Abstract

The significantly less stringent operation of a two-reference swept-source optical coherence tomography (OCT) system for suppressing the mirror image is demonstrated based on the spatially localized image processing method. With this method, the phase difference between the two reference signals is not limited to 90 degrees. Based on the current experimental operation, the mirror image can be effectively suppressed as long as the phase difference is larger than 20 degrees. In other words, the adjustment of the beam splitter orientation for controlling the phase difference becomes much more flexible. Also, based on a phantom experiment, the combination the spatially localized mirror image suppression method with the two-reference OCT operation leads to the implementation of full-range optical Doppler tomography.

© 2012 OSA

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  1. R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett.28(22), 2201–2203 (2003).
    [CrossRef] [PubMed]
  2. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27(16), 1415–1417 (2002).
    [CrossRef] [PubMed]
  3. P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
    [CrossRef]
  4. Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express12(25), 6184–6191 (2004).
    [CrossRef] [PubMed]
  5. J. Zhang, W. Jung, J. Nelson, and Z. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express12(24), 6033–6039 (2004).
    [CrossRef] [PubMed]
  6. E. Götzinger, M. Pircher, R. Leitgeb, and C. Hitzenberger, “High speed full range complex spectral domain optical coherence tomography,” Opt. Express13(2), 583–594 (2005).
    [CrossRef] [PubMed]
  7. S. Yun, G. Tearney, J. de Boer, and B. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express12(20), 4822–4828 (2004).
    [CrossRef] [PubMed]
  8. J. Zhang, J. S. Nelson, and Z. Chen, “Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator,” Opt. Lett.30(2), 147–149 (2005).
    [CrossRef] [PubMed]
  9. A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt.10(6), 064005 (2005).
    [CrossRef] [PubMed]
  10. A. H. Dhalla and J. A. Izatt, “Complete complex conjugate resolved heterodyne swept-source optical coherence tomography using a dispersive optical delay line,” Biomed. Opt. Express2(5), 1218–1232 (2011).
    [CrossRef] [PubMed]
  11. M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers,” Opt. Lett.28(22), 2162–2164 (2003).
    [CrossRef] [PubMed]
  12. K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
    [CrossRef]
  13. S. Zotter, M. Pircher, E. Götzinger, T. Torzicky, M. Bonesi, and C. K. Hitzenberger, “Sample motion-insensitive, full-range, complex, spectral-domain optical-coherence tomography,” Opt. Lett.35(23), 3913–3915 (2010).
    [CrossRef] [PubMed]
  14. K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett.35(7), 1058–1060 (2010).
    [CrossRef] [PubMed]
  15. P. Meemon, K.-S. Lee, and J. P. Rolland, “Doppler imaging with dual-detection full-range frequency domain optical coherence tomography,” Biomed. Opt. Express1(2), 537–552 (2010).
    [CrossRef] [PubMed]
  16. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt.45(8), 1861–1865 (2006).
    [CrossRef] [PubMed]
  17. R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett.90(5), 054103 (2007).
    [CrossRef]
  18. S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express16(12), 8406–8420 (2008).
    [CrossRef] [PubMed]
  19. S. Vergnole, G. Lamouche, and M. L. Dufour, “Artifact removal in Fourier-domain optical coherence tomography with a piezoelectric fiber stretcher,” Opt. Lett.33(7), 732–734 (2008).
    [CrossRef] [PubMed]
  20. K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express17(19), 16820–16833 (2009).
    [CrossRef] [PubMed]
  21. F. Jaillon, S. Makita, M. Yabusaki, and Y. Yasuno, “Parabolic BM-scan technique for full range Doppler spectral domain optical coherence tomography,” Opt. Express18(2), 1358–1372 (2010).
    [CrossRef] [PubMed]
  22. B. Baumann, M. Pircher, E. Götzinger, and C. K. Hitzenberger, “Full range complex spectral domain optical coherence tomography without additional phase shifters,” Opt. Express15(20), 13375–13387 (2007).
    [CrossRef] [PubMed]
  23. L. An and R. K. Wang, “Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography,” Opt. Lett.32(23), 3423–3425 (2007).
    [CrossRef] [PubMed]
  24. R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett.32(23), 3453–3455 (2007).
    [CrossRef] [PubMed]
  25. C. T. Wu, T. T. Chi, C. K. Lee, Y. W. Kiang, C. C. Yang, and C. P. Chiang, “Method for suppressing the mirror image in Fourier-domain optical coherence tomography,” Opt. Lett.36(15), 2889–2891 (2011).
    [CrossRef] [PubMed]
  26. C. T. Wu, T. T. Chi, Y. W. Kiang, and C. C. Yang, “Computation time-saving mirror image suppression method in Fourier-domain optical coherence tomography,” Opt. Express20(8), 8270–8283 (2012), doi:.
    [CrossRef] [PubMed]
  27. J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
    [CrossRef] [PubMed]

2012 (2)

C. T. Wu, T. T. Chi, Y. W. Kiang, and C. C. Yang, “Computation time-saving mirror image suppression method in Fourier-domain optical coherence tomography,” Opt. Express20(8), 8270–8283 (2012), doi:.
[CrossRef] [PubMed]

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

2011 (2)

2010 (4)

2009 (2)

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express17(19), 16820–16833 (2009).
[CrossRef] [PubMed]

K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
[CrossRef]

2008 (2)

2007 (4)

2006 (1)

2005 (3)

2004 (4)

2003 (2)

2002 (1)

An, L.

Aoki, G.

Bajraszewski, T.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett.28(22), 2201–2203 (2003).
[CrossRef] [PubMed]

Baumann, B.

Bonesi, M.

Bouma, B.

Bykov, A. V.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

Chen, M.

Chen, Z.

Chi, T. T.

Chiang, C. P.

Choma, M. A.

A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt.10(6), 064005 (2005).
[CrossRef] [PubMed]

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers,” Opt. Lett.28(22), 2162–2164 (2003).
[CrossRef] [PubMed]

Dallas, W.

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett.35(7), 1058–1060 (2010).
[CrossRef] [PubMed]

K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
[CrossRef]

Davis, A. M.

A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt.10(6), 064005 (2005).
[CrossRef] [PubMed]

de Boer, J.

Dhalla, A. H.

Ding, Z.

Dufour, M. L.

Endo, T.

Fabritius, T.

Fercher, A. F.

Gorczynska, I.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

Götzinger, E.

Hitzenberger, C.

Hitzenberger, C. K.

Hsu, K.

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett.35(7), 1058–1060 (2010).
[CrossRef] [PubMed]

K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
[CrossRef]

Itoh, M.

Izatt, J. A.

Jaillon, F.

Jung, W.

Kalkman, J.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

Kiang, Y. W.

Kowalczyk, A.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27(16), 1415–1417 (2002).
[CrossRef] [PubMed]

Lamouche, G.

Lasser, T.

Lee, C. K.

Lee, K. S.

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett.35(7), 1058–1060 (2010).
[CrossRef] [PubMed]

K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
[CrossRef]

Lee, K.-S.

Leitgeb, R.

Leitgeb, R. A.

Makita, S.

Meemon, P.

Meng, J.

Michaely, R.

Nelson, J.

Nelson, J. S.

Pircher, M.

Rolland, J. P.

Sekhar, S. C.

Streekstra, G. J.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

Sumimura, H.

Szkulmowski, M.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

Targowski, P.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

Tearney, G.

Torzicky, T.

van Leeuwen, T. G.

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

Vergnole, S.

Wang, K.

Wang, R. K.

Wojtkowski, M.

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27(16), 1415–1417 (2002).
[CrossRef] [PubMed]

Wu, C. T.

Yabusaki, M.

Yang, C.

Yang, C. C.

Yasuno, Y.

Yatagai, T.

Yun, S.

Zeng, Y.

Zhang, J.

Zotter, S.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett.90(5), 054103 (2007).
[CrossRef]

Biomed. Opt. Express (2)

J. Biomed. Opt. (1)

A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt.10(6), 064005 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and I. Gorczynska, “Complex spectral OCT in human eye imaging in vivo,” Opt. Commun.229(1-6), 79–84 (2004).
[CrossRef]

Opt. Express (9)

Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express12(25), 6184–6191 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Jung, J. Nelson, and Z. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express12(24), 6033–6039 (2004).
[CrossRef] [PubMed]

E. Götzinger, M. Pircher, R. Leitgeb, and C. Hitzenberger, “High speed full range complex spectral domain optical coherence tomography,” Opt. Express13(2), 583–594 (2005).
[CrossRef] [PubMed]

S. Yun, G. Tearney, J. de Boer, and B. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express12(20), 4822–4828 (2004).
[CrossRef] [PubMed]

S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express16(12), 8406–8420 (2008).
[CrossRef] [PubMed]

K. Wang, Z. Ding, Y. Zeng, J. Meng, and M. Chen, “Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact,” Opt. Express17(19), 16820–16833 (2009).
[CrossRef] [PubMed]

F. Jaillon, S. Makita, M. Yabusaki, and Y. Yasuno, “Parabolic BM-scan technique for full range Doppler spectral domain optical coherence tomography,” Opt. Express18(2), 1358–1372 (2010).
[CrossRef] [PubMed]

B. Baumann, M. Pircher, E. Götzinger, and C. K. Hitzenberger, “Full range complex spectral domain optical coherence tomography without additional phase shifters,” Opt. Express15(20), 13375–13387 (2007).
[CrossRef] [PubMed]

C. T. Wu, T. T. Chi, Y. W. Kiang, and C. C. Yang, “Computation time-saving mirror image suppression method in Fourier-domain optical coherence tomography,” Opt. Express20(8), 8270–8283 (2012), doi:.
[CrossRef] [PubMed]

Opt. Lett. (10)

L. An and R. K. Wang, “Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography,” Opt. Lett.32(23), 3423–3425 (2007).
[CrossRef] [PubMed]

R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett.32(23), 3453–3455 (2007).
[CrossRef] [PubMed]

C. T. Wu, T. T. Chi, C. K. Lee, Y. W. Kiang, C. C. Yang, and C. P. Chiang, “Method for suppressing the mirror image in Fourier-domain optical coherence tomography,” Opt. Lett.36(15), 2889–2891 (2011).
[CrossRef] [PubMed]

S. Vergnole, G. Lamouche, and M. L. Dufour, “Artifact removal in Fourier-domain optical coherence tomography with a piezoelectric fiber stretcher,” Opt. Lett.33(7), 732–734 (2008).
[CrossRef] [PubMed]

S. Zotter, M. Pircher, E. Götzinger, T. Torzicky, M. Bonesi, and C. K. Hitzenberger, “Sample motion-insensitive, full-range, complex, spectral-domain optical-coherence tomography,” Opt. Lett.35(23), 3913–3915 (2010).
[CrossRef] [PubMed]

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett.35(7), 1058–1060 (2010).
[CrossRef] [PubMed]

J. Zhang, J. S. Nelson, and Z. Chen, “Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator,” Opt. Lett.30(2), 147–149 (2005).
[CrossRef] [PubMed]

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers,” Opt. Lett.28(22), 2162–2164 (2003).
[CrossRef] [PubMed]

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett.28(22), 2201–2203 (2003).
[CrossRef] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27(16), 1415–1417 (2002).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

J. Kalkman, A. V. Bykov, G. J. Streekstra, and T. G. van Leeuwen, “Multiple scattering effects in Doppler optical coherence tomography of flowing blood,” Phys. Med. Biol.57(7), 1907–1917 (2012).
[CrossRef] [PubMed]

Proc. SPIE (1)

K. S. Lee, P. Meemon, K. Hsu, W. Dallas, and J. P. Rolland, “Dual-reference full-range frequency domain optical coherence tomography,” Proc. SPIE7170, 717004, 717004-7 (2009).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Setup of the two-reference OCT system. BS1-BS3: beam splitters. FBG: fiber Bragg grating.

Fig. 2
Fig. 2

(a) Un-processed OCT scanning image acquired from balanced detector 1 when a mirror surface is used as the scanning sample and the phase difference, θ, between the two reference signals is around 80 degrees. (b)-(e): Mirror image suppression results based on the quadratic method when θ is 90, 80, 70, and 60 degrees, respectively. (f)-(j): Mirror image suppression results based on the SL method when θ is 90, 40, 30, 20 and 10 degrees, respectively.

Fig. 3
Fig. 3

(a): θ image corresponding to the OCT image in Fig. 2(a). (b): B-mode line-scan profile of θ of the real image (the lower portion in part (a)). (c): B-mode line-scan intensity ratio between the OCT signals from balanced detectors 1 and 2.

Fig. 4
Fig. 4

B-mode averages of the line-scan intensity ratios of the residual mirror image over the real image along A-mode scan corresponding to the results in Fig. 2 when the quadratic (Qd) (a) and SL (b) methods are used.

Fig. 5
Fig. 5

B-mode averages of the mirror image suppression ratios as functions of the phase difference θ for various experimental (Exp.) and simulation (Sim.) cases.

Fig. 6
Fig. 6

OCT images by scanning the skin on a finger of a volunteer. The images in columns 1-4 show the un-processed results obtained from balanced detectors 1 and 2, and the processed results based on the quadratic and SL methods, respectively. Meanwhile, the images in rows 1-4 correspond to the conditions of θ = 90, 80, 30, and 20 degrees, respectively.

Fig. 7
Fig. 7

Setup for the phantom experiment of ODT.

Fig. 8
Fig. 8

OCT images by scanning the capillary tube with motionless bean milk shown in Fig. 7. The images in columns 1-4 show the un-processed results obtained from balanced detectors 1 and 2, and the processed results based on the quadratic and SL methods, respectively. Meanwhile, the images in rows 1-4 correspond to the conditions of θ = 90, 80, 30, and 20 degrees, respectively.

Fig. 9
Fig. 9

ODT phase shift images under various conditions when θ is 90 degrees. The images in rows 1-3 show the un-processed data, the processed results based on the quadratic method, and the processed results based on the SL method, respectively. Meanwhile, the images in columns 1-7 show the results of 0, π/6, π/3, π/2, 2π/3, 5π/6, and π, respectively, in maximum Doppler phase shift around the center of the capillary tube. Arrows are drawn to indicate two dashed lines in the three images of column 7 for line-scan demonstrations later.

Fig. 10
Fig. 10

ODT phase shift images similar to Fig. 9 when θ is 80 degrees.

Fig. 11
Fig. 11

ODT phase shift images similar to Fig. 9 when θ is 30 degrees.

Fig. 12
Fig. 12

ODT phase shift images similar to Fig. 9 when θ is 20 degrees

Fig. 13
Fig. 13

Line-scan profiles of Doppler phase shift along the lower dashed lines in the individual images of the last columns in Figs. 9-12 (indicated by the arrows at the right end) for the cases of θ = 90 (a), 80 (b), 30 (c), and 20 (d) degrees.

Fig. 14
Fig. 14

Line-scan profiles of Doppler phase shift along the upper dashed lines in the individual images of the last columns in Figs. 9-12 (indicated by the arrows at the right end) for the cases of θ = 90 (a), 80 (b), 30 (c), and 20 (d) degrees.

Equations (4)

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S n = r n + m n
S n+1 = r n+1 exp( iθ )+ m n+1 exp( iθ ).
r ˜ n = S n S n+1 exp( iθ ) 1exp( i2θ )
m ˜ n = S n S n+1 exp( iθ ) 1exp( i2θ ) .

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