Abstract

A modified spatial filtering method that improves the sensitivity of single-beam and mode-mismatched thermal lens spectroscopy (TLS) for fluorescence quantum yield measurement is presented. The method is based on the detection of the external part of a laser beam transmitted by the fluorescent sample (eclipsing detection mode). The experimental results show that the signal/noise (S/N) ratio of the absolute quantum yield of Rh6G can be enhanced up to ~1400% using the eclipsing detection mode on the TLS experimental setup. The method was evaluated by measuring the fluorescence quantum yield of varying concentration of ethanolic solutions of Rhodamine 6G.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  39. C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
    [CrossRef]
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    [CrossRef]

2012 (1)

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

2011 (3)

A. M. Brouwer, “Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report),” Pure Appl. Chem.83(12), 2213–2228 (2011).
[CrossRef]

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

2010 (1)

R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys.107(8), 083504 (2010).
[CrossRef]

2009 (1)

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

2008 (1)

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

2007 (1)

2005 (1)

L. S. Rohwer and J. E. Martin, “Measuring the absolute quantum efficiency of luminescent materials,” J. Lumin.115(3–4), 77–90 (2005).
[CrossRef]

2002 (1)

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

2001 (2)

B. Li and R. Gupta, “Optical saturation in continuous-wave photothermal deflection spectroscopy: quantitative investigation of fundamental and harmonic components,” Appl. Opt.40(9), 1563–1569 (2001).
[CrossRef] [PubMed]

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

1999 (1)

C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
[CrossRef]

1997 (1)

Y. M. Biosca and G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in non-polar solvents,” Anal. Chim. Acta345(1–3), 257–263 (1997).
[CrossRef]

1996 (1)

M. Fischer and J. Georges, “Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectroscopy,” Chem. Phys. Lett.260(1–2), 115–118 (1996).
[CrossRef]

1995 (1)

D. R. Snook and R. D. Lowe, “Thermal lens spectroscopy. A review,” Analyst (Lond.)120(8), 2051–2068 (1995).
[CrossRef]

1994 (1)

1993 (1)

A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron.29(6), 1498–1504 (1993).
[CrossRef]

1992 (2)

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys.165(2–3), 385–396 (1992).
[CrossRef]

M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett.197(3), 255–258 (1992).
[CrossRef]

1991 (1)

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

1989 (1)

J. Slaby, “Background illumination filtering in thermal lens spectroscopy,” Anal. Chem.61(22), 2496–2499 (1989).
[CrossRef]

1988 (2)

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

F. López Arbeloa, P. Ruiz Ojeda, and I. López Arbeloa, “The fluorescence quenching mechanisms of rhodamine 6G in concentrated ethanolic solution,” J. Photochem. Photobiol., A45(3), 313–323 (1988).
[CrossRef]

1987 (1)

J. Słaby, “Application of spatial filtering in thermal lensing detection,” Opt. Commun.64(2), 89–93 (1987).
[CrossRef]

1982 (3)

C. E. Buffett and M. D. Morris, “Thermal lens detection for liquid chromatography,” Anal. Chem.54(11), 1824–1825 (1982).
[CrossRef]

R. F. Kubin and A. N. Fletcher, “Fluorescence quantum yields of some rhodamine dyes,” J. Lumin.27(4), 455–462 (1982).
[CrossRef]

S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt.21(9), 1663–1669 (1982).
[CrossRef] [PubMed]

1981 (1)

R. A. Leach and J. M. Harris, “Thermal lens calorimetry,” J. Chromatogr. A218, 15–19 (1981).
[CrossRef]

1980 (1)

T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta115(1), 407–410 (1980).
[CrossRef]

1979 (2)

N. J. Dovichi and J. M. Harris, “Laser induced thermal lens effect for calorimetric trace analysis,” Anal. Chem.51(6), 728–731 (1979).
[CrossRef]

R. R. Hammond, “Selfabsorption of molecular fluorescence, the design of equipment for measurement of fluorescence decay, and the decay times of some laser dyes,” J. Chem. Phys.70(8), 3884–3894 (1979).
[CrossRef]

1978 (2)

G. C. Nieman and S. D. Colson, “Pressure effects on the two-photon spectrum of trans-butadiene as detected by gas phase transient lensing spectroscopy,” J. Chem. Phys.68(6), 2994–2996 (1978).
[CrossRef]

J. H. Brannon and D. J. Magde, “Absolute quantum yield determination by thermal blooming. Fluorescein,” J. Phys. Chem.82(6), 705–709 (1978).
[CrossRef]

1974 (1)

J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res.7(7), 225–231 (1974).
[CrossRef]

1973 (1)

1971 (1)

G. A. Crosby and J. N. Demas, “The measurement of fluorescence quantum yields. Review,” J. Phys. Chem.75(8), 991–1024 (1971).
[CrossRef]

1968 (1)

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys.48(10), 4726–4742 (1968).
[CrossRef]

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

1964 (1)

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett.5(7), 141–143 (1964).
[CrossRef]

Alcantara, P.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

Andrade, A. A.

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

Aramendí, P. F.

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

Baesso, M. L.

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett.197(3), 255–258 (1992).
[CrossRef]

Bindhu, C. V.

C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
[CrossRef]

Biosca, Y. M.

Y. M. Biosca and G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in non-polar solvents,” Anal. Chim. Acta345(1–3), 257–263 (1997).
[CrossRef]

Bloisi, F.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

Brannon, J. H.

J. H. Brannon and D. J. Magde, “Absolute quantum yield determination by thermal blooming. Fluorescein,” J. Phys. Chem.82(6), 705–709 (1978).
[CrossRef]

Braslavsky, S. E.

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

Brouwer, A. M.

A. M. Brouwer, “Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report),” Pure Appl. Chem.83(12), 2213–2228 (2011).
[CrossRef]

Buffett, C. E.

C. E. Buffett and M. D. Morris, “Thermal lens detection for liquid chromatography,” Anal. Chem.54(11), 1824–1825 (1982).
[CrossRef]

Catunda, T.

R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys.107(8), 083504 (2010).
[CrossRef]

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

Cavaliere, P.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

Colson, S. D.

G. C. Nieman and S. D. Colson, “Pressure effects on the two-photon spectrum of trans-butadiene as detected by gas phase transient lensing spectroscopy,” J. Chem. Phys.68(6), 2994–2996 (1978).
[CrossRef]

Crosby, G. A.

G. A. Crosby and J. N. Demas, “The measurement of fluorescence quantum yields. Review,” J. Phys. Chem.75(8), 991–1024 (1971).
[CrossRef]

Cruz, R. A.

R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys.107(8), 083504 (2010).
[CrossRef]

de Araujo, R. E.

de Araújo, C. B.

de Araújo, M. A. C.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

de Lima, E.

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

de Oliveira, P. C.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

Demas, J. N.

G. A. Crosby and J. N. Demas, “The measurement of fluorescence quantum yields. Review,” J. Phys. Chem.75(8), 991–1024 (1971).
[CrossRef]

Dovichi, N. J.

N. J. Dovichi and J. M. Harris, “Laser induced thermal lens effect for calorimetric trace analysis,” Anal. Chem.51(6), 728–731 (1979).
[CrossRef]

Filho, E. L.

Fischer, M.

M. Fischer and J. Georges, “Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectroscopy,” Chem. Phys. Lett.260(1–2), 115–118 (1996).
[CrossRef]

Fletcher, A. N.

R. F. Kubin and A. N. Fletcher, “Fluorescence quantum yields of some rhodamine dyes,” J. Lumin.27(4), 455–462 (1982).
[CrossRef]

Genger, U. R.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

George, N. A.

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

Georges, J.

M. Fischer and J. Georges, “Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectroscopy,” Chem. Phys. Lett.260(1–2), 115–118 (1996).
[CrossRef]

Gomes, A. S. L.

González, M. G.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

Grabolle, M.

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Gupta, R.

Hagan, D. J.

Haisch, C.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

Hammond, E. C.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys.48(10), 4726–4742 (1968).
[CrossRef]

Hammond, R. R.

R. R. Hammond, “Selfabsorption of molecular fluorescence, the design of equipment for measurement of fluorescence decay, and the decay times of some laser dyes,” J. Chem. Phys.70(8), 3884–3894 (1979).
[CrossRef]

Harilal, S. S.

C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
[CrossRef]

Harris, J. M.

R. A. Leach and J. M. Harris, “Thermal lens calorimetry,” J. Chromatogr. A218, 15–19 (1981).
[CrossRef]

N. J. Dovichi and J. M. Harris, “Laser induced thermal lens effect for calorimetric trace analysis,” Anal. Chem.51(6), 728–731 (1979).
[CrossRef]

Hernandes, A. C.

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

Hu, C.

Imasaka, T.

T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta115(1), 407–410 (1980).
[CrossRef]

Ishibashi, N.

T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta115(1), 407–410 (1980).
[CrossRef]

Ishida, H.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Jali, P.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

Kaneko, S.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Knight, L. V.

Kobayashi, A.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Kubin, R. F.

R. F. Kubin and A. N. Fletcher, “Fluorescence quantum yields of some rhodamine dyes,” J. Lumin.27(4), 455–462 (1982).
[CrossRef]

Kurian, A.

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

Lankard, J. R.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys.48(10), 4726–4742 (1968).
[CrossRef]

Leach, R. A.

R. A. Leach and J. M. Harris, “Thermal lens calorimetry,” J. Chromatogr. A218, 15–19 (1981).
[CrossRef]

Lebullenger, R.

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett.5(7), 141–143 (1964).
[CrossRef]

Li, B.

Lima, S. M.

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

López Arbeloa, F.

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

F. López Arbeloa, P. Ruiz Ojeda, and I. López Arbeloa, “The fluorescence quenching mechanisms of rhodamine 6G in concentrated ethanolic solution,” J. Photochem. Photobiol., A45(3), 313–323 (1988).
[CrossRef]

López Arbeloa, I.

F. López Arbeloa, P. Ruiz Ojeda, and I. López Arbeloa, “The fluorescence quenching mechanisms of rhodamine 6G in concentrated ethanolic solution,” J. Photochem. Photobiol., A45(3), 313–323 (1988).
[CrossRef]

Lowe, R. D.

D. R. Snook and R. D. Lowe, “Thermal lens spectroscopy. A review,” Analyst (Lond.)120(8), 2051–2068 (1995).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys.165(2–3), 385–396 (1992).
[CrossRef]

Magde, D. J.

J. H. Brannon and D. J. Magde, “Absolute quantum yield determination by thermal blooming. Fluorescein,” J. Phys. Chem.82(6), 705–709 (1978).
[CrossRef]

Mandelis, A.

A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron.29(6), 1498–1504 (1993).
[CrossRef]

Martellucci, S.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

Martin, J. E.

L. S. Rohwer and J. E. Martin, “Measuring the absolute quantum efficiency of luminescent materials,” J. Lumin.115(3–4), 77–90 (2005).
[CrossRef]

Miyaishi, K.

T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta115(1), 407–410 (1980).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett.5(7), 141–143 (1964).
[CrossRef]

Moreira, S. G. C.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

Morris, M. D.

C. E. Buffett and M. D. Morris, “Thermal lens detection for liquid chromatography,” Anal. Chem.54(11), 1824–1825 (1982).
[CrossRef]

Moruzzi, V. L.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys.48(10), 4726–4742 (1968).
[CrossRef]

Munidasa, M.

A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron.29(6), 1498–1504 (1993).
[CrossRef]

Nampoori, V. P. N.

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
[CrossRef]

Negri, R. M.

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

Nieman, G. C.

G. C. Nieman and S. D. Colson, “Pressure effects on the two-photon spectrum of trans-butadiene as detected by gas phase transient lensing spectroscopy,” J. Chem. Phys.68(6), 2994–2996 (1978).
[CrossRef]

Niessner, R.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

Oishi, S.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Othonos, A.

A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron.29(6), 1498–1504 (1993).
[CrossRef]

Panne, U.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[CrossRef] [PubMed]

Paul, B.

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

Pauli, J.

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Pilla, V.

R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys.107(8), 083504 (2010).
[CrossRef]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

Quartieri, J.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

Ramis-Ramos, G.

Y. M. Biosca and G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in non-polar solvents,” Anal. Chim. Acta345(1–3), 257–263 (1997).
[CrossRef]

Rativa, D.

Resch-Genger, U.

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Rohwer, L. S.

L. S. Rohwer and J. E. Martin, “Measuring the absolute quantum efficiency of luminescent materials,” J. Lumin.115(3–4), 77–90 (2005).
[CrossRef]

Ruiz Ojeda, P.

F. López Arbeloa, P. Ruiz Ojeda, and I. López Arbeloa, “The fluorescence quenching mechanisms of rhodamine 6G in concentrated ethanolic solution,” J. Photochem. Photobiol., A45(3), 313–323 (1988).
[CrossRef]

San Román, E. A.

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

Sheik-Bahae, M.

Sheldon, S. J.

Shen, J.

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys.165(2–3), 385–396 (1992).
[CrossRef]

M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett.197(3), 255–258 (1992).
[CrossRef]

Shiina, Y.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Silva, R.

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

Slaby, J.

J. Slaby, “Background illumination filtering in thermal lens spectroscopy,” Anal. Chem.61(22), 2496–2499 (1989).
[CrossRef]

J. Słaby, “Application of spatial filtering in thermal lensing detection,” Opt. Commun.64(2), 89–93 (1987).
[CrossRef]

Snook, D. R.

D. R. Snook and R. D. Lowe, “Thermal lens spectroscopy. A review,” Analyst (Lond.)120(8), 2051–2068 (1995).
[CrossRef]

Snook, R. D.

M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett.197(3), 255–258 (1992).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys.165(2–3), 385–396 (1992).
[CrossRef]

Sorokin, P. P.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, and E. C. Hammond, “Flashlamp‐pumped organic‐dye lasers,” J. Chem. Phys.48(10), 4726–4742 (1968).
[CrossRef]

Spieles, M.

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Suzuki, K.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Takehira, K.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Thorne, J. M.

Tobita, S.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Tolentino Dominguez, C.

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

Vallabhan, C. P. G.

A. Kurian, N. A. George, B. Paul, V. P. N. Nampoori, and C. P. G. Vallabhan, “Studies on fluorescence efficiency and photodegradation of Rhodamine 6G doped PMMA using a dual beam thermal lens technique,” Laser Chem.20(2–4), 99–110 (2002).
[CrossRef]

C. V. Bindhu, S. S. Harilal, V. P. N. Nampoori, and C. P. G. Vallabhan, “Solvent effect on absolute fluorescence quantum yield of rhodamine 6G determine using transient thermal lens technique,” Mod. Phys. Lett. B13(16), 563–576 (1999).
[CrossRef]

Van Stryland, E. W.

Vicari, L.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martellucci, and J. Quartieri, “Spatial filtering in the detection of transverse phase modulation through a nonlinear thin film,” Opt. Commun.68(6), 391–395 (1988).
[CrossRef]

Whinnery, J. R.

J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res.7(7), 225–231 (1974).
[CrossRef]

C. Hu and J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt.12(1), 72–79 (1973).
[CrossRef] [PubMed]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett.5(7), 141–143 (1964).
[CrossRef]

Würth, C.

C. Würth, M. G. González, R. Niessner, U. Panne, C. Haisch, and U. R. Genger, “Determination of the absolute fluorescence quantum yield of rhodamine 6G with optical and photoacoustic methods--providing the basis for fluorescence quantum yield standards,” Talanta90, 30–37 (2012).
[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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Xia, T.

Yoshihara, T.

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,” Phys. Chem. Chem. Phys.11(42), 9850–9860 (2009).
[CrossRef] [PubMed]

Zalts, A.

R. M. Negri, A. Zalts, E. A. San Román, P. F. Aramendí, and S. E. Braslavsky, “Carboxylated Zinc-Phthalocyanine, influence of dimerization on the spectroscopy properties. An absorption, emission, and thermal lensing study,” Photochem. Photobiol.53(3), 317–322 (1991).
[CrossRef]

Acc. Chem. Res. (1)

J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res.7(7), 225–231 (1974).
[CrossRef]

AIP Adv. (1)

R. Silva, M. A. C. de Araújo, P. Jali, S. G. C. Moreira, P. Alcantara, and P. C. de Oliveira, “Thermal lens spectroscopy: Optimizing amplitude and shortening the transient time,” AIP Adv.1(2), 022154 (2011).
[CrossRef]

Anal. Chem. (4)

C. E. Buffett and M. D. Morris, “Thermal lens detection for liquid chromatography,” Anal. Chem.54(11), 1824–1825 (1982).
[CrossRef]

N. J. Dovichi and J. M. Harris, “Laser induced thermal lens effect for calorimetric trace analysis,” Anal. Chem.51(6), 728–731 (1979).
[CrossRef]

J. Slaby, “Background illumination filtering in thermal lens spectroscopy,” Anal. Chem.61(22), 2496–2499 (1989).
[CrossRef]

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,” Anal. Chem.83(9), 3431–3439 (2011).
[CrossRef] [PubMed]

Anal. Chim. Acta (2)

Y. M. Biosca and G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in non-polar solvents,” Anal. Chim. Acta345(1–3), 257–263 (1997).
[CrossRef]

T. Imasaka, K. Miyaishi, and N. Ishibashi, “Application of the thermal lens effect for determination of iron(II) with 4,7-diphenyl-1,10-phenanthroline disulfonic acid,” Anal. Chim. Acta115(1), 407–410 (1980).
[CrossRef]

Analyst (Lond.) (1)

D. R. Snook and R. D. Lowe, “Thermal lens spectroscopy. A review,” Analyst (Lond.)120(8), 2051–2068 (1995).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: Application to Nd3+-doped fluoride glass,” Appl. Phys. Lett.78(21), 3220 (2001).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurement by mean of the thermal lens effect using a He:Ne laser,” Appl. Phys. Lett.5(7), 141–143 (1964).
[CrossRef]

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys.165(2–3), 385–396 (1992).
[CrossRef]

Chem. Phys. Lett. (3)

M. L. Baesso, J. Shen, and R. D. Snook, “Time-resolved thermal lens measurement of thermal diffusivity of soda-lime glass,” Chem. Phys. Lett.197(3), 255–258 (1992).
[CrossRef]

M. Fischer and J. Georges, “Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectroscopy,” Chem. Phys. Lett.260(1–2), 115–118 (1996).
[CrossRef]

C. Tolentino Dominguez, E. de Lima, P. C. de Oliveira, and F. López Arbeloa, “Using random laser emission to investigate the bonding energy of laser dyes dimers,” Chem. Phys. Lett.464(4–6), 245–248 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Mandelis, M. Munidasa, and A. Othonos, “Single-ended infrared photothermal radiometric measurement of quantum efficiency and metastable lifetime in solid-state laser materials: The Case of Ruby (Cr3+:A1203),” IEEE J. Quantum Electron.29(6), 1498–1504 (1993).
[CrossRef]

J. Appl. Phys. (2)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long transient effects in lasers with inserted liquid samples,” J. Appl. Phys.36(1), 3–8 (1965).
[CrossRef]

R. A. Cruz, V. Pilla, and T. Catunda, “Quantum yield excitation spectrum (UV-visible) of CdSe/ZnS core-shell quantum dots by thermal lens spectrometry,” J. Appl. Phys.107(8), 083504 (2010).
[CrossRef]

J. Chem. Phys. (3)

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Figures (7)

Fig. 1
Fig. 1

Scheme of the geometric position of the laser beams in a dual-beam mode-mismatched TL (DTL) configuration.

Fig. 2
Fig. 2

Experimental setup for S-ETL/D-ETL method. L1 and L7 (f = 3.5 cm), L2 (f = 25 cm), L3 and L4 (f = 10 cm), L5 (f = 15 cm), L6 (f = 20 cm) are spherical lens; M1, M2 and M3 are aluminum mirrors; D is a silicon photodiode.

Fig. 3
Fig. 3

TL signal from a 10−6 M of Rh6G in ethanol solution obtained by (a) single-beam TL and (b) S-ETL methods. The inset image in (b) is a digital image of excitation beam after the wavefront filtering. N and S indicate noise and signal respectively.

Fig. 4
Fig. 4

Fluorescence quantum yield values of Rh6G obtained by S-ETL method as a function of, (a) the excitation power and (b) its molar concentration.

Fig. 5
Fig. 5

Normalized TL signal of a HeNe probe beam (632 nm) passing through a sample of 2 × 10−5 M of Rh6G in ethanol solution when excited by 9 mW from a cw Nd:YAG laser (532 nm). Signal obtained using (a) dual-beam mode mismatched TL (DTL) and (b) D-ETL method. The inset image in (b) is a digital image of the probe beam, before and after the wavefront filter.

Fig. 6
Fig. 6

Fluorescence quantum yield of Rh6G dissolved in ethanol as function of excitation power. Measurements performed (a) with and (b) without a wavefront filter in the dual-beam TL.

Fig. 7
Fig. 7

Fluorescence quantum yield of ethanolic solutions of Rh6G as a function of its molar concentration for different excitation powers measured by D- ETL method.

Tables (4)

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Table 1 Signal/noise ratios for three different beam/filter diameters ratio. The Rh6G concentration was 10−6 M and the excitation power was 8 mW.

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Table 2 Mean values of quantum yield values for different Rh6G concentrations obtained by S-ETL methods.

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Table 3 Ratio S/N between the D-ETL and the conventional DTL techniques. The Rh6G concentration was 2 × 10−5 M.

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Table 4 Mean values of quantum yield values for different Rh6G concentrations obtained by D-ETL method compared with those obtained by other authors

Equations (5)

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I= I 0 [ 1 θ 2 tan 1 ( 2mV [ ( 1+2m ) 2 + V 2 ]( t c / 2t )+1+2m+ V 2 ) ] 2 ,
V=z/ z 0P +( z 0P / z 2 )[ 1+ ( z/ z 0P ) 2 ],
θ= φ P abs k λ p dn dT ,
φ=1η λ ex λ em ,
η=( 1 Θ Θ 0 ) λ em λ ex ,

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