Abstract

We developed a spectral-domain visible-light optical coherence tomography (VIS-OCT) based multimodal imaging technique which can accomplish simultaneous OCT and fluorescence imaging with a single broadband light source. Phantom experiments showed that by using the simultaneously acquired OCT images as a reference, the effect of light attenuation on the intensity of the fluorescent images by materials in front of the fluorescent target can be compensated. This capability of the multimodal imaging technique is of high importance for achieving quantification of the true intensities of autofluorescence (AF) imaging of the retina. We applied the technique in retinal imaging including AF imaging of the retinal pigment epithelium and fluorescein angiography (FA). We successfully demonstrated the effect of compensation on AF and FA images with the simultaneously acquired VIS-OCT images.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [PubMed]

2015 (1)

2014 (2)

2013 (3)

J. Yi, Q. Wei, W. Liu, V. Backman, and H. F. Zhang, “Visible-light optical coherence tomography for retinal oximetry,” Opt. Lett. 38(11), 1796–1798 (2013).
[Crossref] [PubMed]

C. Dai, X. Liu, H. F. Zhang, C. A. Puliafito, and S. Jiao, “Absolute retinal blood flow measurement with a dual-beam Doppler optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. 54(13), 7998–8003 (2013).
[Crossref] [PubMed]

J. I. W. Morgan and E. N. Pugh., “Scanning Laser Ophthalmoscope Measurement of Local Fundus Reflectance and Autofluorescence Changes Arising from Rhodopsin Bleaching and Regeneration,” Invest. Ophthalmol. Vis. Sci. 54(3), 2048–2059 (2013).
[Crossref] [PubMed]

2012 (3)

C. Dai, X. Liu, and S. Jiao, “Simultaneous optical coherence tomography and autofluorescence microscopy with a single light source,” J. Biomed. Opt. 17(8), 080502 (2012).
[Crossref] [PubMed]

J. R. Sparrow, E. Gregory-Roberts, K. Yamamoto, A. Blonska, S. K. Ghosh, K. Ueda, and J. Zhou, “The bisretinoids of retinal pigment epithelium,” Prog. Retin. Eye Res. 31(2), 121–135 (2012).
[Crossref] [PubMed]

X. Zhang, H. F. Zhang, S. Jiao, and S. Jiao, “Optical Coherence Photoacoustic Microscopy: accomplishing optical coherence tomography and photoacoustic microscopy with a single light source,” J. Biomed. Opt. 17(3), 030502 (2012).
[Crossref] [PubMed]

2011 (3)

X. Zhang, H. F. Zhang, C. A. Puliafito, and S. Jiao, “Simultaneous in vivo imaging of melanin and lipofuscin in the retina with multimodal photoacoustic ophthalmoscopy,” J. Biomed. Opt. 16, 080504 (2011).
[Crossref] [PubMed]

X. Zhang, J. Hu, R. W. Knighton, X.-R. Huang, C. A. Puliafito, and S. Jiao, “Dual-band spectral-domain optical coherence tomography for in vivo imaging the spectral contrasts of the retinal nerve fiber layer,” Opt. Express 19(20), 19653–19659 (2011).
[Crossref] [PubMed]

F. Delori, J. P. Greenberg, R. L. Woods, J. Fischer, T. Duncker, J. Sparrow, and R. T. Smith, “Quantitative measurements of autofluorescence with the scanning laser ophthalmoscope,” Invest. Ophthalmol. Vis. Sci. 52(13), 9379–9390 (2011).
[Crossref] [PubMed]

2010 (4)

A. D. Singh, R. N. Belfort, K. Sayanagi, and P. K. Kaiser, “Fourier domain optical coherence tomographic and auto-fluorescence findings in indeterminate choroidal melanocytic lesions,” Br. J. Ophthalmol. 94(4), 474–478 (2010).
[Crossref] [PubMed]

E. J. Johnson, “Age-related macular degeneration and antioxidant vitamins: recent findings,” Curr. Opin. Clin. Nutr. Metab. Care 13(1), 28–33 (2010).
[Crossref] [PubMed]

X. Zhang, M. Jiang, A. A. Fawzi, X. Li, K. K. Shung, C. A. Puliafito, H. F. Zhang, and S. Jiao, “Simultaneous dual molecular contrasts provided by the absorbed photons in photoacoustic microscopy,” Opt. Lett. 35(23), 4018–4020 (2010).
[Crossref] [PubMed]

B. M. Kevany and K. Palczewski, “Phagocytosis of retinal rod and cone photoreceptors,” Physiology (Bethesda) 25(1), 8–15 (2010).
[Crossref] [PubMed]

2005 (4)

J. R. Sparrow and M. Boulton, “RPE lipofuscin and its role in retinal pathobiology,” Exp. Eye Res. 80(5), 595–606 (2005).
[Crossref] [PubMed]

O. Strauss, “The retinal pigment epithelium in visual function,” Physiol. Rev. 85(3), 845–881 (2005).
[Crossref] [PubMed]

S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. Puliafito, “Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography,” Opt. Express 13(2), 444–452 (2005).
[Crossref] [PubMed]

J. R. Sparrow and M. Boulton, “RPE lipofuscin and its role in retinal pathobiology,” Exp. Eye Res. 80(5), 595–606 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

J. R. Sparrow, N. Fishkin, J. Zhou, B. Cai, Y. P. Jang, S. Krane, Y. Itagaki, and K. Nakanishi, “A2E, a byproduct of the visual cycle,” Vision Res. 43(28), 2983–2990 (2003).
[Crossref] [PubMed]

2002 (1)

B. Povazay, A. A. Apolonski, A. Unterhuber, B. Hermann, K. K. Bizheva, H. Sattmann, P. S. J. Russell, F. Krausz, A. F. Fercher, and W. Drexler, “Visible light optical coherence tomography,” Proc. SPIE 4619, 90–94 (2002).
[Crossref]

1998 (1)

F. G. Holz, C. Bellmann, K. Rohrschneider, R. O. W. Burk, and H. E. Völcker, “Simultaneous confocal scanning laser fluorescein and indocyanine green angiography,” Am. J. Ophthalmol. 125(2), 227–236 (1998).
[Crossref] [PubMed]

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 (2)

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995).
[PubMed]

F. C. Delori, G. Staurenghi, O. Arend, C. K. Dorey, D. G. Goger, and J. J. Weiter, “In vivo measurement of lipofuscin in Stargardt’s disease--Fundus flavimaculatus,” Invest. Ophthalmol. Vis. Sci. 36(11), 2327–2331 (1995).
[PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1989 (1)

M. Boulton, N. M. McKechnie, J. Breda, M. Bayly, and J. Marshall, “The formation of autofluorescent granules in cultured human RPE,” Invest. Ophthalmol. Vis. Sci. 30(1), 82–89 (1989).
[PubMed]

1987 (1)

1986 (1)

J. J. Weiter, F. C. Delori, G. L. Wing, and K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27(2), 145–152 (1986).
[PubMed]

1985 (1)

F. C. Delori, S. E. Bursell, A. Yoshida, and J. W. McMeel, “Vitreous fluorophotometry in diabetics: study of artifactual contributions,” Graefes Arch. Clin. Exp. Ophthalmol. 222(4-5), 215–218 (1985).
[Crossref] [PubMed]

1976 (1)

G. De Venecia, M. Davis, and R. Engerman, “Clinicopathologic correlations in diabetic retinopathy. i. histology and fluorescein angiography of microaneurysms,” Arch. Ophthalmol. 94(10), 1766–1773 (1976).
[Crossref] [PubMed]

1962 (1)

E. A. Boettner and J. R. Wolter, “Transmission of the ocular media,” Invest. Ophthalmol. Vis. Sci. 1(6), 776–783 (1962).

Apolonski, A. A.

B. Povazay, A. A. Apolonski, A. Unterhuber, B. Hermann, K. K. Bizheva, H. Sattmann, P. S. J. Russell, F. Krausz, A. F. Fercher, and W. Drexler, “Visible light optical coherence tomography,” Proc. SPIE 4619, 90–94 (2002).
[Crossref]

Arend, O.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995).
[PubMed]

F. C. Delori, G. Staurenghi, O. Arend, C. K. Dorey, D. G. Goger, and J. J. Weiter, “In vivo measurement of lipofuscin in Stargardt’s disease--Fundus flavimaculatus,” Invest. Ophthalmol. Vis. Sci. 36(11), 2327–2331 (1995).
[PubMed]

Backman, V.

Bayly, M.

M. Boulton, N. M. McKechnie, J. Breda, M. Bayly, and J. Marshall, “The formation of autofluorescent granules in cultured human RPE,” Invest. Ophthalmol. Vis. Sci. 30(1), 82–89 (1989).
[PubMed]

Belfort, R. N.

A. D. Singh, R. N. Belfort, K. Sayanagi, and P. K. Kaiser, “Fourier domain optical coherence tomographic and auto-fluorescence findings in indeterminate choroidal melanocytic lesions,” Br. J. Ophthalmol. 94(4), 474–478 (2010).
[Crossref] [PubMed]

Bellmann, C.

F. G. Holz, C. Bellmann, K. Rohrschneider, R. O. W. Burk, and H. E. Völcker, “Simultaneous confocal scanning laser fluorescein and indocyanine green angiography,” Am. J. Ophthalmol. 125(2), 227–236 (1998).
[Crossref] [PubMed]

Berendschot, T. T.

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]

Bizheva, K. K.

B. Povazay, A. A. Apolonski, A. Unterhuber, B. Hermann, K. K. Bizheva, H. Sattmann, P. S. J. Russell, F. Krausz, A. F. Fercher, and W. Drexler, “Visible light optical coherence tomography,” Proc. SPIE 4619, 90–94 (2002).
[Crossref]

Blonska, A.

J. R. Sparrow, E. Gregory-Roberts, K. Yamamoto, A. Blonska, S. K. Ghosh, K. Ueda, and J. Zhou, “The bisretinoids of retinal pigment epithelium,” Prog. Retin. Eye Res. 31(2), 121–135 (2012).
[Crossref] [PubMed]

Boettner, E. A.

E. A. Boettner and J. R. Wolter, “Transmission of the ocular media,” Invest. Ophthalmol. Vis. Sci. 1(6), 776–783 (1962).

Boulton, M.

J. R. Sparrow and M. Boulton, “RPE lipofuscin and its role in retinal pathobiology,” Exp. Eye Res. 80(5), 595–606 (2005).
[Crossref] [PubMed]

J. R. Sparrow and M. Boulton, “RPE lipofuscin and its role in retinal pathobiology,” Exp. Eye Res. 80(5), 595–606 (2005).
[Crossref] [PubMed]

M. Boulton, N. M. McKechnie, J. Breda, M. Bayly, and J. Marshall, “The formation of autofluorescent granules in cultured human RPE,” Invest. Ophthalmol. Vis. Sci. 30(1), 82–89 (1989).
[PubMed]

Breda, J.

M. Boulton, N. M. McKechnie, J. Breda, M. Bayly, and J. Marshall, “The formation of autofluorescent granules in cultured human RPE,” Invest. Ophthalmol. Vis. Sci. 30(1), 82–89 (1989).
[PubMed]

Burk, R. O. W.

F. G. Holz, C. Bellmann, K. Rohrschneider, R. O. W. Burk, and H. E. Völcker, “Simultaneous confocal scanning laser fluorescein and indocyanine green angiography,” Am. J. Ophthalmol. 125(2), 227–236 (1998).
[Crossref] [PubMed]

Bursell, S. E.

F. C. Delori, S. E. Bursell, A. Yoshida, and J. W. McMeel, “Vitreous fluorophotometry in diabetics: study of artifactual contributions,” Graefes Arch. Clin. Exp. Ophthalmol. 222(4-5), 215–218 (1985).
[Crossref] [PubMed]

Cai, B.

J. R. Sparrow, N. Fishkin, J. Zhou, B. Cai, Y. P. Jang, S. Krane, Y. Itagaki, and K. Nakanishi, “A2E, a byproduct of the visual cycle,” Vision Res. 43(28), 2983–2990 (2003).
[Crossref] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Dai, C.

C. Dai, X. Liu, H. F. Zhang, C. A. Puliafito, and S. Jiao, “Absolute retinal blood flow measurement with a dual-beam Doppler optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. 54(13), 7998–8003 (2013).
[Crossref] [PubMed]

C. Dai, X. Liu, and S. Jiao, “Simultaneous optical coherence tomography and autofluorescence microscopy with a single light source,” J. Biomed. Opt. 17(8), 080502 (2012).
[Crossref] [PubMed]

Davis, M.

G. De Venecia, M. Davis, and R. Engerman, “Clinicopathologic correlations in diabetic retinopathy. i. histology and fluorescein angiography of microaneurysms,” Arch. Ophthalmol. 94(10), 1766–1773 (1976).
[Crossref] [PubMed]

De Venecia, G.

G. De Venecia, M. Davis, and R. Engerman, “Clinicopathologic correlations in diabetic retinopathy. i. histology and fluorescein angiography of microaneurysms,” Arch. Ophthalmol. 94(10), 1766–1773 (1976).
[Crossref] [PubMed]

Delori, F.

F. Delori, J. P. Greenberg, R. L. Woods, J. Fischer, T. Duncker, J. Sparrow, and R. T. Smith, “Quantitative measurements of autofluorescence with the scanning laser ophthalmoscope,” Invest. Ophthalmol. Vis. Sci. 52(13), 9379–9390 (2011).
[Crossref] [PubMed]

Delori, F. C.

F. C. Delori, G. Staurenghi, O. Arend, C. K. Dorey, D. G. Goger, and J. J. Weiter, “In vivo measurement of lipofuscin in Stargardt’s disease--Fundus flavimaculatus,” Invest. Ophthalmol. Vis. Sci. 36(11), 2327–2331 (1995).
[PubMed]

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995).
[PubMed]

J. J. Weiter, F. C. Delori, G. L. Wing, and K. A. Fitch, “Retinal pigment epithelial lipofuscin and melanin and choroidal melanin in human eyes,” Invest. Ophthalmol. Vis. Sci. 27(2), 145–152 (1986).
[PubMed]

F. C. Delori, S. E. Bursell, A. Yoshida, and J. W. McMeel, “Vitreous fluorophotometry in diabetics: study of artifactual contributions,” Graefes Arch. Clin. Exp. Ophthalmol. 222(4-5), 215–218 (1985).
[Crossref] [PubMed]

Dorey, C. K.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995).
[PubMed]

F. C. Delori, G. Staurenghi, O. Arend, C. K. Dorey, D. G. Goger, and J. J. Weiter, “In vivo measurement of lipofuscin in Stargardt’s disease--Fundus flavimaculatus,” Invest. Ophthalmol. Vis. Sci. 36(11), 2327–2331 (1995).
[PubMed]

Drexler, W.

B. Povazay, A. A. Apolonski, A. Unterhuber, B. Hermann, K. K. Bizheva, H. Sattmann, P. S. J. Russell, F. Krausz, A. F. Fercher, and W. Drexler, “Visible light optical coherence tomography,” Proc. SPIE 4619, 90–94 (2002).
[Crossref]

Duker, J.

Duncker, T.

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P. D. Kiser, M. Golczak, and K. Palczewski, “Chemistry of the retinoid (visual) cycle,” Chem. Rev. 114(1), 194–232 (2014).
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Povazay, B.

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J. I. W. Morgan and E. N. Pugh., “Scanning Laser Ophthalmoscope Measurement of Local Fundus Reflectance and Autofluorescence Changes Arising from Rhodopsin Bleaching and Regeneration,” Invest. Ophthalmol. Vis. Sci. 54(3), 2048–2059 (2013).
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Puliafito, C. A.

X. Liu, T. Liu, R. Wen, Y. Li, C. A. Puliafito, H. F. Zhang, and S. Jiao, “Optical coherence photoacoustic microscopy for in vivo multimodal retinal imaging,” Opt. Lett. 40(7), 1370–1373 (2015).
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X. Zhang, J. Hu, R. W. Knighton, X.-R. Huang, C. A. Puliafito, and S. Jiao, “Dual-band spectral-domain optical coherence tomography for in vivo imaging the spectral contrasts of the retinal nerve fiber layer,” Opt. Express 19(20), 19653–19659 (2011).
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X. Zhang, M. Jiang, A. A. Fawzi, X. Li, K. K. Shung, C. A. Puliafito, H. F. Zhang, and S. Jiao, “Simultaneous dual molecular contrasts provided by the absorbed photons in photoacoustic microscopy,” Opt. Lett. 35(23), 4018–4020 (2010).
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F. G. Holz, C. Bellmann, K. Rohrschneider, R. O. W. Burk, and H. E. Völcker, “Simultaneous confocal scanning laser fluorescein and indocyanine green angiography,” Am. J. Ophthalmol. 125(2), 227–236 (1998).
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B. Povazay, A. A. Apolonski, A. Unterhuber, B. Hermann, K. K. Bizheva, H. Sattmann, P. S. J. Russell, F. Krausz, A. F. Fercher, and W. Drexler, “Visible light optical coherence tomography,” Proc. SPIE 4619, 90–94 (2002).
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A. D. Singh, R. N. Belfort, K. Sayanagi, and P. K. Kaiser, “Fourier domain optical coherence tomographic and auto-fluorescence findings in indeterminate choroidal melanocytic lesions,” Br. J. Ophthalmol. 94(4), 474–478 (2010).
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Singh, A. D.

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F. Delori, J. P. Greenberg, R. L. Woods, J. Fischer, T. Duncker, J. Sparrow, and R. T. Smith, “Quantitative measurements of autofluorescence with the scanning laser ophthalmoscope,” Invest. Ophthalmol. Vis. Sci. 52(13), 9379–9390 (2011).
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Sparrow, J.

F. Delori, J. P. Greenberg, R. L. Woods, J. Fischer, T. Duncker, J. Sparrow, and R. T. Smith, “Quantitative measurements of autofluorescence with the scanning laser ophthalmoscope,” Invest. Ophthalmol. Vis. Sci. 52(13), 9379–9390 (2011).
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J. R. Sparrow, E. Gregory-Roberts, K. Yamamoto, A. Blonska, S. K. Ghosh, K. Ueda, and J. Zhou, “The bisretinoids of retinal pigment epithelium,” Prog. Retin. Eye Res. 31(2), 121–135 (2012).
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Staurenghi, G.

F. C. Delori, G. Staurenghi, O. Arend, C. K. Dorey, D. G. Goger, and J. J. Weiter, “In vivo measurement of lipofuscin in Stargardt’s disease--Fundus flavimaculatus,” Invest. Ophthalmol. Vis. Sci. 36(11), 2327–2331 (1995).
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D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
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J. R. Sparrow, E. Gregory-Roberts, K. Yamamoto, A. Blonska, S. K. Ghosh, K. Ueda, and J. Zhou, “The bisretinoids of retinal pigment epithelium,” Prog. Retin. Eye Res. 31(2), 121–135 (2012).
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Weiter, J. J.

F. C. Delori, C. K. Dorey, G. Staurenghi, O. Arend, D. G. Goger, and J. J. Weiter, “In vivo fluorescence of the ocular fundus exhibits retinal pigment epithelium lipofuscin characteristics,” Invest. Ophthalmol. Vis. Sci. 36(3), 718–729 (1995).
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Wing, G. L.

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J. R. Sparrow, E. Gregory-Roberts, K. Yamamoto, A. Blonska, S. K. Ghosh, K. Ueda, and J. Zhou, “The bisretinoids of retinal pigment epithelium,” Prog. Retin. Eye Res. 31(2), 121–135 (2012).
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Yoshida, A.

F. C. Delori, S. E. Bursell, A. Yoshida, and J. W. McMeel, “Vitreous fluorophotometry in diabetics: study of artifactual contributions,” Graefes Arch. Clin. Exp. Ophthalmol. 222(4-5), 215–218 (1985).
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X. Liu, T. Liu, R. Wen, Y. Li, C. A. Puliafito, H. F. Zhang, and S. Jiao, “Optical coherence photoacoustic microscopy for in vivo multimodal retinal imaging,” Opt. Lett. 40(7), 1370–1373 (2015).
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Figures (5)

Fig. 1
Fig. 1 Schematic of the imaging system. SC: supercontinuum; SLD: superluminescent diode; DM1-2: dichroic mirror; L1-3: Achromatic lens; LPF: long-pass filter; PH: pinhole; FP1-7: Fiber collimating port; ISO: Isolator; FC1-2: 3dB fiber coupler; PC1-2: Polarization controller; G1-2: BK-7 glass plate; M1-2: Mirror; IRIS1-2: Iris.
Fig. 2
Fig. 2 Phantom simulation experiment. (a) Schematic of the phantom; (b) The AF/OCT (the AF intensity divided by the 2nd boundary OCT intensity, green) signals were not influence by the OD values of the ND filter, unlike the raw AF signals (blue) and OCT signals (red). The linear decrease of AF/OCT was due to accumulated bleaching of the dye.
Fig. 3
Fig. 3 VIS-OCT and AF images simultaneously acquired from a rat retina in vivo. (a) OCT fundus image; (b) AF image; (c) OCT B-scan image. The dotted line in the OCT fundus image marks the location of the OCT B-scan image. Bar: 200 µm
Fig. 4
Fig. 4 The original AF intensities (a) and the normalized AF intensities (b) of four rats followed for a period of four weeks. Normalization was performed using the RPE image intensities calculated from the segmented OCT images.
Fig. 5
Fig. 5 VIS-OCT and AF images simultaneously acquired from a rat retina in vivo. (a) OCT fundus image; (b) AF image; (c) AF/OCT compensated fundus image; (d) OCT B-scan image. The dotted line in the OCT fundus image marks the location of the OCT B-scan image. Bar: 200 µm

Equations (4)

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I pre = I 0 . τ pre ( λ ) 2 . R pre ( λ ) 
I RPE = I 0 . τ pre ( λ ) 2 . [ 1 R pre ( λ ) ] 2 . τ RPE ( λ ) 2 . R RPE ( λ )       
I AFRPE = I 0 . τ pre ( λ ) 2 . [ 1 R pre ( λ ) ] 2 .  ε.C.d.Q. A d  
I AF I RPE = ε.C.d.Q.Ad τ RPE 2 ( λ ). R RPE ( λ )         

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