Abstract

We demonstrate in vivo volumetric bidirectional blood flow imaging in animal models using single-pass flow imaging spectral domain optical coherence tomography. This technique uses a modified Hilbert transform algorithm to separate moving and non-moving scatterers within a depth. The resulting reconstructed image maps the components of moving scatterers flowing into and out of the imaging axis onto opposite image half-planes, enabling volumetric bidirectional flow mapping without manual segmentation.

© 2008 Optical Society of America

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  1. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  11. M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
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    [CrossRef]
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    [CrossRef] [PubMed]
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  15. B. Baumann, M. Pircher, E. Gotzinger, and C. K. Hitzenberger, "Full range complex spectral domain optical coherence tomography without additional phase shifters," Opt. Express 15, 13375 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-13375
    [CrossRef] [PubMed]
  16. 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, 3423 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3423
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    [CrossRef] [PubMed]
  20. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
    [CrossRef] [PubMed]
  21. A. M. Davis, M. A. Choma, and J. A. Izatt, "Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal," J. Biomedical Opt. 10, (2005).
    [CrossRef] [PubMed]
  22. A. H. Bachmann, R. A. Leitgeb, and T. Lasser, "Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution," Opt. Express 14, 1487 (2006). nfobase.org/abstract.cfm?URI=oe-14-4-1487">http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1487
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, "Resonant Doppler flow imaging and optical vivisection of retinal blood vessels," Opt. Express 15, 408 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-408
    [CrossRef] [PubMed]
  25. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
    [CrossRef] [PubMed]
  26. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
    [CrossRef] [PubMed]
  27. T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
    [CrossRef] [PubMed]
  28. V. Hamburger, and H. L. Hamilton, "A series of normal stages in the development of the chick embryo," J. Morphology 88, 54 (1951).
    [CrossRef]
  29. B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
    [CrossRef] [PubMed]

2008 (3)

2007 (9)

R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, "Three dimensional optical angiography," Opt. Express 15, 4083 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4083
[CrossRef] [PubMed]

A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, "Resonant Doppler flow imaging and optical vivisection of retinal blood vessels," Opt. Express 15, 408 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-408
[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, 3453 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3453
[CrossRef]

R. K. Wang, "In vivo full range complex Fourier domain optical coherence tomography," Appl. Phys. Lett. 90, 054103 (2007).

B. Baumann, M. Pircher, E. Gotzinger, and C. K. Hitzenberger, "Full range complex spectral domain optical coherence tomography without additional phase shifters," Opt. Express 15, 13375 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-13375
[CrossRef] [PubMed]

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, 3423 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3423
[CrossRef]

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

B. A. Bower, M. Zhao, R. J. Zawadzki, and J. A. Izatt, "Real-time spectral domain Doppler optical coherence tomography and investigation of human retinal vessel autoregulation," J. Biomedical Opt. 12, 041214 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (4)

2004 (4)

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
[CrossRef] [PubMed]

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

2003 (3)

2002 (1)

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

1994 (1)

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

1986 (1)

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

1951 (1)

V. Hamburger, and H. L. Hamilton, "A series of normal stages in the development of the chick embryo," J. Morphology 88, 54 (1951).
[CrossRef]

Agarwal, N.

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

An, L.

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, 3423 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3423
[CrossRef]

Aoki, G.

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 (2006).
[CrossRef] [PubMed]

Bachman, M.

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

Bachmann, A. H.

Bajraszewski, T.

Baumann, B.

Blatter, C.

Bouma, B. E.

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
[CrossRef] [PubMed]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Bower, B. A.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

B. A. Bower, M. Zhao, R. J. Zawadzki, and J. A. Izatt, "Real-time spectral domain Doppler optical coherence tomography and investigation of human retinal vessel autoregulation," J. Biomedical Opt. 12, 041214 (2007).
[CrossRef] [PubMed]

Cable, A. E.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Cense, B.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Chen, T. C.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Chen, Z.

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

Chen, Z. 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. Biomedical Opt. 10, (2005).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

Constanza, M.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Creazzo, T. L.

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

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. Biomedical Opt. 10, (2005).
[CrossRef] [PubMed]

de Boer, J. F.

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
[CrossRef] [PubMed]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Dewhirst, M. W.

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

Drexler, W.

Duker, J. S.

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Ellerbee, A. K.

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

Endo, T.

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 (2006).
[CrossRef] [PubMed]

Fabritius, T.

Fercher, A. F.

Fujimoto, J. G.

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Gotzinger, E.

Gragoudas, E.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Gruber, A.

Guo, S.

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

Guyer, D.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
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Hamburger, V.

V. Hamburger, and H. L. Hamilton, "A series of normal stages in the development of the chick embryo," J. Morphology 88, 54 (1951).
[CrossRef]

Hamilton, H. L.

V. Hamburger, and H. L. Hamilton, "A series of normal stages in the development of the chick embryo," J. Morphology 88, 54 (1951).
[CrossRef]

Hanson, S. R.

Hardee, M. E.

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

Hitzenberger, C. K.

Hope-Ross, M.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Huang, D.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Hurst, S.

Itoh, M.

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 (2006).
[CrossRef] [PubMed]

Izatt, J. A.

B. A. Bower, M. Zhao, R. J. Zawadzki, and J. A. Izatt, "Real-time spectral domain Doppler optical coherence tomography and investigation of human retinal vessel autoregulation," J. Biomedical Opt. 12, 041214 (2007).
[CrossRef] [PubMed]

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

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

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

Jacques, S. L.

Jiang, J. Y.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Kirby, M. L.

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

Ko, T. H.

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Kowalczyk, A.

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, "Flow velocity estimation using joint Spectral and Time Domain Optical Coherence Tomography," Opt. Express 16, 6008 (2008). http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-9-6008
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Krupsky, S.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Lasser, T.

Leitgeb, R. A.

Li, G. P.

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

Liu, G.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Ma, Z.

Makita, S.

Mariampillai, A.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Michaely, R.

Moeller, B. J.

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

Munce, N. R.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Nassif, N. A.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Nelson, J. S.

Orlock, D.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Park, B. H.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Pierce, M. C.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Pircher, M.

Puliafito, C. A.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Randall, C.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Rohrer, K.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Sarunic, M. V.

Schmetterer, L.

Sekhar, S. C.

Shields, W.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Slakter, J.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Sobel, R.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Sorenson, J.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

Sorg, B. S.

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

Srinivasan, V. J.

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Standish, B. A.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Szkulmowska, A.

Szkulmowski, M.

Tan, O.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Tearney, G. J.

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
[CrossRef] [PubMed]

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Thrane, L.

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

Tindel, L.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Villiger, M. L.

Vitkin, I. A.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Wang, L.

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

Wang, R. K.

R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, "Three dimensional optical angiography," Opt. Express 15, 4083 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4083
[CrossRef] [PubMed]

R. K. Wang, "In vivo full range complex Fourier domain optical coherence tomography," Appl. Phys. Lett. 90, 054103 (2007).

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, 3423 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3423
[CrossRef]

Wang, Y.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography," J. Biomedical Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G. P. Li, and Z. Chen, "Frequency domain phase-resolved optical Doppler and Doppler variance tomography," Opt. Commun. 242, 6 (2004).
[CrossRef]

White, B. R.

B. R. White, M. C. Pierce, N. A. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. De Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 8 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-25-3490
[CrossRef] [PubMed]

Wojtkowski, M.

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, "Flow velocity estimation using joint Spectral and Time Domain Optical Coherence Tomography," Opt. Express 16, 6008 (2008). http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-9-6008
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-Resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12, 2404 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-11-2404.
[CrossRef] [PubMed]

Yang, C.

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt Lett 30, 1162 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183
[CrossRef] [PubMed]

Yang, C. H.

Yang, V. X. D.

A. Mariampillai, B. A. Standish, N. R. Munce, C. Randall, G. Liu, J. Y. Jiang, A. E. Cable, I. A. Vitkin, and V. X. D. Yang, "Doppler optical cardiogram gated 2D color flow imaging at 1000 fps and 4D in vivo visualization of embryonic heart at 45 fps on a swept source OCT system," Optics Express 15, 1627 (2007). http://www.opticsinfobase.org/abstract.cfm?id=127228
[CrossRef] [PubMed]

Yannuzzi, L.

M. Hope-Ross, L. Yannuzzi, E. Gragoudas, D. Guyer, J. Slakter, J. Sorenson, S. Krupsky, D. Orlock, and C. A. Puliafito, "Adverse reactions due to indocyanine green," Ophthalmology 101, 5 (1994).
[PubMed]

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Yasuno, Y.

Yatagai, T.

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 (2006).
[CrossRef] [PubMed]

Yelbuz, T. M.

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

Yun, S. H.

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822 (2004). http://www.opticsexpress.org/abstract.cfm?id=81308
[CrossRef] [PubMed]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Optics Express 12, 10 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367
[CrossRef] [PubMed]

Zang, E.

L. Yannuzzi, K. Rohrer, L. Tindel, R. Sobel, M. Constanza, W. Shields, and E. Zang, "Fluorescein angiography complication survey," Ophthalmology 93, 7 (1986).
[PubMed]

Zawadzki, R. J.

Zhang, J.

Zhao, M.

B. A. Bower, M. Zhao, R. J. Zawadzki, and J. A. Izatt, "Real-time spectral domain Doppler optical coherence tomography and investigation of human retinal vessel autoregulation," J. Biomedical Opt. 12, 041214 (2007).
[CrossRef] [PubMed]

Appl. Opt. (1)

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 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

R. K. Wang, "In vivo full range complex Fourier domain optical coherence tomography," Appl. Phys. Lett. 90, 054103 (2007).

Circulation (1)

T. M. Yelbuz, M. A. Choma, L. Thrane, M. L. Kirby, and J. A. Izatt, "Optical coherence tomography - A new high-resolution imaging technology to study cardiac development in chick embryos," Circulation 106, 2771 (2002).
[CrossRef] [PubMed]

J. Biomedical Opt. (2)

B. S. Sorg, M. E. Hardee, N. Agarwal, B. J. Moeller, and M. W. Dewhirst, "Spectral imaging facilitates visualization and measurements of unstable and abnormal microvascular oxygen transport in tumors," J. Biomedical Opt. 13, (2008).
[CrossRef] [PubMed]

B. A. Bower, M. Zhao, R. J. Zawadzki, and J. A. Izatt, "Real-time spectral domain Doppler optical coherence tomography and investigation of human retinal vessel autoregulation," J. Biomedical Opt. 12, 041214 (2007).
[CrossRef] [PubMed]

J. Biomedical Opt.. (1)

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Supplementary Material (1)

» Media 1: AVI (7726 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Flow chart of SDOCT spectral datacube processing. (a) Spectral inverse Fourier transform of B-scan yields (b,c) conventional SDOCT depth-resolved reflectivity map and lateral Fourier transform yields (d,e) sample spatial frequency information.

Fig. 2.
Fig. 2.

Flow chart of SPFI-SDOCT processing. (a) Lateral Fourier transform of B-scan yields (b) spatial frequency of sample centered around DC and spatial frequency of moving scatterers shifted by their respective Doppler frequencies. (c) Applying a frequency-shifted Heaviside step function and inverse Fourier transform of spatial frequencies recreates (d) the analytic interferometric signal (modified Hilbert transf'rm). (e) Spectral inverse Fourier transform of the analytic interferometric signal maps depth-solved reflectivities of bidirectionally moving scatterers on opposite image half-planes which can then be (f) overlaid for vessel identification.

Fig. 3.
Fig. 3.

SPFI-SDOCT microscope. 2-dimensional scanning was implemented using a galvanometer scanning pair and f/8.5 microscope optics were optimized for a 9μm spot-size. The reference arm was blocked to allow for commonpath imaging.

Fig. 4.
Fig. 4.

Phantom and in vivo flow models.(a) Two micro-capillaries were connected and oriented such that fluid flowed in opposite directions in a B-scan cross-section (line indicates B-scan orientation).(b) Chicken embryo preparation showing live embryo and peripheral vessels on both amnion and yolk surfaces (arrow).(c) Mouse window chamber preparation showing skin fold vasculature and tumor.

Fig. 5.
Fig. 5.

Flow phantom imaging showing (a) conventional SDOCT depth image with complex conjugate mirror image,(b) SPFI processed flow image showing bidirectional flow, and (c) overlaid flow and structure image. Negative flow (blue), positive flow (red), and non-moving structure (orange) are identified.

Fig. 6.
Fig. 6.

3D reconstruction of bidirectional volumetric flow magnitude in chicken embryo model. 3mm × 3mm volume is comprised of nine 1mm × 1mm volumes sampled with 1ms integration time. Vessel sizes of 40μm (purple) to 270μm (orange) were within detection limits. Amionic vessel (blue), amionic vessel branch point (green), and motion artifact (red) are indentified.

Fig. 7.
Fig. 7.

(7.73MB) Movie of 3D rendering of bidirectional flow magnitude in chicken embryo model. [Media 1]

Fig. 8.
Fig. 8.

3D reconstruction of bidirectional volumetric flow magnitude in mouse window chamber model. 3mm × 3mm volume is comprised of nine 1mm × 1mm volumes sampled with 2ms integration time. Vessel sizes of 20μm (purple) to 110μm (green) were within detection limits. Tumor region vasculature (blue) and motion artifact (red) are indicated.

Equations (10)

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s [ k , x ] = m = 1 M A m exp [ ( 2 nk Δ z m + θ h [ x ] + θ m [ x ] ) ]
θ m [ x ] = 2 nk w 0 2 [ x dL D ] v m v x x dL D + w 0 2
s [ k , x ] = m = 1 M A m exp [ i 2 nk Δ z m ] exp [ i θ h [ x ] ] exp [ 2 ink∏ w 0 2 [ x dL D ] v m v x x dL D + w 0 2 ]
= m = 1 M A m exp [ i 2 nk Δ z m ] g [ x ] h [ x ]
FT x u [ I [ k , x ] ] = m = 1 M A m cos [ 2 nk Δ z m ] ⊗Re [ G [ u ] ] ⊗Re [ H [ u ] ] .
Re [ H [ u ] ] = Re [ dL D w 0 2 dL D + w 0 2 exp [ 2 ink v m v x x dL D + w 0 2 ] exp [ iux ] dx ]
= κ cos [ w 0 u 2 nk v m v x ] 1 u 2 nk v m v x
σ h [ u ] = x = 1 L σ h 2 [ x ]
FT x u [ I [ k , x ] ] H [ u f T ] = α ( V + [ k , u + f D , + ] + V __ [ k , u f D , ] )
dv = L λ 0 2 nD τ w 0 cos θ D

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