Abstract

Optical visualization systems are needed in medical applications for determining the localization of deep-seated luminescent markers in biotissues. The spatial resolution of such systems is limited by the scattering of the tissues. We present a novel epi-luminescent technique, which allows a 1.8-fold increase in the lateral spatial resolution in determining the localization of markers lying deep in a scattering medium compared to the traditional visualization techniques. This goal is attained by using NaYF4:Yb3+Tm3+@NaYF4 core/shell nanoparticles and special optical fiber probe with combined channels for the excitation and detection of anti-Stokes luminescence signals.

© 2014 Optical Society of America

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2013 (3)

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

2012 (1)

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

2011 (2)

M. Haase and H. Schäfer, “Upconverting nanoparticles,” Angew. Chem. Int. Ed. Engl.50(26), 5808–5829 (2011).
[CrossRef] [PubMed]

K. Welsher, S. P. Sherlock, and H. J. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. U.S.A.108(22), 8943–8948 (2011).
[CrossRef] [PubMed]

2010 (4)

V. Ntziachristos, “Going Deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

F. Leblond, S. C. Davis, P. A. Valdés, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: Review of instruments, methods and applications,” J. Photochem. Photobiol. B98(1), 77–94 (2010).
[CrossRef] [PubMed]

J. C. Boyer and F. C. J. M. van Veggel, “Absolute quantum yield measurements of colloidal NaYF4: Er3+, Yb3+ upconverting nanoparticles,” Nanoscale2(8), 1417–1419 (2010).
[CrossRef] [PubMed]

P. Svenmarker, C. T. Xu, and S. Andersson-Engels, “Use of nonlinear upconverting nanoparticles provides increased spatial resolution in fluorescence diffuse imaging,” Opt. Lett.35(16), 2789–2791 (2010).
[CrossRef] [PubMed]

2009 (6)

Y. T. Lin, H. Yan, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography with functional and structural a priori information,” Appl. Opt.48(7), 1328–1336 (2009).
[CrossRef] [PubMed]

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A26(5), 1277–1290 (2009).
[CrossRef] [PubMed]

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett.94(25), 251107 (2009).
[CrossRef]

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

X. H. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: from synthesis and properties to biological and biomedical applications,” Adv. Mater.21(48), 4880–4910 (2009).
[CrossRef]

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

2008 (1)

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol.51(16), 3983–4001 (2006).
[CrossRef] [PubMed]

2005 (2)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol.50(17), 4225–4241 (2005).
[CrossRef] [PubMed]

2004 (1)

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Ahn, S.

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

Akhmanov, A. S.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol.50(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Andersson-Engels, S.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

P. Svenmarker, C. T. Xu, and S. Andersson-Engels, “Use of nonlinear upconverting nanoparticles provides increased spatial resolution in fluorescence diffuse imaging,” Opt. Lett.35(16), 2789–2791 (2010).
[CrossRef] [PubMed]

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett.94(25), 251107 (2009).
[CrossRef]

Arridge, S. R.

Axelsson, J.

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett.94(25), 251107 (2009).
[CrossRef]

Badawi, R. D.

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

Barrow, E.

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
[CrossRef] [PubMed]

Bibikova, O. A.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Bogdanov, A.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Boyer, J. C.

J. C. Boyer and F. C. J. M. van Veggel, “Absolute quantum yield measurements of colloidal NaYF4: Er3+, Yb3+ upconverting nanoparticles,” Nanoscale2(8), 1417–1419 (2010).
[CrossRef] [PubMed]

Brooks, D. H.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

Byers, R. J.

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
[CrossRef] [PubMed]

Bykov, A. V.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Chatziioannou, A. F.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol.50(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Chaudhari, A. J.

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

Cherry, S. R.

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

Choe, R.

Clay, V.

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
[CrossRef] [PubMed]

Corlu, A.

Dai, H. J.

K. Welsher, S. P. Sherlock, and H. J. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. U.S.A.108(22), 8943–8948 (2011).
[CrossRef] [PubMed]

Davis, S. C.

F. Leblond, S. C. Davis, P. A. Valdés, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: Review of instruments, methods and applications,” J. Photochem. Photobiol. B98(1), 77–94 (2010).
[CrossRef] [PubMed]

de Kleine, R.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

Deyev, S. M.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Durduran, T.

El-Sayed, M. A.

X. H. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: from synthesis and properties to biological and biomedical applications,” Adv. Mater.21(48), 4880–4910 (2009).
[CrossRef]

Generalova, A. N.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Gibson, A. P.

Graves, E.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Grebenik, E. A.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

Gulsen, G.

Haase, M.

M. Haase and H. Schäfer, “Upconverting nanoparticles,” Angew. Chem. Int. Ed. Engl.50(26), 5808–5829 (2011).
[CrossRef] [PubMed]

Hoyland, J. A.

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
[CrossRef] [PubMed]

Huang, X. H.

X. H. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: from synthesis and properties to biological and biomedical applications,” Adv. Mater.21(48), 4880–4910 (2009).
[CrossRef]

Hyde, D.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

Josephson, L.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Karmenyan, A. V.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Khaydukov, E. V.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Kinnunen, M. T.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Klinov, D. V.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Krucker, T.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
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Leblond, F.

F. Leblond, S. C. Davis, P. A. Valdés, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: Review of instruments, methods and applications,” J. Photochem. Photobiol. B98(1), 77–94 (2010).
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Levenson, R.

A. J. Chaudhari, S. Ahn, R. Levenson, R. D. Badawi, S. R. Cherry, and R. M. Leahy, “Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies,” Phys. Med. Biol.54(15), 4687–4704 (2009).
[CrossRef] [PubMed]

Lin, Y. T.

Liu, H.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

MacLaurin, S. A.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

Messing, M. E.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
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Miller, E.

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
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Nadort, A.

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
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E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
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Nalcioglu, O.

Nechaev, A. V.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
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A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Neretina, S.

X. H. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: from synthesis and properties to biological and biomedical applications,” Adv. Mater.21(48), 4880–4910 (2009).
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Ntziachristos, V.

V. Ntziachristos, “Going Deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

D. Hyde, R. de Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-beta plaques in a murine Alzheimer’s disease model,” Neuroimage44(4), 1304–1311 (2009).
[CrossRef] [PubMed]

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol.51(16), 3983–4001 (2006).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Panagiotou, C.

Panchenko, V. Ya.

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
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A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Pogue, B. W.

F. Leblond, S. C. Davis, P. A. Valdés, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: Review of instruments, methods and applications,” J. Photochem. Photobiol. B98(1), 77–94 (2010).
[CrossRef] [PubMed]

Popov, A. P.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol.50(17), 4225–4241 (2005).
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Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Rosen, M. A.

Schäfer, H.

M. Haase and H. Schäfer, “Upconverting nanoparticles,” Angew. Chem. Int. Ed. Engl.50(26), 5808–5829 (2011).
[CrossRef] [PubMed]

Schellenberger, E. A.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Schnall, M. D.

Schweiger, M.

Semchishen, V. A.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Seminogov, V. N.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Sherlock, S. P.

K. Welsher, S. P. Sherlock, and H. J. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. U.S.A.108(22), 8943–8948 (2011).
[CrossRef] [PubMed]

Sokolov, V. I.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Somayajula, S.

Song, Z.

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

Soubret, A.

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol.51(16), 3983–4001 (2006).
[CrossRef] [PubMed]

Sreenivasan, V. K. A.

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Svenmarker, P.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

P. Svenmarker, C. T. Xu, and S. Andersson-Engels, “Use of nonlinear upconverting nanoparticles provides increased spatial resolution in fluorescence diffuse imaging,” Opt. Lett.35(16), 2789–2791 (2010).
[CrossRef] [PubMed]

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E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
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Tholouli, E.

E. Tholouli, E. Sweeney, E. Barrow, V. Clay, J. A. Hoyland, and R. J. Byers, “Quantum dots light up pathology,” J. Pathol.216(3), 275–285 (2008).
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Tuchin, V. V.

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

Valdés, P. A.

F. Leblond, S. C. Davis, P. A. Valdés, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: Review of instruments, methods and applications,” J. Photochem. Photobiol. B98(1), 77–94 (2010).
[CrossRef] [PubMed]

van Veggel, F. C. J. M.

J. C. Boyer and F. C. J. M. van Veggel, “Absolute quantum yield measurements of colloidal NaYF4: Er3+, Yb3+ upconverting nanoparticles,” Nanoscale2(8), 1417–1419 (2010).
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Wallenberg, L. R.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Welsher, K.

K. Welsher, S. P. Sherlock, and H. J. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. U.S.A.108(22), 8943–8948 (2011).
[CrossRef] [PubMed]

Wu, X.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

Xu, C. T.

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

P. Svenmarker, C. T. Xu, and S. Andersson-Engels, “Use of nonlinear upconverting nanoparticles provides increased spatial resolution in fluorescence diffuse imaging,” Opt. Lett.35(16), 2789–2791 (2010).
[CrossRef] [PubMed]

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett.94(25), 251107 (2009).
[CrossRef]

Yan, H.

Yessayan, D.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an Annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A.101(33), 12294–12299 (2004).
[CrossRef] [PubMed]

Yodh, A. G.

Zubov, V. P.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

Zvyagin, A. V.

E. A. Grebenik, A. Nadort, A. N. Generalova, A. V. Nechaev, V. K. A. Sreenivasan, E. V. Khaydukov, V. A. Semchishen, A. P. Popov, V. I. Sokolov, A. S. Akhmanov, V. P. Zubov, D. V. Klinov, V. Ya. Panchenko, S. M. Deyev, and A. V. Zvyagin, “Feasibility study of the optical imaging of a breast cancer lesion labeled with upconversion nanoparticle biocomplexes,” J. Biomed. Opt.18(7), 076004 (2013).
[CrossRef] [PubMed]

A. P. Popov, A. V. Karmenyan, A. V. Bykov, E. V. Khaydukov, A. V. Nechaev, O. A. Bibikova, V. Ya. Panchenko, V. A. Semchishen, V. N. Seminogov, A. S. Akhmanov, V. I. Sokolov, M. T. Kinnunen, V. V. Tuchin, and A. V. Zvyagin, “High-resolution deep-tissue optical imaging using anti-Stokes phosphors,” Proc. SPIE8801, 88010C (2013).
[CrossRef]

A. Nadort, V. K. A. Sreenivasan, Z. Song, E. A. Grebenik, A. V. Nechaev, V. A. Semchishen, V. Ya. Panchenko, and A. V. Zvyagin, “Quantitative Imaging of Single Upconversion Nanoparticles in Biological Tissue,” PLoS ONE8(5), e63292 (2013).
[CrossRef] [PubMed]

ACS Nano (1)

C. T. Xu, P. Svenmarker, H. Liu, X. Wu, M. E. Messing, L. R. Wallenberg, and S. Andersson-Engels, “High-resolution fluorescence diffuse optical tomography developed with nonlinear upconverting nanoparticles,” ACS Nano6(6), 4788–4795 (2012).
[CrossRef] [PubMed]

Adv. Mater. (1)

X. H. Huang, S. Neretina, and M. A. El-Sayed, “Gold nanorods: from synthesis and properties to biological and biomedical applications,” Adv. Mater.21(48), 4880–4910 (2009).
[CrossRef]

Angew. Chem. Int. Ed. Engl. (1)

M. Haase and H. Schäfer, “Upconverting nanoparticles,” Angew. Chem. Int. Ed. Engl.50(26), 5808–5829 (2011).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett.94(25), 251107 (2009).
[CrossRef]

J. Biomed. Opt. (1)

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Figures (9)

Fig. 1
Fig. 1

Size distribution histogram of the NaYF4:Yb3+Tm3+@NaYF4 core/shell nanoparticles. The inset is a TEM photograph of the nanoparticles.

Fig. 2
Fig. 2

PL spectrum of the NaYF4:Yb3+Tm3+@NaYF4 core/shell nanoparticles irradiated with 975 nm laser light. Excitation intensity is 1 W/cm2. Presented in the inset is the PL intensity at a wavelength of 800 nm as a function of the exciting radiation intensity.

Fig. 3
Fig. 3

Schematic illustration of the epiluminescent methods studied: (а) wide-field imaging (WFI); (b) raster scanning fiber imaging (RSFI).

Fig. 4
Fig. 4

A schematic diagram of the scattering of the light beam incident on a spatially inhomogeneous medium. The extended and narrow light beam geometries are considered. (N) is a normal to the surface z = 0, rp is the coordinate of the center of the incident beam, r0 is the coordinate of the sampling point situated at the plane z = 0, rs is the coordinate of the photoluminescent marker, (R)0s = r0 - rs, Ii(r0 - rp) denotes the intensity of the light beam, Δσ( r 0 ) –the fiber probe cross-section, ΔS( r s ) –the photoluminescent marker surface site of the size small compared with the light beam intensity variation, θ is the angle between (N) and (R)0s.

Fig. 5
Fig. 5

The case of single UCNPs marker strip. Experiment: full circles – PL detection by the WFI technique; open circles – PL detection by the RSFI technique. Solid lines 1 and 2 – theoretical calculations.

Fig. 6
Fig. 6

The case of two marker strips localized in the plane z = d. Experiment: full circles – PL detection by the WFI technique; open circles – PL detection by the RSFI technique. Solid lines 1 and 2 – theoretical calculations. The distance between the marker strips is (xbxa) = 5.1 mm.

Fig. 7
Fig. 7

Parameter R (xa, xb) as a function of the distance between the marker strips (xbxa). Curve 1 (RSFI technique) is constructed by formulas (10), (12), while curve 2 (WFI technique), by formulas (11), (12). The curve segments with open circles indicate the regions wherein the Rayleigh criterion is satisfied.

Fig. 8
Fig. 8

Experimental dependence of the intensity of the PL signal (λ = 800 nm) obtained by moving the probe along the intersection line of the planes z = 0 and y = yp = const (open circles, see Fig. 6). Solid curves 1 through 3 are constructed by formula (10) at μa = 0.2 cm–1, xa = 33.4 mm, xb = 38.5 mm, F( R a0 )=F( R b0 )const , and Aprobe ≈const. The distance between the marker strips is (xbxa) = 5.1 mm. The thickness of the phantom: d = 3.5 mm (1), d = 3.5 mm (2), d = 4.5 mm (3).

Fig. 9
Fig. 9

Normalized distributions I RSFI 1 as a function of the coordinate x of the first probe, xs = 0, μa = 0.2 cm–1, h = 6 mm. The thickness of the phantom: d = 4 mm (1), d = 3.5 mm (2), d = 4.5 mm (3).

Equations (19)

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B z=0 ( r s , r 0 )= ΔΦ( r 0 ) Δσ( r 0 )cosθ( r s , r 0 )ΔΩ , ΔΩ( r s , r 0 )=sinθ( r s , r 0 )Δθ( r s , r 0 )Δϕ= ΔS( r s )cosθ( r s , r 0 ) R s0 2 , R s0 = ( x s x 0 ) 2 + ( y s y 0 ) 2 + d 2 ,cosθ( r s , r 0 )=d/ R s0 .
I i ( r 0 r p )= B z=0 ( θ,ϕ ) cosθdΩ( θ,ϕ )= - B z=0 ( | R s0 | ) d 2 R s0 4 d x s d y s .
B z=0 ( | R s0 | )= I i ( r 0 r p )F( R s0 ), B z=d ( | R s0 | )= I i ( r 0 r p )F( R s0 )exp( μ a R s0 ),
F( R s0 ) d 2 R s0 4 d x s d y s =1.
B z=d ( | R s0 | )= I i ( r 0 r p ) π ,F( R s0 )= 1 π .
I λ=975 ( x s , y s ,z=d)= F( R s0 ) I i ( r 0 r p )exp( μ a R s0 ) d R s0 3 d x 0 d y 0 .
I λ=800 ( x s , y s ,z=d )=η | I λ=975 ( x s , y s ,z=d ) | 2 = =η | F( R s0 ) I i ( r 0 r p )exp( μ a R s0 ) ( d R s0 ) 3 d x 0 d y 0 d 2 | 2 .
B λ=800 z=d ( x s , y s )=F( R s1 ) I λ=800 ( x s , y s ,z=d ), R s1 = ( x 1 x s ) 2 + ( y 1 y s ) 2 + d 2 .
F( R s0 ) I i ( r 0 r p ) B λ=800 z=d ( x s , y s ), R s0 R s1 ,d x 0 d y 0 d x s d y s .
I λ=800 beam ( x 1 , y 1 ,z=0 )= A beam ( r s , r p )F( R s1 ) ( d/ R s1 ) 3 exp( μ a R s1 ), A beam ( r s , r p )=η ΔS( r s ) z 0 2 | F( R s0 ) I i ( r 0 r p )exp( μ a R s0 ) ( d/ R s0 ) 3 d x 0 d y 0 d 2 |,
I i ( r 0 r p )={ I i0 =const, if | r 0 r p | r probe 0,if| r 0 r p |> r probe }.
I λ=800 probe ( x 0 , y 0 ,z=0 )= A probe ( R s0 ) [ F( R s0 ) ] 3 ( d/ R s0 ) 9 exp( 3 μ a R s0 ), A probe ( R s0 )=η I i0 2 ( Δ S probe d 2 ) 2 ( ΔS( r s ) d 2 )=const,
I λ=800 probe ( x 0 , y 0 ,z=0 ) A probe [ F( R s0 ) ] 3 = ( I λ=800 beam ( x 0 , y 0 ,z=0 ) A beam F( R s0 ) ) 3 .
I λ=800 probe ( x 0 , y 0 ,z=0 )= A probe { [ F( R a0 ) ] 3 ( d/ R a0 ) 9 exp( 3 μ a R a0 )+ + [ F( R b0 ) ] 3 ( d/ R b0 ) 9 exp( 3 μ a R b0 ) }
I λ=800 beam ( x 0 , y 0 ,z=0 )= A beam { F( R a0 ) ( d/ R a0 ) 3 exp( μ a R a0 )+ + F( R b0 ) ( d/ R b0 ) 3 exp( μ a R b0 ) }, R a0 = ( x 0 x a ) 2 + ( y 0 y a ) 2 + d 2 , R b0 = ( x 0 x b ) 2 + ( y 0 y b ) 2 + d 2 ,
R( x a , x b )= I max ( x a , x b ) I min ( x a , x b ) I max ( x a , x b ) ×10020%.
I λ=975 beam ( x 0 , y 0 ,z=0 )= D beam F( R s0 ) ( d/ R s0 ) 3 exp( μ a R s0 ),
I λ=975 probe ( x 0 , y 0 ,z=0 )= D probe [ F( R s0 ) ] 2 ( d/ R s0 ) 6 exp( 2 μ a R s0 ),
I RSFI 1 = I λ=800 probe (x,y= y s ,z=0)= D probe [ ( d/ R 1 ) 3 exp( μ a R 1 )+ ( d/ R 2 ) 3 exp( μ a R 2 ) ] 2 ( d/ R 1 ) 3 exp( μ a R 1 ), R 1 = (x x s ) 2 +d , R 2 = (x+h x s ) 2 + d 2 , D probe =const.

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