Abstract

We extend the applicability of inverse scattering for optical coherence tomography (OCT) to the case of high numerical aperture focusing optics. We include the effects of tight focusing so that the approach is applicable to any interferometric microscopy method. The applicability to modalities, such as OCT and optical coherence microscopy, enables computed reconstruction of three-dimensional volumes from en face temporal ranging data. Simulations show that the computed structure outside of the focal plane exhibits spatially invariant resolution on par with the resolution achieved at the focal plane.

© 2006 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
  2. B. E. Bouma and J. G. Tearny, The Handbook of Optical Coherence Tomography (Marcel Dekker, 2001).
  3. C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
    [PubMed]
  4. J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
    [CrossRef] [PubMed]
  5. S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
    [CrossRef] [PubMed]
  6. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, J. Opt. Soc. Am. A 23, 1027 (2006).
    [CrossRef]
  7. O. Bruno and J. Chaubell, Opt. Lett. 21, 2049 (2003).
    [CrossRef]
  8. B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, M. Vetterlein, and E. Scherzer, Opt. Lett. 27, 1800 (2002).
    [CrossRef]
  9. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, Opt. Lett. 19, 590 (1994).
    [CrossRef] [PubMed]
  10. C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
    [CrossRef]
  11. J. F. deBoer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, Opt. Lett. 28, 2067 (2003).
    [CrossRef]
  12. M. Choma, M. Sarunic, C. Yang, and J. Izatt, Opt. Express 11, 2183 (2003).
    [CrossRef] [PubMed]

2006

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, J. Opt. Soc. Am. A 23, 1027 (2006).
[CrossRef]

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

2003

2002

1998

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

1995

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

1994

1991

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Apolonski, A.

Bizheva, K.

Boppart, S. A.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, J. Opt. Soc. Am. A 23, 1027 (2006).
[CrossRef]

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

Bouma, B. E.

J. F. deBoer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, Opt. Lett. 28, 2067 (2003).
[CrossRef]

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

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

Brezinski, M. E.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

Bruno, O.

O. Bruno and J. Chaubell, Opt. Lett. 21, 2049 (2003).
[CrossRef]

Carney, P. S.

Cense, B.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chaubell, J.

O. Bruno and J. Chaubell, Opt. Lett. 21, 2049 (2003).
[CrossRef]

Choma, M.

deBoer, J. F.

Drexler, W.

Duker, J. S.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Eckhaus, M.

J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
[CrossRef] [PubMed]

Fercher, A. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, Opt. Lett. 19, 590 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hee, M.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Hee, M. R.

Hee, R.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hermann, B.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Izatt, J.

Izatt, J. A.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, Opt. Lett. 19, 590 (1994).
[CrossRef] [PubMed]

Knight, J. C.

Knuttel, A.

J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
[CrossRef] [PubMed]

Lin, C.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Luo, W.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

Marks, D. L.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, J. Opt. Soc. Am. A 23, 1027 (2006).
[CrossRef]

Owen, G. M.

Park, B. H.

Pierce, M. C.

Pitris, C.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

Povazay, B.

Puliafito, C.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Ralston, T. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, J. Opt. Soc. Am. A 23, 1027 (2006).
[CrossRef]

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

Reichel, E.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Russell, P. S. J.

Sarunic, M.

Sattmann, H.

Scherzer, E.

Schmitt, J.

J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
[CrossRef] [PubMed]

Schuman, J.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Southern, J. F.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, Opt. Lett. 19, 590 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tan, W.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

Tearney, G. J.

Tearny, J. G.

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

Unterhuber, A.

Vetterlein, M.

Vinegoni, C.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

Wadsworth, W. J.

Yadlowsky, M.

J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
[CrossRef] [PubMed]

Yang, C.

Appl. Phys. Lett.

C. Vinegoni, T. S. Ralston, W. Tan, W. Luo, D. L. Marks, and S. A. Boppart, Appl. Phys. Lett. 88, 053901 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Med.

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

Ophthalmology

C. Puliafito, M. Hee, C. Lin, E. Reichel, J. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto, Ophthalmology 102, 217 (1995).
[PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

J. Schmitt, A. Knuttel, M. Yadlowsky, and M. Eckhaus, Phys. Med. Biol. 39, 1705 (1994).
[CrossRef] [PubMed]

Science

D. Huang, E. A. Swanson, C. P. Lin, W. G. Stinson, W. Chang, R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other

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

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Figures (2)

Fig. 1
Fig. 1

System diagram for spectral-domain optical coherence microscopy. The system is composed of a broadband source, a fiber-based interferometer, and a spectral detector. Note that data are collected at the camera as the optical Fourier transform.

Fig. 2
Fig. 2

Simulated volume of point scatterers imaged with OCM to demonstrate spatially invariant resolution. Projection of (a) unprocessed and (b) processed data on a 2D plane, and full 3D rendering of (c) unprocessed and (d) processed volume of point scatterers. All axes are labeled in units of wavelength. Arrows in (c) indicate wavefront interference, which is resolved in (d).

Equations (13)

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g ( r r 0 , k ) = 1 ( 2 π ) 2 d 2 q exp [ i q ( r r 0 ) ] exp [ i k z ( q ) ( z z 0 ) ] g ̃ 0 ( q , k ) ,
U s ( r , r 0 , k ) = A ( k ) d 3 r G ( r , r , k ) g ( r r 0 , k ) η ( r ) .
S ( r 0 , k ) = A ( k ) z = 0 d 2 r d 3 r G ( r , r , k ) g ( r r 0 , k ) g ( r r 0 , k ) η ( r ) .
G ( r , r , k ) = i 2 π d 2 q exp [ i q ( r r ) ] exp [ i k z ( q ) ( z z ) ] k z ( q ) ,
S ̃ ( Q , k ) = i 2 π A ( k ) d 2 q d z 1 k z ( q ) exp [ i k z ( q ) ( z z 0 ) ] exp [ i k z ( q Q ) ( z z 0 ) ] exp ( α 2 q 2 2 k 2 ) exp ( α 2 q Q 2 2 k 2 ) η ̃ ( Q , z ) .
S ̃ ( Q , k ) = i 2 π A ( k ) d 2 q d z 1 k z ( q ) exp [ i k z ( q ) ( z z 0 ) ] exp [ i k z ( q Q ) ( z z 0 ) ] exp [ α 2 Q 2 4 k 2 ] exp [ α 2 q Q 2 2 k 2 ] η ̃ ( Q , z ) .
exp { i [ k z ( q ) + k z ( q Q ) ] ( z z 0 ) } k z ( q ) = exp [ 2 i k z ( Q 2 ) ( z z 0 ) ] k z ( Q 2 ) + ( q Q 2 ) q exp { i [ k z ( q ) + k z ( q Q ) ] ( z z 0 ) } k z ( q ) q = Q 2 + ,
S ̃ ( Q , k ) = i 2 π A ( k ) exp ( α 2 Q 2 4 k 2 ) d z exp [ 2 i k z ( Q 2 ) ( z z 0 ) ] k z ( Q 2 ) d 2 q exp ( α 2 q Q 2 2 k 2 ) η ̃ ( Q , z ) .
S ̃ ( Q , k ) = k 2 α 2 i 2 π 2 A ( k ) exp [ 2 i k z ( Q 2 ) z 0 ] k z ( Q 2 ) exp ( α 2 Q 2 4 k 2 ) η ̃ ̃ [ Q , 2 k z ( Q 2 ) ] ,
H ( Q , k , β ) = k 2 α 2 i 2 π 2 A ( k ) exp [ 2 i k z ( Q 2 ) z 0 ] k z ( Q 2 ) exp ( α 2 Q 2 4 k 2 ) δ [ β + 2 k z ( Q 2 ) ] f ( Q , k , β ) δ [ β + 2 k z ( Q 2 ) ] .
H * H ( Q , β , β ) f ( Q , 1 2 β 2 + Q 2 , β ) 2 β 2 β 2 + Q 2 δ ( β β ) ,
H + ( Q , k ; β ) = f * ( Q , k , β ) δ ( k 1 2 β 2 + Q 2 ) f ( Q , k , β ) 2 + 2 N k k z ( Q 2 ) .
η ̃ ̃ + ( Q , β ) = [ f * ( Q , k , β ) S ̃ ( Q , k ) f ( Q , k , β ) 2 + 2 N k k z ( Q 2 ) ] k = 1 2 β 2 + Q 2 .

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