Abstract

A three-dimensional optical coherence tomography imaging method based on Lissajous scanning is presented. This method was designed to correct eye motion in OCT images. A Lissajous scanning pattern, which has a trajectory that frequently overlaps with itself, is adopted as the OCT scanning protocol to obtain measurement data. Eye motion artifacts are then corrected automatically by software. By comparing the images without and with motion correction, we show the effectiveness of our method. We performed an experiment and compared the results obtained by our method with the ground truths to verify its validity. The experimental results showed that our method effectively corrects eye motion artifacts. Furthermore, the sufficient repeatability of our method was confirmed.

© 2017 Optical Society of America

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  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]
  2. W. Drexler and J. G. Fujimoto, eds., Optical Coherence Tomography - Technology and Applications (Springer, 2015), 2nd ed.
    [Crossref]
  3. M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
    [Crossref] [PubMed]
  4. U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
    [Crossref] [PubMed]
  5. Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
    [Crossref] [PubMed]
  6. M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
    [Crossref]
  7. V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
    [Crossref] [PubMed]
  8. H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
    [Crossref]
  9. O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
    [Crossref] [PubMed]
  10. K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
    [Crossref] [PubMed]
  11. S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
    [Crossref] [PubMed]
  12. M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
    [Crossref] [PubMed]
  13. T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
    [Crossref]
  14. D. Hammer, R. D. Ferguson, N. Iftimia, T. Ustun, G. Wollstein, H. Ishikawa, M. Gabriele, W. Dilworth, L. Kagemann, and J. Schuman, “Advanced scanning methods with tracking optical coherence tomography,” Opt. Express 13(20), 7937–7947 (2005).
    [Crossref] [PubMed]
  15. M. Pircher, B. Baumann, E. Götzinger, H. Sattmann, and C. K. Hitzenberger, “Simultaneous SLO/OCT imaging of the humanretina with axial eye motion correction,” Opt. Express 15(25), 16922–16932 (2007).
    [Crossref] [PubMed]
  16. K. V. Vienola, B. Braaf, C. K. Sheehy, Q. Yang, P. Tiruveedhula, D. W. Arathorn, J. F. de Boer, and A. Roorda, “Real-time eye motion compensation for OCT imaging with tracking SLO,” Biomed. Opt. Express 3(11), 2950–2963 (2012).
    [Crossref] [PubMed]
  17. R. D. Ferguson, D. Hammer, L. A. Paunescu, S. Beaton, and J. S. Schuman, “Tracking optical coherence tomography,” Opt. Lett. 29(18), 2139–2141 (2004).
    [Crossref] [PubMed]
  18. M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012).
    [Crossref] [PubMed]
  19. M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
    [Crossref] [PubMed]
  20. H. C. Hendargo, R. Estrada, S. J. Chiu, C. Tomasi, S. Farsiu, and J. A. Izatt, “Automated non-rigid registration and mosaicing for robust imaging of distinct retinal capillary beds using speckle variance optical coherence tomography,” Biomed. Opt. Express 4(6), 803–821 (2013).
    [Crossref] [PubMed]
  21. P. Zang, G. Liu, M. Zhang, C. Dongye, J. Wang, A. D. Pechauer, T. S. Hwang, D. J. Wilson, D. Huang, D. Li, and Y. Jia, “Automated motion correction using parallel-strip registration for wide-field en face OCT angiogram,” Biomed. Opt. Express 7(7), 2823–2836 (2016).
    [Crossref] [PubMed]
  22. A. Bazaei, Y. K. Yong, and S. O. R. Moheimani, “High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues,” Rev. Sci. Instrum. 83(6), 063701 (2012).
    [Crossref] [PubMed]
  23. 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).
    [Crossref] [PubMed]

2016 (1)

2014 (1)

2013 (2)

2012 (3)

2011 (1)

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

2010 (1)

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

2009 (4)

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

2008 (1)

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

2007 (2)

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

M. Pircher, B. Baumann, E. Götzinger, H. Sattmann, and C. K. Hitzenberger, “Simultaneous SLO/OCT imaging of the humanretina with axial eye motion correction,” Opt. Express 15(25), 16922–16932 (2007).
[Crossref] [PubMed]

2005 (4)

D. Hammer, R. D. Ferguson, N. Iftimia, T. Ustun, G. Wollstein, H. Ishikawa, M. Gabriele, W. Dilworth, L. Kagemann, and J. Schuman, “Advanced scanning methods with tracking optical coherence tomography,” Opt. Express 13(20), 7937–7947 (2005).
[Crossref] [PubMed]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

2004 (1)

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]

Adler, D. C.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

Agawa, T.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Ahlers, C.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Akiba, M.

Arathorn, D. W.

Baumann, B.

Bazaei, A.

A. Bazaei, Y. K. Yong, and S. O. R. Moheimani, “High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues,” Rev. Sci. Instrum. 83(6), 063701 (2012).
[Crossref] [PubMed]

Beaton, S.

Bock, R.

Braaf, B.

Branchini, L.

Budai, A.

Chan, K.-P.

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, C.-L.

Chen, Y.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

Chiu, S. J.

Chong, C.

Chopra, V.

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

de Boer, J. F.

Dilworth, W.

Dongye, C.

Drexler, W.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Duan, L.

Duker, J. S.

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Esmaeelpour, M.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Estrada, R.

Fabritius, T.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Farsiu, S.

Fercher, A. F.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Ferguson, R. D.

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]

Friberg, T. R.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

Fujimoto, J. G.

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref] [PubMed]

M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

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]

Fukuda, S.

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

Gabriele, M.

Gabriele, M. L.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

Gorczynska, I.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

Goto, H.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Gotoh, N.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Götzinger, E.

Gregory, K.

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]

Hammer, D.

Hangai, M.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Hee, M. R.

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]

Hendargo, H. C.

Hermann, B.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Hitzenberger, C. K.

Hofer, B.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Hong, Y.-J.

Hornegger, J.

Huang, D.

P. Zang, G. Liu, M. Zhang, C. Dongye, J. Wang, A. D. Pechauer, T. S. Hwang, D. J. Wilson, D. Huang, D. Li, and Y. Jia, “Automated motion correction using parallel-strip registration for wide-field en face OCT angiogram,” Biomed. Opt. Express 7(7), 2823–2836 (2016).
[Crossref] [PubMed]

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

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]

Huber, R.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

Hwang, T. S.

Iftimia, N.

Ikuno, Y.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Inoue, R.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Ishikawa, H.

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

D. Hammer, R. D. Ferguson, N. Iftimia, T. Ustun, G. Wollstein, H. Ishikawa, M. Gabriele, W. Dilworth, L. Kagemann, and J. Schuman, “Advanced scanning methods with tracking optical coherence tomography,” Opt. Express 13(20), 7937–7947 (2005).
[Crossref] [PubMed]

Itoh, M.

Iwasaki, T.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Izatt, J. A.

Jia, Y.

Ju, M. J.

Kagemann, L.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

D. Hammer, R. D. Ferguson, N. Iftimia, T. Ustun, G. Wollstein, H. Ishikawa, M. Gabriele, W. Dilworth, L. Kagemann, and J. Schuman, “Advanced scanning methods with tracking optical coherence tomography,” Opt. Express 13(20), 7937–7947 (2005).
[Crossref] [PubMed]

Kajic, V.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Kapoor, K.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Kawana, K.

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

Kim, J.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

Kita, M.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Kiuchi, T.

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

Ko, T.

Kowalczyk, A.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Kraus, M. F.

Kurokawa, K.

Leitgeb, R. A.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Li, D.

Lim, Y.

Lin, C. P.

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]

Liu, G.

Liu, J. J.

Lu, A. T.-H.

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

Madjarova, V. D.

Makita, S.

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).
[Crossref] [PubMed]

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

Mayer, M. A.

Michels, S.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Miura, M.

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).
[Crossref] [PubMed]

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Moheimani, S. O. R.

A. Bazaei, Y. K. Yong, and S. O. R. Moheimani, “High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues,” Rev. Sci. Instrum. 83(6), 063701 (2012).
[Crossref] [PubMed]

Morosawa, A.

Nishida, K.

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

North, R. V.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Ojima, Y.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Oshika, T.

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

Paunescu, L. A.

Pechauer, A. D.

Pircher, M.

Potsaid, B.

Považay, B.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Puliafito, C. A.

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]

Roorda, A.

Sacu, S.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Sakai, T.

Sattmann, H.

M. Pircher, B. Baumann, E. Götzinger, H. Sattmann, and C. K. Hitzenberger, “Simultaneous SLO/OCT imaging of the humanretina with axial eye motion correction,” Opt. Express 15(25), 16922–16932 (2007).
[Crossref] [PubMed]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Schmidt-Erfurth, U.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Scholda, C.

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Schottenhamml, J.

Schuman, J.

Schuman, J. S.

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

R. D. Ferguson, D. Hammer, L. A. Paunescu, S. Beaton, and J. S. Schuman, “Tracking optical coherence tomography,” Opt. Lett. 29(18), 2139–2141 (2004).
[Crossref] [PubMed]

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]

Sheehy, C. K.

Sheen, N. J. L.

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

Srinivasan, V.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Srinivasan, V. J.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

Stinson, W. G.

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]

Sung, K. R.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

Swanson, E. A.

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]

Tan, O.

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

Tang, S.

Tiruveedhula, P.

Tomasi, C.

Townsend, K. A.

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

Ustun, T.

Varma, R.

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

Vienola, K. V.

Wang, J.

Wilson, D. J.

Wojtkowski, M.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Wollstein, G.

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

D. Hammer, R. D. Ferguson, N. Iftimia, T. Ustun, G. Wollstein, H. Ishikawa, M. Gabriele, W. Dilworth, L. Kagemann, and J. Schuman, “Advanced scanning methods with tracking optical coherence tomography,” Opt. Express 13(20), 7937–7947 (2005).
[Crossref] [PubMed]

Yamanari, M.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Yang, Q.

Yasuno, Y.

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).
[Crossref] [PubMed]

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

Yatagai, T.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

Yong, Y. K.

A. Bazaei, Y. K. Yong, and S. O. R. Moheimani, “High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues,” Rev. Sci. Instrum. 83(6), 063701 (2012).
[Crossref] [PubMed]

Yoshimura, N.

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Zang, P.

Zhang, M.

Biomed. Opt. Express (5)

M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012).
[Crossref] [PubMed]

K. V. Vienola, B. Braaf, C. K. Sheehy, Q. Yang, P. Tiruveedhula, D. W. Arathorn, J. F. de Boer, and A. Roorda, “Real-time eye motion compensation for OCT imaging with tracking SLO,” Biomed. Opt. Express 3(11), 2950–2963 (2012).
[Crossref] [PubMed]

H. C. Hendargo, R. Estrada, S. J. Chiu, C. Tomasi, S. Farsiu, and J. A. Izatt, “Automated non-rigid registration and mosaicing for robust imaging of distinct retinal capillary beds using speckle variance optical coherence tomography,” Biomed. Opt. Express 4(6), 803–821 (2013).
[Crossref] [PubMed]

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3d-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref] [PubMed]

P. Zang, G. Liu, M. Zhang, C. Dongye, J. Wang, A. D. Pechauer, T. S. Hwang, D. J. Wilson, D. Huang, D. Li, and Y. Jia, “Automated motion correction using parallel-strip registration for wide-field en face OCT angiogram,” Biomed. Opt. Express 7(7), 2823–2836 (2016).
[Crossref] [PubMed]

Graefe’s Arch. Clin. Exp. Ophthalmol. (1)

T. Agawa, M. Miura, Y. Ikuno, S. Makita, T. Fabritius, T. Iwasaki, H. Goto, K. Nishida, and Y. Yasuno, “Choroidal thickness measurement in healthy Japanese subjects by three-dimensional high-penetration optical coherence tomography,” Graefe’s Arch. Clin. Exp. Ophthalmol. 249(10), 1485–1492 (2011).
[Crossref]

Invest. Ophthalmol. Vis. Sci. (4)

M. Esmaeelpour, B. Považay, B. Hermann, B. Hofer, V. Kajic, K. Kapoor, N. J. L. Sheen, R. V. North, and W. Drexler, “Three-dimensional 1060-nm OCT: choroidal thickness maps in normal subjects and improved posterior segment visualization in cataract patients,” Invest. Ophthalmol. Vis. Sci. 51(10), 5260–5266 (2010).
[Crossref] [PubMed]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head,” Invest. Ophthalmol. Vis. Sci. 49(11), 5103–5110 (2008).
[Crossref] [PubMed]

H. Ishikawa, J. Kim, T. R. Friberg, G. Wollstein, L. Kagemann, M. L. Gabriele, K. A. Townsend, K. R. Sung, J. S. Duker, J. G. Fujimoto, and J. S. Schuman, “Three-dimensional optical coherence tomography (3d-OCT) image enhancement with segmentation-free contour modeling C-mode,” Invest. Ophthalmol. Vis. Sci. 50(3), 1344–1349 (2009).
[Crossref]

U. Schmidt-Erfurth, R. A. Leitgeb, S. Michels, B. Považay, S. Sacu, B. Hermann, C. Ahlers, H. Sattmann, C. Scholda, A. F. Fercher, and W. Drexler, “Three-dimensional ultrahigh-resolution optical coherence tomography of macular diseases,” Invest. Ophthalmol. Vis. Sci. 46(9), 3393–3402 (2005).
[Crossref] [PubMed]

Ophthalmology (5)

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

O. Tan, V. Chopra, A. T.-H. Lu, J. S. Schuman, H. Ishikawa, G. Wollstein, R. Varma, and D. Huang, “Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography,” Ophthalmology 116(12), 2305–2314 (2009).
[Crossref] [PubMed]

K. Kawana, T. Kiuchi, Y. Yasuno, and T. Oshika, “Evaluation of trabeculectomy blebs using 3-dimensional cornea and anterior segment optical coherence tomography,” Ophthalmology 116(5), 848 – 855 (2009).
[Crossref] [PubMed]

S. Fukuda, K. Kawana, Y. Yasuno, and T. Oshika, “Anterior ocular biometry using 3-dimensional optical coherence tomography,” Ophthalmology 116(5), 882 – 889 (2009).
[Crossref] [PubMed]

M. Hangai, Y. Ojima, N. Gotoh, R. Inoue, Y. Yasuno, S. Makita, M. Yamanari, T. Yatagai, M. Kita, and N. Yoshimura, “Three-dimensional imaging of macular holes with high-speed optical coherence tomography,” Ophthalmology 114(4), 763–773 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

A. Bazaei, Y. K. Yong, and S. O. R. Moheimani, “High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues,” Rev. Sci. Instrum. 83(6), 063701 (2012).
[Crossref] [PubMed]

Science (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]

Other (1)

W. Drexler and J. G. Fujimoto, eds., Optical Coherence Tomography - Technology and Applications (Springer, 2015), 2nd ed.
[Crossref]

Supplementary Material (4)

NameDescription
» Visualization 1: MP4 (6712 KB)      Fly-through cross-section of ONH.
» Visualization 2: MP4 (6633 KB)      Fly-through cross-section of macula.
» Visualization 3: MP4 (871 KB)      Three-dimensional volume rendering of ONH.
» Visualization 4: MP4 (580 KB)      Three-dimensional volume rendering of macula.

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Figures (12)

Fig. 1
Fig. 1 Example of a Lissajous scanning pattern containing 64 A-lines per single horizontal cycle (n = 64) (a) and its magnified image in the center region (b). The black dots on the scanning trajectory represent A-line sampling points. The yellow, green and blue curves are examples of a single horizontal cycle. The green and blue curves are adjacent horizontal cycles.

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Fig. 2
Fig. 2 Flowchart of rough lateral motion correction.

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Fig. 3
Fig. 3 Division each strip into four sub-strips.

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Fig. 4
Fig. 4 Comparison of the en face projection images without (a) and with (b) lateral motion correction demonstrates the effectiveness of the lateral motion correction.

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Fig. 5
Fig. 5 A comparison of the cross-sectional images without (a) and with (b) axial motion correction demonstrates the effectiveness of the axial motion correction.

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Fig. 6
Fig. 6 Validation of the lateral motion correction: comparison of the motion-corrected en face projection images with the SLO ground truth. (a) ONH, (b) macula. The cyan images are obtained by SLO and the motion corrected OCT images (yellow) are overlaid on the SLO images.

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Fig. 7
Fig. 7 Validity of the axial motion correction: comparison of the motion-corrected cross-sectional image with the fast B-scan ground truth. (a)–(e) ONH and (f)–(j) macula. Two volumes for each ONH and macula are from the same eye but from different measurements. First row: motion corrected en face projections. Second row: horizontal cross-sections taken from the motion corrected volumes. Third row: Green-magenta compositions of cross-sections. (e) is made from (c) and (d), while (j) is made from (h) and (j). Since green and magenta are complementary to each other, the nearly monochromatic (gray) appearance in (e) and (j) validates good performance of motion correction.

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Fig. 8
Fig. 8 Repeatability evaluation. Top row: En face projection images of two motion corrected volumes (a)–(d). Middle row: checkerboard images of en face projection images (e) and (g). (e) is from (a) and (b), and (g) is from (c) and (d). (f) and (h) are magnified images of (e) and (g), respectively. Bottom row: magenta-green composite cross-sectional images in the corresponding positions for two motion-corrected volumes (the colors of the bounding boxes correspond to the lines of the same colors in the top row). (i) and (j) are compositions of cross-sections taken from (a) and (b), and (k) and (l) are compositions of (c) and (d).

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Fig. 9
Fig. 9 The en face projection image with blinking before Cartesian remapping. The acquisition starts from the bottom left to the right, bottom to top, and ends at the top right. The horizontal black region (arrow) is caused by eye blink.

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Fig. 10
Fig. 10 Motion-corrected en face projection image (a) and two cross-sectional images (b) and (c) crossing the center of macula. The colors of the bounding boxes of (b) and (c) correspond to the lines of the same colors in (a).

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Fig. 11
Fig. 11 Fly-through cross-sectional movies. (a) ONH and (b) macula.

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Fig. 12
Fig. 12 Three-dimensional volume rendering movies. (a) ONH and (b) macula.

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Tables (1)

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Table 1 Comparison of raster and Lissajous scans.

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Equations (33)

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x ( t ) = A x cos ( 2 π ⋅ f x ⋅ t ) ,
y ( t ) = A y cos ( 2 π ⋅ f y ⋅ t ) ,
f x = 2 N ⋅ f ,
f y = ( 2 N − 1 ) ⋅ f ,
f = 1 / T ,
f = f A / ( n ⋅ 2 N ) ,
A ≡ A x = A y .
N = n / 4 .
x ( t i ) = A ⋅ cos ( 2 π ⋅ f A n ⋅ t i ) ,
y ( t i ) = A ⋅ cos ( 2 π ⋅ f A ⋅ ( n − 2 ) n 2 ⋅ t i ) ,
R ( l ) = ∑ k ( I E ( t k   + ( l − 1 ) ⋅ n ) − I E l ¯ ) ⋅ ( I E ( t k + l ⋅ n ) − I E l + 1 ¯ ) ∑ k ( I E ( t k   + ( l − 1 ) ⋅ n ) − I E l ¯ ) 2 ⋅ ∑ k ( I E ( t k   + l ⋅ n ) − I E l + 1 ¯ ) 2 ,
σ = − 1 n / 2 − 2 ∑ l = 1 n / 2 − 2 ( Δ R ( l ) − Δ R ¯ ) 2 ,
R ( l ) = S ( l ) M ( l ) ,
d R ( l ) d l = d S ( l ) d l M ( l ) + S ( l ) d M ( l ) d l .
d S ( l ) d l ≃ 0 .
d R ( l ) d l ≃ S ( l ) d M ( l ) d l .
| d R ( l ) d l | { ≃ 0 if no motion exists ≃ 0 if only slow motion exists ≫ 0 if quick motion exists .
ρ ( r ′ ) = σ f g 2 ( r ′ ) σ f 2 ( r ′ ) σ g 2 ( r ′ ) ,
f ′ ( r ) ≡ { f ( r ) within the image area of f ( r ) , Arbitary value for the other area .
m f ( r ) ≡ { 1 within the image area of f ( r ) , 0 for the other area .
σ f g 2 ( r ′ ) = 〈 { f ( r ) − 〈 f ( r ) 〉 M } { g ( r + r ′ ) − 〈 g ( r + r ′ ) 〉 M } 〉 M = ∑ M { f ′ ( r ) − 〈 f ′ ( r ) 〉 M } { g ′ ( r + r ′ ) − 〈 g ′ ( r + r ′ ) 〉 M } ∑ R m f ( r ) m g ( r + r ′ ) ,
〈 f ′ ( r ) 〉 M = ∑ M f ′ ( r ) ∑ R m f ( r ) m g ( r + r ′ ) = ∑ R f ′ ( r ) m f ( r ) m g ( r + r ′ ) ∑ R m f ( r ) m g ( r + r ′ ) = ( f ′ m f ) ⊗ m g m f ⊗ m g .
∑ M h ( r ) = ∑ R h ( r ) m f ( r ) m g ( r + r ′ ) ,
〈 g ′ ( r + r ′ ) 〉 M = ∑ M g ′ ( r + r ′ ) ∑ R m f ( r ) m g ( r + r ′ ) = ∑ R m f ( r ) g ′ ( r + r ′ ) m g ( r + r ′ ) ∑ R m f ( r ) m g ( r + r ′ ) = m f ⊗ ( g ′ m g ) m f ⊗ m g .
σ f g ( r ′ ) = 1 m f ⊗ m g ∑ M [ f ′ ( r ) g ′ ( r + r ′ ) − m f ⊗ ( g ′ m g ) m f ⊗ m g f ′ ( r ) − ( f ′ m f ) ⊗ m g m f ⊗ m g g ′ ( r + r ′ ) + [ ( f ′ m f ⊗ m g ) ] [ m f ⊗ ( g ′ m g ) ] ( m f ⊗ m g ) 2 ]
∑ M f ′ ( r ) g ′ ( r + r ′ ) = ∑ R f ′ ( r ) m f ( r ) g ′ ( r + r ′ ) m g ( r + r ′ ) = ( f ′ m f ) ⊗ ( g ′ m g )
− m f ⊗ ( g ′ m g ) m f ⊗ m g ∑ M f ′ ( r ) = − m f ⊗ ( g ′ m g ) m f ⊗ m g ∑ R f ′ ( r ) m f ( r ) m g ( r + r ′ ) = − [ m f ⊗ ( g ′ m g ) ] [ ( f ′ m f ) ⊗ m g ] m f ⊗ m g .
− ( f ′ m f ) ⊗ m g m f ⊗ m g ∑ M g ′ ( r + r ′ ) = − ( f ′ m f ) ⊗ m g m f ⊗ m g ∑ R m f ( r ) g ′ ( r + r ′ ) m g ( r + r ′ ) = − [ ( f ′ m f ) ⊗ m g ] [ m f ⊗ ( g ′ m g ) ] m f ⊗ m g .
[ ( f ′ m f ⊗ m g ) ] [ m f ⊗ ( g ′ m g ) ] ( m f ⊗ m g ) 2 ∑ M 1 = [ ( f ′ m f ⊗ m g ) ] [ m f ⊗ ( g ′ m g ) ] m f ⊗ m g ,
σ f g ( r ′ ) = ( m f ⊗ m g ) − 1 [ ( f ′ m f ) ⊗ ( g ′ m g ) − { ( f ′ m f ) ⊗ m g } { m f ⊗ ( g ′ m g ) m f ⊗ m g ] .
σ f 2 ( r ′ ) = 〈 [ f ′ ( r ) − 〈 f ′ ( r ) 〉 M ] 2 〉 M = ∑ M [ f ′ ( r ) − ( f ′ m f ) ⊗ m g m f ⊗ m g ] 2 / ( m f ⊗ m g ) = [ ( f ′ m f ) 2 ⊗ m g − { ( f ′ m f ) ⊗ m g } 2 m f ⊗ m g ] / ( m f ⊗ m g ) ,
σ g 2 ( r ′ ) = [ m f ⊗ ( g ′ m g ) 2 − { m f ⊗ ( g ′ m g ) } 2 m f ⊗ m g ] / ( m f ⊗ m g ) .
ρ ( r ′ ) = ( f ′ m f ) ⊗ ( g ′ m g ) − { ( f ′ m f ) ⊗ m g } { m f ⊗ ( g ′ m g ) } / m f ⊗ m g [ ( f ′ m f ) 2 ⊗ m g − { ( f ′ m f ) ⊗ m g } 2 m f ⊗ m g ] [ m f ⊗ ( g ′ m g ) 2 − { m f ⊗ ( g ′ m g ) } 2 m f ⊗ m g ] .

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