Abstract

Full-field optical coherence tomography (OCT) is able to image an entire en face plane of scatterers simultaneously, but typically the focus is scanned through the volume to acquire three-dimensional structure. By solving the inverse scattering problem for full-field OCT, we show it is possible to computationally reconstruct a three-dimensional volume while the focus is fixed at one plane inside the sample. While a low-numerical-aperture (NA) OCT system can tolerate defocus because the depth of field is large, for high NA it is critical to correct for defocus. By deriving a solution to the inverse scattering problem for full-field OCT, we propose and simulate an algorithm that recovers object structure both inside and outside the depth of field, so that even for high NA the focus can be fixed at a particular plane within the sample without compromising resolution away from the focal plane.

© 2007 Optical Society of America

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A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, "Ultrahigh-resolution full-field optical coherence tomography," Appl. Opt. 43, 2874-2883 (2004).
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[CrossRef] [PubMed]

A. V. Zvyagin, "Fourier-domain optical coherence tomography: optimization of signal-to-noise ratio in full space," Opt. Commun. 242, 97-108 (2004).
[CrossRef]

2003 (4)

2002 (3)

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E. Beaurepaire and A.-C. Boccara, "Full-field optical coherence microscopy," Opt. Lett. 23, 244-246 (1998).
[CrossRef]

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[CrossRef] [PubMed]

1996 (1)

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

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1994 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

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1968 (1)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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P. Blazkiewicz, M. Gourlay, J. R. Tucker, A. D. Rakic, and A. V. Zvyagin, "Signal-to-noise ratio study of full-field Fourier-domain optical coherence tomography," Appl. Opt. 34, 7722-7729 (2005).
[CrossRef]

A. V. Zvyagin, P. Blazkiewicz, and J. Vintrou, "Image reconstruction in full-field Fourier-domain optical coherence tomography," J. Opt. A 7, 350-356 (2005).
[CrossRef]

Bocarra, A.-C.

Bocarra, C.

Boccara, A.-C.

Boccara, C.

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J. M. Schmitt, M. J. Yadlowsky, and R. F. Bonner, "Subsurface imaging of living skin with optical coherence microscopy," Dermatology (Basel) 191, 93-98 (1995).
[CrossRef]

Boppart, S. A.

Bouma, B. E.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[CrossRef] [PubMed]

B. E. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, "High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser," Opt. Lett. 20, 1486-1488 (1995).
[CrossRef] [PubMed]

Brezinski, M. E.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[CrossRef] [PubMed]

B. E. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, "High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser," Opt. Lett. 20, 1486-1488 (1995).
[CrossRef] [PubMed]

Carney, P. S.

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]

Changhuei, Y.

Choma, M.

De Martino, A.

Drevillon, B.

Drexler, W.

Dubois, A.

Fercher, A. F.

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).
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Fujimoto, J. G.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gourlay, M.

P. Blazkiewicz, M. Gourlay, J. R. Tucker, A. D. Rakic, and A. V. Zvyagin, "Signal-to-noise ratio study of full-field Fourier-domain optical coherence tomography," Appl. Opt. 34, 7722-7729 (2005).
[CrossRef]

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]

Grieve, K.

Hariharan, P.

P. Hariharan, Optical Interferometry (Academic, 2003).

Hayasaka, Y.

Hee, M. R.

Hermann, B.

Hitzenberger, C. K.

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]

Ippen, E. P.

Izatt, J.

Izatt, J. A.

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[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]

Kartner, F. X.

Kobayashi, M. W.

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

Kulkarni, H.-W.

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

Laude, B.

Le Gargasson, J.-F.

Lecaque, R.

Leitgeb, R.

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]

Lorlette, V.

Marks, D. L.

Moneron, G.

Moreau, J.

Morgner, U.

Oldenburg, A. L.

Owen, G. M.

Paques, M.

Pitris, C.

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. Li, E. P. Ippen, and J. G. Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999).
[CrossRef]

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[CrossRef] [PubMed]

Povazay, B.

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]

Rakic, A. D.

P. Blazkiewicz, M. Gourlay, J. R. Tucker, A. D. Rakic, and A. V. Zvyagin, "Signal-to-noise ratio study of full-field Fourier-domain optical coherence tomography," Appl. Opt. 34, 7722-7729 (2005).
[CrossRef]

Ralston, T. S.

Reynolds, J. J.

Rhodes, W. T.

Sahel, J.

Sarunic, M.

Sato, M.

Sattmann, H.

Schmitt, J. M.

J. M. Schmitt, M. J. Yadlowsky, and R. F. Bonner, "Subsurface imaging of living skin with optical coherence microscopy," Dermatology (Basel) 191, 93-98 (1995).
[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]

Schwartz, L.

Simonutti, M.

Sitter, D. N.

Sivak, M. W.

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

Southern, J. F.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[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]

Swanson, E. A.

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]

Tanno, N.

Tearney, G. J.

Tucker, J. R.

P. Blazkiewicz, M. Gourlay, J. R. Tucker, A. D. Rakic, and A. V. Zvyagin, "Signal-to-noise ratio study of full-field Fourier-domain optical coherence tomography," Appl. Opt. 34, 7722-7729 (2005).
[CrossRef]

Unterhuber, A.

Vabre, L.

Vintrou, J.

A. V. Zvyagin, P. Blazkiewicz, and J. Vintrou, "Image reconstruction in full-field Fourier-domain optical coherence tomography," J. Opt. A 7, 350-356 (2005).
[CrossRef]

Wang, K.

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

Watanabe, Y.

Yadlowsky, M. J.

J. M. Schmitt, M. J. Yadlowsky, and R. F. Bonner, "Subsurface imaging of living skin with optical coherence microscopy," Dermatology (Basel) 191, 93-98 (1995).
[CrossRef]

Zvyagin, A. V.

P. Blazkiewicz, M. Gourlay, J. R. Tucker, A. D. Rakic, and A. V. Zvyagin, "Signal-to-noise ratio study of full-field Fourier-domain optical coherence tomography," Appl. Opt. 34, 7722-7729 (2005).
[CrossRef]

A. V. Zvyagin, P. Blazkiewicz, and J. Vintrou, "Image reconstruction in full-field Fourier-domain optical coherence tomography," J. Opt. A 7, 350-356 (2005).
[CrossRef]

A. V. Zvyagin, "Fourier-domain optical coherence tomography: optimization of signal-to-noise ratio in full space," Opt. Commun. 242, 97-108 (2004).
[CrossRef]

Appl. Opt. (7)

Dermatology (Basel) (1)

J. M. Schmitt, M. J. Yadlowsky, and R. F. Bonner, "Subsurface imaging of living skin with optical coherence microscopy," Dermatology (Basel) 191, 93-98 (1995).
[CrossRef]

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

J. A. Izatt, H.-W. Kulkarni, K. Wang, M. W. Kobayashi, and M. W. Sivak, "Optical coherence tomography and microscopy in gastrointestinal tissues," IEEE J. Sel. Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

J. Opt. A (1)

A. V. Zvyagin, P. Blazkiewicz, and J. Vintrou, "Image reconstruction in full-field Fourier-domain optical coherence tomography," J. Opt. A 7, 350-356 (2005).
[CrossRef]

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

Nat. Med. (1)

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, "In vivo cellular optical coherence tomography imaging," Nat. Med. 4, 861-864 (1998).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. V. Zvyagin, "Fourier-domain optical coherence tomography: optimization of signal-to-noise ratio in full space," Opt. Commun. 242, 97-108 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (6)

Phys. Med. Biol. (1)

A. Dubois, G. Moneron, K. Grieve, and A.-C. Boccara, "Three-dimensional cellular-level imaging using full-field optical coherence tomography," Phys. Med. Biol. 49, 1227-1234 (2004).
[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 (2)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

P. Hariharan, Optical Interferometry (Academic, 2003).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of full-field OCT using frequency scanning and the focus of the objective fixed at the sample surface.

Fig. 2
Fig. 2

Calculated band volume shape for a full-field OCT system. All units are in terms of the maximum spatial frequency of the illumination.

Fig. 3
Fig. 3

Simulation of inverse scattering in full-field OCT. (a) The magnitude of the raw interference patterns recorded as a function of illumination spatial frequency. (b) A projection of the time-domain data for a collection of randomly placed point scatterers imaged with full-field OCT. (c) A projection of the computed reconstruction of the scatterers. All length units are in the center wavelength of the illumination, and spatial frequencies are inverse wavelength units. Three planes are denoted that are shown as en face images in Fig. 5.

Fig. 4
Fig. 4

(a) Resampling grid to compute synthetic data D ̃ ( q ; k ) from object η ̃ ( Q ) . (b) Resampling grid to compute reconstruction of η ̃ ( Q ) from D ̃ ( q ; k ) . Note that the transverse components of Q are the same as M q , and the axial component of Q is β. To form the full 3-D Fourier space, both grids are revolved around their respective vertical axes.

Fig. 5
Fig. 5

Three pairs of en face images of the time-domain data (left) and the reconstructed volume (right). (a)–(c) Pairs of images corresponding, respectively, to the planes A, B, and C marked in Fig. 3. All dimensions are in wavelength units.

Fig. 6
Fig. 6

Three-dimensional volumes representing the (a) time-domain data and (b) reconstructed volume. All dimensions are in wavelength units.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

E i ( r ; k ) = A ( k ) exp ( i k r z ̂ ) ,
E s ( r ; k ) = V d 3 r E i ( r ; k ) η ( r ) exp ( i k r r ) r r .
E ̃ s ( q ; k ) = 2 π i A ( k ) V d 3 r η ( r ) exp { i [ q r ] + i z [ k + k z ( q ) ] } k z ( q ) 1 ,
E ̃ s ( q ; k ) = 2 π i A ( k ) k z ( q ) 1 η ̃ { q + z ̂ [ k + k z ( q ) ] } .
E f ( r ; k ) = M 1 d 2 r E s ( r ; k ) P ( r M r ; k ) .
E ̃ f ( q ; k ) = M E ̃ s ( M q ; k ) P ̃ ( M q ; k ) = 2 π i M A ( k ) P ̃ ( M q ; k ) k z ( M q ) 1 η ̃ { M q + z ̂ [ k + k z ( M q ) ] } .
E r ( r ; k , τ ) = A ( k ) exp [ i ω ( k ) τ ] ,
I ( r ; k , τ ) = A ( k ) 2 + E f ( r ; k ) 2 + 2 A ( k ) Re { E f ( r ; k ) exp [ i ω ( k ) τ ] } .
D ( r ; k ) = 1 i 4 I ( r ; k , 0 ) 1 + i 4 I ( r ; k , π ω ) + i 2 I ( r ; k , π 2 ω ) .
D ̃ ( q ; k ) = K ̃ ( q ; k ) η ̃ { M q + z ̂ [ k + k z ( M q ) ] } ,
K ̃ ( q , k ) = 2 π i M A ( k ) 2 P ̃ ( M q ; k ) k z 1 ( M q ) .
D ̃ = K ̃ η ̃ = d 3 Q K ̃ ( q ; k ) η ̃ ( Q ) δ ( 2 ) ( Q M q ) δ [ β k k z ( M q ) ] ,
I T ( r ; τ ) = 1 2 π [ d k ( d ω d k ) ( A ( k ) 2 + E f ( r ; k ) 2 ) ] + 1 π Re { d k ( d ω d k ) D ( r ; k ) exp [ i ω ( k ) τ ] } .
D ̃ ( q ; k ) = D ̃ ( q ; k ) exp { i z 0 [ k k z ( M q ) ] } .
D ( r ; k ) = K η = d 3 r K ( r , r ; k ) η ( r ) ,
K ( r , r ; k ) = M 1 A ( k ) 2 exp ( i k r z ̂ ) r z ̂ = 0 d 2 r exp ( i k r r ) r r P ( r M r ; k ) .
η + ( r ) = arg min η D K η 2 = arg min η d 2 r d k D ( r ; k ) K η ( r ) 2 .
η ̃ A = K ̃ * D ̃ = d 2 q d k K ̃ * ( q ; k ) D ̃ ( q ; k ) δ ( 2 ) ( Q M q ) δ [ β k k z ( M q ) ] = K ̃ * ( M 1 Q ; Q 2 + β 2 2 β ) D ̃ ( M 1 Q ; Q 2 + β 2 2 β ) M 2 β β + β 2 + Q 2 ,
η ̃ + ( Q ) = D ̃ ( M 1 Q ; Q 2 + β 2 2 β ) K ̃ * ( M 1 Q ; Q 2 + β 2 2 β ) K ̃ ( M 1 Q ; Q 2 + β 2 2 β ) 2 + γ M 2 β + β 2 + Q 2 β .
P ̃ ( q ; k ) = 1 for q ( NA ) k ,
P ̃ ( q ; k ) = 0 for q > ( NA ) k .
k min < Q 2 ( 2 Q z ̂ ) < k max ,
( 2 Q z ̂ ) Q 2 ( Q z ̂ ) 2 Q 2 < NA .

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