Abstract

Light is being detected by the two distinct types of photoreceptors in the human retina: cones and rods. Before light arrives at the photoreceptors, it must traverse the whole retina, along its array of higher-index Müller cells serving as natural waveguides. Here we analyze this optical process of light propagation through Müller cells by two independent optical methods: numerical beam propagation and analytical modal analysis. We show that the structure and refractive index profile of the Müller cells create a unique spatio-spectral distribution of light. This distribution corresponds to the positions and spectral sensitivities of both cones and rods to improve their light absorption.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (1)

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
[Crossref] [PubMed]

2013 (2)

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

G. Westheimer, “Retinal light distributions, the Stiles-Crawford effect and apodization,” J. Opt. Soc. Am. A 30(7), 1417–1421 (2013).
[Crossref] [PubMed]

2011 (1)

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

2010 (2)

A. M. Labin and E. N. Ribak, “Retinal glial cells enhance human vision acuity,” Phys. Rev. Lett. 104(15), 158102 (2010).
[Crossref] [PubMed]

V. G. Kravets and A. N. Grigorenko, “Retinal light trapping in textured photovoltaic cells,” Appl. Phys. Lett. 97(14), 143701 (2010).
[Crossref]

2007 (1)

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

2005 (1)

1999 (1)

A. Roorda and D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature 397(6719), 520–522 (1999).
[Crossref] [PubMed]

1997 (1)

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

1981 (1)

1973 (2)

A. W. Snyder and C. Pask, “The Stiles-Crawford effect - explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13(12), 2185–2194 (1973).
[Crossref] [PubMed]

1972 (1)

W. H. Miller and A. W. Snyder, “Optical function of myoids,” Vision Res. 12(11), 1841–1848 (1972).
[Crossref] [PubMed]

1971 (1)

1964 (1)

P. K. Brown and G. Wald, “Visual pigments in single rods and cones of the human retina,” Science 144(3614), 45–52 (1964).
[Crossref] [PubMed]

Agte, S.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Artal, P.

Biedermann, B.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Brown, P. K.

P. K. Brown and G. Wald, “Visual pigments in single rods and cones of the human retina,” Science 144(3614), 45–52 (1964).
[Crossref] [PubMed]

Buse, E.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Chao, T. I.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Drommer, W.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Erdmann, I.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Faude, F.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Foja, C.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Francke, M.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Franze, K.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Friedrich, K. J.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Fujii, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Gloge, D.

Grigorenko, A. N.

V. G. Kravets and A. N. Grigorenko, “Retinal light trapping in textured photovoltaic cells,” Appl. Phys. Lett. 97(14), 143701 (2010).
[Crossref]

Grosche, J.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Guck, J.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Hiramoto, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Iglesias, I.

Junek, S.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Käs, J. A.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Kasper, M.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Kravets, V. G.

V. G. Kravets and A. N. Grigorenko, “Retinal light trapping in textured photovoltaic cells,” Appl. Phys. Lett. 97(14), 143701 (2010).
[Crossref]

Kuhrt, H.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Labin, A. M.

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
[Crossref] [PubMed]

A. M. Labin and E. N. Ribak, “Retinal glial cells enhance human vision acuity,” Phys. Rev. Lett. 104(15), 158102 (2010).
[Crossref] [PubMed]

Lagasse, P. E.

Matthias, S.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Miller, W. H.

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13(12), 2185–2194 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of myoids,” Vision Res. 12(11), 1841–1848 (1972).
[Crossref] [PubMed]

Mühle, C.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Nakamura, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Nishiwaki, S.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Pannicke, T.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Pask, C.

A. W. Snyder and C. Pask, “The Stiles-Crawford effect - explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973).
[Crossref] [PubMed]

Perlman, I.

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
[Crossref] [PubMed]

Pritz-Hohmeier, S.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Reichelt, W.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Reichenbach, A.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Ribak, E. N.

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
[Crossref] [PubMed]

A. M. Labin and E. N. Ribak, “Retinal glial cells enhance human vision acuity,” Phys. Rev. Lett. 104(15), 158102 (2010).
[Crossref] [PubMed]

Roorda, A.

A. Roorda and D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature 397(6719), 520–522 (1999).
[Crossref] [PubMed]

Safuri, S. K.

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
[Crossref] [PubMed]

Schild, D.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Schinkinger, S.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Skatchkov, S. N.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and C. Pask, “The Stiles-Crawford effect - explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13(12), 2185–2194 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of myoids,” Vision Res. 12(11), 1841–1848 (1972).
[Crossref] [PubMed]

Suzuki, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Travis, K.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Uckermann, O.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Ulbricht, E.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
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van der Donk, J.

Van Roey, J.

Vohnsen, B.

Wald, G.

P. K. Brown and G. Wald, “Visual pigments in single rods and cones of the human retina,” Science 144(3614), 45–52 (1964).
[Crossref] [PubMed]

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A. Roorda and D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature 397(6719), 520–522 (1999).
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Wulst, M.

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

Wurm, A.

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

V. G. Kravets and A. N. Grigorenko, “Retinal light trapping in textured photovoltaic cells,” Appl. Phys. Lett. 97(14), 143701 (2010).
[Crossref]

Biophys. J. (1)

S. Agte, S. Junek, S. Matthias, E. Ulbricht, I. Erdmann, A. Wurm, D. Schild, J. A. Käs, and A. Reichenbach, “Müller Glial Cell-Provided Cellular Light Guidance through the Vital Guinea-Pig Retina,” Biophys. J. 101(11), 2611–2619 (2011).
[Crossref] [PubMed]

J. Neurocytol. (1)

T. I. Chao, J. Grosche, K. J. Friedrich, B. Biedermann, M. Francke, T. Pannicke, W. Reichelt, M. Wulst, C. Mühle, S. Pritz-Hohmeier, H. Kuhrt, F. Faude, W. Drommer, M. Kasper, E. Buse, and A. Reichenbach, “Comparative studies on mammalian Müller (retinal glial) cells,” J. Neurocytol. 26(7), 439–454 (1997).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nat. Commun. (1)

A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5, 4319 (2014).
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Nat. Photonics (1)

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 248–254 (2013).
[Crossref]

Nature (1)

A. Roorda and D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature 397(6719), 520–522 (1999).
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A. M. Labin and E. N. Ribak, “Retinal glial cells enhance human vision acuity,” Phys. Rev. Lett. 104(15), 158102 (2010).
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Proc. Natl. Acad. Sci. U.S.A. (1)

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Muller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. U.S.A. 104(20), 8287–8292 (2007).
[Crossref] [PubMed]

Science (1)

P. K. Brown and G. Wald, “Visual pigments in single rods and cones of the human retina,” Science 144(3614), 45–52 (1964).
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Other (3)

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, Wiley-VCH (2000).

A. Reichenbach, and, A. Bringmann, Müller Cells in the Healthy and Diseased Retina (Springer 2010).

K. Okamoto, Fundamentals of Optical Waveguides, Academic Press (2006).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic representation of the photoreceptors layer. The high sensitivity rods (represented in orange) surround the lower sensitivity cones, with three spectral peak sensitivities: blue (430nm), green (530nm) and red-yellow (560nm). (b) Side view of the retina, where the Müller cells concentrate and channel light from the top layer to the photoreceptors, down from a ~12 µm diameter into a cone of 2.4 µm diameter. (c) Refractive index profile of a human Müller cell and vicinity neurons, and (d) the corresponding structure. The refractive index in the cell is higher than its surrounding by ~1%-3%.
Fig. 2
Fig. 2 (a) Light intensity distribution propagating along a Müller cell for blue (450 nm), green (530 nm) and red (650 nm) wavelengths (notice different scales). (b) Light intensity inside Müller cells (normalized to the input power), as a function of propagation distance along the cell (~130 µm) for the same three colors. Most of the energy leaks out to the surrounding rods during propagation. The waveguide confinement of green light (delivered to the cone) is higher than the corresponding red and blue. (c) Normalized light intensity as function of propagation distance inside the cell for 25 wavelengths.
Fig. 3
Fig. 3 RGB representation of Müller cell’s light transmission. (a) The spatial distributions at the bottom of a Müller cell for 25 discrete wavelengths (three shown). (b) CIE standard observer color matching functions (xyz) used for a transformation from wavelengths to RGB. (c) True color spatial distribution at the bottom of a Müller cell, reconstructed by composing the red, green and blue distributions. High concentration of medium wavelengths into the center is evident.
Fig. 4
Fig. 4 Spectral transmission by a human Müller cell: modal analysis (left) and BPM (right). (a) Mode power confined within the cell’s core (mean radius 1.2 µm, no funnel), normalized by the total power for the mode. (b) Normalized total core power (summed over all modes) for a characteristic distribution of cells widths (1-1.4 µm), only for the cylindrical constant width part of the cell. (c) Transmission within the whole cell obtained by BPM for normal incidence (blue curve) and averaged tilted field (red curve) for the whole cell. (d) Normalized total intensity for the characteristic cell’s radius distribution obtained by the BPM for normal-incidence field (average of 20 realizations each).

Equations (6)

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2 E( r ¯ )+ k 2 n 2 E( r ¯ )=0.
φ z =i 1 2k n 0 2 φik( n n 0 )φ.
Ai 1 2k n 0 2 ; Bik( n n 0 ).
φ z =(A+B)φ.
φ(z+h,r)= F 1 [ e A f h F{ e Bh φ(z,r)}],
h J l+1 (ha) J l (ha) =q K l+1 (qa) K l (qa) ,

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