Abstract

We propose using maximum a-posteriori (MAP) estimation to improve the image signal-to-noise ratio (SNR) in polarization diversity (PD) optical coherence tomography. PD-detection removes polarization artifacts, which are common when imaging highly birefringent tissue or when using a flexible fiber catheter. However, dividing the probe power to two polarization detection channels inevitably reduces the SNR. Applying MAP estimation to PD-OCT allows for the removal of polarization artifacts while maintaining and improving image SNR. The effectiveness of the MAP-PD method is evaluated by comparing it with MAP-non-PD, intensity averaged PD, and intensity averaged non-PD methods. Evaluation was conducted in vivo with human eyes. The MAP-PD method is found to be optimal, demonstrating high SNR and artifact suppression, especially for highly birefringent tissue, such as the peripapillary sclera. The MAP-PD based attenuation coefficient image also shows better differentiation of attenuation levels than non-MAP attenuation images.

© 2017 Optical Society of America

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2017 (1)

2016 (2)

A. C. Chan, K. Kurokawa, S. Makita, M. Miura, and Y. Yasuno, “Maximum a posteriori estimator for high-contrast image composition of optical coherence tomography,” Opt. Lett. 41(2), 321–324 (2016).
[Crossref] [PubMed]

D. S. Sugiyama, Y. Ikuno, D. Alonso-Caneiro, M. Yamanari, S. Fukuda, T. Oshika, Y.-J. Hong, E. Li, S. Makita, M. Miura, and Y. Yasuno, “Accurate and quantitative polarization-sensitive OCT by unbiased birefringence estimator with noise-stochastic correction,” Proc. SPIE 9697, 96971I (2016).
[Crossref]

2015 (4)

M. G. O. Grafe, L. S. Wilk, B. Braaf, J. H. de Jong, J. Novosel, K. A. Vermeer, and J. F. de Boer, “Quantification of retinal blood flow in swept-source Doppler OCT,” Invest. Ophthalmol. Vis. Sci. 56, 5948 (2015).

M. Tanaka, M. Hirano, K. Murashima, H. Obi, R. Yamaguchi, and T. Hasegawa, “1.7-μm spectroscopic spectral-domain optical coherence tomography for imaging lipid distribution within blood vessel,” Opt. Express 23(5), 6645–6655 (2015).
[Crossref] [PubMed]

S. Sugiyama, Y.-J. Hong, D. Kasaragod, S. Makita, S. Uematsu, Y. Ikuno, M. Miura, and Y. Yasuno, “Birefringence imaging of posterior eye by multi-functional Jones matrix optical coherence tomography,” Biomed. Opt. Express 6(12), 4951–4974 (2015).
[Crossref] [PubMed]

J. Kim, W. Brown, J. R. Maher, H. Levinson, and A. Wax, “Functional optical coherence tomography: principles and progress,” Phys. Med. Biol. 60(10), 211–237 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (1)

2012 (2)

2010 (1)

Y. Yasuno, M. Yamanari, K. Kawana, M. Miura, S. Fukuda, S. Makita, S. Sakai, and T. Oshika, “Visibility of trabecular meshwork by standard and polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(6), 061705 (2010).
[Crossref]

2009 (1)

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, “Three-dimensional microscopy of the tumor microenvironment in vivo using optical frequency domain imaging,” Nat. Med. 15(10), 1219–1223 (2009).
[Crossref] [PubMed]

2008 (4)

W. Drexler and J. G. Fujimoto, “State-of-the-art retinal optical coherence tomography,” Prog. Retin. Eye Res. 27(1), 45–88 (2008).
[Crossref]

L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438–11452 (2008).
[Crossref] [PubMed]

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16(8), 5892–5906 (2008).
[Crossref] [PubMed]

R. F. Spaide, H. Koizumi, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 146(4), 496–500 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (2)

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[Crossref] [PubMed]

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006).
[Crossref] [PubMed]

2005 (2)

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express. 13(25), 10217–10229 (2005).
[Crossref] [PubMed]

M. Pierce, M. Shishkov, B. Park, N. Nassif, B. Bouma, G. Tearney, and J. de Boer, “Effects of sample arm motion in endoscopic polarization-sensitive optical coherence tomography,” Opt. Express 13(15), 5739–5749 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (2)

2002 (1)

2000 (1)

1997 (3)

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 J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1975 (1)

P. Tan and C. Drossos, “Invariance properties of maximum likelihood estimators,” Mathematics Magazine 48(1), 37 (1975).
[Crossref]

1966 (1)

P. W. Zehna, “Invariance of Maximum Likelihood Estimators,” Ann. Math. Statist. 37(3), 744 (1966).
[Crossref]

Akiba, M.

Alonso-Caneiro, D.

D. S. Sugiyama, Y. Ikuno, D. Alonso-Caneiro, M. Yamanari, S. Fukuda, T. Oshika, Y.-J. Hong, E. Li, S. Makita, M. Miura, and Y. Yasuno, “Accurate and quantitative polarization-sensitive OCT by unbiased birefringence estimator with noise-stochastic correction,” Proc. SPIE 9697, 96971I (2016).
[Crossref]

An, L.

Bajraszewski, T.

Bartlett, L. A.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, “Three-dimensional microscopy of the tumor microenvironment in vivo using optical frequency domain imaging,” Nat. Med. 15(10), 1219–1223 (2009).
[Crossref] [PubMed]

Baumann, B.

Beheregaray, S.

Boppart, S.

Boppart, S. A.

A. L. Oldenburg, C. Xu, and S. A. Boppart, “Spectroscopic Optical Coherence Tomography and Microscopy,” IEEE J. Sel. Top. Quant. Electron. 13(6), 1629–1640 (2007).
[Crossref]

Bouma, B.

Bouma, B. E.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, “Three-dimensional microscopy of the tumor microenvironment in vivo using optical frequency domain imaging,” Nat. Med. 15(10), 1219–1223 (2009).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[Crossref] [PubMed]

B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical coherence tomography,” Opt. Express 11(25), 3490–3497 (2003).
[Crossref] [PubMed]

Braaf, B.

M. G. O. Grafe, L. S. Wilk, B. Braaf, J. H. de Jong, J. Novosel, K. A. Vermeer, and J. F. de Boer, “Quantification of retinal blood flow in swept-source Doppler OCT,” Invest. Ophthalmol. Vis. Sci. 56, 5948 (2015).

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]

Brown, W.

J. Kim, W. Brown, J. R. Maher, H. Levinson, and A. Wax, “Functional optical coherence tomography: principles and progress,” Phys. Med. Biol. 60(10), 211–237 (2015).
[Crossref] [PubMed]

Casella, G.

E. L. Lehmann and G. Casella, Theory of Point Estimation (Springer-Verlag, 1998), 2nd ed.

Cense, B.

Chan, A. C.

Chan, R. C.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[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 J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Chen, T. C.

Chen, Z.

Choi, W.

de Boer, J.

de Boer, J. F.

M. G. O. Grafe, L. S. Wilk, B. Braaf, J. H. de Jong, J. Novosel, K. A. Vermeer, and J. F. de Boer, “Quantification of retinal blood flow in swept-source Doppler OCT,” Invest. Ophthalmol. Vis. Sci. 56, 5948 (2015).

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]

K. A. Vermeer, J. Mo, J. J. A. Weda, H. G. Lemij, and J. F. de Boer, “Depth-resolved model-based reconstruction of attenuation coefficients in optical coherence tomography,” Biomed. Opt. Express 5(1), 322–337 (2014).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[Crossref] [PubMed]

B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical coherence tomography,” Opt. Express 11(25), 3490–3497 (2003).
[Crossref] [PubMed]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[Crossref] [PubMed]

de Groot, M.

de Jong, J. H.

M. G. O. Grafe, L. S. Wilk, B. Braaf, J. H. de Jong, J. Novosel, K. A. Vermeer, and J. F. de Boer, “Quantification of retinal blood flow in swept-source Doppler OCT,” Invest. Ophthalmol. Vis. Sci. 56, 5948 (2015).

Desjardins, A. E.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[Crossref] [PubMed]

Do, M.

Drexler, W.

Drossos, C.

P. Tan and C. Drossos, “Invariance properties of maximum likelihood estimators,” Mathematics Magazine 48(1), 37 (1975).
[Crossref]

Duan, L.

Dudewicz, E. J.

E. J. Dudewicz and S. N. Mishra, Modern Mathematical Statistics (John Wiley & Sons, Inc, 1988).

Duker, J. S.

Ellis, J. D.

J. D. Ellis, Field Guide to Displacement Measuring Interferometry (SPIE Field Guides, 2014).
[Crossref]

Evans, J. A.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2006).
[Crossref] [PubMed]

Fercher, A. F.

Flotte, T.

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 J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Fujimoto, J. G.

Fukuda, S.

D. S. Sugiyama, Y. Ikuno, D. Alonso-Caneiro, M. Yamanari, S. Fukuda, T. Oshika, Y.-J. Hong, E. Li, S. Makita, M. Miura, and Y. Yasuno, “Accurate and quantitative polarization-sensitive OCT by unbiased birefringence estimator with noise-stochastic correction,” Proc. SPIE 9697, 96971I (2016).
[Crossref]

D. Kasaragod, S. Makita, S. Fukuda, S. Beheregaray, T. Oshika, and Y. Yasuno, “Bayesian maximum likelihood estimator of phase retardation for quantitative polarization-sensitive optical coherence tomography,” Opt. Express 22(13), 16472–16492 (2014).
[Crossref] [PubMed]

Y. Yasuno, M. Yamanari, K. Kawana, M. Miura, S. Fukuda, S. Makita, S. Sakai, and T. Oshika, “Visibility of trabecular meshwork by standard and polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 15(6), 061705 (2010).
[Crossref]

Fukumura, D.

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Figures (10)

Fig. 1
Fig. 1 Intensity images of the macula and ONH. The four images on the left-hand side, (a), (b), (e), and (f), use non-PD OCT. The four on the right (c), (d), (g), and (h), are PD-OCT images. The images in the first row are composed by intensity averaging four repeated B-scans. Images in the second row are composed by MAP estimation from the same four repeated B-scans. Zero dB corresponds to the 99.9th percentile intensity in each image. The SIRs between the retinal pigment epithelium and vitreous, calculated from the macula images, are 31.1 dB for the MAP non-PD-OCT (e), 24.5 dB for averaging non-PD-OCT (a), 28.4 dB for MAP PD-OCT (g), and 21.7 dB for averaged PD-OCT (c).
Fig. 2
Fig. 2 Contour plots of 2D histograms of MAP and average intensities of corresponding pixels in non-PD (a) and PD (b) images of the ONH. The red line is the line of equal intensities for MAP and averaging.
Fig. 3
Fig. 3 Histograms of the intensity images from the macula and ONH, corresponding to the images in Fig. 1. The same labels are assigned to the corresponding sub-figures in Fig. 1. Zero dB corresponds to the 99.9th percentile intensity in each image. The histograms on the left-hand side, (a), (b), (e), and (f), correspond to non-PD images. The histograms on the right-hand side, (c), (d), (g), and (h), correspond to PD images. The first row corresponds to intensity-averaged images. The second row corresponds to MAP images.
Fig. 4
Fig. 4 Binary map represents the location of pixels where intensities less than −50 dB in Fig. 1(h). Black means pixel has intensity larger than or equal to −50 dB and white means less than −50 dB. There are many pixels in the MPD ONH image with intensities less than −50 dB. They are located in both the vitreous and deep regions.
Fig. 5
Fig. 5 Maps of MAP intensity precision (first row) and the reliability (squared-intensity-to-error ratio, second row). The first and second columns are for MAP non-PD-OCT estimation, and the third and fourth columns are for MAP-PD-OCT. The first and third columns are of the macula, while the second and fourth columns are of the ONH.
Fig. 6
Fig. 6 Contour plots of 2D histograms of MPD intensity and reliability (a), and MPD intensity and precision (b) of the macula.
Fig. 7
Fig. 7 Attenuation images of the macula and ONH. The four images on the left-hand side, (a), (b), (e), and (f), are for non-PD OCT. The four images on the right-hand side, (c), (d), (g), and (h), are for PD-OCT. The images in the first row are composed using the intensity averaging of four repeated B-scans. Images in the second row are composed by MAP estimation from the same B-scans.
Fig. 8
Fig. 8 Contour plots of 2D histgrams of attenuations of corresponding pixels in MAP and averaged images of the ONH. Sub-figure (a) is from comparing attenuations of corresponding pixels in Fig. 7(f) and Fig. 7(b). Sub-figure (b) is from comparing attenuations of corresponding pixels in Fig. 7(h) and Fig. 7(d). The red line represents the location of equal attenuation.
Fig. 9
Fig. 9 Histograms of attenuation images of the macula and ONH, corresponding to Fig. 7. The same labels are assigned to the corresponding sub-figures in Fig. 7. The four histograms on the left-hand side, (a), (b), (e), and (f), are from the non-PD OCT images, and those on the right-hand side, (c), (d), (g), and (h), are from the PD-OCT images. The histograms in the first row are from the intensity averaged images and those in the second row are from the MAP images. It is clear that the attenuation images based on MAP in the first row have broader dynamic ranges and better attenuation coefficient differentiation than the attenuation images based on averaging (second row).
Fig. 10
Fig. 10 Attenuation estimation precision (first row) and reliability (squared-attenuation-coefficient-to-error ratio). The first and second columns are for MAP non-PD-OCT, while the third and fourth columns are for MAP PD-OCT. The first and third columns are of the macula, and the second and fourth columns are of the ONH.

Tables (1)

Tables Icon

Table 1 A summary of OCT composition methods.

Equations (24)

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p ( a | α , σ 2 ) = a σ 2 exp [ ( a 2 + α 2 ) 2 σ 2 ] I 0 ( a α σ 2 ) ,
f ( α ; a , σ 2 ) p ( a | α , σ 2 ) .
l ( α ; a , σ 2 ) = n = 1 N f ( α ; a n , σ 2 ) .
α ^ arg max α [ l ( α ; a , σ 2 ) π ( α ) ] = arg max α [ n = 1 N f ( α ; a n , σ 2 ) π ( α ) ] ,
υ ^ = arg max υ [ l υ ( υ ; i , σ 2 ) π ( υ ) ]
υ ^ = α ^ 2 .
T ( α ) = 2 log [ l ( α ^ ; σ 2 ) l ( α ; σ 2 ) ] .
p ( a n | α , σ 2 ) = a n σ 2 exp { ( a n 2 + α 2 ) 2 σ 2 } I 0 ( a n α σ 2 ) = a n σ 2 exp { ( a n α ) 2 2 a n α 2 σ 2 } I 0 ( a n α σ 2 ) = a n σ 2 exp { ( a n α ) 2 2 σ 2 } [ I 0 ( a n α σ 2 ) exp ( a n α σ 2 ) ] ,
I SPD = | E h ( z ) | 2 ¯ + | E v ( z ) | 2 ¯ ,
I MPD ( z ) = | E h ( z ) ^ | 2 + | E v ( z ) ^ | 2 ,
E cc ( z ) = 1 2 [ E h ( z ) e i θ + E v ( z ) ] ,
I SnPD = | E cc ( z ) | 2 ¯ ,
I MnPD = | E cc ( z ) ^ | 2 ,
μ ( z i ) = 1 2 Δ I ( z i ) j = i + 1 M I ( z j ) ,
C ( z i ) = SNR ( z i ) σ 2 ( z i ) .
I PD ( z i ) | E h ( z i ) ˜ | 2 C h ( z i ) + | E v ( z i ) ˜ | 2 C v ( z i ) ,
σ μ 2 ( z i ) = ( μ ( z i ) I ( z i ) ) 2 σ υ 2 ( z i ) + j = i + 1 M ( μ ( z i ) I ( z j ) ) 2 σ υ 2 ( z j ) ,
σ μ 2 ( z i ) = μ ( z i ) 2 I 2 ( z i ) σ υ 2 ( z i ) + { μ ( z i ) 2 [ k = i + 1 M I ( z k ) ] 2 } j = i + 1 M σ υ 2 ( z j ) .
θ h , v arg ( z E h , v ( 2 ) ( z ) E h , v ( 1 ) * ( z ) ) ,
E h , v ( z ) E h , v ( 1 ) ( z ) + E h , v ( 2 ) ( z ) e i θ h , v .
p ( α | a ) l ( α ; a ) π ( α ) ,
MAP ( α ) arg max α [ p ( α | a ) ] = arg max α [ l ( α ; a ) ] MLE ( α ) .
p Y ( y | θ ) = p X ( g 1 ( y ) | θ ) | x y | .
arg max α [ l ( θ ; y ) ] = arg max θ [ | x y | l ( θ ; g 1 ( y ) ) ] = arg max θ [ l ( θ ; x ) ] .

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