Abstract

The dynamic range of fiber-optic fluorescent probes such as single fibers and fiber bundles is calculated for strongly absorbing samples, such as process liquids, foodstuffs, and lubricants. The model assumes an excitation beam profile based on a Lambertian light source and uses analytical forms of the collection efficiency, followed by an Abel transformation and numerical integration. It is found that the effect of primary absorption of the excitation light and secondary absorption of the fluorescence is profound. For fiber bundles and bifurcated fiber probes, the upper accessible concentration limit is roughly given by the absorption length of the primary and secondary absorption. Fluorescence detectors that are placed at right angles to the excitation beam axis or collinear to the beam axis are equally strongly affected by secondary absorption. A probe in which the same fiber is used for excitation and for collection of the fluorescence emerges as the fiber probe with the largest accessible concentration range.

© 2012 Optical Society of America

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2012 (3)

2011 (2)

2009 (2)

G. K. Bhowmick, N. Gautam, and L. M. Gantayet, “Design optimization of fiber optic probes for remote fluorescence spectroscopy,” Opt. Commun. 282, 2676–2684 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

2008 (2)

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

2007 (1)

2006 (1)

M. L. Nahorniak and K. S. Booksh, “Excitation-emission matrix fluorescence spectroscopy in conjunction with multiway analysis for PAH detection in complex matrices,” Analyst 131, 1308–1315 (2006).
[CrossRef]

2005 (2)

T. J. Pfefer, A. Agrawal, and R. A. Drezek, “Oblique-incidence illumination and collection for depth-selective fluorescence spectroscopy,” J. Biomed. Opt. 10, 044016 (2005).
[CrossRef]

J. M. Dixon, M. Taniguchi, and J. S. Lindsey, “PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations,” Photochem. Photobiol. 81, 212–213 (2005).
[CrossRef]

2004 (2)

2003 (1)

A. Larson, V. Iyer, T. Hoogland, and P. Saggau, “Fiber-coupled non-descanned 4π detection with a commercial confocal microscope modified for multiphoton imaging,” Proc. SPIE 4963, 239–251 (2003).
[CrossRef]

2001 (2)

P. T. Tran and F. Chang, “Transmitted light fluorescence microscopy revisited,” Biol. Bull. 201, 235–236 (2001).
[CrossRef]

T. J. Pfefer, K. T. Schomacker, and N. S. Nishioka, “Effect of fiber optic probe design on fluorescent light propagation in tissue,” Proc. SPIE 4257, 410–416 (2001).
[CrossRef]

2000 (1)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

1998 (2)

E. V. Trujillo, D. R. Sandison, U. Utzinger, N. Ramanujam, M. F. Mitchell, and R. Richards-Kortum, “Method to determine tissue fluorescence efficiency in vivo and predict signal-to-noise ratio for spectrometers,” Appl. Spectrosc. 52, 943–951(1998).
[CrossRef]

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

1996 (4)

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

K. R. Rogers and E. J. Poziomek, “Fiber optic sensors for environmental monitoring,” Chemosphere 33, 1151–1174 (1996).
[CrossRef]

T. F. Cooney, H. T. Skinner, and S. M. Angel, “Comparative study of some fiber-optic remote Raman probe designs. Part I: model for liquids and transparent solids,” Appl. Spectrosc. 50, 836–848 (1996).
[CrossRef]

T. F. Cooney, H. T. Skinner, and S. M. Angel, “Comparative study of some fiber-optic remote Raman probe designs. Part II: tests of single-fiber, lensed, and flat- and bevel-tip multi-fiber probes,” Appl. Spectrosc. 50, 849–860 (1996).
[CrossRef]

1991 (1)

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

1986 (1)

Agrawal, A.

T. J. Pfefer, A. Agrawal, and R. A. Drezek, “Oblique-incidence illumination and collection for depth-selective fluorescence spectroscopy,” J. Biomed. Opt. 10, 044016 (2005).
[CrossRef]

Angel, S. M.

Atkinson, N.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Attilio, C.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Barnes, J. A.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Bhowmick, G. K.

G. K. Bhowmick, N. Gautam, and L. M. Gantayet, “Design optimization of fiber optic probes for remote fluorescence spectroscopy,” Opt. Commun. 282, 2676–2684 (2009).
[CrossRef]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Bock, W. J.

Booksh, K. S.

Y. C. Kim, J. A. Jordan, D. Chavez, and K. S. Booksh, “Coaxial fiber-optic chemical-sensing excitation—emission matrix fluorometer,” Opt. Lett. 36, 355–357 (2011).
[CrossRef]

M. L. Nahorniak and K. S. Booksh, “Excitation-emission matrix fluorescence spectroscopy in conjunction with multiway analysis for PAH detection in complex matrices,” Analyst 131, 1308–1315 (2006).
[CrossRef]

Brightwell, A.

Buonocore, G.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Carnohan, M.

Chai, T. Y.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Chang, F.

P. T. Tran and F. Chang, “Transmitted light fluorescence microscopy revisited,” Biol. Bull. 201, 235–236 (2001).
[CrossRef]

Chavez, D.

Cheng, T. H.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Chiniforooshan, Y.

Choi, H. Y.

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Ciaccheri, L.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Cimato, A.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Cooney, T. F.

Corkan, L. A.

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

Cottone, G.

Cucci, C.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Cuomo, F. W.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

Dall’Asta, C.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Del Nobile, M. A.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Díaz-Herrera, N.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

Dixon, J. M.

J. M. Dixon, M. Taniguchi, and J. S. Lindsey, “PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations,” Photochem. Photobiol. 81, 212–213 (2005).
[CrossRef]

Dossena, A.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Drezek, R. A.

T. J. Pfefer, A. Agrawal, and R. A. Drezek, “Oblique-incidence illumination and collection for depth-selective fluorescence spectroscopy,” J. Biomed. Opt. 10, 044016 (2005).
[CrossRef]

Du, H.

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

Dudelzak, A. E.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Faccini, A.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Fang, Q. Y.

Fevrier, H.

Francalanci, S.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

Fuh, R. C. A.

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

Galaverna, G.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Gantayet, L. M.

G. K. Bhowmick, N. Gautam, and L. M. Gantayet, “Design optimization of fiber optic probes for remote fluorescence spectroscopy,” Opt. Commun. 282, 2676–2684 (2009).
[CrossRef]

Gautam, N.

G. K. Bhowmick, N. Gautam, and L. M. Gantayet, “Design optimization of fiber optic probes for remote fluorescence spectroscopy,” Opt. Commun. 282, 2676–2684 (2009).
[CrossRef]

Gerevini, M.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Gord, J. R.

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Grimaldi, M. F.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Hao, W. H.

He, G.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

Hindle, F. P.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Hoogland, T.

A. Larson, V. Iyer, T. Hoogland, and P. Saggau, “Fiber-coupled non-descanned 4π detection with a commercial confocal microscope modified for multiphoton imaging,” Proc. SPIE 4963, 239–251 (2003).
[CrossRef]

Hsu, P. S.

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Iyer, V.

A. Larson, V. Iyer, T. Hoogland, and P. Saggau, “Fiber-coupled non-descanned 4π detection with a commercial confocal microscope modified for multiphoton imaging,” Proc. SPIE 4963, 239–251 (2003).
[CrossRef]

Jiang, N. B.

John, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Jones, L. R.

Jordan, J. A.

Jouan, M.

Jung, Y. M.

Kim, K. T.

Kim, Y. C.

Kulatilaka, W. D.

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed. (Springer, 2006), Chap. 5.

Larson, A.

A. Larson, V. Iyer, T. Hoogland, and P. Saggau, “Fiber-coupled non-descanned 4π detection with a commercial confocal microscope modified for multiphoton imaging,” Proc. SPIE 4963, 239–251 (2003).
[CrossRef]

Lee, B. H.

Leonard, S. W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Li, J. Z.

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

Lindsey, J. S.

J. M. Dixon, M. Taniguchi, and J. S. Lindsey, “PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations,” Photochem. Photobiol. 81, 212–213 (2005).
[CrossRef]

H. Du, R. C. A. Fuh, J. Z. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68, 141–142 (1998).
[CrossRef]

Loock, H.-P.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Ma, J. J.

Mahadevan-Jansen, A.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Malpica, A.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Marcu, L.

Mastroianni, M.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

McCann, H.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Mencaglia, A. A.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Mentana, A.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Meseguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Mignani, A. G.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Mitchell, M. F.

Mitchell, M. Follen

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Mondia, J. P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Monti, D.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Nahorniak, M. L.

M. L. Nahorniak and K. S. Booksh, “Excitation-emission matrix fluorescence spectroscopy in conjunction with multiway analysis for PAH detection in complex matrices,” Analyst 131, 1308–1315 (2006).
[CrossRef]

Nguyen, Q. D.

Nishioka, N. S.

T. J. Pfefer, K. T. Schomacker, and N. S. Nishioka, “Effect of fiber optic probe design on fluorescent light propagation in tissue,” Proc. SPIE 4257, 410–416 (2001).
[CrossRef]

Omrani, H.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Ottevaere, H.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Ozanyan, K. B.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Ozin, G. A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Paccagnini, A.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

Paolesse, R.

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Papaioannou, T.

Pavone, F. S.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

Pfefer, T. J.

T. J. Pfefer, A. Agrawal, and R. A. Drezek, “Oblique-incidence illumination and collection for depth-selective fluorescence spectroscopy,” J. Biomed. Opt. 10, 044016 (2005).
[CrossRef]

T. J. Pfefer, K. T. Schomacker, and N. S. Nishioka, “Effect of fiber optic probe design on fluorescent light propagation in tissue,” Proc. SPIE 4257, 410–416 (2001).
[CrossRef]

Plaza, P.

Poolton, N. R. J.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Poziomek, E. J.

K. R. Rogers and E. J. Poziomek, “Fiber optic sensors for environmental monitoring,” Chemosphere 33, 1151–1174 (1996).
[CrossRef]

Preyer, N. W.

Ramanujam, N.

E. V. Trujillo, D. R. Sandison, U. Utzinger, N. Ramanujam, M. F. Mitchell, and R. Richards-Kortum, “Method to determine tissue fluorescence efficiency in vivo and predict signal-to-noise ratio for spectrometers,” Appl. Spectrosc. 52, 943–951(1998).
[CrossRef]

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Richards-Kortum, R.

E. V. Trujillo, D. R. Sandison, U. Utzinger, N. Ramanujam, M. F. Mitchell, and R. Richards-Kortum, “Method to determine tissue fluorescence efficiency in vivo and predict signal-to-noise ratio for spectrometers,” Appl. Spectrosc. 52, 943–951(1998).
[CrossRef]

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Rogers, K. R.

K. R. Rogers and E. J. Poziomek, “Fiber optic sensors for environmental monitoring,” Chemosphere 33, 1151–1174 (1996).
[CrossRef]

Rong, W. F.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Ross, R.

Roy, S.

Saggau, P.

A. Larson, V. Iyer, T. Hoogland, and P. Saggau, “Fiber-coupled non-descanned 4π detection with a commercial confocal microscope modified for multiphoton imaging,” Proc. SPIE 4963, 239–251 (2003).
[CrossRef]

Saisse, H.

Sandison, D. R.

Schomacker, K. T.

T. J. Pfefer, K. T. Schomacker, and N. S. Nishioka, “Effect of fiber optic probe design on fluorescent light propagation in tissue,” Proc. SPIE 4257, 410–416 (2001).
[CrossRef]

Skinner, H. T.

Staerkel, G.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Tan, K. L.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Taniguchi, M.

J. M. Dixon, M. Taniguchi, and J. S. Lindsey, “PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations,” Photochem. Photobiol. 81, 212–213 (2005).
[CrossRef]

Thienpont, H.

A. G. Mignani, L. Ciaccheri, N. Díaz-Herrera, A. A. Mencaglia, H. Ottevaere, H. Thienpont, S. Francalanci, A. Paccagnini, and F. S. Pavone, “Optical fiber spectroscopy for measuring quality indicators of lubricant oils,” Meas. Sci. Technol. 20, 034011 (2009).
[CrossRef]

A. G. Mignani, L. Ciaccheri, C. Cucci, A. A. Mencaglia, A. Cimato, C. Attilio, H. Ottevaere, H. Thienpont, R. Paolesse, M. Mastroianni, D. Monti, M. Gerevini, G. Buonocore, M. A. Del Nobile, A. Mentana, M. F. Grimaldi, C. Dall’Asta, A. Faccini, G. Galaverna, and A. Dossena, “EAT-by-LIGHT: fiber-optic and micro-optic devices for food quality and safety assessment,” IEEE Sens. J. 8, 1342–1354 (2008).
[CrossRef]

Thomsen, S. L.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Toader, O.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Tran, P. T.

P. T. Tran and F. Chang, “Transmitted light fluorescence microscopy revisited,” Biol. Bull. 201, 235–236 (2001).
[CrossRef]

Trujillo, E. V.

Utzinger, U.

van Driel, H. M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[CrossRef]

Waechter, H.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Wang, L.

Wang, Y. X.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Wang, Z. Y.

Wright, T.

N. Ramanujam, M. Follen Mitchell, A. Mahadevan-Jansen, S. L. Thomsen, G. Staerkel, A. Malpica, T. Wright, N. Atkinson, and R. Richards-Kortum, “Cervical precancer detection using a multivariate statistical algorithm based on laser-induced fluorescence spectra at multiple excitation wavelengths,” Photochem. Photobiol. 64, 720–735 (1996).
[CrossRef]

Yeo, T. L.

K. B. Ozanyan, T. L. Yeo, F. P. Hindle, N. R. J. Poolton, H. McCann, and K. L. Tan, “Fiber-based UV laser-diode fluorescence sensor for commercial gasolines,” IEEE Sens. J. 4, 681–690 (2004).
[CrossRef]

Yeo, Y. K.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Zhou, M. T.

W. F. Rong, Y. X. Wang, T. Y. Chai, Y. K. Yeo, M. T. Zhou, and T. H. Cheng, “Bandwidth enhancement of multimode fiber based on a cost-effective periodic mode-scrambling method,” Opt. Eng. 47, 115002 (2008).
[CrossRef]

Analyst (2)

M. L. Nahorniak and K. S. Booksh, “Excitation-emission matrix fluorescence spectroscopy in conjunction with multiway analysis for PAH detection in complex matrices,” Analyst 131, 1308–1315 (2006).
[CrossRef]

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation-emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Appl. Opt. (3)

Appl. Spectrosc. (3)

Biol. Bull. (1)

P. T. Tran and F. Chang, “Transmitted light fluorescence microscopy revisited,” Biol. Bull. 201, 235–236 (2001).
[CrossRef]

Chemosphere (1)

K. R. Rogers and E. J. Poziomek, “Fiber optic sensors for environmental monitoring,” Chemosphere 33, 1151–1174 (1996).
[CrossRef]

IEEE Sens. J. (2)

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Figures (7)

Fig. 1.
Fig. 1.

Sketch of the four different detection configurations (see text for details).

Fig. 2.
Fig. 2.

(a) Two-dimensional representation, Iexc(r,z), of the light intensity emitted from a multimode fiber as calculated using the model by He and Cuomo [22]. (b) Abel transform of (a), Iexc(x,z), as described in Eq. (1).

Fig. 3.
Fig. 3.

False-color 2D cross section of the spatial distribution of light following absorption and emission from a multimode fiber with a 50 μm core into Eosin Y dye solution in basic ethanol. The left images assume an Eosin Y concentration of 3 μM, and the right images assume 440 μM. Intensities have been rescaled to cover the entire dynamic range of the image. (a) Primary absorption of excitation light calculated using the model by He and Cuomo [22]. (b) Fluorescence collection probability assuming that the excitation fiber also collects fluorescence (case 1). (c) Fluorescence collection probability assuming that light is collected by a detector placed 5 mm above the image plane (case 2). (d) Fluorescence collection probability assuming that a detector looking into the fiber is placed 5 mm “downstream” of the light emission (case 3). (e)–(f) Fluorescence collection probability of two fibers aligned parallel to the center emission fiber, where the emission and collection fibers have (e) a 50 μm core and 125 μm cladding diameter or (f) a 125 μm core and no cladding (F) (case 4).

Fig. 4.
Fig. 4.

Calculated total intensity for the four different cases. The simulation assumes NA=0.20 and nsolution=1.362 and absorption coefficients of Eosin Y dye at the excitation wavelength of 532 nm (ε=86,400lmol1cm1) and at the center of the emission spectrum at 543.5 nm (ε=24,500lmol1cm1). The intensity of a cube with 500 μm sides is integrated except in case 2 (yoff=5000μm; yellow squares) when the length of the region was 2.5 mm, in case 4 (113 and 125 μm core) when the sides of the cube were 1 mm long, and in case 4 (400 μm core) when the sides were 4 mm long.

Fig. 5.
Fig. 5.

Eosin Y fluorescence images. Left: false-color images detected through a microscope. The concentrations correspond to a dilution series of a 0.857 mM solution to 12, 14, 18 and 116 (top to bottom). Right: simulated fluorescence profiles using case 2 and yoff=3mm. The absorption coefficients were the same as in Fig. 4. Each of the 10 images is 500 μm high.

Fig. 6.
Fig. 6.

Geometry of the 50/125μm fiber bundle.

Fig. 7.
Fig. 7.

Left, collection efficiency of two fibers together with the fiber excitation cone (center); right, resulting fluorescence collection assuming a 440 μM concentration of Eosin Y [akin to Fig. 4(a)].

Equations (14)

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I(x,z)=2x02πI(r,ρ,z)rr2x2dρdr=4πxI(r,z)rr2x2dr.
Iprim(r,z)=Iexc(r,z)×{exp(αexcz),ifr<r0,exp(αexcz2+(rr0)2,ifr>r0.
Idetect(r,z)=Iprim(r,z)×CE(r,z)×{exp(αemz),ifr<r0,exp(αemz2+(rr0)2),ifr>r0.
CE(r,z)={arctan(r+r0z)+arctan(rr0z),ifr<r0,arctan(r+r0z)arctan(rr0z),ifr>r0.
Idetect(x,z)=2x02πIprim(r,ρ,z)exp[αem(yoffrsinρ)]rr2x2dρdr.
Idetect(r,z)=Iprim(r,z)CEprim(r,z)exp[αem(zoffz)].
CE(r,z)=arctan(rdetect+rzoffz)arctan(rdetectr0zoffz).
Idetect(r,z)={Iprim(r,z)×CEA(r,z)×exp(αemz2+(r2rcl)2),ifr>2rcl+r0,Iprim(r,z)×CEB(r,z)×exp(αemz2+(rclr)2),ifr<2rclr0,Iprim(r,z)×CEC(r,z)×exp(αemz),if2rclr0<r<2rcl+r0.
CEA(r,z)=Γ(r,z)×(arctan(r2rclr0z)arctan(r2rcl+r0z)),ifr>2rcl+r0;CEB(r,z)=Γ(r,z)×(arctan(2rclr0rz)arctan(2rcl+r0rz)),ifr<2rclr0;CEC(r,z)=Γ(r,z)×(arctan(2rcl+r0rz)+arctan(r2rcl+r0z)),if2rclr0<r<2rcl+r0.
Γ(r,z)=6πarctan{16rcl2r2[4rcl2r02(z)+r2]24rcl2r02(z)+r2}.
r0(z)=r0(0)(1+zn2/NA21).
Γ=6α(r,z)/2π.
α(r,z)=2arctan{16rcl2r2[4rcl2r02(z)+r2]24rcl2r02(z)+r2}.
r0(z)=r0(0)(1+zn2/NA21).

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