Abstract

Quantitative flow velocimetry in Optical Coherence Tomography is used to determine both the axial and lateral flow component at the level of individual voxels. The lateral flow is determined by analyzing the statistical properties of reflected electro-magnetic fields for repeated measurements at (nearly) the same location. The precision or statistical fluctuation of the quantitative velocity estimation depends on the number of repeated measurements and the method to determine quantitative flow velocity. In this paper, both a method to determine quantitative flow velocity and a model for the prediction of the statistical fluctuations of velocity estimations are developed to analyze and optimize the estimation precision for phase-based velocimetry methods. The method and model are validated by phantom measurements in a bulk scattering medium as well as in intralipid solution in a capillary. Based on the model, the number of repeated measurements to achieve a certain velocimetry precision is predicted.

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

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2017 (4)

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

C. L. Chen and R. K. Wang, “Optical coherence tomography based angiography [Invited],” Biomed. Opt. Express 8(2), 1056–1082 (2017).
[Crossref] [PubMed]

I. Popov, A. Weatherbee, and I. A. Vitkin, “Statistical properties of dynamic speckles from flowing Brownian scatterers in the vicinity of the image plane in optical coherence tomography,” Biomed. Opt. Express 8(4), 2004–2017 (2017).
[Crossref] [PubMed]

2016 (4)

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

R. Haindl, W. Trasischker, A. Wartak, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Total retinal blood flow measurement by three beam Doppler optical coherence tomography,” Biomed. Opt. Express 7(2), 287–301 (2016).
[Crossref] [PubMed]

A. Wartak, R. Haindl, W. Trasischker, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Active-passive path-length encoded (APPLE) Doppler OCT,” Biomed. Opt. Express 7(12), 5233–5251 (2016).
[Crossref] [PubMed]

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

2015 (3)

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23(3), 3448–3459 (2015).
[Crossref] [PubMed]

R. F. Spaide, J. G. Fujimoto, and N. K. Waheed, “Image Artifacts in Optical Coherence Tomography Angiography,” Retina 35(11), 2163–2180 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (3)

2012 (4)

2009 (1)

B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Statistical properties of phase-decorrelation in phase-resolved Doppler optical coherence tomography,” IEEE Trans. Med. Imaging 28(6), 814–821 (2009).
[Crossref] [PubMed]

2007 (2)

2006 (1)

2005 (2)

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

B. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[Crossref] [PubMed]

2002 (2)

2000 (1)

M. H. M. Cuypers, J. S. Kasanardjo, and B. C. P. Polak, “Retinal blood flow changes in diabetic retinopathy measured with the Heidelberg scanning laser Doppler flowmeter,” Graefes Arch. Clin. Exp. Ophthalmol. 238(12), 935–941 (2000).
[Crossref] [PubMed]

1997 (3)

1988 (1)

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
[Crossref] [PubMed]

1966 (1)

Akcay, C.

Barry, S.

Barton, J. K.

Baumann, B.

Berclaz, C.

Boas, D. A.

Bolmont, T.

Bouma, B.

Bouma, B. E.

B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Statistical properties of phase-decorrelation in phase-resolved Doppler optical coherence tomography,” IEEE Trans. Med. Imaging 28(6), 814–821 (2009).
[Crossref] [PubMed]

Bouwens, A.

Braaf, B.

Brecke, K. M.

Cable, A. E.

Cense, B.

Chan, A. C.

A. C. Chan, V. J. Srinivasan, and E. Y. Lam, “Maximum likelihood Doppler frequency estimation under decorrelation noise for quantifying flow in optical coherence tomography,” IEEE Trans. Med. Imaging 33(6), 1313–1323 (2014).
[Crossref] [PubMed]

Chan, K. K. W.

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Chen, C. L.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

C. L. Chen and R. K. Wang, “Optical coherence tomography based angiography [Invited],” Biomed. Opt. Express 8(2), 1056–1082 (2017).
[Crossref] [PubMed]

Chen, Z.

Cheung, C. Y.

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Chico-Calero, I.

Choi, W.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Cole, E. D.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Cuypers, M. H. M.

M. H. M. Cuypers, J. S. Kasanardjo, and B. C. P. Polak, “Retinal blood flow changes in diabetic retinopathy measured with the Heidelberg scanning laser Doppler flowmeter,” Graefes Arch. Clin. Exp. Ophthalmol. 238(12), 935–941 (2000).
[Crossref] [PubMed]

Dave, D.

de Boer, J.

de Boer, J. F.

de Carlo, T. E.

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

de Groot, M.

Ding, Z.

Duan, L.

Duker, J. S.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

Duong, T. Q.

E. R. Muir, R. C. Rentería, and T. Q. Duong, “Reduced ocular blood flow as an early indicator of diabetic retinopathy in a mouse model of diabetes,” Invest. Ophthalmol. Vis. Sci. 53(10), 6488–6494 (2012).
[Crossref] [PubMed]

Dupont, J. C.

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

Fingler, J.

Fraser, S. E.

Fujimoto, J. G.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

R. F. Spaide, J. G. Fujimoto, and N. K. Waheed, “Image Artifacts in Optical Coherence Tomography Angiography,” Retina 35(11), 2163–2180 (2015).
[Crossref] [PubMed]

Gahm, J. K.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Grunwald, J. E.

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

Hager, A.

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

Haindl, R.

Heussen, F. M.

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

Hitzenberger, C. K.

Hong, Y.

Hong, Y. J.

Hornegger, J.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Husvogt, L.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Izatt, J. A.

Jiang, J. Y.

Ju, M. J.

Kalkman, J.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23(3), 3448–3459 (2015).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 88(4), 042312 (2013).
[Crossref] [PubMed]

Kasanardjo, J. S.

M. H. M. Cuypers, J. S. Kasanardjo, and B. C. P. Polak, “Retinal blood flow changes in diabetic retinopathy measured with the Heidelberg scanning laser Doppler flowmeter,” Graefes Arch. Clin. Exp. Ophthalmol. 238(12), 935–941 (2000).
[Crossref] [PubMed]

Kashani, A. H.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Koch, E.

Kogelnik, H.

Kulkarni, M. D.

Kurokawa, K.

Lagendijk, A.

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
[Crossref] [PubMed]

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
[Crossref] [PubMed]

Lam, E. Y.

A. C. Chan, V. J. Srinivasan, and E. Y. Lam, “Maximum likelihood Doppler frequency estimation under decorrelation noise for quantifying flow in optical coherence tomography,” IEEE Trans. Med. Imaging 33(6), 1313–1323 (2014).
[Crossref] [PubMed]

Lasser, T.

Lee, B.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Lee, J.

Li, T.

Lim, Y.

Lo, E. H.

Maguire, M. G.

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

Maier, A.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Makita, S.

Malekafzali, A.

Mandeville, E. T.

Metelitsina, T. I.

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

Milner, T. E.

Miura, M.

Moult, E. M.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Muir, E. R.

E. R. Muir, R. C. Rentería, and T. Q. Duong, “Reduced ocular blood flow as an early indicator of diabetic retinopathy in a mouse model of diabetes,” Invest. Ophthalmol. Vis. Sci. 53(10), 6488–6494 (2012).
[Crossref] [PubMed]

Mujat, M.

Nam, A. S.

Nelson, J. S.

Novais, E. A.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Ouyang, Y.

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

Park, B.

Parrein, P.

Pierce, M. C.

Pircher, M.

Ploner, S. B.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Polak, B. C. P.

M. H. M. Cuypers, J. S. Kasanardjo, and B. C. P. Polak, “Retinal blood flow changes in diabetic retinopathy measured with the Heidelberg scanning laser Doppler flowmeter,” Graefes Arch. Clin. Exp. Ophthalmol. 238(12), 935–941 (2000).
[Crossref] [PubMed]

Popov, I.

Potsaid, B.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Radhakrishnan, H.

Ren, H.

Rentería, R. C.

E. R. Muir, R. C. Rentería, and T. Q. Duong, “Reduced ocular blood flow as an early indicator of diabetic retinopathy in a mouse model of diabetes,” Invest. Ophthalmol. Vis. Sci. 53(10), 6488–6494 (2012).
[Crossref] [PubMed]

Richter, G. M.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Rolland, J. P.

Romano, A.

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

Rosenfeld, P. J.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Schottenhamml, J.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

Schwartz, D.

Shao, Q.

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

Shi, Y.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Spaide, R. F.

R. F. Spaide, J. G. Fujimoto, and N. K. Waheed, “Image Artifacts in Optical Coherence Tomography Angiography,” Retina 35(11), 2163–2180 (2015).
[Crossref] [PubMed]

Srinivas, S.

Srinivasan, V. J.

A. C. Chan, V. J. Srinivasan, and E. Y. Lam, “Maximum likelihood Doppler frequency estimation under decorrelation noise for quantifying flow in optical coherence tomography,” IEEE Trans. Med. Imaging 33(6), 1313–1323 (2014).
[Crossref] [PubMed]

V. J. Srinivasan, H. Radhakrishnan, E. H. Lo, E. T. Mandeville, J. Y. Jiang, S. Barry, and A. E. Cable, “OCT methods for capillary velocimetry,” Biomed. Opt. Express 3(3), 612–629 (2012).
[Crossref] [PubMed]

Szkulmowski, M.

Szlag, D.

Tang, F.

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Tang, S.

Tearney, G.

Tearney, G. J.

B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Statistical properties of phase-decorrelation in phase-resolved Doppler optical coherence tomography,” IEEE Trans. Med. Imaging 28(6), 814–821 (2009).
[Crossref] [PubMed]

Tham, C. C. Y.

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Trasischker, W.

Vakoc, B. J.

A. S. Nam, I. Chico-Calero, and B. J. Vakoc, “Complex differential variance algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 5(11), 3822–3832 (2014).
[Crossref] [PubMed]

B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Statistical properties of phase-decorrelation in phase-resolved Doppler optical coherence tomography,” IEEE Trans. Med. Imaging 28(6), 814–821 (2009).
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van Albada, M. P.

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
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van Albada, MP

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
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van der Mark, MB

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
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van Gemert, M. J. C.

van Leeuwen, T. G.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23(3), 3448–3459 (2015).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 88(4), 042312 (2013).
[Crossref] [PubMed]

Vermeer, K. A.

Vienola, K. V.

Vitkin, I. A.

Waheed, N. K.

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

R. F. Spaide, J. G. Fujimoto, and N. K. Waheed, “Image Artifacts in Optical Coherence Tomography Angiography,” Retina 35(11), 2163–2180 (2015).
[Crossref] [PubMed]

Walther, J.

Wang, R. K.

C. L. Chen and R. K. Wang, “Optical coherence tomography based angiography [Invited],” Biomed. Opt. Express 8(2), 1056–1082 (2017).
[Crossref] [PubMed]

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Wang, X.

Wartak, A.

Weatherbee, A.

Weiss, N.

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23(3), 3448–3459 (2015).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 88(4), 042312 (2013).
[Crossref] [PubMed]

Welch, A. J.

Wojtkowski, M.

Wu, W.

Yamanari, M.

Yang, C.

Yasuno, Y.

Yatagai, T.

Yazdanfar, S.

Ying, G. S.

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

Young, A. L.

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Yun, S. H.

Zeimer, R.

R. Zeimer, “Nature is teaching us to be humble in our quest to measure structure and function in glaucoma,” Br. J. Ophthalmol. 91(1), 2–3 (2007).
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Zhao, Y.

Zheng, F.

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Zhu, B.

Appl. Opt. (2)

Biomed. Opt. Express (7)

B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive OCT of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5(8), 2736–2758 (2014).
[Crossref] [PubMed]

V. J. Srinivasan, H. Radhakrishnan, E. H. Lo, E. T. Mandeville, J. Y. Jiang, S. Barry, and A. E. Cable, “OCT methods for capillary velocimetry,” Biomed. Opt. Express 3(3), 612–629 (2012).
[Crossref] [PubMed]

I. Popov, A. Weatherbee, and I. A. Vitkin, “Statistical properties of dynamic speckles from flowing Brownian scatterers in the vicinity of the image plane in optical coherence tomography,” Biomed. Opt. Express 8(4), 2004–2017 (2017).
[Crossref] [PubMed]

C. L. Chen and R. K. Wang, “Optical coherence tomography based angiography [Invited],” Biomed. Opt. Express 8(2), 1056–1082 (2017).
[Crossref] [PubMed]

A. S. Nam, I. Chico-Calero, and B. J. Vakoc, “Complex differential variance algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 5(11), 3822–3832 (2014).
[Crossref] [PubMed]

R. Haindl, W. Trasischker, A. Wartak, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Total retinal blood flow measurement by three beam Doppler optical coherence tomography,” Biomed. Opt. Express 7(2), 287–301 (2016).
[Crossref] [PubMed]

A. Wartak, R. Haindl, W. Trasischker, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Active-passive path-length encoded (APPLE) Doppler OCT,” Biomed. Opt. Express 7(12), 5233–5251 (2016).
[Crossref] [PubMed]

BMJ Open Ophthalmol (1)

K. K. W. Chan, F. Tang, C. C. Y. Tham, A. L. Young, and C. Y. Cheung, “Retinal vasculature in glaucoma: a review,” BMJ Open Ophthalmol 1(1), e000032 (2017).
[Crossref] [PubMed]

Br. J. Ophthalmol. (1)

R. Zeimer, “Nature is teaching us to be humble in our quest to measure structure and function in glaucoma,” Br. J. Ophthalmol. 91(1), 2–3 (2007).
[Crossref] [PubMed]

Eur. J. Ophthalmol. (1)

Q. Shao, F. M. Heussen, Y. Ouyang, and A. Hager, “Retinal vessel diameter changes in different severities of diabetic retinopathy by SD-OCT,” Eur. J. Ophthalmol. 26(4), 342–346 (2016).
[Crossref] [PubMed]

Graefes Arch. Clin. Exp. Ophthalmol. (1)

M. H. M. Cuypers, J. S. Kasanardjo, and B. C. P. Polak, “Retinal blood flow changes in diabetic retinopathy measured with the Heidelberg scanning laser Doppler flowmeter,” Graefes Arch. Clin. Exp. Ophthalmol. 238(12), 935–941 (2000).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (2)

B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Statistical properties of phase-decorrelation in phase-resolved Doppler optical coherence tomography,” IEEE Trans. Med. Imaging 28(6), 814–821 (2009).
[Crossref] [PubMed]

A. C. Chan, V. J. Srinivasan, and E. Y. Lam, “Maximum likelihood Doppler frequency estimation under decorrelation noise for quantifying flow in optical coherence tomography,” IEEE Trans. Med. Imaging 33(6), 1313–1323 (2014).
[Crossref] [PubMed]

Int. J. Retina Vitreous (1)

T. E. de Carlo, A. Romano, N. K. Waheed, and J. S. Duker, “A review of optical coherence tomography angiography (OCTA),” Int. J. Retina Vitreous 1(1), 5 (2015).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

J. E. Grunwald, T. I. Metelitsina, J. C. Dupont, G. S. Ying, and M. G. Maguire, “Reduced foveolar choroidal blood flow in eyes with increasing AMD severity,” Invest. Ophthalmol. Vis. Sci. 46(3), 1033–1038 (2005).
[Crossref] [PubMed]

E. R. Muir, R. C. Rentería, and T. Q. Duong, “Reduced ocular blood flow as an early indicator of diabetic retinopathy in a mouse model of diabetes,” Invest. Ophthalmol. Vis. Sci. 53(10), 6488–6494 (2012).
[Crossref] [PubMed]

Opt. Express (9)

B. Braaf, K. A. Vermeer, K. V. Vienola, and J. F. de Boer, “Angiography of the retina and the choroid with phase-resolved OCT using interval-optimized backstitched B-scans,” Opt. Express 20(18), 20516–20534 (2012).
[Crossref] [PubMed]

J. Lee, W. Wu, J. Y. Jiang, B. Zhu, and D. A. Boas, “Dynamic light scattering optical coherence tomography,” Opt. Express 20(20), 22262–22277 (2012).
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A. Bouwens, D. Szlag, M. Szkulmowski, T. Bolmont, M. Wojtkowski, and T. Lasser, “Quantitative lateral and axial flow imaging with optical coherence microscopy and tomography,” Opt. Express 21(15), 17711–17729 (2013).
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M. J. Ju, Y. J. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura, S. Tang, and Y. Yasuno, “Advanced multi-contrast Jones matrix optical coherence tomography for Doppler and polarization sensitive imaging,” Opt. Express 21(16), 19412–19436 (2013).
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S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23(3), 3448–3459 (2015).
[Crossref] [PubMed]

J. Fingler, D. Schwartz, C. Yang, and S. E. Fraser, “Mobility and transverse flow visualization using phase variance contrast with spectral domain optical coherence tomography,” Opt. Express 15(20), 12636–12653 (2007).
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B. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
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J. Walther and E. Koch, “Relation of joint spectral and time domain optical coherence tomography (jSTdOCT) and phase-resolved Doppler OCT,” Opt. Express 22(19), 23129–23146 (2014).
[Crossref] [PubMed]

Opt. Lett. (5)

Phys. Rev. B Condens. Matter (1)

A. Lagendijk, M. P. van Albada, A. Lagendijk, MB van der Mark, and MP van Albada, “Light scattering in strongly scattering media: Multiple scattering and weak localization,” Phys. Rev. B Condens. Matter 37(7), 3575–3592 (1988).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 88(4), 042312 (2013).
[Crossref] [PubMed]

Prog. Retin. Eye Res. (1)

A. H. Kashani, C. L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retin. Eye Res. 60, 66–100 (2017).
[Crossref] [PubMed]

Retina (2)

S. B. Ploner, E. M. Moult, W. Choi, N. K. Waheed, B. Lee, E. A. Novais, E. D. Cole, B. Potsaid, L. Husvogt, J. Schottenhamml, A. Maier, P. J. Rosenfeld, J. S. Duker, J. Hornegger, and J. G. Fujimoto, “Toward quantitative optical coherence tomography angiography: Visualizing Blood Flow Speeds in Ocular Pathology Using Variable Interscan Time Analysis,” Retina 36(Suppl 1), S118–S126 (2016).
[Crossref] [PubMed]

R. F. Spaide, J. G. Fujimoto, and N. K. Waheed, “Image Artifacts in Optical Coherence Tomography Angiography,” Retina 35(11), 2163–2180 (2015).
[Crossref] [PubMed]

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J. W. Goodman, Statistical optics, Wiley classics library ed., Wiley classics library (Wiley, New York, 2000), pp. xvii, 550 p.

H. L. V. Trees, Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise (Krieger Publishing Co., Inc., 1992), p. 646.

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Figures (7)

Fig. 1
Fig. 1 Schematic illustration of the incident and backpropagating field focused by a lens or objective onto a sample. The fields are considered as superpositions of plane waves with the wave vectors p in and p out which are weighed by m in ( p in ) and m out ( p out ), respectively.
Fig. 2
Fig. 2 In blue graphs of the PDF P(φ|α) given in Eq. (19) for different ratios of displacement. a) δr/ w 0 =0.05. b) δr/ w 0 =1. In red the fits with a Gaussian (Eq. (20)) are shown. In b) a and hfrom Eq. (20) are indicated c) The ratio h/a as a function of δr/ w 0 . The ratio increases with increasing displacement.
Fig. 3
Fig. 3 Simulation of the estimated velocity and the velocity precision as a function of actual velocity determined by three estimation methods: Gauss. fit (blue), second moment (red) and MLE (black). Velocity is expressed as a ratio of δr/ w 0 . a) estimated velocity as a function of input velocity. Crosses show the average estimated velocity and the full error bar length indicates two times the standard deviation. b) zoom in from a) while omitting the error bars. The solid line represents a slope of 1 (indication when estimated is the same as set ratio). c) standard deviation of the fluctuation as a function of average velocity, showing the estimation precision. d) zoom in from c) for a better visibility of the differences between second moment and MLE. Additionally, the Cramér-Rao lower bound (CRLB, solid black line) was included. The MLE comes closest to the Cramér-Rao lower bound indicating a low estimation uncertainty. Each simulation was based on N = 290 samples, each simulation was repeated 5000 times for a given actual velocity.
Fig. 4
Fig. 4 Interferometer for phase sensitive measurements as well as polarization sensitive acquisition. PDU: polarization delay unit, P: polarizer, PC: polarization controller, PBS: polarization beam splitter, FBG: fiber-bragg-grating, PD: photo diode
Fig. 5
Fig. 5 a) Schematic drawing of the flow phantom setup in front of the ophthalmic interface (same as in [31]). f: lens of 15 mm focal length, Ph: phantom consisting of a scattering medium with embedded capillary with 150 µm inner diameter, R: reservoir for intralipid. b) Structural image of a single B-scan. The part of the static medium used for the analysis is delineated in yellow and the inner boundary circle of the capillary delineated in red.
Fig. 6
Fig. 6 Analysis of the velocity estimation uncertainties for measurements (dots) compared to simulations (solid line) for the cases of 290 samples per estimation (a and b) and 33 samples per estimation (c and d). Flow is mimicked by a motion of the beam with respect to a static medium (a and c) and by pumping intralipid with a constant flow rate through a capillary (b and d). Three estimators were used (see 2. Theory & Simulations): Gauss. fit (blue), second moment (red) and MLE (black).
Fig. 7
Fig. 7 Double logarithmic plot of the velocity estimation uncertainty for a set normalized velocity of 0.92 and varying samples per velocity estimation for the Gauss. fit method (blue) and the MLE (black). The dashed lines indicate a fit of a linear function with slope −0.5, indicating that the velocity estimation uncertainty is inversely proportional to the square root of the number of samples per estimation.

Equations (23)

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E in (r)= m in ( p in ) e ir p in d p , in
E S ( r 2 ; p out )= n G( r 2 , r 1 ; p out ) F n ( r 1 ) E in ( r 1 )d r 1
G( r 2 , r 1 ; p out )= e i p out ( r 1 r) | r 1 r 2 | e ikf f e i p out r 1
E(f,k)= m out ( p out ) E s (f, p out ) d p ,out
E( r n ,k)= k 2 e ikf f n m in ( p in ) exp[ i r n p in ]d p ,in E in × m out ( p out ) exp[ i r n p out ]d p ,out E out .
E(r,k) e z 2 / l c 2 m in ( p in ) exp[ ir p in ]d p ,in E in (r) × m out ( p out ) exp[ ir p out ]d p ,out E out (r)
p z =k 1 p x 2 k 2 p y 2 k 2 k( 1 p x 2 2 k 2 p y 2 2 k 2 )
E in (r)= e izk e k 2 w 0 2 ( x 2 + y 2 ) k 2 w 0 4 +2 z 2 e ( x 2 + y 2 ) w (z) 2 e i 2zk( x 2 + y 2 ) k 2 w 0 4 +4 z 2 e i k( x 2 + y 2 ) 2R(z) w 0 2 w 0 2 i 2z k w 0 w(z) e iζ(z)
Γ B = μ A Γ A + μ C Γ C ,
E A (r)= E in (r) E out (r)exp( z 2 / l c 2 )
α= E B (x+δx,y,z+δz) E A (x,y,z) d 3 r E B (x+δx,y,z+δz) E B (x+δx,y,z+δz) d 3 r E A (x,y,z) E A (x,y,z) d 3 r
E B (r+δr) E A (r) d 3 r = e i2 k 0 δz e δ z 2 2 l c 2 × w 0 2 w (zΔz+δz) 2 w 0 2 w (zΔz) 2 e i(ζ(zΔz)ζ(zΔz+δz)) × e [ 2[ (x+δx) 2 + y 2 ] w (zΔz+δz) 2 + 2( x 2 + y 2 ) w (zΔz) 2 ] e i k[ (x+δx) 2 + y 2 ] R(zΔz+δz) +i k( x 2 + y 2 ) R(zΔz) dxdy e 2 (zΔz+δz/2) 2 l c 2 dz
E B E A d 3 r = e i2 k 0 δz e δ z 2 2 l c 2 ( w 0 2 w ( z ) 2 ) 2 e 2 ( z +δz/2) 2 l c 2 × e [ 2[ (x+δx) 2 + x 2 +2 y 2 ] w ( z ) 2 ] e i k[ (x+δx) 2 x 2 ] R( z ) dxdyd z .
E B E A d 3 r = e i2 k 0 δz e δ z 2 2 l c 2 ( w 0 2 w (ξ) 2 ) 2 × e [ 2[ (x+δx) 2 + x 2 +2 y 2 ] w (ξ) 2 ] e i k[ (x+δx) 2 x 2 ] R(ξ) dxdy × e 2 ( z +δz) 2 l c 2 d z .
α= e i2 k 0 δz e δ x 2 w 0 2 e δ z 2 2 l c 2
P A ( x Γ , y Γ | μ A )= 2 x Γ μ A 2 exp( x Γ 2 μ A 2 )
P C ( x Γ , y Γ | μ C )= 1 π μ C 2 exp( x Γ 2 + y Γ 2 μ A 2 )
P B = 1 π e ( ( x Γ 2 + y Γ 2 )/(1 α 2 ) ) + α 2 π(1 α 2 ) x Γ e ( ( x Γ 2 + y Γ 2 α 2 x Γ 2 )/(1 α 2 ) ) erfc( x Γ α 2 1 α 2 )
P(φ|α)= 1 α 2 2π(1 α 2 cos 2 φ) [ 1+ αcosφ 1 α 2 cos 2 φ ( tan 1 [ αcosφ 1 α 2 cos 2 φ ]+ π 2 ) ]
C=aexp( φ 2 2 σ 2 )+h
( δr w 0 ) MLE = argmax δr/ w 0 j logP( φ j |δr/ w 0 )
σ CR 2 = { E[ 2 lnp(x|θ) 2 θ ] } 1
E out ¯ (z)= 1 4 [ E 11 (z)+ e i θ 12 E 12 (z)+ e i θ 21 E 21 (z)+ e i θ 22 E 22 (z) ]

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