Abstract

Decades of experimental and theoretical investigations have established that photoreceptors capture light based on the principles of optical waveguiding. Yet considerable uncertainty remains, even for the most basic prediction as to whether photoreceptors support more than a single waveguide mode. To test for modal behavior in human cone photoreceptors in the near infrared, we took advantage of adaptive-optics optical coherence tomography (AO-OCT, λc = 785 nm) to noninvasively image in three dimensions the reflectance profile of cones. Modal content of reflections generated at the cone inner segment and outer segment junction (IS/OS) and cone outer segment tip (COST) was examined over a range of cone diameters in 1,802 cones from 0.6° to 10° retinal eccentricity. Second moment analysis in conjunction with theoretical predictions indicate cone IS and OS have optical properties consistent of waveguides, which depend on segment diameter and refractive index. Cone IS was found to support a single mode near the fovea (≤3°) and multiple modes further away (>4°). In contrast, no evidence of multiple modes was found in the cone OSs. The IS/OS and COST reflections share a common optical aperture, are most circular near the fovea, show no orientation preference, and are temporally stable. We tested mode predictions of a conventional step-index fiber model and found that in order to fit our AO-OCT results required a lower estimate of the IS refractive index and introduction of an IS focusing/tapering effect.

© 2015 Optical Society of America

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References

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2015 (2)

Z. Liu, O. P. Kocaoglu, T. L. Turner, and D. T. Miller, “Imaging modal content of cone photoreceptors using adaptive optics optical coherence tomography,” Proc. SPIE 9307, 930712 (2015).
[Crossref]

J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

2014 (3)

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
[Crossref] [PubMed]

F. Felberer, J. S. Kroisamer, B. Baumann, S. Zotter, U. Schmidt-Erfurth, C. K. Hitzenberger, and M. Pircher, “Adaptive optics SLO/OCT for 3D imaging of human photoreceptors in vivo,” Biomed. Opt. Express 5(2), 439–456 (2014).
[Crossref] [PubMed]

T. Liu, L. Thibos, G. Marin, and M. Hernandez, “Evaluation of a global algorithm for wavefront reconstruction for Shack-Hartmann wave-front sensors and thick fundus reflectors,” Ophthalmic Physiol. Opt. 34(1), 63–72 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (2)

2011 (2)

2010 (1)

T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
[Crossref] [PubMed]

2009 (6)

2008 (5)

2007 (2)

2005 (3)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
[Crossref]

B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. Soc. Am. A 22(11), 2318–2328 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (2)

A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vis. 2(5), 404–412 (2002).
[Crossref] [PubMed]

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, “Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation,” Vis. Neurosci. 19(4), 395–407 (2002).
[Crossref] [PubMed]

1999 (1)

1998 (1)

1997 (1)

J. M. Gorrand and F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44(3), 473–491 (1997).
[Crossref]

1996 (1)

J. van de Kraats, T. T. Berendschot, and D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36(15), 2229–2247 (1996).
[Crossref] [PubMed]

1995 (1)

1994 (1)

1993 (1)

1991 (2)

M. S. Banks, A. B. Sekuler, and S. J. Anderson, “Peripheral spatial vision: limits imposed by optics, photoreceptors, and receptor pooling,” J. Opt. Soc. Am. A 8(11), 1775–1787 (1991).
[Crossref] [PubMed]

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

1990 (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref] [PubMed]

1988 (1)

1987 (1)

1980 (2)

1978 (1)

A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. A 68(3), 297–309 (1978).
[Crossref]

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]

1963 (1)

J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. A 53(1), 71–85 (1963).
[Crossref]

1956 (1)

B. K. Johnson and K. Tansley, “The cones of the grass snake’s eye,” Nature 178(4545), 1285–1286 (1956).
[Crossref] [PubMed]

1951 (1)

1949 (1)

1946 (1)

1933 (1)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond. B Biol. Sci. 112(778), 428–450 (1933).
[Crossref]

Abouraddy, A. F.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Allen, K. A.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

Anderson, S. J.

Applegate, R. A.

Artal, P.

Baek, S.

Banks, M. S.

Baumann, B.

Bengtsson, J.

Berendschot, T. T.

T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
[Crossref] [PubMed]

J. van de Kraats, T. T. Berendschot, and D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36(15), 2229–2247 (1996).
[Crossref] [PubMed]

Birks, T. A.

Borghi, R.

Brambilla, G.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Bruning, R.

J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

Burns, S. A.

Calvo, M. L.

Carroll, J.

Cense, B.

Chen, C. L.

Chen, Z.

Chui, T. Y.

Chui, Y. T.

Chung, C. K.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, “Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation,” Vis. Neurosci. 19(4), 395–407 (2002).
[Crossref] [PubMed]

Codemard, C.

Cooper, R. F.

Crawford, B. H.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond. B Biol. Sci. 112(778), 428–450 (1933).
[Crossref]

Curcio, C. A.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, “Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation,” Vis. Neurosci. 19(4), 395–407 (2002).
[Crossref] [PubMed]

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref] [PubMed]

Delori, F.

Delori, F. C.

J. M. Gorrand and F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44(3), 473–491 (1997).
[Crossref]

Derby, J. C.

Ditto, D.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
[Crossref]

Doly, M.

Dubis, A. M.

Dubra, A.

Duparre, M.

J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

Duparré, M.

Easter, S. S.

Elsner, A. E.

Engheta, N.

Enoch, J. M.

J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. A 53(1), 71–85 (1963).
[Crossref]

Fang, Z.

Felberer, F.

Feng, X.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Flamm, D.

Francia, G. T. D.

Gao, W.

Ghalmi, S.

Gori, F.

Gorrand, J. M.

J. M. Gorrand and M. Doly, “Alignment parameters of foveal cones,” J. Opt. Soc. Am. A 26(5), 1260–1267 (2009).
[Crossref] [PubMed]

J. M. Gorrand and F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44(3), 473–491 (1997).
[Crossref]

Guattari, G.

Halme, S. J.

He, J. C.

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref] [PubMed]

Herde, A. E.

Hernandez, M.

T. Liu, L. Thibos, G. Marin, and M. Hernandez, “Evaluation of a global algorithm for wavefront reconstruction for Shack-Hartmann wave-front sensors and thick fundus reflectors,” Ophthalmic Physiol. Opt. 34(1), 63–72 (2014).
[Crossref] [PubMed]

Hitzenberger, C. K.

Hoang, Q. V.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, “Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation,” Vis. Neurosci. 19(4), 395–407 (2002).
[Crossref] [PubMed]

Horak, P.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Hurley, J. B.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

Iglesias, I.

Jeong, Y.

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
[Crossref] [PubMed]

Johnson, B. K.

B. K. Johnson and K. Tansley, “The cones of the grass snake’s eye,” Nature 178(4545), 1285–1286 (1956).
[Crossref] [PubMed]

Jonnal, R. S.

Jung, Y. M.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Kaiser, T.

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref] [PubMed]

Kanis, M. J.

T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
[Crossref] [PubMed]

Klock, I. B.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

Knight, J. C.

Kocaoglu, O. P.

Koizumi, F.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Koukharenko, E.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
[Crossref]

Kroisamer, J. S.

Lakshminarayanan, V.

Lee, J.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
[Crossref]

Lee, S.

Lee, S. H.

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
[Crossref] [PubMed]

S. H. Lee, J. S. Werner, and R. J. Zawadzki, “Improved visualization of outer retinal morphology with aberration cancelling reflective optical design for adaptive optics - optical coherence tomography,” Biomed. Opt. Express 4(11), 2508–2517 (2013).
[Crossref] [PubMed]

Lerea, C. L.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

Li, X.

Liang, F.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
[Crossref]

Linsenmeier, R. A.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, “Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation,” Vis. Neurosci. 19(4), 395–407 (2002).
[Crossref] [PubMed]

Liu, T.

T. Liu, L. Thibos, G. Marin, and M. Hernandez, “Evaluation of a global algorithm for wavefront reconstruction for Shack-Hartmann wave-front sensors and thick fundus reflectors,” Ophthalmic Physiol. Opt. 34(1), 63–72 (2014).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, O. P. Kocaoglu, T. L. Turner, and D. T. Miller, “Imaging modal content of cone photoreceptors using adaptive optics optical coherence tomography,” Proc. SPIE 9307, 930712 (2015).
[Crossref]

Z. Liu, O. P. Kocaoglu, and D. T. Miller, “In-the-plane design of an off-axis ophthalmic adaptive optics system using toroidal mirrors,” Biomed. Opt. Express 4(12), 3007–3029 (2013).
[Crossref] [PubMed]

Marcos, S.

Marin, G.

T. Liu, L. Thibos, G. Marin, and M. Hernandez, “Evaluation of a global algorithm for wavefront reconstruction for Shack-Hartmann wave-front sensors and thick fundus reflectors,” Ophthalmic Physiol. Opt. 34(1), 63–72 (2014).
[Crossref] [PubMed]

Milam, A. H.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

Miller, D. T.

Z. Liu, O. P. Kocaoglu, T. L. Turner, and D. T. Miller, “Imaging modal content of cone photoreceptors using adaptive optics optical coherence tomography,” Proc. SPIE 9307, 930712 (2015).
[Crossref]

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
[Crossref] [PubMed]

Z. Liu, O. P. Kocaoglu, and D. T. Miller, “In-the-plane design of an off-axis ophthalmic adaptive optics system using toroidal mirrors,” Biomed. Opt. Express 4(12), 3007–3029 (2013).
[Crossref] [PubMed]

R. S. Jonnal, O. P. Kocaoglu, Q. Wang, S. Lee, and D. T. Miller, “Phase-sensitive imaging of the outer retina using optical coherence tomography and adaptive optics,” Biomed. Opt. Express 3(1), 104–124 (2012).
[Crossref] [PubMed]

O. P. Kocaoglu, S. Lee, R. S. Jonnal, Q. Wang, A. E. Herde, J. C. Derby, W. Gao, and D. T. Miller, “Imaging cone photoreceptors in three dimensions and in time using ultrahigh resolution optical coherence tomography with adaptive optics,” Biomed. Opt. Express 2(4), 748–763 (2011).
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W. Gao, R. S. Jonnal, B. Cense, O. P. Kocaoglu, Q. Wang, and D. T. Miller, “Measuring directionality of the retinal reflection with a Shack-Hartmann wavefront sensor,” Opt. Express 17(25), 23085–23097 (2009).
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W. Gao, B. Cense, Y. Zhang, R. S. Jonnal, and D. T. Miller, “Measuring retinal contributions to the optical Stiles-Crawford effect with optical coherence tomography,” Opt. Express 16(9), 6486–6501 (2008).
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Miller, W. H.

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13(12), 2185–2194 (1973).
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G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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Nicholson, J. W.

Nilsson, J.

O’Brien, B.

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

Philippov, V.

Pircher, M.

Pugh, E. N.

Qi, X.

Ramachandran, S.

Reichard, K.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
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Rha, J.

Richardson, D. J.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vis. 2(5), 404–412 (2002).
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Ruffin, P.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
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Saijonmaa, J.

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Schmidt-Erfurth, U.

Schroter, S.

J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

Schröter, S.

Schulze, C.

J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

Sekuler, A. B.

Sessions, N. P.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005).
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Sharma, A. B.

Sloan, K. R.

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
[Crossref] [PubMed]

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
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Snyder, A. W.

A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. A 68(3), 297–309 (1978).
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A. W. Snyder and C. Pask, “The Stiles-Crawford effect--explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973).
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W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13(12), 2185–2194 (1973).
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Song, H.

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B. K. Johnson and K. Tansley, “The cones of the grass snake’s eye,” Nature 178(4545), 1285–1286 (1956).
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Teague, M. R.

Thibos, L.

T. Liu, L. Thibos, G. Marin, and M. Hernandez, “Evaluation of a global algorithm for wavefront reconstruction for Shack-Hartmann wave-front sensors and thick fundus reflectors,” Ophthalmic Physiol. Opt. 34(1), 63–72 (2014).
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Turner, T. L.

Z. Liu, O. P. Kocaoglu, T. L. Turner, and D. T. Miller, “Imaging modal content of cone photoreceptors using adaptive optics optical coherence tomography,” Proc. SPIE 9307, 930712 (2015).
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T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
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T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
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J. van de Kraats, T. T. Berendschot, and D. van Norren, “The pathways of light measured in fundus reflectometry,” Vision Res. 36(15), 2229–2247 (1996).
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Wadsworth, W. J.

Wang, Q.

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R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
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S. H. Lee, J. S. Werner, and R. J. Zawadzki, “Improved visualization of outer retinal morphology with aberration cancelling reflective optical design for adaptive optics - optical coherence tomography,” Biomed. Opt. Express 4(11), 2508–2517 (2013).
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J. Wilde, C. Schulze, R. Bruning, M. Duparre, and S. Schroter, “Selective higher order fiber mode excitation using a monolithic setup of a phase plate at a fiber facet,” Proc. SPIE 9343, 93431P (2015).

Wilkinson, J. S.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vis. 2(5), 404–412 (2002).
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Witkowska, A.

Wu, S.

Xu, F.

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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Yablon, A. D.

Yang, Y.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
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Yin, S. Z.

Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, “Fabrication and implementation of a multi-to-single mode converter based on a tapered multimode fiber,” Opt. Commun. 249(1-3), 129–137 (2005).
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Yin, X.

Young, W. R.

A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. A 68(3), 297–309 (1978).
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Zawadzki, R. J.

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
[Crossref] [PubMed]

S. H. Lee, J. S. Werner, and R. J. Zawadzki, “Improved visualization of outer retinal morphology with aberration cancelling reflective optical design for adaptive optics - optical coherence tomography,” Biomed. Opt. Express 4(11), 2508–2517 (2013).
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Zhang, Y.

Zhao, L.

Zhao, Y.

Zotter, S.

Adv. Opt. Photonics (1)

G. Brambilla, F. Xu, P. Horak, Y. M. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photonics 1(1), 107–161 (2009).
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Appl. Opt. (3)

Biomed. Opt. Express (7)

R. F. Cooper, A. M. Dubis, A. Pavaskar, J. Rha, A. Dubra, and J. Carroll, “Spatial and temporal variation of rod photoreceptor reflectance in the human retina,” Biomed. Opt. Express 2(9), 2577–2589 (2011).
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Y. N. Sulai and A. Dubra, “Adaptive optics scanning ophthalmoscopy with annular pupils,” Biomed. Opt. Express 3(7), 1647–1661 (2012).
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Z. Liu, O. P. Kocaoglu, and D. T. Miller, “In-the-plane design of an off-axis ophthalmic adaptive optics system using toroidal mirrors,” Biomed. Opt. Express 4(12), 3007–3029 (2013).
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O. P. Kocaoglu, S. Lee, R. S. Jonnal, Q. Wang, A. E. Herde, J. C. Derby, W. Gao, and D. T. Miller, “Imaging cone photoreceptors in three dimensions and in time using ultrahigh resolution optical coherence tomography with adaptive optics,” Biomed. Opt. Express 2(4), 748–763 (2011).
[Crossref] [PubMed]

R. S. Jonnal, O. P. Kocaoglu, Q. Wang, S. Lee, and D. T. Miller, “Phase-sensitive imaging of the outer retina using optical coherence tomography and adaptive optics,” Biomed. Opt. Express 3(1), 104–124 (2012).
[Crossref] [PubMed]

S. H. Lee, J. S. Werner, and R. J. Zawadzki, “Improved visualization of outer retinal morphology with aberration cancelling reflective optical design for adaptive optics - optical coherence tomography,” Biomed. Opt. Express 4(11), 2508–2517 (2013).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (1)

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S. H. Lee, J. S. Werner, and D. T. Miller, “The cellular origins of the outer retinal bands in optical coherence tomography images,” Invest. Ophthalmol. Vis. Sci. 55(12), 7904–7918 (2014).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

T. T. Berendschot, J. van de Kraats, M. J. Kanis, and D. van Norren, “Directional model analysis of the spectral reflection from the fovea and para-fovea,” J. Biomed. Opt. 15(6), 065005 (2010).
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J. Comp. Neurol. (2)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref] [PubMed]

C. A. Curcio, K. A. Allen, K. R. Sloan, C. L. Lerea, J. B. Hurley, I. B. Klock, and A. H. Milam, “Distribution and morphology of human cone photoreceptors stained with anti-blue opsin,” J. Comp. Neurol. 312(4), 610–624 (1991).
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J. Opt. Soc. Am. (4)

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J. Vis. (1)

A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vis. 2(5), 404–412 (2002).
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Nature (1)

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Supplementary Material (1)

NameDescription
» Visualization 1: AVI (5598 KB)      A fly through movie of the volume at 7° temporal retina is shown in Media 1, restricted to the photoreceptor and RPE layers. A projected log B-scan is included next to the linear en face, which is globally normalized.

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Figures (14)

Fig. 1
Fig. 1 Cone model. (a) Simplistic cone model composed of two cylinders, IS and OS, of homogeneous refractive index and surrounded by interphotoreceptor matrix. (b) Cone segment diameters (solid curves) [30, 31] and theoretical V numbers (dashed curves) increase monotonically as function of retinal eccentricity for IS (red) and OS (blue). V number was calculated from V = π d i , o λ n i , o 2 n s 2 , where di,o is the cone IS or OS diameter, ni,o is the refractive index of IS or OS, ns is the refractive index of interphotoreceptor matrix, and λ is the wavelength, 785 nm for this study. V number predicts the mode cutoff frequencies of the cone model, as for example when V<2.405, all modes with exception of fundamental LP01 mode are cut off. Linear polarized (LP) modes are a common descriptor for circularly symmetric waveguides and often used to characterize cone photoreceptor models [13], as was done here.
Fig. 2
Fig. 2 Representative AO-OCT en face projections through the IS/OS and COST layers at 3° retinal eccentricity for three different focus levels: (left) 0.05 D, (middle) 0.15 D, and (right) 0.25 D. Positive focus corresponds to a vitreal focal shift.
Fig. 3
Fig. 3 Power spectra analysis to determine optimal focus for cone imaging. (a) Circumferentially-averaged power of the (left) IS/OS and (right) COST layers for 16 different levels of focus (−0.125 D to 0.25 D), which are color coded. Positive focus corresponds to a vitreal shift relative to zero diopters reported by the SHWS after AO correction. (b) Power at the cone fundamental frequency is plotted as a function of system focus averaged across eight retinal eccentricities on two subjects. Power for each retinal eccentricity was determined from the circumferentially-averaged power spectra of the IS/OS (red) and COST (blue) layers, as for example those in (a). Error bar denotes standard error.
Fig. 4
Fig. 4 (Visualization 1) Representative AO-OCT images of cone photoreceptors with best focus at 0.6°, 3°, 7° and 10° temporal to fovea. Top and bottom rows show the reflectance from the IS/OS and COST layers of the same volume. Colored labels denote IS/OS and COST reflections of the same cone. Note that the scale of enlarged cones below each cone mosaic image varies with retinal eccentricity. A fly through movie of the volume at 7° temporal retina is shown in Media 1, restricted to the photoreceptor and RPE layers. A projected log B-scan is included next to the linear en face, which is globally normalized.
Fig. 5
Fig. 5 Average (Mode) and variance (Var) maps of the IS/OS and COST reflections. Maps were computed from the 50 to 100 cones selected at each retinal eccentricity and share the same color bar (bottom right).
Fig. 6
Fig. 6 Second moment analysis applied to the waveguided LP modes predicted for the circular ISs of cones at 7° temporal retina. (a) Shown are the theoretical en face intensity distributions of Ex for the six modes supported by cone IS. Second moment analysis gives (b) second moment value, (c) circularity, and (d) orientation. Note (b-d) results are color coded with the six modes in (a).
Fig. 7
Fig. 7 Second moment value s as function of retinal eccentricity for subjects (symbols) and predicted modes of the step index fiber model described in Fig. 1 (curves). Second moments are for the IS/OS (red) and COST (blue) reflections. Solid symbols are the average s of cones at each retinal eccentricity. Open symbols are s of the average cone. Error bars denote standard error for the selected 50 to 100 cones per retinal eccentricity. The red and blue curves are theoretical predictions of LP01 (dash) and LP11 (solid) modes for IS and OS, respectively. As shown, LP11 for IS is not supported below 2° retinal eccentricity.
Fig. 8
Fig. 8 Cone circularity (c) as function of retinal eccentricity, subject, and photoreceptor reflection: IS/OS (red) and COST (blue). Solid symbols are average of c for the selected 50 to 100 cones per retinal eccentricity. Open symbols are c of the average cone. Error bars denote standard error.
Fig. 9
Fig. 9 Cone orientation (θ) as function of retinal eccentricity, subject, and photoreceptor reflection: IS/OS (red) and COST (blue). Black circles denote mean for the selected 50 to 100 cones per retinal eccentricity.
Fig. 10
Fig. 10 En face spacing and size of the cone reflections. (a) Fovea cone projection through IS/OS and COST is shown with foveal center at bottom left corner of image. (b) Cone OS spot size is shown as measured by visual inspection (solid circles) and by converting second moment size to an equivalent diameter, 2 × s (open circles) (see main text). For comparison the histology OS (blue trace) and IS (red trace) diameters from Fig. 1(b) are replotted. Error bars denote standard error.
Fig. 11
Fig. 11 Temporal stability of the IS/OS reflection of individual cones as imaged with AO-OCT. A total of 12 cones are shown, each imaged six times over a ~2.5 s duration. See text for details.
Fig. 12
Fig. 12 Predicted coupling efficiency into cone IS modes as a function of AO-OCT beam offset in the cone IS aperture. False colored images are shown of the (left) modeled AO-OCT beam profile at the cone aperture, (middle) predicted modes LP01 and LP11 supported by the cone IS with c of 0.75, and (right) predicted coupling efficiency into the cone IS as a function of beam offset and mode. Solid white line denotes edge of cone IS. Double arrow indicates the polarization orientation, which is parallel to the major axis of cone. See text for details.
Fig. 13
Fig. 13 (a) Modified cone model to test hypotheses one and two. (b-c) Test of hypothesis one by determining values of IS diameter, d, and refractive index, ni, that allow the predicted and measured second moment size s to match. Three retinal eccentricities were selected. Predicted size was computed from a step-index fiber model. (b) Colored curves are model predictions of s for (dashed) LP01 and (solid) LP11 modes. Each color denotes a unique IS diameter (2.5-7.4 μm). Not all combinations of d and ni support LP01 and LP11 modes, thus the curves are of different lengths. The horizontal gray bands correspond to the measured second moments at 0.6°, 3°, and 8.5° eccentricities from Fig. 8 with band widths equal to the stand errors in the same figure. For comparison of d values, the histologic IS diameters at the three eccentricities are given in parentheses. (c) To summarize the results of (b), colored polygons superimposed on the d-versus-ni plot enclose the combinations of d and ni values in (b) that enable the predicted s to equal the measured s. The two black curves are the theoretical V number cutoff for LP11 (solid) and LP21, 02 (dashed) modes.
Fig. 14
Fig. 14 Test of hypothesis two. Testing centered on determining a common ni that allows predicted second moment size s and mode profile to match those of the measured IS/OS reflection for three retinal eccentricities: 0.6°, 3° and 8.5°. For ni axis, ns was fixed at 1.347. (a) Predicted size was computed from a step-index fiber model. Colored curves are model predictions of s at the three retinal eccentricities and for (dashed) LP01 and (solid) LP11 modes. The horizontal gray bands correspond to the measured second moments at 0.6°, 3°, and 8.5° eccentricities from Fig. 7 (s) with band widths equal to the stand errors in the same figure. (b) Plot is identical to that in (a) except minification factor and error bars were applied to the predicted curves. See text for how minification factor was computed. Because the minification factor has measurement error, predicted colored curves consist of two lines, the separation being the standard error calculated from OS diameter measurements in Fig. 10(c). (c) To summarize the results of (b), colored lines superimposed on the d-versus-ni plot represent the combinations of d and ni values in (b) that enable the predicted s to equal the measured s. The two black curves are the theoretical V number cutoff for LP11 and LP21, 02 modes.

Equations (6)

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μ p q = i = 1 n j = 1 m ( x i x ¯ ) p ( y j y ¯ ) q I ( x i , y j ) i = 1 n j = 1 m I ( x i , y j ) ,
x ¯ = i = 1 n j = 1 m x i I ( x i , y j ) i = 1 n j = 1 m I ( x i , y j ) , and y ¯ = i = 1 n j = 1 m y i I ( x i , y j ) i = 1 n j = 1 m I ( x i , y j ) .
C = c o v ( I ( x , y ) ) = [ μ 20 μ 11 μ 11 μ 02 ] ,
[ V , Λ ] = e i g e n [ C ] ,
a = 2 × Λ 1 , b = 2 × Λ 2 ( Λ 1 < Λ 2 )
θ = a n g l e ( b , x ) . ( 0 ° < q 18 0 ° )

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