Abstract

We present an experimental and theoretical study of confocal fluorescence polarization microscopy in turbid media. We have performed an experimental study using a fluorophore-embedded polymer rod immersed in aqueous suspensions of 0.1 and 0.5μm diameter polystyrene microspheres. A Monte Carlo approach to simulate confocal fluorescence polarization imaging in scattering media is also presented. It incorporates a detailed model of polarized fluorescence generation that includes sampling of elliptical polarization, excited-state molecular rotational Brownian motion, and dipole fluorescence emission. Using both approaches, we determine the effects of the number of scattering events, target depth, photon scattering statistics, objective numerical aperture, and pinhole size on confocal anisotropy imaging. From this detailed analysis and comparison of experiment with simulation, we determine that fluorescence polarization is maintained to depths at which meaningful intensity images can be acquired.

© 2006 Optical Society of America

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2005

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

2004

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

2003

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

C. E. Bigelow, D. L. Conover, and T. H. Foster, "Confocal fluorescence spectroscopy and anisotropy imaging system," Opt. Lett. 28, 695-697 (2003).
[CrossRef] [PubMed]

2002

X. Wang and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

2001

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, "Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy," Chem. Phys. Lett. 336, 88-96 (2001).
[CrossRef]

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

2000

S. P. Schilders and M. Gu, "Limiting factors on image quality in imaging through turbid media under single-photon and two-photon excitation," Microsc. Microanal. 6, 156-160 (2000).
[PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

M. Gu, S. P. Schilders, and X. Gan, "Two-photon fluorescence imaging of microspheres embedded in turbid media," J. Mod. Opt. 47, 959-965 (2000).
[CrossRef]

S. Bartel and A. H. Hielscher, "Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media," Appl. Opt. 39, 1580-1588 (2000).
[CrossRef]

1999

X. Gan and M. Gu, "Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media," Opt. Lett. 24, 741-743 (1999).
[CrossRef]

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

1996

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

J. M. Schmitt and K. Ben-Letaief, "Efficient Monte Carlo simulation of confocal microscopy in biological tissue," J. Opt. Soc. Am. A 13, 952-961 (1996).
[CrossRef]

1995

L. V. Wang, S. L. Jacques, and L. Zheng, "MCML: Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1994

1993

1992

A. Entwistle and M. Noble, "The use of polarization analysis in the quantification of fluorescent emission: general principles," J. Microsc. 165, 331-346 (1992).
[CrossRef]

1989

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

1988

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

1979

S. A. Allison and J. M. Schurr, "Torsion dynamics and depolarization of fluorescence of linear macromolecules. I. Theory and application to DNA," Chem. Phys. 41, 35-59 (1979).
[CrossRef]

1972

S. C. Harvey and H. C. Cheung, "Computer simulation of fluorescence depolarization due to Brownian motion," Proc. Natl. Acad. Sci. U.S.A. 69, 3670-3672 (1972).
[CrossRef] [PubMed]

1969

F. W. J. Teale, "Fluorescence depolarization by light-scattering in turbid solutions," Photochem. Photobiol. 10, 363-374 (1969).
[CrossRef] [PubMed]

T. Tao, "Time-dependent fluorescence depolarization and Brownian rotational diffusion coefficients of macromolecules," Biopolymers 8, 609-632 (1969).
[CrossRef]

Allison, S. A.

S. A. Allison and J. M. Schurr, "Torsion dynamics and depolarization of fluorescence of linear macromolecules. I. Theory and application to DNA," Chem. Phys. 41, 35-59 (1979).
[CrossRef]

Barker, M. G.

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Bartel, S.

Ben-Letaief, K.

Beretta, S.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Beth, A. H.

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

Bigelow, C. E.

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

C. E. Bigelow, D. L. Conover, and T. H. Foster, "Confocal fluorescence spectroscopy and anisotropy imaging system," Opt. Lett. 28, 695-697 (2003).
[CrossRef] [PubMed]

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

C. E. Bigelow, "Biological applications of confocal fluorescence polarization microscopy" (University of Rochester, Rochester, N.Y., 2005), http://hdl.handle.net/1802/2358.

Billinton, N.

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Blackman, S. M.

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley InterScience, 1983).

Cahill, P. A.

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

Calkins, D. J.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

Cannone, F.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Cantor, C. R.

C. R. Cantor and P. R. Schimmel, Biophysical Chemistry. Part II: Techniques for the Study of Biological Structure and Function (Freeman, 1980).

Cheung, H. C.

S. C. Harvey and H. C. Cheung, "Computer simulation of fluorescence depolarization due to Brownian motion," Proc. Natl. Acad. Sci. U.S.A. 69, 3670-3672 (1972).
[CrossRef] [PubMed]

Chirico, G.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Cobb, C. E.

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

Conover, D. L.

C. E. Bigelow, D. L. Conover, and T. H. Foster, "Confocal fluorescence spectroscopy and anisotropy imaging system," Opt. Lett. 28, 695-697 (2003).
[CrossRef] [PubMed]

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Coppey, J.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Coppey-Moisan, M.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Denjean, P.

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Diaspro, A.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Dickens, B. F.

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

Durieux, C.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Entwistle, A.

A. Entwistle and M. Noble, "The use of polarization analysis in the quantification of fluorescent emission: general principles," J. Microsc. 165, 331-346 (1992).
[CrossRef]

Federici, F.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Feld, M. S.

Fielden, P. R.

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Foster, T. H.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

C. E. Bigelow, D. L. Conover, and T. H. Foster, "Confocal fluorescence spectroscopy and anisotropy imaging system," Opt. Lett. 28, 695-697 (2003).
[CrossRef] [PubMed]

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Frelinger, J. G.

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

Gan, X.

M. Gu, S. P. Schilders, and X. Gan, "Two-photon fluorescence imaging of microspheres embedded in turbid media," J. Mod. Opt. 47, 959-965 (2000).
[CrossRef]

X. Gan and M. Gu, "Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media," Opt. Lett. 24, 741-743 (1999).
[CrossRef]

Gautier, I.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

Georgakoudi, I.

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Goddard, N. J.

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Green, V.

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

Griffiths, D. J.

D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, 1989).

Gu, M.

S. P. Schilders and M. Gu, "Limiting factors on image quality in imaging through turbid media under single-photon and two-photon excitation," Microsc. Microanal. 6, 156-160 (2000).
[PubMed]

M. Gu, S. P. Schilders, and X. Gan, "Two-photon fluorescence imaging of microspheres embedded in turbid media," J. Mod. Opt. 47, 959-965 (2000).
[CrossRef]

X. Gan and M. Gu, "Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media," Opt. Lett. 24, 741-743 (1999).
[CrossRef]

Harkrider, C. J.

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Harvey, S. C.

S. C. Harvey and H. C. Cheung, "Computer simulation of fluorescence depolarization due to Brownian motion," Proc. Natl. Acad. Sci. U.S.A. 69, 3670-3672 (1972).
[CrossRef] [PubMed]

Hielscher, A. H.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley InterScience, 1983).

Jacques, S. L.

L. V. Wang, S. L. Jacques, and L. Zheng, "MCML: Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, A Monte Carlo Model of Light Propagation in Tissue, Proc. SPIE Institute Series Vol. IS 5 (SPIE, 1989), pp. 102-111.

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, A Monte Carlo Model of Light Propagation in Tissue, Proc. SPIE Institute Series Vol. IS 5 (SPIE, 1989), pp. 102-111.

Kemnitz, K.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Knight, A. W.

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Knüttel, A.

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum, 1999).

Lavrentovich, O. D.

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, "Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy," Chem. Phys. Lett. 336, 88-96 (2001).
[CrossRef]

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Mitra, S.

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Nichols, M. G.

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Nicolas, J. C.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

Noble, M.

A. Entwistle and M. Noble, "The use of polarization analysis in the quantification of fluorescent emission: general principles," J. Microsc. 165, 331-346 (1992).
[CrossRef]

Pansu, R. B.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Pearson, B. D.

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Piston, D. W.

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, A Monte Carlo Model of Light Propagation in Tissue, Proc. SPIE Institute Series Vol. IS 5 (SPIE, 1989), pp. 102-111.

Rajadhyaksha, M.

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Rava, R. P.

Robello, M.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

Schilders, S. P.

M. Gu, S. P. Schilders, and X. Gan, "Two-photon fluorescence imaging of microspheres embedded in turbid media," J. Mod. Opt. 47, 959-965 (2000).
[CrossRef]

S. P. Schilders and M. Gu, "Limiting factors on image quality in imaging through turbid media under single-photon and two-photon excitation," Microsc. Microanal. 6, 156-160 (2000).
[PubMed]

Schimmel, P. R.

C. R. Cantor and P. R. Schimmel, Biophysical Chemistry. Part II: Techniques for the Study of Biological Structure and Function (Freeman, 1980).

Schmitt, J. M.

Schurr, J. M.

S. A. Allison and J. M. Schurr, "Torsion dynamics and depolarization of fluorescence of linear macromolecules. I. Theory and application to DNA," Chem. Phys. 41, 35-59 (1979).
[CrossRef]

Sheppard, C. J. R.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Shiyanovskii, S. V.

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, "Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy," Chem. Phys. Lett. 336, 88-96 (2001).
[CrossRef]

Smalyukh, I. I.

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, "Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy," Chem. Phys. Lett. 336, 88-96 (2001).
[CrossRef]

Snow, T. R.

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

Sun, C.-W.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Sun, F. F.

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

Tao, T.

T. Tao, "Time-dependent fluorescence depolarization and Brownian rotational diffusion coefficients of macromolecules," Biopolymers 8, 609-632 (1969).
[CrossRef]

Taylor, B. M.

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

Teale, F. W. J.

F. W. J. Teale, "Fluorescence depolarization by light-scattering in turbid solutions," Photochem. Photobiol. 10, 363-374 (1969).
[CrossRef] [PubMed]

Tong, D. M.

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

Tramier, M.

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

Vishwasrao, H. D.

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

Walmsley, R. M.

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Wang, L. V.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

L. V. Wang, S. L. Jacques, and L. Zheng, "MCML: Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Wang, X.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

Weglicki, W. B.

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

Weitz, D. A.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, A Monte Carlo Model of Light Propagation in Tissue, Proc. SPIE Institute Series Vol. IS 5 (SPIE, 1989), pp. 102-111.

Wilson, J. D.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

T. Wilson, Confocal Microscopy (Academic, 1990).

Wu, J.

Wu, Y.

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

Yadlowsky, M.

Yang, C.-C.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Zheng, L.

L. V. Wang, S. L. Jacques, and L. Zheng, "MCML: Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Zhu, J. X.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Anal. Commun.

A. W. Knight, N. J. Goddard, P. R. Fielden, M. G. Barker, N. Billinton, and R. M. Walmsley, "Fluorescence polarisation of green fluorescent protein (GFP). A strategy for improved wavelength discrimination for GFP determinations," Anal. Commun. 36, 113-117 (1999).
[CrossRef]

Appl. Opt.

Biophys. J.

S. M. Blackman, C. E. Cobb, A. H. Beth, and D. W. Piston, "The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy," Biophys. J. 71, 194-208 (1996).
[CrossRef] [PubMed]

I. Gautier, M. Tramier, C. Durieux, J. Coppey, R. B. Pansu, J. C. Nicolas, K. Kemnitz, and M. Coppey-Moisan, "Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins," Biophys. J. 80, 3000-3008 (2001).
[CrossRef] [PubMed]

Y. Wu, F. F. Sun, D. M. Tong, and B. M. Taylor, "Changes in membrane properties during energy depletion-induced cell injury studied with fluorescence microscopy," Biophys. J. 71, 91-100 (1996).
[CrossRef] [PubMed]

M. Tramier, K. Kemnitz, C. Durieux, J. Coppey, P. Denjean, R. B. Pansu, and M. Coppey-Moisan, "Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells," Biophys. J. 78, 2614-2627 (2000).
[CrossRef] [PubMed]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, "Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling," Biophys. J. 88, 2929-2938 (2005).
[CrossRef] [PubMed]

Biopolymers

T. Tao, "Time-dependent fluorescence depolarization and Brownian rotational diffusion coefficients of macromolecules," Biopolymers 8, 609-632 (1969).
[CrossRef]

Chem. Phys.

S. A. Allison and J. M. Schurr, "Torsion dynamics and depolarization of fluorescence of linear macromolecules. I. Theory and application to DNA," Chem. Phys. 41, 35-59 (1979).
[CrossRef]

Chem. Phys. Lett.

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, "Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy," Chem. Phys. Lett. 336, 88-96 (2001).
[CrossRef]

Comput. Methods Programs Biomed.

L. V. Wang, S. L. Jacques, and L. Zheng, "MCML: Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

J. Biochem. Biophys. Methods

A. W. Knight, N. J. Goddard, N. Billinton, P. A. Cahill, and R. M. Walmsley, "Fluorescence polarization discriminates green fluorescent protein from interfering autofluorescence in a microplate assay for genotoxicity," J. Biochem. Biophys. Methods 51, 165-177 (2002).
[CrossRef] [PubMed]

J. Biomed. Opt.

A. Diaspro, G. Chirico, F. Federici, F. Cannone, S. Beretta, and M. Robello, "Two-photon microscopy and spectroscopy based on a compact confocal scanning head," J. Biomed. Opt. 6, 300-310 (2001).
[CrossRef] [PubMed]

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

J. Microsc.

C. E. Bigelow, H. D. Vishwasrao, J. G. Frelinger, and T. H. Foster, "Imaging enzyme activity with polarization-sensitive confocal fluorescence microscopy," J. Microsc. 215, 24-33 (2004).
[CrossRef] [PubMed]

A. Entwistle and M. Noble, "The use of polarization analysis in the quantification of fluorescent emission: general principles," J. Microsc. 165, 331-346 (1992).
[CrossRef]

J. Mod. Opt.

M. Gu, S. P. Schilders, and X. Gan, "Two-photon fluorescence imaging of microspheres embedded in turbid media," J. Mod. Opt. 47, 959-965 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Microsc. Microanal.

S. P. Schilders and M. Gu, "Limiting factors on image quality in imaging through turbid media under single-photon and two-photon excitation," Microsc. Microanal. 6, 156-160 (2000).
[PubMed]

Mol. Cell. Biochem.

B. F. Dickens, T. R. Snow, V. Green, and W. B. Weglicki, "The effect of erythrocyte associated light scattering on membrane fluorescence polarization," Mol. Cell. Biochem. 79, 91-94 (1988).
[CrossRef] [PubMed]

Opt. Lett.

Photochem. Photobiol.

F. W. J. Teale, "Fluorescence depolarization by light-scattering in turbid solutions," Photochem. Photobiol. 10, 363-374 (1969).
[CrossRef] [PubMed]

T. H. Foster, B. D. Pearson, S. Mitra, and C. E. Bigelow, "Fluorescence anisotropy imaging reveals localization of meso-tetrahydroxyphenyl chlorin in the nuclear envelope," Photochem. Photobiol. 81, 1544-1547 (2005).
[CrossRef] [PubMed]

Phys. Rev. B

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

S. C. Harvey and H. C. Cheung, "Computer simulation of fluorescence depolarization due to Brownian motion," Proc. Natl. Acad. Sci. U.S.A. 69, 3670-3672 (1972).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

C. E. Bigelow, C. J. Harkrider, D. L. Conover, T. H. Foster, I. Georgakoudi, S. Mitra, M. G. Nichols, and M. Rajadhyaksha, "Retrofitted confocal laser scanner for a commercial inverted fluorescence microscope," Rev. Sci. Instrum. 72, 3407-3410 (2001).
[CrossRef]

Other

T. Wilson, Confocal Microscopy (Academic, 1990).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum, 1999).

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, 1989).

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, A Monte Carlo Model of Light Propagation in Tissue, Proc. SPIE Institute Series Vol. IS 5 (SPIE, 1989), pp. 102-111.

C. E. Bigelow, "Biological applications of confocal fluorescence polarization microscopy" (University of Rochester, Rochester, N.Y., 2005), http://hdl.handle.net/1802/2358.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley InterScience, 1983).

C. R. Cantor and P. R. Schimmel, Biophysical Chemistry. Part II: Techniques for the Study of Biological Structure and Function (Freeman, 1980).

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Figures (9)

Fig. 1
Fig. 1

Schematic of setup used to quantify the degradation of the measured anisotropy due to scattering at depth in turbid media.

Fig. 2
Fig. 2

Mechanics of body-fixed coordinate system rotation. (a) Light initially traveling along the z n axis is incident on a scattering particle. The photon packet is defined relative to the initial coordinate system ( x n , y n , z n ) and the scattering plane Ψ n , which contains the x n and z n axes. (b) An intermediate coordinate system is found by rotating by ϕ s about z n to yield the orientation of the new scattering plane Ψ n + 1 . (c) The final local coordinate system of the outgoing photon packet ( x n + 1 , y n + 1 , z n + 1 ) is determined by rotating through θ s about the y n + 1 axis.

Fig. 3
Fig. 3

Experimental results indicating the effect of NA and pinhole size on the fidelity of anisotropy at depth in scattering media. Both plots contain data acquired with 0.1 μ m microspheres, with (a) and (b) corresponding to the 4 × , NA 0.13 objective and the 10 × , NA 0.45 objective, respectively. Pinhole diameter v p is given relative to the optimal size

Fig. 4
Fig. 4

Experimental results indicating the effect of the scattering phase function on the fidelity of anisotropy at depth in scattering media. Both plots contain data acquired with the 10 × , 0.45 NA objective. Pinhole radius v p is given relative to the optimal size v 0 .

Fig. 5
Fig. 5

Monte Carlo simulations of the anisotropy returned from a planar fluorescent target located 100 μ m into an aqueous suspension of 0.1 μ m diameter microspheres and imaged with a 0.45 NA objective. (a) The effect on r of increasing the pinhole diameter from 1 to 1000 times the optimal value. (b) The mean value of r from (a) along with the mean number of scattering events experienced by excitation and fluorescence photons for each pinhole size. (c) and (d) Histograms of the number of scattering events for each pinhole size for the excitation (Ex) and fluorescence (Em), respectively. Error bars are standard error of the mean.

Fig. 6
Fig. 6

Monte Carlo simulations of the anisotropy returned from a planar fluorescent target located 100 μ m into an aqueous suspension of 0.511 μ m diameter microspheres and imaged with a 0.45 NA objective. In (a)–(d) the parameters are the same as those in Figs. 5a, 5b, 5c, 5d.

Fig. 7
Fig. 7

Monte Carlo simulations of the anisotropy returned from a planar fluorescent target located 200 μ m into an aqueous suspension of 0.511 μ m diameter microspheres and imaged with a 0.45 NA objective. In (a)–(d) the parameters are the same as those in Figs. 5a, 5b, 5c, 5d.

Fig. 8
Fig. 8

Monte Carlo results illustrating the change in the mean number of scattering events experienced by excitation photons that lead to detected fluorescence photons for a given pinhole size. Results are plotted for both 0.1 and 0.511 μ m beads with a target located at a depth of 100 μ m . (a) The ratio of the number of photons scattered once ( N 1 ) to the number of ballistic (unscattered) photons ( N 0 ) . (b) The ratio of the number of photons scattered ten times, N 10 , to the number of ballistic photons. The inset contains a rescaled plot of the results for v p 100 v 0 to reveal differences between the two bead sizes in this range. (c) The mean anisotropy as a function of pinhole size for suspensions of both bead sizes. Error bars are standard error of the mean.

Fig. 9
Fig. 9

Monte Carlo simulations of the uncertainty in r measurements as a function of pinhole size. The mean anisotropy and standard error of the mean (SEM) are shown for a target 100 μ m deep into an aqueous suspension of 0.511 μ m diameter polystyrene microspheres.

Tables (1)

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Table 1 Parameters Used in Monte Carlo Simulation of the Fluorophore-Containing Rod in an Aqueous Suspension of Polystyrene Microspheres a

Equations (16)

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r = I I I + 2 I .
η ( ω ) = a b ( a 2 sin 2 ω + b 2 cos 2 ω ) 1 2 ,
P { 0 ω Ω } = 0 Ω ( a b ) 2 a 2 sin 2 ( ω ) + b 2 cos 2 ( ω ) d ω 0 π 2 ( a b ) 2 a 2 sin 2 ( ω ) + b 2 cos 2 ( ω ) d ω = 2 π tan 1 ( a b tan ( Ω ) ) .
p ( θ b , t ) = 1 4 π τ [ 1 + exp ( t τ r ) ( 3 cos 2 θ b 1 ) ] exp ( t τ ) ,
t = τ ln ξ .
p ( θ b t ) = 1 2 [ 1 + exp ( t τ r ) ( 3 cos 2 θ b 1 ) ] .
P { 0 ϑ θ b } = 1 2 [ 1 + ( exp ( t τ r ) 4 1 ) cos θ b exp ( t τ r ) 4 cos 3 θ b ] .
3 4 0 θ d sin 2 ϑ sin ϑ d ϑ = ξ .
r total = n r n i n = n r n ( 3 I n Q n ) 2 T i ,
d W ( θ b , ϕ b , t ) d t = D rot 2 W ( θ b , ϕ b , t ) ,
W ( θ b , ϕ b , t ) = 0 2 π d ϕ b , 0 0 π sin θ b , 0 W ( θ b , 0 , ϕ b , 0 ) G ( θ b , 0 , ϕ b , 0 θ b , ϕ b , t ) d θ b , 0 ,
G ( θ b , 0 , ϕ b , 0 θ b , ϕ b , t ) = l = 0 m = l l c l ( t ) Y l , m * ( θ b , 0 , ϕ b , 0 ) Y l , m ( θ b , ϕ b ) ,
W ( θ b , 0 , ϕ b , 0 , 0 ) = 3 4 π cos 2 θ b , 0 = 1 4 π [ 1 + 2 P 2 ( cos θ b , 0 ) ] .
W ( θ b , ϕ b , t ) = 1 4 π [ 1 + 2 exp ( t τ r ) P 2 ( cos θ ) ] .
Γ ( θ b , ϕ b , t ) = W ( θ b , ϕ b , t ) exp ( t τ ) = 1 4 π [ 1 + 2 exp ( t τ r ) P 2 ( cos θ b ) ] exp ( t τ ) ,
p ( θ b , t ) = 1 4 π τ [ 1 + exp ( t τ r ) ( 3 cos 2 θ b 1 ) ] exp ( t τ ) ,

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