Abstract

Photoreceptor outer segments have been modeled as stacked arrays of discs or membrane infoldings containing visual pigments with light-induced dipole moments. Waveguiding has been excluded so fields diffract beyond the physical boundaries of each photoreceptor cell. Optical reciprocity is used to argue for identical radiative and light gathering properties of pigments to model vision. Two models have been introduced: one a macroscopic model that assumes a uniform pigment density across each layer and another microscopic model that includes the spatial location of each pigment molecule within each layer. Both models result in highly similar directionality at the pupil plane which proves to be insensitive to the exact details of the outer-segment packing being predominantly determined by the first and last contributing layers as set by the fraction of bleaching. The versatility of the microscopic model is demonstrated with an array of examples that includes the Stiles-Crawford effect, visibility of a focused beam of light and the role of defocus.

© 2014 Optical Society of America

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2013

P. Bedggood and A. Mehta, “Optical imaging of human cone photoreceptors directly following the capture of light,” Plos One8(11), e79251 (2013).

B. Lochocki and B. Vohnsen, “Defocus-corrected analysis of the foveal Stiles–Crawford effect of the first kind across the visible spectrum,” J. Opt.15(12), 125301 (2013).
[CrossRef]

S. Castillo and B. Vohnsen, “Exploring the Stiles-Crawford effect of the first kind with coherent light and dual Maxwellian sources,” Appl. Opt.52(1), A1–A8 (2013).
[CrossRef] [PubMed]

2012

2011

2010

2008

A. Hajiaboli and M. Popovic, “Human retinal photoreceptors: electrodynamic model of optical microfilters,” IEEE Sel. Top. Quantum Electron.14(1), 126–130 (2008).
[CrossRef]

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. Express16(9), 6486–6501 (2008).
[CrossRef] [PubMed]

2007

2005

B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. Soc. Am. A22(11), 2318–2328 (2005).
[CrossRef] [PubMed]

A. M. Pozo, F. Pérez-Ocón, and J. R. Jiménez, “FDTD analysis of the light propagation in the cones of the human retina: an approach to the Stiles-Crawford effect of the first kind,” J. Opt. A: Pure Appl. Opt.7(8), 357 (2005).

2003

A. Pallikaris, D. R. Williams, and H. Hofer, “The reflectance of single cones in the living human eye,” Invest. Ophthalmol. Vis. Sci.44(10), 4580–4592 (2003).
[CrossRef] [PubMed]

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

N. P. Zagers, T. T. Berendschot, and D. van Norren, “Wavelength dependence of reflectometric cone photoreceptor directionality,” J. Opt. Soc. Am. A20(1), 18–23 (2003).
[CrossRef] [PubMed]

2002

A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vision2(5), 54 (2002).

1999

1997

1996

M. P. Rowe, J. M. Corless, N. Engheta, and E. N. Pugh., “Scanning interferometry of sunfish cones. I.Longitudinal variation in single-cone refractive index,” J. Opt. Soc. Am. A13(11), 2141–2150 (1996).
[CrossRef]

O. S. Packer, D. R. Williams, and D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci.16(7), 2251–2260 (1996).
[PubMed]

1993

M. J. Piket-May, A. Taflove, and J. B. Troy, “Electrodynamics of visible-light interactions with the vertebrate retinal rod,” Opt. Lett.18(8), 568–570 (1993).
[CrossRef] [PubMed]

O. Keller, M. Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci.280(1–2), 217–230 (1993).
[CrossRef]

1992

A. Hendrickson and D. Drucker, “The development of parafoveal and mid-peripheral human retina,” Behav. Brain Res.49(1), 21–31 (1992).
[CrossRef] [PubMed]

1983

M. Alpern, C. C. Ching, and K. Kitahara, “The directional sensitivity of retinal rods,” J. Physiol.343(1), 577–592 (1983).
[PubMed]

1980

R. H. Steinberg, S. K. Fisher, and D. H. Anderson, “Disc morphogenesis in vertebrate photoreceptors,” J. Comp. Neurol.190(3), 501–518 (1980).
[CrossRef] [PubMed]

1975

D. C. Petersen and R. A. Cone, “The electric dipole moment of rhodopsin solubilized in Triton X-100,” Biophys. J.15(12), 1181–1200 (1975).
[CrossRef] [PubMed]

1973

F. L. Tobey and J. M. Enoch, “Directionality and waveguide properties of optically isolated rat rods,” Invest. Ophthalmol.12(12), 873–880 (1973).
[PubMed]

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

J. M. Enoch and G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol.12(7), 497–503 (1973).
[PubMed]

1971

J. R. Coble and W. A. Rushton, “Stiles-Crawford effect and the bleaching of cone pigments,” J. Physiol.217(1), 231–242 (1971).
[PubMed]

A. M. Laties and J. M. Enoch, “An analysis of retinal receptor orientation. I. Angular relationship of neighboring photoreceptors,” Invest. Ophthalmol.10(1), 69–77 (1971).
[PubMed]

1968

W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res.8(10), 1271–1284 (1968).
[CrossRef] [PubMed]

1967

G. Westheimer, “Dependence of the magnitude of the Stiles-Crawford effect on retinal location,” J. Physiol.192(2), 309–315 (1967).
[PubMed]

1966

P. L. Walraven, “Recovery from the increase of the Stiles-Crawford effect after bleaching,” Nature210(5033), 311–312 (1966).
[CrossRef] [PubMed]

1963

1958

1957

R. L. Sidman, “The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy,” J. Biophys. Biochem. Cytol.3(1), 15–30 (1957).
[CrossRef] [PubMed]

1951

1949

1937

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. Lond. B Biol. Sci.123(830), 90–118 (1937).
[CrossRef]

Alpern, M.

M. Alpern, C. C. Ching, and K. Kitahara, “The directional sensitivity of retinal rods,” J. Physiol.343(1), 577–592 (1983).
[PubMed]

Anderson, D. H.

R. H. Steinberg, S. K. Fisher, and D. H. Anderson, “Disc morphogenesis in vertebrate photoreceptors,” J. Comp. Neurol.190(3), 501–518 (1980).
[CrossRef] [PubMed]

Artal, P.

P. Artal, C. Schwarz, C. Cánovas, and A. Mira-Agudelo, “Night myopia studied with an adaptive optics visual analyzer,” Plos One7(7), e40239 (2012).

B. Vohnsen, I. Iglesias, and P. Artal, “Guided light and diffraction model of human-eye photoreceptors,” J. Opt. Soc. Am. A22(11), 2318–2328 (2005).
[CrossRef] [PubMed]

Bedggood, P.

P. Bedggood and A. Mehta, “Optical imaging of human cone photoreceptors directly following the capture of light,” Plos One8(11), e79251 (2013).

Bensinger, D. G.

O. S. Packer, D. R. Williams, and D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci.16(7), 2251–2260 (1996).
[PubMed]

Berendschot, T. T.

Besecker, J. R.

Boyde, L.

Bozhevolnyi, S.

O. Keller, M. Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci.280(1–2), 217–230 (1993).
[CrossRef]

Bozhevolnyi, S. I.

Burns, S. A.

Cánovas, C.

P. Artal, C. Schwarz, C. Cánovas, and A. Mira-Agudelo, “Night myopia studied with an adaptive optics visual analyzer,” Plos One7(7), e40239 (2012).

Carroll, J.

Castillo, S.

Cense, B.

Chalut, K. J.

Ching, C. C.

M. Alpern, C. C. Ching, and K. Kitahara, “The directional sensitivity of retinal rods,” J. Physiol.343(1), 577–592 (1983).
[PubMed]

Coble, J. R.

J. R. Coble and W. A. Rushton, “Stiles-Crawford effect and the bleaching of cone pigments,” J. Physiol.217(1), 231–242 (1971).
[PubMed]

Cone, R. A.

D. C. Petersen and R. A. Cone, “The electric dipole moment of rhodopsin solubilized in Triton X-100,” Biophys. J.15(12), 1181–1200 (1975).
[CrossRef] [PubMed]

Cooper, R. F.

Corless, J. M.

Derby, J. C.

Drucker, D.

A. Hendrickson and D. Drucker, “The development of parafoveal and mid-peripheral human retina,” Behav. Brain Res.49(1), 21–31 (1992).
[CrossRef] [PubMed]

Dubis, A. M.

Dubra, A.

Elsner, A. E.

Engel, A.

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

Engheta, N.

Enoch, J. M.

F. L. Tobey and J. M. Enoch, “Directionality and waveguide properties of optically isolated rat rods,” Invest. Ophthalmol.12(12), 873–880 (1973).
[PubMed]

J. M. Enoch and G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol.12(7), 497–503 (1973).
[PubMed]

A. M. Laties and J. M. Enoch, “An analysis of retinal receptor orientation. I. Angular relationship of neighboring photoreceptors,” Invest. Ophthalmol.10(1), 69–77 (1971).
[PubMed]

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

J. M. Enoch and G. A. Fry, “Characteristics of a model retinal receptor studied at microwave frequencies,” J. Opt. Soc. Am.48(12), 899–911 (1958).
[CrossRef] [PubMed]

Filipek, S.

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

Fischer, L.

Fisher, S. K.

R. H. Steinberg, S. K. Fisher, and D. H. Anderson, “Disc morphogenesis in vertebrate photoreceptors,” J. Comp. Neurol.190(3), 501–518 (1980).
[CrossRef] [PubMed]

Fotiadis, D.

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

Fry, G. A.

Gao, W.

Götzinger, E.

M. Pircher, E. Götzinger, H. Sattmann, R. A. Leitgeb, and C. K. Hitzenberger, “In vivo investigation of human cone photoreceptors with SLO/OCT in combination with 3D motion correction on a cellular level,” Biomed. Opt. Express18(13), 13935–13944 (2010).

Guck, J.

Hajiaboli, A.

A. Hajiaboli and M. Popovic, “Human retinal photoreceptors: electrodynamic model of optical microfilters,” IEEE Sel. Top. Quantum Electron.14(1), 126–130 (2008).
[CrossRef]

Harmening, W. M.

He, J. C.

Hendrickson, A.

A. Hendrickson and D. Drucker, “The development of parafoveal and mid-peripheral human retina,” Behav. Brain Res.49(1), 21–31 (1992).
[CrossRef] [PubMed]

Hitzenberger, C. K.

M. Pircher, E. Götzinger, H. Sattmann, R. A. Leitgeb, and C. K. Hitzenberger, “In vivo investigation of human cone photoreceptors with SLO/OCT in combination with 3D motion correction on a cellular level,” Biomed. Opt. Express18(13), 13935–13944 (2010).

Hofer, H.

A. Pallikaris, D. R. Williams, and H. Hofer, “The reflectance of single cones in the living human eye,” Invest. Ophthalmol. Vis. Sci.44(10), 4580–4592 (2003).
[CrossRef] [PubMed]

Hope, G. M.

J. M. Enoch and G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol.12(7), 497–503 (1973).
[PubMed]

Iglesias, I.

Jiménez, J. R.

A. M. Pozo, F. Pérez-Ocón, and J. R. Jiménez, “FDTD analysis of the light propagation in the cones of the human retina: an approach to the Stiles-Crawford effect of the first kind,” J. Opt. A: Pure Appl. Opt.7(8), 357 (2005).

Jonnal, R. S.

Keller, O.

O. Keller, M. Xiao, and S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci.280(1–2), 217–230 (1993).
[CrossRef]

Kitahara, K.

M. Alpern, C. C. Ching, and K. Kitahara, “The directional sensitivity of retinal rods,” J. Physiol.343(1), 577–592 (1983).
[PubMed]

Kocaoglu, O. P.

Kreysing, M.

Laties, A. M.

A. M. Laties and J. M. Enoch, “An analysis of retinal receptor orientation. I. Angular relationship of neighboring photoreceptors,” Invest. Ophthalmol.10(1), 69–77 (1971).
[PubMed]

Leitgeb, R. A.

M. Pircher, E. Götzinger, H. Sattmann, R. A. Leitgeb, and C. K. Hitzenberger, “In vivo investigation of human cone photoreceptors with SLO/OCT in combination with 3D motion correction on a cellular level,” Biomed. Opt. Express18(13), 13935–13944 (2010).

Liang, Y.

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

Lochocki, B.

B. Lochocki and B. Vohnsen, “Defocus-corrected analysis of the foveal Stiles–Crawford effect of the first kind across the visible spectrum,” J. Opt.15(12), 125301 (2013).
[CrossRef]

Makous, W. L.

W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res.8(10), 1271–1284 (1968).
[CrossRef] [PubMed]

Marcos, S.

Mehta, A.

P. Bedggood and A. Mehta, “Optical imaging of human cone photoreceptors directly following the capture of light,” Plos One8(11), e79251 (2013).

Miller, D. T.

Mira-Agudelo, A.

P. Artal, C. Schwarz, C. Cánovas, and A. Mira-Agudelo, “Night myopia studied with an adaptive optics visual analyzer,” Plos One7(7), e40239 (2012).

Norris, J. L.

O’Brien, B.

Packer, O. S.

O. S. Packer, D. R. Williams, and D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci.16(7), 2251–2260 (1996).
[PubMed]

Palczewski, K.

D. Fotiadis, Y. Liang, S. Filipek, D. A. Saperstein, A. Engel, and K. Palczewski, “Atomic-force microscopy: Rhodopsin dimers in native disc membranes,” Nature421(6919), 127–128 (2003).
[CrossRef] [PubMed]

Pallikaris, A.

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A. M. Pozo, F. Pérez-Ocón, and J. R. Jiménez, “FDTD analysis of the light propagation in the cones of the human retina: an approach to the Stiles-Crawford effect of the first kind,” J. Opt. A: Pure Appl. Opt.7(8), 357 (2005).

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D. Rativa and B. Vohnsen, “Analysis of individual cone-photoreceptor directionality using scanning laser ophthalmoscopy,” Biomed. Opt. Express2(6), 1423–1431 (2011).
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[CrossRef] [PubMed]

IEEE Sel. Top. Quantum Electron.

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

J. Mod. Opt.

D. Rativa and B. Vohnsen, “Single- and multimode characteristics of the foveal cones: the super-Gaussian function,” J. Mod. Opt.58(19–20), 1809–1816 (2011).
[CrossRef]

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O. S. Packer, D. R. Williams, and D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci.16(7), 2251–2260 (1996).
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J. Opt.

B. Lochocki and B. Vohnsen, “Defocus-corrected analysis of the foveal Stiles–Crawford effect of the first kind across the visible spectrum,” J. Opt.15(12), 125301 (2013).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

A. M. Pozo, F. Pérez-Ocón, and J. R. Jiménez, “FDTD analysis of the light propagation in the cones of the human retina: an approach to the Stiles-Crawford effect of the first kind,” J. Opt. A: Pure Appl. Opt.7(8), 357 (2005).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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G. Westheimer, “Dependence of the magnitude of the Stiles-Crawford effect on retinal location,” J. Physiol.192(2), 309–315 (1967).
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A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vision2(5), 54 (2002).

Nature

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Plos One

P. Artal, C. Schwarz, C. Cánovas, and A. Mira-Agudelo, “Night myopia studied with an adaptive optics visual analyzer,” Plos One7(7), e40239 (2012).

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Figures (12)

Fig. 1
Fig. 1

Photoreceptor outer-segment model: (a) schematic of a stacked-aperture array with N layers to represent the radiative and collective properties of visual pigments in the cone membrane infoldings or rhodopsin molecules of rod discs giving rise to a diffracted field, Ediffr. (b) Stacked array of outer-segment dipoles driven by an incident field, E0, and the resulting Rayleigh-scattered field, Esc, from dipole (n,m) propagated a distance, R.

Fig. 2
Fig. 2

Calculated light distribution in the pupil plane of a schematic eye model for d = 2.0 µm apertures representing photoreceptor outer-segment discs or membrane infoldings, for N = 1, 1000 and 2000 equally contributing layers for a single outer segment. The wavelength of the light is λ = 0.550 µm and all pupil intensities have been fitted (optimized Levenberg Marquardt) with a solid line to the Stiles-Crawford function giving the following directionality parameters: ρ 1disc =0.0562/ mm 2 , ρ 1000discs =0.0763/ mm 2 , and ρ 2000discs =0.1130/ mm 2 , respectively.

Fig. 3
Fig. 3

Calculated light distribution in the pupil plane of a schematic eye model for d = 2 µm apertures (representing photoreceptor outer-segment discs or membrane infoldings) for N = 1000 equally contributing layers for a single outer segment. The wavelength of the light is 0.450 µm, 0.550 µm and 0.650 µm, respectively, and all pupil intensities have been fitted (optimized Levenberg Marquardt) to the Stiles-Crawford function (solid lines) resulting in the directionality parameters ρ 450nm =0.1063/ mm 2 , ρ 550nm =0.0763/ mm 2 , and ρ 650nm =0.0578/ mm 2 , respectively.

Fig. 4
Fig. 4

Calculated role of pigment bleaching ( = 1- absorption) on the light distribution in the pupil plane of a schematic eye model for d = 2 µm apertures (representing photoreceptor outer-segment discs or membrane infoldings) for N = 2000 contributing layers for a single outer segment. The wavelength of the light is 0.550 µm. All pupil intensities have been fitted (optimized Levenberg Marquardt) to the Stiles-Crawford function resulting in the directionality parameters: ρ 100% =0.1130/ mm 2 , ρ 1% =0.1008/ mm 2 , ρ 0.001% =0.0764/ mm 2 and ρ 0.000001% =0.0660/ mm 2 , respectively. For comparison, also the single-aperture case is shown. Three selected pupil intensity images are shown corresponding to 100% full bleach (same as Fig. 2 with N = 2000) compared with 1% and 0.001% partially-bleached conditions.

Fig. 5
Fig. 5

Light distribution in the pupil plane of a schematic eye model for d = 2.0 µm discs, representing photoreceptor outer-segment discs or membrane infoldings, for N = 1, 1000 and 2000 equally contributing layers containing 740 dipoles in each for a single outer segment. The wavelength of the light is λ = 0.550 µm and all pupil intensities have been fitted (optimized Levenberg Marquardt) to the Stiles-Crawford function (solid lines) resulting in the directionality parameters: ρ 1disc =0.0567/ mm 2 , ρ 1000discs =0.0766/ mm 2 , and ρ 2000discs =0.1133/ mm 2 , respectively.

Fig. 6
Fig. 6

Radiative far-field component of scattered light intensities for an isolated outer segment (OS) propagated from the middle inside of the OS (left) towards the inner segment (IS) and pupil (right) when including N = 1 (top), 100 (middle) and 1000 (bottom) equally contributing layers containing 740 dipoles in each. The molecular arrangement of dipolar pigments within a single layer is shown in the top-left corner. OS: outer segment and IS: inner segment.

Fig. 7
Fig. 7

Scattered light intensities from the dipoles in one isolated outer segment seen in xy cross sections (middle) at the middle and near the far end of the outer segment, and in xz cross sections (left and right) when illuminated by a plane wave at different angles of incidence, θ, from 0° to 15° (the last value is slightly beyond the angle achievable with a dilated 8 mm pupil). The dotted white circle shows the 2.0 µm diameter of the outer segment that contains N = 1000 layers with 172 dipoles in each. The dotted white line in the yz cross sections shows the external boundary of the outer segment.

Fig. 8
Fig. 8

Scattered light intensities in the middle of the outer segment from the dipoles in the central part of an array containing 19 outer segments each with d = 2.0 µm diameter and a center-to-center spacing of 1.22d. The incident light is a plane wave at different angles of incidence, θ. The dotted white circle shows the 2.0 µm diameter of the outer segment for one of the outer segments. Each outer segment contains N = 1000 layers that each contain 12 dipoles.

Fig. 9
Fig. 9

Role of defocus seen in a cross section through the middle of the outer segments for an array of 19 hexagonally-packed outer segments each with N = 1000 layers each containing 12 dipoles. The array is illuminated by an incident Gaussian beam with beam waist (radius) w0 = 1.00 µm striking axially onto the central photoreceptor and scattered by the array. The defocus in diopters refers to defocus of the focused incident beam with respect to the outer-segment entrance so that −0.05D is focused near the far end of the outer segment and positive values are focused before the outer segment is reached. The schematic drawings of a single outer segment show the case of focusing the incident light near the (a) upper entrance and (b) far-end exit. Blue arrows indicate the direction of back-scattered light from each layer causing a focusing effect when focused within or beyond the outer segment.

Fig. 10
Fig. 10

Cross section at the middle of the outer segments for an array of 19 hexagonally-packed outer segments each with N = 1000 layers that each contain 12 dipoles. A Gaussian beam of light with waist (radius) w0 = 1.00 µm is axially incident and focused on the entrance facet at different horizontal locations of the outer-segment array and scattered. Left: the entire array is seen when illuminated by a plane wave, the following images towards the right show the scattering produced when the Gaussian beam is shifted increasingly towards the right. On the right-hand side: the beam is incident at the midpoint between two outer segments. For the centrally incident beam (0,0) cone ‘b’ carries only 5.6% of the power contained in cone ‘a’ and thus all 6 cones surrounding cone ‘a’ carry 33% of the power; when the beam is displaced by 25% of the outer-segment spacing cone ‘b’ carries 21% of the power with respect to the power in cone ‘a’; and when displaced to the midpoint between two outer segments the ratio cone ‘a’ and ‘b’ carry an equal amount of power. In this case, the total power within the outer segments is 67% when compared to the on-axis case. θ. The dotted white circles show the 2.0 µm diameter of each outer segment.

Fig. 11
Fig. 11

Cross sections in the xz-plane of light scattering produced when a Gaussian beam is focused to a spot size w0 = 1.00 μm at the top (left) and bottom (right) of an outer segment, respectively. Both a d = 2 μm diameter cylindrical and conical outer segment is shown. Each outer segment contains N = 1000 layers with 172 dipoles in each for the cylindrical case and a linear reduction in dipoles with depth in the conical case. The dotted white lines show the external boundaries of the outer segments.

Fig. 12
Fig. 12

Cross sections in the xz-plane of light scattering produced when an outer segment is illuminated at different wavelengths for λ = 450 nm, 550 nm, and 650 nm for an L = 20 μm outer segment with 172 dipoles in each layer. The spacing between outer-segment layers is δ = 20 nm (left), δ = 200 nm (middle), and δ = 2000 nm (right) with corresponding layers N = 1000, 100 and 10, respectively. The dotted white lines show the external boundaries of the outer segments.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E diffr ( r p )= n=1 N E 0,n iλ z n exp( ik[ z n + r p 2 2 z n ] )[ 2 J 1 ( k r p d/2 z n ) k r p d/2 z n ] ,
T( z )= e σ N V | z | = e β| z | ,
η 0 =1 e βL
E sc (r)= α R 4π ε 0 k 2 n=1 N m=1 M R m,n R m,n R m,n 2 U R m,n 3 E 0 ( r m,n )exp(ik R m,n ) ,
E sc (r)= α R 4π ε 0 k 2 n=1 N m=1 M 1 R m,n 3 ( x m,n 2 R m,n 2 x m,n y m,n x m,n z m,n ) E 0,x ( r m,n )exp(ik R m,n ) .
E 0,x ( r ˜ p ;z)= w 0 w(z) e r ˜ p 2 / w 2 (z) e ik r ˜ p 2 /(2R(z)) e i[ kzatan( λz π n eye w 0 2 ) ]
η( r p )= ( 2 J 1 (α r p ) α r p ) 2 .

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