϕ_{r} = ρ ϕ_{e} + Δ μ β ϕ_{e} = D ϕ_{e},

\begin{array}{l} ϕ_{t} = ϕ_{1} + ϕ_{2} + ϕ_{3} + \dots \\ = D_{f} ϕ_{o} + \bar{D} D_{f} ϕ_{o} + {\bar{D}}^{2} D_{f} ϕ_{o} + \dots \\ = [I + \bar{D} + {\bar{D}}^{2} + \dots] D_{f} ϕ_{o} \\ = M D_{f} ϕ_{o} . \end{array}

Δ μ = \frac{\int_{- \infty}^{\infty} x e (τ) d τ}{x e (0)},

v_{j} = K M D_{f} ϕ_{o, j},

V_{s} = K M D_{s} Φ_{o},

V_{r} = K M D_{r} Φ_{o} .

D_{s} = D_{r} Φ_{o} V_{r}^{- 1} V_{s} Φ_{o}^{- 1} .

Q Y (μ) = \frac{\int_{350}^{700} λ β_{s} (λ, μ) d λ / μ}{1 - ρ_{s} (μ)},

X_{j} (μ) = ϕ_{o} (μ_{j}) x (μ - μ_{j}),

E_{i} (λ) = A (λ_{i}) e (λ - λ_{i}),

ϕ_{j}^{1} (λ) = \int_{0}^{\infty} [ρ_{f} (μ) δ (μ - λ) + β_{f} (λ, μ)] X_{j} (μ) d μ,

\begin{array}{l} v_{i j}^{1} = \int_{0}^{\infty} E_{i} (λ) ϕ_{j}^{1} (λ) d λ \\ = \int_{0}^{\infty} E_{i} (λ) \int_{0}^{\infty} X_{j} (μ) [ρ_{f} (μ) δ (μ - λ) + β_{f} (λ, μ)] d μ d λ \\ \approx A (λ_{i}) ϕ_{o} (μ_{j}) ρ_{f} (μ_{j}) δ_{i j} \int_{0}^{\infty} e (λ - λ_{i}) x (λ - λ_{i}) d λ \\ + A (λ_{i}) ϕ_{o} (μ_{j}) β_{f} (λ_{i}, μ_{j}) \int_{0}^{\infty} e (λ - λ_{i}) d λ \int_{0}^{\infty} x (μ - μ_{j}) d μ \\ \approx K_{i} [ρ_{f} (μ_{j}) δ_{i j} + Δ μ β_{f} (λ_{i}, μ_{j})] ϕ_{o} (μ_{j}) \\ \approx K_{i} D_{f, i j} ϕ_{o} (μ_{j}) . \end{array}

K_{i} = A (λ_{i}) \int_{0}^{\infty} d λ e (λ - λ_{i}) x (λ - λ_{i}),

Δ μ = \frac{\int_{0}^{\infty} x (μ - μ_{j}) d μ \int_{0}^{\infty} e (λ - λ_{j}) d λ}{\int_{0}^{\infty} x (λ - λ_{j}) e (λ - λ_{j}) d λ} = \frac{\int_{- \infty}^{\infty} x e (τ) d τ}{x e (0)},

v_{j}^{1} = K D_{f} ϕ_{o, j} .

ϕ_{j}^{2} (λ) = \int_{0}^{\infty} [\bar{ρ} (γ) δ (γ - λ) + \bar{β} (λ, γ)] ϕ_{j}^{1} (γ) d γ

\begin{array}{l} v_{i j}^{2} = \int_{0}^{\infty} E_{i} (λ) ϕ_{j}^{2} (λ) d λ \\ = A (λ_{i}) \int_{0}^{\infty} e (λ - λ_{i}) \bar{ρ} (λ) ϕ_{1}^{j} (λ) d λ + A (λ_{i}) \int_{0}^{\infty} e (λ - λ_{i}) \bar{β} (λ, γ) ϕ_{1}^{j} (γ) d γ d λ \\ \approx K_{i} \bar{ρ} (λ_{i}) D_{f, i j} ϕ_{o} (μ_{j}) + A (λ_{i}) ϕ_{o} (μ_{j}) \int_{0}^{\infty} \int_{0}^{\infty} e (λ - λ_{i}) \bar{β} (λ, γ) ρ_{f} (γ) x (γ - μ_{j}) d γ d λ \\ + A (λ_{i}) ϕ_{o} (μ_{j}) \int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty} e (λ - λ_{i}) \bar{β} (λ, γ) β_{f} (γ, μ) x (μ - μ_{j}) d γ d λ d μ \\ \approx K_{i} \bar{ρ} (λ_{i}) D_{f, i j} ϕ_{o} (μ_{j}) + A (λ_{i}) ϕ_{o} (μ_{j}) ρ_{f} (μ_{j}) \bar{β} (λ_{i}, μ_{j}) \int_{0}^{\infty} e (λ - λ_{i}) d λ \int_{0}^{\infty} x (γ - μ_{j}) d γ \\ + A (λ_{i}) ϕ_{o} (μ_{j}) \int_{0}^{\infty} \bar{β} (λ_{i}, γ) β_{f} (γ, μ_{j}) d γ \int_{0}^{\infty} e (λ - λ_{i}) d λ \int_{0}^{\infty} x (μ - μ_{j}) d μ \\ \approx K_{i} \bar{ρ} (λ_{i}) D_{f, i j} ϕ_{o} (μ_{j}) + K_{i} Δ μ ρ_{f} (μ_{j}) \bar{β} (λ_{i}, μ_{j}) ϕ_{o} (μ_{j}) \\ + K_{i} Δ μ ϕ_{o} (μ_{j}) \int_{0}^{\infty} \bar{β} (λ_{i}, γ) β_{f} (γ, μ_{j}) d γ \\ \approx K_{i} \bar{ρ} (λ_{i}) D_{f, i j} ϕ_{o} (μ_{j}) + K_{i} Δ μ ρ_{f} (μ_{j}) \bar{β} (λ_{i}, μ_{j}) ϕ_{o} (μ_{j}) \\ + K_{i} {(Δ μ)}^{2} ϕ_{o} (μ_{j}) \sum_{l = 0}^{m} \bar{β} (λ_{i}, γ_{l}) β_{f} (γ_{l}, μ_{j}) . \end{array}

\begin{array}{l} v_{j}^{2} \approx K \bar{ρ} D_{f} ϕ_{o, j} + Δ μ K \bar{β} ρ_{f} ϕ_{o, j} + {(Δ μ)}^{2} K \bar{β} β_{f} ϕ_{o, j} \\ \approx K [\bar{ρ} + Δ μ \bar{β}] D_{f} ϕ_{o, j} \\ \approx K \bar{D} D_{f} ϕ_{o, j} \end{array}

v_{j} = K [I + \bar{D} + {\bar{D}}^{2} + \dots] D_{f} ϕ_{o, j} = K M D_{f} ϕ_{o, j} .

Sphere diameter (cm)	Port diameter (cm)	Fractional port area $a_{p o r t}$
20.3	3.8	$8.8 \times 10^{- 3}$
30.0	3.8	$4.0 \times 10^{- 3}$