Abstract

In several modes of retinal imaging, the primary means of visualizing cone photoreceptors is from reflected light. Understanding how such images are formed, particularly when adaptive optics techniques are used, will help to guide their interpretation. Toward this end, we used finite difference beam propagation to model reflections from cone photoreceptors. We investigated the formation of cone images in adaptive optics scanning laser ophthalmoscopy (AOSLO) and optical coherence tomography (AOOCT). Three cone models were tested, one made up of three segments of varying refractive index, the other two having additional boundaries at the inner/outer segment junction and outer segment tip. Images formed by the first model did not correspond to AOOCT observations in the literature, while the latter two did. The predicted distributions of reflected light intensity from the latter cone models were compared to the distribution from AOSLO images, both studied with light sources of varied coherence length. The cone model with the most reflections at the inner/outer segment junction best fit the data measured in vivo. These results show that variance in cone reflection can originate from light interfering from reflectors much more closely spaced than the outer segment length. We also show that subtracting images taken with different coherence length sources highlights these changes in interference. Differential coherence images of cones occasionally revealed an annular reflection profile, which modeling showed to be very sensitive to cone size and the gaps bracketing the outer segment, suggesting that such imaging may be useful for probing photoreceptor morphology.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

S. A. Burns, A. E. Elsner, K. A. Sapoznik, R. L. Warner, and T. J. Gast, “Adaptive optics imaging of the human retina,” Prog. Retin. Eye Res. 68, 1–30 (2019).
[Crossref]

M. Azimipour, J. V. Migacz, R. J. Zawadzki, J. S. Werner, and R. S. Jonnal, “Functional retinal imaging using adaptive optics swept-source OCT at 16 MHz,” Optica 6(3), 300–303 (2019).
[Crossref]

2018 (6)

N. Cuenca, I. Ortuño-Lizarán, and I. Pinilla, “Cellular characterization of OCT and outer retinal bands Using Specific Immunohistochemistry Markers and Clinical Implications,” Ophthalmology 125(3), 407–422 (2018).
[Crossref]

C. A. Curcio, J. R. Sparrow, V. L. Bonilha, A. Pollreisz, and B. J. Lujan, “Re: Cuenca, et al.: Cellular characterization of OCT and outer retinal bands using specific immunohistochemistry markers and clinical implications,” Ophthalmology 125(3), 407–422 (2018).
[Crossref]

A. Meadway and L. C. Sincich, “Light propagation and capture in cone photoreceptors,” Biomed. Opt. Express 9(11), 5543–5565 (2018).
[Crossref]

K. M. Litts, Y. Zhang, K. Bailey Freund, and C. A. Curcio, “Optical coherence tomography and histology of age-related macular degeneration support mitochondria as reflectivity sources,” Retina 38(3), 445–461 (2018).
[Crossref]

J. Liu, H. W. Jung, A. Dubra, and J. Tam, “Cone photoreceptor cell segmentation and diameter measurement on adaptive optics images using circularly constrained active contour model,” Invest. Ophthalmol. Visual Sci. 59(11), 4639–4652 (2018).
[Crossref]

B. S. Sajdak, B. A. Bell, T. R. Lewis, G. Luna, G. S. Cornwell, S. K. Fisher, D. K. Merriman, and J. Carroll, “Assessment of outer retinal remodeling in the hibernating 13-lined ground squirrel,” Invest. Ophthalmol. Visual Sci. 59(6), 2538–2547 (2018).
[Crossref]

2017 (5)

P. Zhang, R. J. Zawadzki, M. Goswami, P. T. Nguyen, V. Yarov-Yarovoy, M. E. Burns, and E. N. Pugh, “In vivo optophysiology reveals that G-protein activation triggers osmotic swelling and increased light scattering of rod photoreceptors,” Proc. Natl. Acad. Sci. 114(14), E2937–E2946 (2017).
[Crossref]

M. Pircher and R. J. Zawadzki, “Review of adaptive optics OCT (AO-OCT): principles and applications for retinal imaging,” Biomed. Opt. Express 8(5), 2536–2562 (2017).
[Crossref]

R. F. Cooper, W. S. Tuten, A. Dubra, D. H. Brainard, and J. I. W. Morgan, “Non-invasive assessment of human cone photoreceptor function,” Biomed. Opt. Express 8(11), 5098–5112 (2017).
[Crossref]

R. S. Jonnal, I. Gorczynska, J. V. Migacz, M. Azimipour, R. J. Zawadzki, and J. S. Werner, “The properties of outer retinal band three investigated with adaptive-optics optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 58(11), 4559–4568 (2017).
[Crossref]

J. H. Tu, K. G. Foote, B. J. Lujan, K. Ratnam, J. Qin, M. B. Gorin, E. T. Cunningham, W. S. Tuten, J. L. Duncan, and A. Roorda, “Dysflective cones: Visual function and cone reflectivity in long-term follow-up of acute bilateral foveolitis,” Am. J. Ophthalmol. Case Reports 7, 14–19 (2017).
[Crossref]

2016 (7)

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
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O. P. Kocaoglu, Z. Liu, F. Zhang, K. Kazuhiro, R. S. Jonnal, and D. T. Miller, “Photoreceptor disc shedding in the living human eye,” Biomed. Opt. Express 7(11), 4554–4568 (2016).
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L. Mariotti, N. Devaney, G. Lombardo, and M. Lombardo, “Understanding the changes of cone reflectance in adaptive optics flood illumination retinal images over three years,” Biomed. Opt. Express 7(7), 2807–2822 (2016).
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J. I. W. Morgan, “The fundus photo has met its match: Optical coherence tomography and adaptive optics ophthalmoscopy are here to stay,” Ophthalmic Physiol. Opt. 36(3), 218–239 (2016).
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R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, Z. Liu, D. T. Miller, and J. S. Werner, “A review of adaptive optics optical coherence tomography: Technical advances, scientific applications, and the future,” Invest. Ophthalmol. Visual Sci. 57(9), OCT51–OCT68 (2016).
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Y. Li, R. N. Fariss, J. W. Qian, E. D. Cohen, and H. Qian, “Light-induced thickening of photoreceptor outer segment layer detected by ultra-high resolution OCT imaging,” Invest. Ophthalmol. Vis. Sci. 57(9), OCT105–OCT111 (2016).
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D. Hillmann, H. Spahr, C. Pfäffle, H. Sudkamp, G. Franke, and G. Hüttmann, “In vivo optical imaging of physiological responses to photostimulation in human photoreceptors,” Proc. Natl. Acad. Sci. 113(46), 13138–13143 (2016).
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2015 (6)

K. S. Bruce, W. M. Harmening, B. R. Langston, W. S. Tuten, A. Roorda, and L. C. Sincich, “Normal perceptual sensitivity arising from weakly reflective cone photoreceptors,” Invest. Ophthalmol. Visual Sci. 56(8), 4431–4438 (2015).
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Z. Liu, O. P. Kocaoglu, T. L. Turner, and D. T. Miller, “Modal content of living human cone photoreceptors,” Biomed. Opt. Express 6(9), 3378–3404 (2015).
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A. Roorda and J. L. Duncan, “Adaptive Optics Ophthalmoscopy,” Annu. Rev. Vis. Sci. 1(1), 19–50 (2015).
[Crossref]

R. F. Spaide, “Outer retinal bands,” Invest. Ophthalmol. Visual Sci. 56(4), 2505–2506 (2015).
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R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, S.-H. Lee, J. S. Werner, and D. T. Miller, “Author response: Outer retinal bands,” Invest. Ophthalmol. Visual Sci. 56(4), 2507–2510 (2015).
[Crossref]

Q. Wang, W. S. Tuten, B. J. Lujan, J. Holland, P. S. Bernstein, S. D. Schwartz, J. L. Duncan, and A. Roorda, “Adaptive optics microperimetry and OCT images show preserved function and recovery of cone visibility in macular telangiectasia type 2 retinal lesions,” Invest. Ophthalmol. Visual Sci. 56(2), 778–786 (2015).
[Crossref]

2014 (6)

D. Scoles, Y. Sulai, and C. Langlo, “In vivo imaging of human cone photoreceptor inner segments,” Invest. Ophthalmol. Visual Sci. 55(7), 4244–4251 (2014).
[Crossref]

B. Vohnsen, “Directional sensitivity of the retina: A layered scattering model of outer-segment photoreceptor pigments,” Biomed. Opt. Express 5(5), 1569–1587 (2014).
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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).
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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. Visual Sci. 55(12), 7904–7918 (2014).
[Crossref]

G. Staurenghi, S. Sadda, U. Chakravarthy, and R. F. Spaide, “Proposed lexicon for anatomic landmarks in normal posterior segment spectral-domain optical coherence tomography: the IN•OCT consensus,” Ophthalmology 121(8), 1572–1578 (2014).
[Crossref]

W. M. Harmening, W. S. Tuten, A. Roorda, and L. C. Sincich, “Mapping the perceptual grain of the human retina,” J. Neurosci. 34(16), 5667–5677 (2014).
[Crossref]

2013 (3)

A. Panorgias, R. J. Zawadzki, A. G. Capps, A. A. Hunter, L. S. Morse, and J. S. Werner, “Multimodal assessment of microscopic morphology and retinal function in patients with geographic atrophy,” Invest. Ophthalmol. Visual Sci. 54(6), 4372–4384 (2013).
[Crossref]

A. Meadway, C. A. Girkin, and Y. Zhang, “A dual-modal retinal imaging system with adaptive optics,” Opt. Express 21(24), 29792–29807 (2013).
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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), 3007–3030 (2013).
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2012 (5)

2011 (6)

H. Song, T. Y. P. Chui, Z. Zhong, A. E. Elsner, and S. A. Burns, “Variation of cone photoreceptor packing density with retinal eccentricity and age,” Invest. Ophthalmol. Visual Sci. 52(10), 7376–7384 (2011).
[Crossref]

D. Rativa and B. Vohnsen, “Analysis of individual cone-photoreceptor directionality using scanning laser ophthalmoscopy,” Biomed. Opt. Express 2(6), 1423 (2011).
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S. Ooto, M. Hangai, A. Tomidokoro, H. Saito, M. Araie, T. Otani, S. Kishi, K. Matsushita, N. Maeda, M. Shirakashi, H. Abe, S. Ohkubo, K. Sugiyama, A. Iwase, and N. Yoshimura, “Effects of age, sex, and axial length on the three-dimensional profile of normal macular layer structures,” Invest. Ophthalmol. Visual Sci. 52(12), 8769–8779 (2011).
[Crossref]

R. F. Spaide and C. A. Curcio, “Anatomical correlates to the bands seen in the outer retina by optical coherence tomogrphy: literature review and model,” Retina 31(8), 1609–1619 (2011).
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M. Pircher, J. S. Kroisamer, F. Felberer, H. Sattmann, E. Götzinger, and C. K. Hitzenberger, “Temporal changes of human cone photoreceptors observed in vivo with SLO / OCT,” Biomed. Opt. Express 2(1), 100–112 (2011).
[Crossref]

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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2010 (4)

2009 (1)

2008 (3)

2007 (3)

2005 (2)

2004 (2)

2003 (1)

A. Pallikaris, D. R. Williams, and H. Hofer, “The reflectance of single cones in the living human eye,” Invest. Ophthalmol. Visual Sci. 44(10), 4580–4592 (2003).
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2002 (3)

A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
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A. Roorda and D. R. Williams, “Optical fiber properties of individual human cones,” J. Vis. 2(5), 4 (2002).
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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).
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2000 (1)

A. Stockman and L. T. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype,” Vision Res. 40(13), 1711–1737 (2000).
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1997 (1)

J.-M. Gorrand and F. C. Delori, “A model for the assesment of cone directionality,” J. Mod. Opt. 44(3), 473–491 (1997).
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1993 (1)

W. P. Huang and C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29(10), 2639–2649 (1993).
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1992 (1)

W. P. Huang, C. L. Xu, and S. K. Chaudhuri, “A finite-difference vector beam propagation method for three-dimensional waveguide structures,” IEEE Photonics Technol. Lett. 4(2), 148–151 (1992).
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1991 (2)

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “A vector beam propagation method for guided-wave optics,” IEEE Photonics Technol. Lett. 3(10), 910–913 (1991).
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C. A. Curcio and A. E. Hendrickson, “Organization and development of the primate photoreceptor mosaic,” Prog. Retin. Res. 10, 89–120 (1991).
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1989 (1)

1987 (1)

C. R. Braekevelt, “Photoreceptor fine structure in the vervet monkey (Cercopithecus aethiops),” Histol. Histopathol. 2(4), 433–439 (1987).

1980 (1)

R. H. Steinberg, S. K. Fisher, and D. H. Anderson, “Disc morphogenesis in vertebrate photoreceptors,” J. Comp. Neurol. 190, 501–518 (1980).
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1975 (2)

D. G. Stavenga, “Waveguide modes and refractive index in photoreceptors of vertebrates,” Vision Res. 15(3), 323–330 (1975).
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1974 (1)

1973 (1)

A. W. Snyder and C. Pask, “The Stiles-Crawford effect—explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973).
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1972 (1)

A. W. Snyder and M. Hamer, “The light-capture area of a photoreceptor,” Vision Res. 12(10), 1749–1753 (1972).
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1970 (1)

A. W. Snyder, “Coupling of modes on a tapered dielectric cylinder,” IEEE Trans. Microw. Theory Tech. 18(7), 383–392 (1970).
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1969 (1)

B. B. Boycott, J. E. Dowling, and H. Kolb, “Organization of the primate retina: light microscopy,” Proc. R. Soc. London, Ser. B, Biol. Sci. 255(799), 109–184 (1969).
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1963 (1)

1961 (1)

J. M. Enoch, “Wave-guide modes in retinal receptors,” Science 133(3461), 1353–1354 (1961).
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1960 (1)

1957 (2)

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).
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a Leitgeb, R.

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S. Ooto, M. Hangai, A. Tomidokoro, H. Saito, M. Araie, T. Otani, S. Kishi, K. Matsushita, N. Maeda, M. Shirakashi, H. Abe, S. Ohkubo, K. Sugiyama, A. Iwase, and N. Yoshimura, “Effects of age, sex, and axial length on the three-dimensional profile of normal macular layer structures,” Invest. Ophthalmol. Visual Sci. 52(12), 8769–8779 (2011).
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M. D. Abramoff, P. J. Magalhães, and S. J. J. Ram, “Image processing with ImageJ,” Biophotonics Int. 11, 36–43 (2004).

Anderson, D. H.

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

S. Ooto, M. Hangai, A. Tomidokoro, H. Saito, M. Araie, T. Otani, S. Kishi, K. Matsushita, N. Maeda, M. Shirakashi, H. Abe, S. Ohkubo, K. Sugiyama, A. Iwase, and N. Yoshimura, “Effects of age, sex, and axial length on the three-dimensional profile of normal macular layer structures,” Invest. Ophthalmol. Visual Sci. 52(12), 8769–8779 (2011).
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Arathorn, D. W.

Arganda-carreras, I.

I. Arganda-carreras, C. O. S. Sorzano, R. Marabini, J. M. Carazo, C. Oritz-de-Solorzano, and J. Kybic, “Consistent and elastic registration of histological sections using vector-spline regularization,” in CVAMIA: Computer Vision Approaches to Medical Image Analysis (2006), pp. 85–95.

Artal, P.

Azimipour, M.

M. Azimipour, J. V. Migacz, R. J. Zawadzki, J. S. Werner, and R. S. Jonnal, “Functional retinal imaging using adaptive optics swept-source OCT at 16 MHz,” Optica 6(3), 300–303 (2019).
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R. S. Jonnal, I. Gorczynska, J. V. Migacz, M. Azimipour, R. J. Zawadzki, and J. S. Werner, “The properties of outer retinal band three investigated with adaptive-optics optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 58(11), 4559–4568 (2017).
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Bailey Freund, K.

K. M. Litts, Y. Zhang, K. Bailey Freund, and C. A. Curcio, “Optical coherence tomography and histology of age-related macular degeneration support mitochondria as reflectivity sources,” Retina 38(3), 445–461 (2018).
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Barer, R.

Baumann, B.

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P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Visual Sci. 53(7), 3673–3681 (2012).
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Bell, B. A.

B. S. Sajdak, B. A. Bell, T. R. Lewis, G. Luna, G. S. Cornwell, S. K. Fisher, D. K. Merriman, and J. Carroll, “Assessment of outer retinal remodeling in the hibernating 13-lined ground squirrel,” Invest. Ophthalmol. Visual Sci. 59(6), 2538–2547 (2018).
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Bernstein, P. S.

Q. Wang, W. S. Tuten, B. J. Lujan, J. Holland, P. S. Bernstein, S. D. Schwartz, J. L. Duncan, and A. Roorda, “Adaptive optics microperimetry and OCT images show preserved function and recovery of cone visibility in macular telangiectasia type 2 retinal lesions,” Invest. Ophthalmol. Visual Sci. 56(2), 778–786 (2015).
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Besecker, J. R.

Bonilha, V. L.

C. A. Curcio, J. R. Sparrow, V. L. Bonilha, A. Pollreisz, and B. J. Lujan, “Re: Cuenca, et al.: Cellular characterization of OCT and outer retinal bands using specific immunohistochemistry markers and clinical implications,” Ophthalmology 125(3), 407–422 (2018).
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Boycott, B. B.

B. B. Boycott, J. E. Dowling, and H. Kolb, “Organization of the primate retina: light microscopy,” Proc. R. Soc. London, Ser. B, Biol. Sci. 255(799), 109–184 (1969).
[Crossref]

Braaf, B.

Braekevelt, C. R.

C. R. Braekevelt, “Photoreceptor fine structure in the vervet monkey (Cercopithecus aethiops),” Histol. Histopathol. 2(4), 433–439 (1987).

Brainard, D. H.

Bruce, K. S.

K. S. Bruce, W. M. Harmening, B. R. Langston, W. S. Tuten, A. Roorda, and L. C. Sincich, “Normal perceptual sensitivity arising from weakly reflective cone photoreceptors,” Invest. Ophthalmol. Visual Sci. 56(8), 4431–4438 (2015).
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Burns, M. E.

P. Zhang, R. J. Zawadzki, M. Goswami, P. T. Nguyen, V. Yarov-Yarovoy, M. E. Burns, and E. N. Pugh, “In vivo optophysiology reveals that G-protein activation triggers osmotic swelling and increased light scattering of rod photoreceptors,” Proc. Natl. Acad. Sci. 114(14), E2937–E2946 (2017).
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Burns, S. A.

S. A. Burns, A. E. Elsner, K. A. Sapoznik, R. L. Warner, and T. J. Gast, “Adaptive optics imaging of the human retina,” Prog. Retin. Eye Res. 68, 1–30 (2019).
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H. Song, T. Y. P. Chui, Z. Zhong, A. E. Elsner, and S. A. Burns, “Variation of cone photoreceptor packing density with retinal eccentricity and age,” Invest. Ophthalmol. Visual Sci. 52(10), 7376–7384 (2011).
[Crossref]

Campbell, M. C. W.

Capps, A. G.

A. Panorgias, R. J. Zawadzki, A. G. Capps, A. A. Hunter, L. S. Morse, and J. S. Werner, “Multimodal assessment of microscopic morphology and retinal function in patients with geographic atrophy,” Invest. Ophthalmol. Visual Sci. 54(6), 4372–4384 (2013).
[Crossref]

Carazo, J. M.

I. Arganda-carreras, C. O. S. Sorzano, R. Marabini, J. M. Carazo, C. Oritz-de-Solorzano, and J. Kybic, “Consistent and elastic registration of histological sections using vector-spline regularization,” in CVAMIA: Computer Vision Approaches to Medical Image Analysis (2006), pp. 85–95.

Carroll, J.

B. S. Sajdak, B. A. Bell, T. R. Lewis, G. Luna, G. S. Cornwell, S. K. Fisher, D. K. Merriman, and J. Carroll, “Assessment of outer retinal remodeling in the hibernating 13-lined ground squirrel,” Invest. Ophthalmol. Visual Sci. 59(6), 2538–2547 (2018).
[Crossref]

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
[Crossref]

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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J. Rha, B. Schroeder, P. Godara, and J. Carroll, “Variable optical activation of human cone photoreceptors visualized using a short coherence light source,” Opt. Lett. 34(24), 3782–3784 (2009).
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Cense, B.

Chakravarthy, U.

G. Staurenghi, S. Sadda, U. Chakravarthy, and R. F. Spaide, “Proposed lexicon for anatomic landmarks in normal posterior segment spectral-domain optical coherence tomography: the IN•OCT consensus,” Ophthalmology 121(8), 1572–1578 (2014).
[Crossref]

Chaudhuri, S. K.

W. P. Huang, C. L. Xu, and S. K. Chaudhuri, “A finite-difference vector beam propagation method for three-dimensional waveguide structures,” IEEE Photonics Technol. Lett. 4(2), 148–151 (1992).
[Crossref]

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “A vector beam propagation method for guided-wave optics,” IEEE Photonics Technol. Lett. 3(10), 910–913 (1991).
[Crossref]

Choi, S. S.

Chu, S. T.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, “A vector beam propagation method for guided-wave optics,” IEEE Photonics Technol. Lett. 3(10), 910–913 (1991).
[Crossref]

Chui, T. Y. P.

H. Song, T. Y. P. Chui, Z. Zhong, A. E. Elsner, and S. A. Burns, “Variation of cone photoreceptor packing density with retinal eccentricity and age,” Invest. Ophthalmol. Visual Sci. 52(10), 7376–7384 (2011).
[Crossref]

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]

Cohen, E. D.

Y. Li, R. N. Fariss, J. W. Qian, E. D. Cohen, and H. Qian, “Light-induced thickening of photoreceptor outer segment layer detected by ultra-high resolution OCT imaging,” Invest. Ophthalmol. Vis. Sci. 57(9), OCT105–OCT111 (2016).
[Crossref]

Collison, F. T.

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
[Crossref]

Connor, T. B.

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
[Crossref]

Cooper, R. F.

R. F. Cooper, W. S. Tuten, A. Dubra, D. H. Brainard, and J. I. W. Morgan, “Non-invasive assessment of human cone photoreceptor function,” Biomed. Opt. Express 8(11), 5098–5112 (2017).
[Crossref]

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
[Crossref]

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).
[Crossref]

Cornwell, G. S.

B. S. Sajdak, B. A. Bell, T. R. Lewis, G. Luna, G. S. Cornwell, S. K. Fisher, D. K. Merriman, and J. Carroll, “Assessment of outer retinal remodeling in the hibernating 13-lined ground squirrel,” Invest. Ophthalmol. Visual Sci. 59(6), 2538–2547 (2018).
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Cuenca, N.

N. Cuenca, I. Ortuño-Lizarán, and I. Pinilla, “Cellular characterization of OCT and outer retinal bands Using Specific Immunohistochemistry Markers and Clinical Implications,” Ophthalmology 125(3), 407–422 (2018).
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Cunningham, E. T.

J. H. Tu, K. G. Foote, B. J. Lujan, K. Ratnam, J. Qin, M. B. Gorin, E. T. Cunningham, W. S. Tuten, J. L. Duncan, and A. Roorda, “Dysflective cones: Visual function and cone reflectivity in long-term follow-up of acute bilateral foveolitis,” Am. J. Ophthalmol. Case Reports 7, 14–19 (2017).
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Curcio, C. A.

C. A. Curcio, J. R. Sparrow, V. L. Bonilha, A. Pollreisz, and B. J. Lujan, “Re: Cuenca, et al.: Cellular characterization of OCT and outer retinal bands using specific immunohistochemistry markers and clinical implications,” Ophthalmology 125(3), 407–422 (2018).
[Crossref]

K. M. Litts, Y. Zhang, K. Bailey Freund, and C. A. Curcio, “Optical coherence tomography and histology of age-related macular degeneration support mitochondria as reflectivity sources,” Retina 38(3), 445–461 (2018).
[Crossref]

R. F. Spaide and C. A. Curcio, “Anatomical correlates to the bands seen in the outer retina by optical coherence tomogrphy: literature review and model,” Retina 31(8), 1609–1619 (2011).
[Crossref]

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]

C. A. Curcio and A. E. Hendrickson, “Organization and development of the primate photoreceptor mosaic,” Prog. Retin. Res. 10, 89–120 (1991).
[Crossref]

de Boer, J. F.

Delori, F. C.

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

Derby, J. C.

Devaney, N.

Donnelly, W. J.

Dowling, J. E.

B. B. Boycott, J. E. Dowling, and H. Kolb, “Organization of the primate retina: light microscopy,” Proc. R. Soc. London, Ser. B, Biol. Sci. 255(799), 109–184 (1969).
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Drexler, W.

Dubis, A. M.

Dubra, A.

J. Liu, H. W. Jung, A. Dubra, and J. Tam, “Cone photoreceptor cell segmentation and diameter measurement on adaptive optics images using circularly constrained active contour model,” Invest. Ophthalmol. Visual Sci. 59(11), 4639–4652 (2018).
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R. F. Cooper, W. S. Tuten, A. Dubra, D. H. Brainard, and J. I. W. Morgan, “Non-invasive assessment of human cone photoreceptor function,” Biomed. Opt. Express 8(11), 5098–5112 (2017).
[Crossref]

M. M. Razeen, R. F. Cooper, C. S. Langlo, M. R. Goldberg, M. A. Wilk, D. P. Han, T. B. Connor, G. A. Fishman, F. T. Collison, Y. N. Sulai, A. Dubra, J. Carroll, and K. E. Stepien, “Correlating photoreceptor mosaic structure to clinical findings in Stargardt disease,” Transl. Vis. Sci. Technol. 5(2), 6 (2016).
[Crossref]

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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Figures (11)

Fig. 1.
Fig. 1. Propagation of reflected light compared across three cone models. Depicted are the input electric fields (ψ0), the forward propagations, the refractive index maps (n) of each cone model, and the reflected propagations and output fields at the ELM (z = 0) from each reflective boundary. The output fields are used to calculate the power returned to a detector. The electric fields (ψ) are normalized to the peak condition in each propagation set, and are shown only for light polarized in the x direction. ELM reflections are not shown. The OCT
Fig. 2.
Fig. 2. Estimation of gap size distributions from OCT band widths. (A) For Models 2 and 3, the predicted OCT band width was first calculated as a function of extracellular gap size. OCT widths (B, from [15,16]) were used to derive gap size distributions (C) from the functions in A, based on 100,000 draws from the distributions in B. Inner segment diameter, d0, was
Fig. 3.
Fig. 3. Variation of predicted cone reflected light intensity for Models 2 and 3 with different coherence length sources (low coherence: lc = 4.81 µm, high coherence: lc = 14.7 µm, values in air) and varying extracellular gap sizes. Inner segment diameter, d0, was 6.36 µm, corresponding to 2° eccentricity. Reflectance values are interpolated based on a gap step size of 0.2 µm and normalized to the mean of the Model 2 high coherence condition.
Fig. 4.
Fig. 4. AOSLO images of the cone photoreceptor mosaic at 1.7° inferior retinal eccentricity taken with (A) the high coherence source, and (B) the low coherence source. (C) Normalized differential coherence image (B minus A) showing the direction and magnitude of intensity changes due to interference. Four example cones are highlighted: red = cones with negative differential intensity, blue = cones with positive differential intensity.
Fig. 5.
Fig. 5. Selection of cones for intensity measurements from in vivo AOSLO images. (A) Cone mosaic from one subject at 2.2° naso-inferior retinal eccentricity. (B) Motion contrast image of the overlying vasculature. (C) Blood vessel mask created from B. (D) The blood vessel mask superimposed on the motion contrast image. (E) Red dots indicate the selected cones to be used for quantification that are free from light path disruption from overlying vessels.
Fig. 6.
Fig. 6. Comparison of differential coherence cone contrast between modeled cones and in vivo AOSLO images. The variation in cone intensity vs. contrast in Models 2 (A) and 3 (B) is relatively low on the intensity axis because the cones have no noise included in their computed reflectance. Cone intensity data are normalized to the mean. The variation present is due only to interference effects (N = 100,000). Incorporating a generic noise factor in the reflectance intensity (C, D) spreads the modeled data along this axis, allowing for unaccounted sources of intensity variation. (E) Cone intensity vs. contrast distribution measured in AOSLO images
Fig. 7.
Fig. 7. Comparison of modeled vs. measured probability distributions of cone reflection intensity. (A) Normalized cone intensity data in Model 2 matches the measured data in the low coherence condition (red) but not the high coherence condition (black). (B). Normalized cone intensities data from Model 3 matches both coherence sources. Both models incorporate the optimal noise factor derived for Fig. 6.
Fig. 8.
Fig. 8. Comparison of simulated and actual AOSLO images. Images with the high coherence source have consistently higher variation in cone intensities than images produced with a low coherence source. Cone positions and gap sizes are identical in all modeled images. Images are normalized to the high coherence condition. Actual images were taken at an inferior eccentricity of 1.7°. Differential coherence images (low minus high, right column) exhibit variation in reflection due to interference as well as occasional annular intensity profiles centered on cones. Differential data are represented in root mean square (RMS) units. Bottom panels show magnified views of 4 matched examples from the modeled and in vivo data (outlined in yellow and red), illustrating annuli with two types of polarity between center and annulus.
Fig. 9.
Fig. 9. Cone reflection intensity as a function of extracellular gap size. A cone that exhibited an annulus with Model 3 in Fig. 8 was chosen as a starting condition (IS/OS gap = 1.28 µm, OST gap = 2.27  µm). The gap sizes were varied independently in steps of 0.05 µm. Variation of cone intensity is more obvious in the high coherence condition, and is greatest when the IS/OS gap is varied. The visibility of the annulus in the differential coherence images is dependent on both the IS/OS and OST gap sizes. Cone images are normalized to the maximum value among coherence conditions; differential images are normalized to the maximum deviation.
Fig. 10.
Fig. 10. Cone reflection intensity as a function of inner and outer segment diameter. Example cone reflectance from a high coherence (A) and low coherence source (B) for a cone with an IS/OS gap = 1.40 µm and OST gap = 1.17 µm. Differential coherence images (C) show that the presence of an annulus is sensitive to segment diameters. Varying the gap sizes will yield different reflectance profiles, including cases with negative difference images (see Fig. 9).
Fig. 11.
Fig. 11. Polarization and IS/OS dependency of annular differential coherence images. (A) Reflection patterns as a function of outer segment diameter for a cone with IS/OS gap = 1.28 µm and OST gap = 2.27 µm. The difference image is ring-like for unpolarized light. If light is polarized, the image has waveguide features containing an LP11 mode. (B) Intensity profiles of individual reflections in the x direction with unpolarized light. IS/OS 1, 2 and 3 are the reflections from the three interfaces at this junction (from proximal to distal), while OST 1 and 2 are the reflections from the proximal and distal interfaces bracketing this gap. Larger outer segments increase the IS/OS profile width compared to the OST, and can be bimodal. (C) Cone images for the examples in B, grouping the reflections from just IS/OS or OST. Images are normalized within each set, with a zero value for the differential coherence images set to the middle gray level.

Equations (21)

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2 i n 0 k 0 z ψ x = H ψ x ,
2 i n 0 k 0 z ψ x = ( A x + A y ) ψ x ,
A x ψ x x ( 1 n 2 x ( n 2 ψ x ) ) + 1 2 k 0 2 ( n 2 n 0 2 ) ψ x
A y ψ x 2 ψ x y 2 + 1 2 k 0 2 ( n 2 n 0 2 ) ψ x .
2 i n 0 u m + 1 u m Δ z = ( A x + A y ) u m + 1 + u m 2 ,
M y u i , j m + 1 / 2 = q y .
a j = 1 Δ y 2 , b j = 4 i n 0 k 0 Δ z + 2 Δ y 2 1 2 k 0 2 [ ( n i , j m + 1 / 2 ) 2 n 0 2 ] , c j = 1 Δ y 2 ,
q j = 1 Δ y 2 [ u i , j 1 m + u i , j + 1 m ] + { 4 i n 0 k 0 Δ z 2 Δ y 2 + 1 2 k 0 2 [ ( n i , j m ) 2 n 0 2 ] } u i , j m .
M x u i , j m + 1 = q x
a i = 1 Δ x 2 T i 1 , j m + 1 , b i = 4 i n 0 k 0 Δ z + 2 Δ x 2 R i , j 1 2 k 0 2 [ ( n i , j m + 1 ) 2 n 0 2 ] , c i = 1 Δ x 2 T i + 1 , j m + 1 , q i = 1 Δ x 2 [ T i 1 , j m + 1 / 2 u i , j 1 m + 1 / 2 + T i + 1 , j m + 1 / 2 u i , j + 1 m + 1 / 2 ] + { 4 i n 0 k 0 Δ z 2 R i , j m + 1 / 2 Δ x 2 + 1 2 k 0 2 [ ( n i , j m + 1 / 2 ) 2 n 0 2 ] } u i , j m + 1 / 2 ,
T i ± 1 , j 2 n i ± 1 , j 2 n i + 1 , j 2 + n i , j 2
R i , j 2 T i + 1 , j + T i 1 , j 2 .
P = 0 r p | ψ r h | 2 d r ,
ψ + z = ψ z ψ z ,
d = { d o s d 0 l i s 2 z 2 + d 0  for  0 z < l i s d o s  for  z l i s ,
ρ = 0.061 ε 2 + 1.50 ε + 3.26
d 0 = 0.09 ρ + 8.2
P = i = 1 N P i + i = 1 , j = 2 N [ 2 P i P j γ ] , for  j > i ,
γ = Re { exp [ 2 i π L λ ] exp [ ( π L 2 l c ) 2 ] } ,
Δ P = P 1 P 2 ,
Δ P = i = 1 , j = 2 N [ 2 P i P j γ 1 ] i = 1 , j = 2 N [ 2 P i P j γ 2 ] , for  j > i .