Abstract

Optical coherence tomography (OCT) is a high-resolution imaging technology based on low-coherence interferometry. When OCT imaging is performed in biological tissue, dispersion almost inevitably occurs. We quantify the group-velocity dispersion that a grating-based optical delay line may induce and its contribution to the axial point-spread function of OCT. Among the practical reasons for modeling the dispersion in grating-based optical delay line is that, at maximum compensation, it can provide insight into the dispersive properties of tissues.

© 2003 Optical Society of America

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References

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  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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. R. C. Youngquist, S. Carr, D. E. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett. 13, 186–190 (1987).
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    [CrossRef] [PubMed]
  5. J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
    [PubMed]
  6. M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
    [CrossRef] [PubMed]
  7. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  15. E. D. J. Smith, A. V. Zvyagin, D. D. Sampson, “Real-time dispersion compensation in scanning interferometry,” Opt. Lett. 27, 1998–2000 (2002).
    [CrossRef]
  16. M. R. Hee, “Optical coherence tomography: theory,” in Handbook of Optical Coherence Tomography, B. E. Bouma, G. J. Tearney, eds. (Marcel Dekker, N.Y., 2002), pp. 45–48.

2002

1999

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

1998

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154, 179–185 (1998).
[CrossRef]

1997

G. J. Tearney, M. E. Brezinski, B. E. Bouma, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

1996

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

1993

1991

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1987

Baumgartner, A.

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154, 179–185 (1998).
[CrossRef]

Becker, P. C.

Boppart, S. A.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

S. A. Boppart, “Surgical diagnostics, guidance, and intervention using optical coherence tomography,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., 1998).

Bouma, B. E.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

Brezinski, M. E.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

Brito Cruz, C. H.

Carr, 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chida, K.

Chu, K. C.

Davies, D. E.

Dienes, A.

Fercher, A. F.

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154, 179–185 (1998).
[CrossRef]

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fork, R. L.

Fujimoto, J. G.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Golubovic, B.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

M. R. Hee, “Optical coherence tomography: theory,” in Handbook of Optical Coherence Tomography, B. E. Bouma, G. J. Tearney, eds. (Marcel Dekker, N.Y., 2002), pp. 45–48.

Heritage, J. P.

Herrmann, J.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

Hitzenberger, C. K.

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154, 179–185 (1998).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

Jesser, C. A.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

Kwong, K. F.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Noda, J.

Pitris, C.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sampson, D. D.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Shank, C. V.

Smith, E. D. J.

Southern, J. F.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

Stamper, D. L.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Takada, K.

Tearney, G. J.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

G. J. Tearney, “Optical biopsy of in vivo tissue using optical coherence tomography,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., 1996).

Yankelevich, D.

Yokohama, I.

Youngquist, R. C.

Zvyagin, A. V.

Am. J. Gastroenterol.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, S. A. Boppart, J. G. Fujimoto, “Optical biopsy in human gastrointestinal tissue using optical coherence tomography,” Am. J. Gastroenterol. 92, 1800–1804 (1997).
[PubMed]

Appl. Opt.

Circulation

M. E. Brezinski, G. J. Tearney, B. E. Bouma, J. A. Izatt, M. R. Hee, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical coherence tomography for optical biopsy: properties and demonstration of vascular pathology,” Circulation 93, 1206–1213 (1996).
[CrossRef] [PubMed]

J. Rheumatol.

J. Herrmann, C. Pitris, B. E. Bouma, S. A. Boppart, C. A. Jesser, D. L. Stamper, J. G. Fujimoto, M. E. Brezinski, “High resolution imaging of normal and osteoarthritic cartilage with optical coherence tomography,” J. Rheumatol. 26, 627–635 (1999).
[PubMed]

J. Surg. Res.

M. E. Brezinski, G. J. Tearney, S. A. Boppart, E. A. Swanson, J. F. Southern, J. G. Fujimoto, “Optical biopsy with optical coherence tomography, feasibility for surgical diagnostics,” J. Surg. Res. 71, 32–37 (1997).
[CrossRef] [PubMed]

Opt. Commun.

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154, 179–185 (1998).
[CrossRef]

Opt. Lett.

Science

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Other

G. J. Tearney, “Optical biopsy of in vivo tissue using optical coherence tomography,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., 1996).

S. A. Boppart, “Surgical diagnostics, guidance, and intervention using optical coherence tomography,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., 1998).

M. R. Hee, “Optical coherence tomography: theory,” in Handbook of Optical Coherence Tomography, B. E. Bouma, G. J. Tearney, eds. (Marcel Dekker, N.Y., 2002), pp. 45–48.

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Figures (3)

Fig. 1
Fig. 1

Optical arrangement for single-path, grating-based optical delay line.

Fig. 2
Fig. 2

Optical arrangement for double-path, grating-based optical delay line.

Fig. 3
Fig. 3

Experimental results of the PSF at two different focus positions. The x axis is the number of pixels, and the y axis represents arbitrary units of intensity.

Equations (20)

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

l=2|PO|-|PP|+|MN|.
|PO|=L cos Δθ+fcos Δθ, |PP|=-2L-fsin Δθ×tan θλ, |MN|=-2L-fsin Δθ×sin θicos θλ, Δθ=θλ-θ0.
sin θi-sin θλ=mλ/d,
l=2L cos Δθ+fcos Δθ-2L-fsin Δθ mλd cos θλ.
l=2L+f-2L-fΔθ mλd cos θλ=2L+f-2L-fdθλdλ Δλ mλd cos θλ, Δλ=λ-λ0.
dθλdλ=-md cos θλ.
l=2L+f+2L-fm2λd2 cos2 θ0 Δλ.
lD=4L+f+4L-fm2λd2 cos2 θ0 Δλ.
lD=cτg=c ϕω.
GVDω=2ϕω2=1clDω=1clDλdλdω
=1c 4L-fm2λd2 cos2 θ0-2πcω2, where λ=2πcω.
GVDω0=-16π2cm2ω03d2 cos2 θ0L-f.
GVD=-2m2λ03πc2d2 cos2 θ0L-f.
τcrit=2|L-f|m2λ03πc2d2 cos2 θ01/2.
2σ˜τ=2στ1+τcritστ41/2,
2στ=2/σω.
2σ˜τ=2|τcrit2|στ=4|L-f|m2λ03σωπc2d2 cos2 θ0.
2σ˜τ=4|L-f|m2λ0cd2 cos2 θ0 Δλ.
PSF=4|L-f|m2λ0d2 cos2 θ0 Δλ.
PSF=2στc=λ02/πΔλ.

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