Abstract

The spectral shape of a source is of prime importance in optical coherence imaging because it determines several aspects of image quality, especially longitudinal resolution. Wide spectral bandwidth, which provides short coherence length, is sought to obtain high-resolution imaging. To estimate longitudinal resolution, the spectral shape of a source is usually assumed to be Gaussian, although the spectra of real sources are typically non-Gaussian. We discuss the limit of this assumption regarding the estimation of longitudinal resolution. To this end, we also investigate how coherence length is related to longitudinal resolution through the evaluation of different definitions of the coherence length. To demonstrate our purpose, the coherence length for several theoretical and real spectral shapes of sources having the same spectral bandwidth and central wavelength is computed. The reliability of coherence length computations toward the estimation of longitudinal resolution is discussed.

© 2002 Optical Society of America

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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]
  2. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
    [CrossRef]
  3. A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1, 157–173 (1996).
    [CrossRef] [PubMed]
  4. J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
    [CrossRef]
  5. J. K. Barton, A. J. Welch, J. A. Izatt, “Investigating pulsed dye laser-blood vessel interaction with color Doppler optical coherence tomography,” Opt. Express 3, 251–256 (1998); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  6. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chaps. 5 and 7.
  7. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 8.
  8. R. K. Wang, “Resolution improved optical coherence-gated tomography for imaging through biological tissues,” J. Mod. Opt. 46, 1905–1912 (1999).
  9. C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
    [CrossRef] [PubMed]
  10. B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett. 20, 1486–1488 (1995).
    [CrossRef] [PubMed]
  11. R. E. Ziemer, W. H. Tranter, Principles of Communications (Wiley, New York, 1995), Chap. 2.
  12. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 4.
    [CrossRef]
  13. Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
    [CrossRef]
  14. Y. Pan, R. Birngruber, J. Rosperich, R. Engelhardt, “Low-coherence optical tomography in turbid tissue: theoretical analysis,” Appl. Opt. 34, 6564–6575 (1995).
    [CrossRef] [PubMed]
  15. W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).
  16. S. R. Chinn, E. A. Swanson, “Blindness limitations in optical coherence domain reflectrometry,” Electron. Lett. 29, 2025–2027 (1993).
    [CrossRef]
  17. J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
    [CrossRef] [PubMed]
  18. M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
    [CrossRef]

2001 (1)

Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
[CrossRef]

1999 (4)

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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

R. K. Wang, “Resolution improved optical coherence-gated tomography for imaging through biological tissues,” J. Mod. Opt. 46, 1905–1912 (1999).

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

1998 (2)

1997 (1)

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

1996 (2)

A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1, 157–173 (1996).
[CrossRef] [PubMed]

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

1995 (2)

1993 (1)

S. R. Chinn, E. A. Swanson, “Blindness limitations in optical coherence domain reflectrometry,” Electron. Lett. 29, 2025–2027 (1993).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Barton, J. K.

Baumgartner, A.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

Birngruber, R.

Boppart, S. A.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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

Bouma, B.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 8.

Brezinski, M. E.

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]

Chinn, S. R.

S. R. Chinn, E. A. Swanson, “Blindness limitations in optical coherence domain reflectrometry,” Electron. Lett. 29, 2025–2027 (1993).
[CrossRef]

Drexler, W.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

Engelhardt, R.

Fercher, A. F.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1, 157–173 (1996).
[CrossRef] [PubMed]

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]

Fujimoto, J. G.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chaps. 5 and 7.

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.

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

Hitzenberger, C. K.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

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]

Ippen, E. P.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

Izatt, J. A.

J. K. Barton, A. J. Welch, J. A. Izatt, “Investigating pulsed dye laser-blood vessel interaction with color Doppler optical coherence tomography,” Opt. Express 3, 251–256 (1998); http://www.opticsexpress.org .
[CrossRef] [PubMed]

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

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

Kärtner, F. X.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

Kobayashi, K.

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

Kulkarni, M. D.

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

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

Li, X. D.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 4.
[CrossRef]

Morgner, U.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

Pan, Y.

Pitris, C.

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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]

Rosperich, J.

Sato, M.

Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
[CrossRef]

Schmitt, J. M.

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

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

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]

Sivak, M. V.

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

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.

S. R. Chinn, E. A. Swanson, “Blindness limitations in optical coherence domain reflectrometry,” Electron. Lett. 29, 2025–2027 (1993).
[CrossRef]

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]

Tanno, N.

Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
[CrossRef]

Tearney, G. J.

Thomas, C. W.

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

Tranter, W. H.

R. E. Ziemer, W. H. Tranter, Principles of Communications (Wiley, New York, 1995), Chap. 2.

Wang, H.

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

Wang, R. K.

R. K. Wang, “Resolution improved optical coherence-gated tomography for imaging through biological tissues,” J. Mod. Opt. 46, 1905–1912 (1999).

Welch, A. J.

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 4.
[CrossRef]

Zhang, Y.

Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
[CrossRef]

Ziemer, R. E.

R. E. Ziemer, W. H. Tranter, Principles of Communications (Wiley, New York, 1995), Chap. 2.

Appl. Opt. (1)

Electron. Lett. (2)

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

S. R. Chinn, E. A. Swanson, “Blindness limitations in optical coherence domain reflectrometry,” Electron. Lett. 29, 2025–2027 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

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

J. A. Izatt, M. D. Kulkarni, H. Wang, K. Kobayashi, M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissue,” IEEE J. Sel. Top. Quantum Electron. 2, 1017–1028 (1996).
[CrossRef]

J. Biomed. Opt. (3)

A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1, 157–173 (1996).
[CrossRef] [PubMed]

C. K. Hitzenberger, A. Baumgartner, W. Drexler, A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4, 144–151 (1999).
[CrossRef] [PubMed]

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

R. K. Wang, “Resolution improved optical coherence-gated tomography for imaging through biological tissues,” J. Mod. Opt. 46, 1905–1912 (1999).

Opt. Commun. (1)

Y. Zhang, M. Sato, N. Tanno, “Numerical investigations of optimal synthesis of several low coherence source for resolution improvement,” Opt. Commun. 192, 183–192 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

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

W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1486–1488 (1999).

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

Other (4)

R. E. Ziemer, W. H. Tranter, Principles of Communications (Wiley, New York, 1995), Chap. 2.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 4.
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chaps. 5 and 7.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 8.

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Figures (6)

Fig. 1
Fig. 1

Two-layer model to determine the longitudinal resolution.

Fig. 2
Fig. 2

(a) Measured PSD of the SLD: the normalized Gaussian PSD and the normalized Lorentzian PSD (λ0 = 950 nm, Δλ = 62 nm for each). (b) Modulus of the corresponding complex degree of temporal coherence functions.

Fig. 3
Fig. 3

Gaussian PSD with a 100-nm -3-dB bandwidth centered at 940 nm (dashed curve) and PSDs of the same bandwidth and center wavelength with different spectral dip amplitudes.

Fig. 4
Fig. 4

Computed coherence length is presented as a function of the amplitude percentage of the spectral dip with metric 1 (FWHM criterion) and metric 2 (from integration). The circle and the triangle on the vertical axis represent, respectively, the coherence length of the Gaussian PSD, where Gaussian 1 corresponds to the FWHM and Gaussian 2 corresponds to the integration.

Fig. 5
Fig. 5

|γ(τ)| of the PSDs of the 100-nm bandwidth centered at a 940-nm source with a selected percentage of spectral dip.

Fig. 6
Fig. 6

Envelopes of the interferometric signals I 1 and I 2 that are due to backreflections from two successive layers (left column, Δz = l c FWHM /2; right column, Δz = l c /2) and the resulting signal I for a source with (a) Gaussian PSD, (b) Lorentzian PSD, (c) SLD-471 presented in Fig. 2(a), (d) PSD with 8.04% spectral dip amplitude, (e) PSD with 49.13% spectral dip amplitude presented in Fig. 3.

Tables (1)

Tables Icon

Table 1 Coherence Length of Sources with Different-Shaped PSDsa

Equations (13)

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

Iτ  ReA ERr, t+τES* r, tdr,
lcFWHM=cτ-τ=cτFWHM,
lc=c - |γτ|2dτ.
Iτ  ReA ERr, t+τE1*r, tdr+ReA ERr, t+τE2*r, t-2nΔzcdr.
Iτ  Reγτ+α Reγτ-2nΔzc.
Sλ=2ln 2 λ02πcΔλexp-2ln 21λ-1λ0Δλλ022,
Γτ=exp-πcΔλτλ02 2ln 22exp-j2πcτλ0,
lcFWHM=4 ln 2πλ02Δλ,
lc=2 ln 2πλ02Δλ.
Slznλ=2πc Δλλ021+2 1λ-1λ0Δλλ022-1,
Γlznτ=exp-πcΔλλ02 |τ|exp-j2πcτλ0.
lcFWHM=2 ln2πλ02Δλ.
lc=λ02πΔλ.

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