Abstract

Inverse scattering theory for optical coherence tomography (OCT) is developed. The results are used to produce algorithms to resolve three-dimensional object structure, taking into account the finite beam width, diffraction, and defocusing effects. The resolution normally achieved only in the focal plane of the OCT system is shown to be available for all illuminated depths in the object without moving the focal plane. Spatially invariant resolution is verified with numerical simulations and indicates an improvement of the high-resolution cross-sectional imaging capabilities of OCT.

© 2006 Optical Society of America

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  1. P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 1192.
  24. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, 1989), pp. 142-147.
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    [CrossRef]
  26. C. Pozrikidis, Numerical Computation in Science and Engineering (Oxford U. Press, 1998), pp. 406-408.

2005 (2)

O. Bruno and J. Chaubell, "One-dimensional inverse scattering problem for optical coherence tomography," Inverse Probl. 21, 499-524 (2005).
[CrossRef]

M. J. Cobb, X. Liu, and X. Li, "Continuous focus tracking for real-time optical coherence tomography," Opt. Lett. 30, 1680-1682 (2005).
[CrossRef] [PubMed]

2004 (3)

B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, "Adaptive-optics ultrahigh-resolution optical coherence tomography," Opt. Lett. 29, 2142-2144 (2004).
[CrossRef] [PubMed]

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

2003 (6)

2002 (2)

Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, "High-resolution optical coherence tomography over a large depth range with an axicon lens," Opt. Lett. 27, 243-245 (2002).
[CrossRef]

T. Blu, H. Bay, and M. Unser, "A new high-resolution processing method for the deconvolution of optical coherence tomography signals," presented at the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July 7-11, 2002.

2001 (2)

B.E.Bouma and J.G.Tearney, eds., The Handbook of Optical Coherence Tomography (Marcel Dekker, 2001).

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

1999 (1)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

1998 (1)

C. Pozrikidis, Numerical Computation in Science and Engineering (Oxford U. Press, 1998), pp. 406-408.

1997 (3)

P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 33, 1365-1367 (1997).
[CrossRef]

1995 (2)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 1192.

1994 (1)

1992 (1)

P. C. Hansent, "Numerical tools for analysis and solution of Fredholm integral equations of the first kind," Inverse Probl. 8, 849-872 (1992).
[CrossRef]

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, 1178-1181 (1991).
[CrossRef] [PubMed]

1989 (1)

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, 1989), pp. 142-147.

Andersen, P. E.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Andersson-Engels, S.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Artal, P.

Bay, H.

T. Blu, H. Bay, and M. Unser, "A new high-resolution processing method for the deconvolution of optical coherence tomography signals," presented at the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July 7-11, 2002.

Bendsoe, N.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Blu, T.

T. Blu, H. Bay, and M. Unser, "A new high-resolution processing method for the deconvolution of optical coherence tomography signals," presented at the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July 7-11, 2002.

Boppart, S. A.

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, "Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media," Appl. Opt. 42, 204-217 (2003).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

Bouma, B. E.

Brezinski, M. E.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

Bruno, O.

O. Bruno and J. Chaubell, "One-dimensional inverse scattering problem for optical coherence tomography," Inverse Probl. 21, 499-524 (2005).
[CrossRef]

O. Bruno and J. Chaubell, "Inverse scattering problem for optical coherence tomography," Opt. Lett. 28, 2049-2051 (2003).
[CrossRef] [PubMed]

Cense, B.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Charalambous, I.

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

Chaubell, J.

O. Bruno and J. Chaubell, "One-dimensional inverse scattering problem for optical coherence tomography," Inverse Probl. 21, 499-524 (2005).
[CrossRef]

O. Bruno and J. Chaubell, "Inverse scattering problem for optical coherence tomography," Opt. Lett. 28, 2049-2051 (2003).
[CrossRef] [PubMed]

Chen, Z.

Cobb, M. J.

Cooper, P. S.

P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, 1989), pp. 142-147.

deBoer, J. F.

Ding, Z.

Dogariu, A.

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

Drexler, W.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Feng, Y.

Fercher, A. F.

B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, "Adaptive-optics ultrahigh-resolution optical coherence tomography," Opt. Lett. 29, 2142-2144 (2004).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fernandez, E. J.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Fornaro, G.

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

Fujimoto, J. G.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Gaskell, A. P.

P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Hansent, P. C.

P. C. Hansent, "Numerical tools for analysis and solution of Fredholm integral equations of the first kind," Inverse Probl. 8, 849-872 (1992).
[CrossRef]

Hee, M. R.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, 1989), pp. 142-147.

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Huang, D.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 33, 1365-1367 (1997).
[CrossRef]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[CrossRef] [PubMed]

Jensen, L. K.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Kulkarni, M. D.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 33, 1365-1367 (1997).
[CrossRef]

Lanari, R.

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

Li, X.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Liu, X.

Luo, W.

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 1192.

Marks, D. L.

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, "Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media," Appl. Opt. 42, 204-217 (2003).
[CrossRef] [PubMed]

Nelson, J. S.

Oldenburg, A. L.

Owen, G. M.

Park, B. H.

Pedersen, F.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Pierce, M. C.

Plesea, L.

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

Podoleanu, A.

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

Pozrikidis, C.

C. Pozrikidis, Numerical Computation in Science and Engineering (Oxford U. Press, 1998), pp. 406-408.

Prieto, P. M.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Ren, H.

Reynolds, J. J.

Rosen, R.

A. Podoleanu, I. Charalambous, L. Plesea, A. Dogariu, and R. Rosen, "Correction of distortions in optical coherence tomography imaging of the eye," Phys. Med. Biol. 49, 1277-1294 (2004).
[CrossRef] [PubMed]

Sansosti, E.

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

Sattmann, H.

Schmitt, J. M.

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

Schuman, J. S.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Serafino, F.

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

Singletary, K. W.

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

Southern, J. F.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Svanberg, K.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Svanberg, S.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Swanson, E. A.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

Thomas, C. W.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 33, 1365-1367 (1997).
[CrossRef]

Thrane, L.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Tierney, G. J.

Tycho, A.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

Unser, M.

T. Blu, H. Bay, and M. Unser, "A new high-resolution processing method for the deconvolution of optical coherence tomography signals," presented at the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July 7-11, 2002.

Unterhuber, A.

Wang, R. K.

Wang, Y.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 1192.

Wons, A. F.

P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.

Zhao, Y.

Zoffoli, S.

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

Appl. Opt. (1)

Breast Cancer Res. Treat. (1)

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, "Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer," Breast Cancer Res. Treat. 84, 85-97 (2004).
[CrossRef] [PubMed]

Electron. Lett. (1)

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 33, 1365-1367 (1997).
[CrossRef]

IEE Proc., Radar Sonar Navig. (1)

R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, "New approach for hybrid strip-map/spotlight SAR data focusing," IEE Proc., Radar Sonar Navig. 148, 363-372 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

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[CrossRef]

O. Bruno and J. Chaubell, "One-dimensional inverse scattering problem for optical coherence tomography," Inverse Probl. 21, 499-524 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Surg. Res. (1)

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, "Optical biopsy with optical coherence tomography: feasibility for surgical diagnostics," J. Surg. Res. 71, 32-40 (1997).
[CrossRef] [PubMed]

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[CrossRef]

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[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (7)

B.E.Bouma and J.G.Tearney, eds., The Handbook of Optical Coherence Tomography (Marcel Dekker, 2001).

P. S. Cooper, A. F. Wons, and A. P. Gaskell, "High resolution synthetic aperture radar using a multiple sub-band technique," in IEEE Proceedings of Radar Systems, Conf. Publ. 449 (IEEE Press, 1997), pp. 263-267.

L. K. Jensen, L. Thrane, P. E. Andersen, A. Tycho, F. Pedersen, S. Andersson-Engels, N. Bendsoe, S. Svanberg, and K. Svanberg, "Optical coherence tomography in clinical examinations of nonpigmented skin malignancies," in Optical Coherence Tomography and Coherence Techniques, W.Drexler, ed., Proc. SPIE 5140, 160-167 (2003).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 1192.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, 1989), pp. 142-147.

C. Pozrikidis, Numerical Computation in Science and Engineering (Oxford U. Press, 1998), pp. 406-408.

T. Blu, H. Bay, and M. Unser, "A new high-resolution processing method for the deconvolution of optical coherence tomography signals," presented at the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July 7-11, 2002.

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Figures (9)

Fig. 1
Fig. 1

(a) Typical Michelson interferometer for use in OCT. BS is the beam splitter, P S is the sample path, P R is the reference path, and h is the distance traveled by the reference mirror. (b) Interferogram of an impulse response for an OCT system with a low-coherence source having a Gaussian spectrum and a full width at half-maximum (FWHM) coherence length L c .

Fig. 2
Fig. 2

Geometry of a Gaussian beam for low- and high-numerical-aperture (NA) lenses. These geometries are contrasted with the assumption of a collimated axial OCT scan. b is the confocal parameter, w 0 is the beam radius at the focus, and L c is the coherence length of the source.

Fig. 3
Fig. 3

(Color online) Illustration of the notation and relation to the scattering and measurement process. The field emerges from the fiber and is projected by a thin lens in the z = z l plane to produce a beam with normalized profile g ( r r 0 , k ) . The field interacts with the sample to produce, from each point r in the sample, a scattered field U ( r , r 0 , k ) = η ( r ) G ( r , r , k ) . This field is then collected and projected back into the fiber to produce the signal S ( r 0 , k ) .

Fig. 4
Fig. 4

Sampling lattice of the spatial frequencies in the object space ( Q , β ) on a uniform grid of the spatial frequencies in the signal space ( Q , k ) . The curves shown are lines of constant β.

Fig. 5
Fig. 5

(a) Original object model of point scatterers and (b) simulated OCT image with SNR = 35 dB .

Fig. 6
Fig. 6

(a) Original object model of point scatterers and (b) simulated OCT image with SNR = 5 dB .

Fig. 7
Fig. 7

(a) Unfiltered reconstruction and (b) Tikhonov regularized solution, λ = 60 , for SNR values of 35 dB .

Fig. 8
Fig. 8

(a) Unfiltered reconstruction and (b) Tikhonov regularized solution, λ = 60 , for SNR values of 5 dB .

Fig. 9
Fig. 9

(Color online) Illustration of the coupling of light (a) out of and (b) into the fiber.

Tables (6)

Tables Icon

Table 1 Steps in the Simulations Using the Thin-Sample Approximation

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Table 2 Steps in the Calculation of S ( r 0 , k ) from η ( r 0 ; z ) Using the Thin-Sample Approximation

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Table 3 Steps in the Calculation of S t ( r 0 , t ) from S k ( r 0 , k )

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Table 4 Steps in the Calculation of S k ( r 0 , k ) from S t ( r 0 , t )

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Table 5 Steps in the Calculation of η A ( r 0 ; z ) from S ( r 0 , k ) Using the Thin-Sample Approximation

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Table 6 Steps in the Calculation of η ̂ ( r 0 ; z ) from η A ( r 0 ; z ) Using the Thin-Sample Approximation

Equations (56)

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S ( r 0 , t ) = d t E r ( t ) E s * ( r 0 , t t ) ,
S ( r 0 , ω ) = E r ( ω ) E s * ( r 0 , ω ) .
S k ( r , k ) = S ω ( r , ω ) ( k / ω ) 1 .
S = K η ,
W 0 ( k ) = α k ,
g 0 ( r , k ) = 1 2 π W 0 2 ( k ) e r 2 / ( 2 W 0 2 ( k ) ) ,
g ( r r 0 , k ) = 1 ( 2 π ) 2 d 2 q e i q ( r r 0 ) g ˜ ( q , z z 0 , k ) ,
g ˜ ( q , z , k ) = e i k z ( q ) z g ˜ 0 ( q , k ) ,
k z ( q ) = k 2 q 2 ,
g ˜ 0 ( q , k ) = e q 2 ( W 0 2 ( k ) ) / 2 = e q 2 ( α 2 / 2 k 2 ) .
U ( r , r 0 , k ) = A ( k ) V d 3 r G ( r , r , k ) g ( r r 0 , k ) η ( r ) ,
S ( r 0 , k ) = Σ d 2 r U ( r , r 0 , k ) g ( r r 0 , k ) ,
S ( r 0 , k ) = A ( k ) Σ d 2 r V d 3 r G ( r , r , k ) g ( r r 0 , k ) η ( r ) g ( r r 0 , k ) .
G ( r , r , k ) = 1 ( 2 π ) 2 d 2 q e i q ( r r ) G ˜ ( q , z z , k ) .
S ˜ ( Q , z 0 , k ) = A ( k ) d 2 q d z e i k z ( q + Q ) ( z z 0 ) e i k z ( q ) z 0 G ˜ ( q , z , k ) g ˜ 0 ( q + Q , k ) g ˜ 0 ( q , k ) η ˜ ( Q ; z ) ,
G ˜ ( q , z z , k ) = i 2 π k z ( q ) e i k z ( q ) ( z z ) ,
S ˜ ( Q , k ) = A ( k ) d 2 q d z i 2 π k z ( q ) e i k z ( q ) z e i k z ( q + Q ) ( z z 0 ) e i k z ( q ) z 0 g ˜ 0 ( q + Q , k ) g ˜ 0 ( q , k ) η ˜ ( Q ; z ) .
S ˜ ( Q , k ) = A ( k ) d 2 q d z i 2 π k z ( q ) e i k z ( q ) ( z z 0 ) g ˜ 0 ( q , k ) × e i k z ( Q q ) ( z z 0 ) g ˜ 0 ( Q q , k ) η ˜ ( Q ; z ) .
S ˜ ( Q , k ) = i 2 π A ( k ) d z H ( Q , z , k ) η ˜ ( Q ; z ) ,
H ( Q , z , k ) = d 2 q k z 1 ( q ) e i k z ( q ) ( z z 0 ) g ˜ 0 ( q , k ) e i k z ( Q q ) ( z z 0 ) g ˜ 0 ( Q q , k ) .
H ( q , z , k ) = k 1 ( f ˜ f ˜ ) ( q , z , k ) ,
S ( r 0 , k ) = i 2 π A ( k ) k 1 d 3 r f ( r r 0 , k ) 2 η ( r ) ,
f ( r , k ) = ( 2 π ) 2 d 2 q e i q r f ˜ ( q , z , k ) .
f ˜ ( q , z , k ) = e i ( z z 0 ) k 2 q 2 e q 2 ( α 2 / 2 k 2 ) .
k 2 q 2 k 1 2 q 2 k ,
f ˜ ( q , z , k ) = e i ( z z 0 ) k e q 2 ( α 2 / 2 k 2 + i ( z z 0 ) / 2 k ) .
H ( Q , z , k ) = ( f ˜ f ˜ ) ( Q , z , k ) = 1 4 π ( α 2 k 2 + i ( z z 0 ) k ) 1 e 2 i ( z z 0 ) k e Q 2 / 2 ( α 2 / 2 k 2 + i ( z z 0 ) / 2 k ) .
S ˜ ( Q , k ) = i 2 π A ( k ) d z d 2 Q δ ( 2 ) ( Q Q ) H ( Q , z , k ) η ˜ ( Q ; z ) .
S ˜ ( Q , k ) = K η ˜ ˜ ( Q ; β ) = i A ( k ) d β d 2 Q δ ( 2 ) ( Q Q ) H ˜ ( Q , β , k ) η ͌ ( Q ; β ) ,
η + = ( K * K ) 1 K * S = K + S ,
η A = K * S .
η ˜ A ( Q ; β ) = i d k d 2 Q δ ( 2 ) ( Q Q ) A ( k ) H ˜ * ( Q , β , k ) S ˜ ( Q , k ) .
K * K ( Q , β , Q , β ) = d k A ( k ) 2 H ˜ * ( Q , β , k ) H ˜ ( Q , β , k ) δ ( 2 ) ( Q Q ) .
K * K ( Q , β , Q , β ) = 1 4 d k A 2 ( k ) k 2 e i z 0 ( β β ) e α 2 / k ( β + β + 4 k ) u ( β + 2 k Q 2 4 k ) u ( β + 2 k Q 2 4 k ) δ ( 2 ) ( Q Q ) .
H ( Q , z , k ) = I ( Q , z , k ) e i ϕ ( Q , z , k ) ,
I ( Q , z , k ) = 1 4 π ( α 2 k 2 + i ( z z 0 ) k ) 1 e Q 2 / 2 ( α 2 / 2 k 2 )
ϕ ( Q , z , k ) = 2 ( z z 0 ) k Q 2 ( z z 0 ) 4 k .
I ( Q , z , k ) = I k ( Q , k ) = k 2 4 π α 2 e Q 2 / 2 ( α 2 / 2 k 2 ) .
H ˜ ( Q , β , k ) = I k ( Q , k ) e i z 0 β δ ( β + 2 k Q 2 / 4 k ) .
S ˜ ( Q , k ) = i A ( k ) d β d 2 Q δ ( 2 ) ( Q + Q ) I k ( Q , k ) δ ( β ( Q 2 4 k 2 k ) ) e i z 0 β η ͌ ( Q ; β ) ,
η ͌ A ( Q ; β ) = i d k d 2 Q δ ( 2 ) ( Q + Q ) A ( k ) I k ( Q , k ) δ ( k 1 2 ( β 2 + ( β 2 ) 2 + Q * 2 2 ) ) 2 + Q 2 4 k 2 1 e i z 0 ( 2 k Q 2 / 4 k ) S ˜ ( Q , k ) .
K * K ( Q , β , Q , β ) = δ ( 2 ) ( Q Q ) δ ( β β ) 2 + Q 2 4 k 2 1 A ( k ) 2 I k ( Q , k ) 2 k = 1 / 2 ( β / 2 + ( β / 2 ) 2 + Q 2 / 2 ) ,
η ͌ + ( Q , β ) = d k d 2 Q δ ( 2 ) ( Q + Q ) δ ( k 1 2 ( β 2 + ( β 2 ) 2 + Q 2 2 ) ) × ( A ( k ) I k ( Q , k ) ) 1 e i z 0 ( 2 k Q 2 / 4 k ) S ˜ ( Q , k ) .
S ˜ ( Q , k ) = i 2 π A ( k ) d z d 2 Q δ ( 2 ) ( Q + Q ) I k ( Q , k ) [ η ˜ ( Q ; z ) I z ( z ) ] .
H ˜ ( Q , β , k ) = I k ( Q , k ) e i z 0 β δ ( β + 2 k Q 2 4 k ) .
η ͌ ̂ = ( K * K + λ L * L ) 1 K * S ˜ ,
S n = S t ( r 0 , t ) + n ,
P ( n ) = 1 σ n 2 π e n 2 / ( 2 σ n 2 ) .
SNR ( dB ) = 10 log 10 ( σ S 2 / σ n 2 ) .
σ n = σ s / 10 SNR / 10 .
U i ( r ) = A ( k ) d 2 r P ( r , r ) ϕ ( r ) ,
g ( r ) = z = z l d 2 r L ( r ) z = 0 d 2 r P ( r , r ) ϕ ( r ) P ( r , r ) .
U s ( r ) z = 0 = z = z l d 2 r P ( r , r ) L ( r ) Σ d 2 r P ( r , r ) U s ( r ) .
S = z = 0 d 2 r ϕ * ( r ) U s ( r ) .
S = z = 0 d 2 r ϕ * ( r ) z = z l d 2 r P ( r , r ) L ( r ) Σ d 2 r P ( r , r ) U s ( r ) .
S = Σ d 2 r g ( r ) U s ( r ) .

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