Abstract

This paper presents an approach to remove motion artifacts based on a spatial-spectral encoded parallel OCT (SSE-POCT) system, where encoded rectangular illumination is employed. Motion artifacts within a B-scan are avoided due to parallel detection intrinsic to parallel OCT, while those between successive B-scans are estimated and corrected by a proposed overlapped data correlation (ODC) algorithm. To preserve axial resolution, decoded B-scan corresponding to complete spectrum is stitched from successive encoded B-scans after motion correction. Imaging is conducted on several samples under preset motion trajectories, and OCT images with unnoticed motion artifacts and well-preserved resolutions are reconstructed. The approach based on the developed SSE-POCT system and the proposed ODC algorithm for motion correction can be applicable for in vivo imaging where uncontrolled motion is usually unavoidable.

© 2017 Optical Society of America

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References

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2015 (2)

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Z. Chen, Y. Shen, W. Bao, P. Li, X. Wang, and Z. Ding, “Identification of surface defects on glass by parallel spectral domain optical coherence tomography,” Opt. Express 23(18), 23634–23646 (2015).
[Crossref] [PubMed]

2014 (1)

2012 (3)

2011 (2)

2010 (2)

2009 (2)

Z. Yaqoob, W. Choi, S. Oh, N. Lue, Y. Park, C. Fang-Yen, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Improved phase sensitivity in spectral domain phase microscopy using line-field illumination and self phase-referencing,” Opt. Express 17(13), 10681–10687 (2009).
[Crossref] [PubMed]

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

2008 (1)

2007 (3)

2004 (1)

1998 (1)

G. Haüsler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998).
[Crossref] [PubMed]

1993 (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]

Andre, R.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

Badizadegan, K.

Bao, W.

Baumann, B.

Beaton, S.

Biedermann, B. R.

Boas, D. A.

Bock, R.

Bonin, T.

Cable, A.

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, M.

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Chen, Y.

Chen, Z.

Chen, Z. Y.

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Choi, W.

Dasari, R. R.

Ding, Z.

Ding, Z. H.

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Drexler, W.

Eigenwillig, C. M.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

Fang-Yen, C.

Fechtig, D. J.

Feld, M. S.

Fercher, A. F.

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]

Franke, G.

Fujimoto, J. G.

Gorczynska, I.

Götzinger, E.

Grajciar, B.

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]

Hagen-Eggert, M.

Hammer, D. X.

Haüsler, G.

G. Haüsler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998).
[Crossref] [PubMed]

Hee, M. R.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18(21), 1864–1866 (1993).
[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]

Hitzenberger, C. K.

Hornegger, J.

Huang, D.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18(21), 1864–1866 (1993).
[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.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

Hüttmann, G.

Ishikawa, H.

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Itoh, M.

Izatt, J. A.

Jiang, J.

Klein, T.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

Koch, P.

Kraus, M. F.

Lee, J.

Lehareinger, Y.

Leitgeb, R. A.

Li, P.

Z. Chen, Y. Shen, W. Bao, P. Li, X. Wang, and Z. Ding, “Identification of surface defects on glass by parallel spectral domain optical coherence tomography,” Opt. Express 23(18), 23634–23646 (2015).
[Crossref] [PubMed]

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Liew, Y. M.

Lin, C. P.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18(21), 1864–1866 (1993).
[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]

Lindner, M. W.

G. Haüsler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998).
[Crossref] [PubMed]

Liu, J. J.

Lue, N.

Makita, S.

Mayer, M. A.

McLaughlin, R. A.

Nakamura, Y.

Oh, S.

Park, Y.

Paunescu, L. A.

Pfeiffer, T.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

Pircher, M.

Potsaid, B.

Puliafito, C. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18(21), 1864–1866 (1993).
[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]

Radhakrishnan, H.

Ricco, S.

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Sampson, D. D.

Sattmann, H.

Schmoll, T.

Schuman, J.

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Schuman, J. S.

Shen, Y.

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Z. Chen, Y. Shen, W. Bao, P. Li, X. Wang, and Z. Ding, “Identification of surface defects on glass by parallel spectral domain optical coherence tomography,” Opt. Express 23(18), 23634–23646 (2015).
[Crossref] [PubMed]

Srinivasan, V.

Srinivasan, V. J.

Stifter, D.

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88(3), 337–357 (2007).
[Crossref]

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]

Swanson, E. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18(21), 1864–1866 (1993).
[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]

Wang, X.

Wang, X. P.

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Wieser, W.

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

Wollstein, G.

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Wood, F. M.

Yamanari, M.

Yaqoob, Z.

Yasuno, Y.

Yatagai, T.

Zhao, C.

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Appl. Phys. B (1)

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88(3), 337–357 (2007).
[Crossref]

Biomed. Opt. Express (2)

J. Biomed. Opt. (1)

G. Haüsler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998).
[Crossref] [PubMed]

Med. Image Comput. Comput. Assist. Interv. (1)

S. Ricco, M. Chen, H. Ishikawa, G. Wollstein, and J. Schuman, “Correcting motion artifacts in retinal spectral domain optical coherence tomography via image registration,” Med. Image Comput. Comput. Assist. Interv. 12(Pt 1), 100–107 (2009).
[PubMed]

Opt. Commun. (1)

Z. Y. Chen, C. Zhao, Y. Shen, P. Li, X. P. Wang, and Z. H. Ding, “Ultrawide-field parallel spectral domain optical coherence tomography for nondestructive inspection of glass,” Opt. Commun. 341, 122–130 (2015).
[Crossref]

Opt. Express (8)

Z. Chen, Y. Shen, W. Bao, P. Li, X. Wang, and Z. Ding, “Identification of surface defects on glass by parallel spectral domain optical coherence tomography,” Opt. Express 23(18), 23634–23646 (2015).
[Crossref] [PubMed]

Z. Yaqoob, W. Choi, S. Oh, N. Lue, Y. Park, C. Fang-Yen, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Improved phase sensitivity in spectral domain phase microscopy using line-field illumination and self phase-referencing,” Opt. Express 17(13), 10681–10687 (2009).
[Crossref] [PubMed]

B. Grajciar, Y. Lehareinger, A. F. Fercher, and R. A. Leitgeb, “High sensitivity phase mapping with parallel Fourier domain optical coherence tomography at 512 000 A-scan/s,” Opt. Express 18(21), 21841–21850 (2010).
[Crossref] [PubMed]

J. Lee, V. Srinivasan, H. Radhakrishnan, and D. A. Boas, “Motion correction for phase-resolved dynamic optical coherence tomography imaging of rodent cerebral cortex,” Opt. Express 19(22), 21258–21270 (2011).
[Crossref] [PubMed]

B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, “Ultrahigh speed spectral / Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second,” Opt. Express 16(19), 15149–15169 (2008).
[Crossref] [PubMed]

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

Y. Nakamura, S. Makita, M. Yamanari, M. Itoh, T. Yatagai, and Y. Yasuno, “High-speed three-dimensional human retinal imaging by line-field spectral domain optical coherence tomography,” Opt. Express 15(12), 7103–7116 (2007).
[Crossref] [PubMed]

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

Opt. Lett. (4)

Proc. SPIE (1)

T. Klein, W. Wieser, R. Andre, T. Pfeiffer, C. M. Eigenwillig, and R. Huber, “Multi-MHz FDML OCT: Snapshot retinal imaging at 6.7 million axial-scans per second,” Proc. SPIE 8213, 82131E (2012).

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)

J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, Optical Coherence Tomography of Ocular Diseases, 2nd ed. (SLACK Inc., 2004), pp. xii, 714 p.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the developed SSE-POCT system. Ls, lenses (focus lengths of achromatic lenses L1, L2, L3, L4, L6 and L7 are 50 mm, 200 mm, 100 mm, 100 mm, 250 mm and 250 mm, respectively; L5 is a compound-lens composed of two lenses with focus lengths of 50 mm and −150 mm, respectively); Cl1 and Cl2, cylindrical lenses with the same focus lengths of 75mm; DP, dispersive prism; KEP, knife-edge prism; NPBS, non-polarizing beam splitter 50:50; ND, neutral density filter.

Fig. 2
Fig. 2

Illustration of x-k encodings. (a) Illustration of x-k encodings in the sample plane and camera plane. (b) Ideal (blue solid curve) and actual (red dashed curve) x-k encoding functions.

Fig. 3
Fig. 3

Expansion view of x-k encodings in the sample plane and camera plane for two successive steps. (a) x-k encoding rule. (b1) (b2) Distribution of k on the sample plane for steps n-1 and n during C-scan. (c1) (c2) Distribution of x on the camera plane for steps n-1 and n during C-scan. Overlapped data for motion estimation are indicated by arrows.

Fig. 4
Fig. 4

Illustration of wavenumber calibration. (a) Original B-scan spectrum on camera plane with nonuniform k. (b)–(d) Common-path interference signals corresponding to a specific y position: (b) original interference intensity with nonuniform k, (c) original (blue) and resampled (red) interference phases, and (d) resampled interference intensity with uniform k. (e) Resampled B-scan spectrum with uniform k. Non-uniform in k here is exaggerated for better illustration.

Fig. 5
Fig. 5

Flow diagram of the ODC algorithm. (a) Correction for bulk image shifts. (b) Correction for global phase fluctuations. (c) Spectrum stitching [1­–4] are the operations expressed by Eqs. (6) , (7), (18), and (19).

Fig. 6
Fig. 6

Flow charts and processing time of the CDC algorithm and the ODC algorithm.

Fig. 7
Fig. 7

Reconstruction results of a resolution test target under deliberately introduced motion. (a1) Uncorrected and (a2) corrected 3D images. (b) True and estimated shift trajectories. (c1) Uncorrected phase map. (c2) Unwrapped phase map of (c1). (c3) Phase map corrected by the CDC algorithm. (c4) Phase map corrected by the proposed ODC algorithm.

Fig. 8
Fig. 8

Phase differences between encoded frames under deliberately introduced motion. (a) Cross-sectional intensity image. (b1) (b2) Phase difference images based on Eqs. (15) and (16), respectively. Pixels with intensity below threshold are eliminated (in black color). (c1) (c2) Distribution histograms of all the phase difference data from (b1) and (b2), respectively.

Fig. 9
Fig. 9

Reconstruction results of a multilayer sample under deliberately introduced motion. (a1) Uncorrected and (a2) corrected 3D images. Blue line indicates the motion trajectory. (b1)–(b3) Phase maps of the layer point out by red arrow: (b1) before corrected, (b2) after corrected by CDC algorithm and (b3) after corrected by ODC algorithm. (c) En-face intensity image of the layer point out by blue arrow. The dark line is the shadow of the optical fiber.

Fig. 10
Fig. 10

Reconstruction results of a NIR detector card under deliberately introduced motion. (a1) Uncorrected and (a2) corrected 3D images. One corner of the top layer is removed (by post-processing) to reveal the internal structures. Blue line indicates the motion trajectory. (b1)–(b3) Cross-sectional images reconstructed from: (b1) original encoded spectrum, (b2) incorrectly stitched spectrum and (b3) correctly stitched spectrum.

Fig. 11
Fig. 11

Reconstruction results of a piece of slightly curved leather under deliberately introduced motion. (a) Motion trajectory. (b1)–(b3) 3D images of the leather: (b1) before corrected, (b2) after corrected by CDC algorithm and (b3) after corrected by ODC algorithm. (c) Top-view (x-y) projection of the sample. (d1)–(d3) Side-view (x-z) projections of (b1)–(b3), respectively. Solid arrows point out the real scratch while hollow arrows point out the fake scratch (artifacts). Blue solid lines indicate the true shape while red dashed lines indicate the estimated shapes.

Fig. 12
Fig. 12

Reconstruction results of a fresh leaf under deliberately introduced motion. (a1) 3D image, (a2) top-view height projection and (a3) side-view projection before motion correction. (b1) 3D image, (b2) top-view (x-y) height projection and (b3) side-view (x-z) projection after motion correction. Solid arrows point out the real vein while hollow arrows point out the fake vein and the distorted area. (c) Photo of the leaf. The red rectangle indicates the region imaged by SSE-POCT. (d1)–(d5) En-face images at five different depths before motion correction. (e1)–(e5) Corresponding en-face images after motion correction.

Equations (20)

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x( k )={ fsin(2α)[ n ( k m/2 ) 2 sin ( θ i ) 2 n (k) 2 sin ( θ i ) 2 ] k< k 0 fsin(2α)[ n ( k m/2 ) 2 sin ( θ i ) 2 + n (k) 2 sin ( θ i ) 2 ] k k 0 .
n(k)= 1+ 1.738 13.341× 10 4 × k 2 + 0.3138 11.578× 10 3 × k 2 + 1.899 13.93× k 2 .
R n1 ( z,y )= k { I n1 ( k,y ) H ( k ) },
R n ( z,y )= k { I n ( k,y ) H ( k ) }.
Γ n ( ζ,y )= z R n ( zζ,y ) R n1 * ( z,y ) z | R n ( zζ,y ) | 2 z | R n1 ( z,y ) | 2 .
Δ z ^ n ( y )=arg max ζ | Γ n ( ζ,y ) |.
I n ( k,y ):= I n ( k,y ) e j2kΔ z ^ n ( y ) ,
Δ Φ n ( y )=2 k 0 δ z n ( y )
Δ Φ ^ n ( y )=angle[ Γ n ( Δ z ^ n ,y ) ]=angle[ z R n ( zΔ z ^ n ,y ) R n1 * ( z,y ) ],
r n ( 1 ) ( z,y )= k { I n ( k,y );k[ k 3 , k 1 ] }
r n1 ( 2 ) ( z,y )= k { I n1 ( k,y );k[ k 2 , k 0 ] }
r n1 ( 3 ) ( z,y )= k { I n1 ( k,y );k[ k 0 , k 2 ] }
r n ( 4 ) ( z,y )= k { I n ( k,y );k[ k 1 , k 3 ] }
Δ φ n ( z,y )=angle[ r n (1) r n1 (2) * ]=2( k 2 k 1 )z+2 k 2 δ z ^ n ( y ).
Δ φ n + ( z,y )=angle[ r n (4) r n1 (3) * ]=2( k 2 k 1 )z+2 k 2 δ z ^ n ( y ).
[ Δ φ n ( z,y )+Δ φ n + ( z,y ) ] /2 =2 k 0 δ z ^ n ( y ),
Δ Φ ^ n ( y )=2 k 0 δ z ^ n ( y )=angle[ z ( r n (1) r n1 (2) * + r n1 (3) * r n (4) ) ].
Δ Φ ^ n ( y )= 1 2 angle[ z ( | r n (1) r n1 (2) * |+| r n1 (3) * r n (4) | ) e i( Δ ϕ n +Δ ϕ n + ) ].
I n ( k,y ):= I n ( k,y ) e jΔ Φ ^ n ( y ) .
Γ n ( ζ,ψ )= z,y R n ( zζ,yψ ) R n1 * ( z,y ) z,y | R n ( zζ,yψ ) | 2 z,y | R n1 ( z,y ) | 2 .

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