Abstract

Using a novel heterodyne technique, we measure optical phase-space distributions in momentum and position for low-coherence light. Quantitative information is obtained simultaneously about the longitudinal and the transverse coherence properties as well as the wave-front curvature of the light field. This method can be used to monitor these optical parameters directly for signal fields scattered from samples of interest, for tomographic imaging.

© 1999 Optical Society of America

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  1. A. F. Fercher, J. Biomed. Opt. 1, 157 (1996); C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, J. Biomed. Opt. 4, 144 (1999).
    [CrossRef] [PubMed]
  2. B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
    [CrossRef] [PubMed]
  3. G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.
  4. J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
    [CrossRef] [PubMed]
  5. A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
    [CrossRef] [PubMed]
  6. A. Wax and J. E. Thomas, J. Opt. Soc. A 15, 1896 (1998).
    [CrossRef]
  7. A. Wax, “Optical phase space distributions for Coherence Tomography,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).
  8. M. J. Bastiaans, J. Opt. Soc. A 3, 1227 (1986).
    [CrossRef]
  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995), Chap. 5.
    [CrossRef]
  10. A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).
  11. A. Wax and J. E. Thomas, Proc. SPIE 3598, 2 (1999).
    [CrossRef]
  12. A. Wax and J. E. Thomas, Proc. SPIE 3726, 494 (1999).
    [CrossRef]

1999 (3)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef] [PubMed]

A. Wax and J. E. Thomas, Proc. SPIE 3598, 2 (1999).
[CrossRef]

A. Wax and J. E. Thomas, Proc. SPIE 3726, 494 (1999).
[CrossRef]

1998 (2)

A. Wax and J. E. Thomas, J. Opt. Soc. A 15, 1896 (1998).
[CrossRef]

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

1996 (2)

A. F. Fercher, J. Biomed. Opt. 1, 157 (1996); C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, J. Biomed. Opt. 4, 144 (1999).
[CrossRef] [PubMed]

A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
[CrossRef] [PubMed]

1986 (1)

M. J. Bastiaans, J. Opt. Soc. A 3, 1227 (1986).
[CrossRef]

Alphonse, G. A.

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).

Bali, S.

A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).

Bastiaans, M. J.

M. J. Bastiaans, J. Opt. Soc. A 3, 1227 (1986).
[CrossRef]

Bouma, B. E.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Brezinski, M. E.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Connolly, J. C.

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

Fercher, A. F.

A. F. Fercher, J. Biomed. Opt. 1, 157 (1996); C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, J. Biomed. Opt. 4, 144 (1999).
[CrossRef] [PubMed]

Fujimoto, J. G.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Gilbert, D. B.

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

Harvey, M. G.

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

Jones, D. J.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995), Chap. 5.
[CrossRef]

Morris, N.

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

Nelson, L. E.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef] [PubMed]

Tearney, G. J.

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

Thomas, J. E.

A. Wax and J. E. Thomas, Proc. SPIE 3726, 494 (1999).
[CrossRef]

A. Wax and J. E. Thomas, Proc. SPIE 3598, 2 (1999).
[CrossRef]

A. Wax and J. E. Thomas, J. Opt. Soc. A 15, 1896 (1998).
[CrossRef]

A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
[CrossRef] [PubMed]

A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).

Wax, A.

A. Wax and J. E. Thomas, Proc. SPIE 3598, 2 (1999).
[CrossRef]

A. Wax and J. E. Thomas, Proc. SPIE 3726, 494 (1999).
[CrossRef]

A. Wax and J. E. Thomas, J. Opt. Soc. A 15, 1896 (1998).
[CrossRef]

A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
[CrossRef] [PubMed]

A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).

A. Wax, “Optical phase space distributions for Coherence Tomography,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995), Chap. 5.
[CrossRef]

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef] [PubMed]

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef] [PubMed]

J. Biomed. Opt. (3)

A. F. Fercher, J. Biomed. Opt. 1, 157 (1996); C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, J. Biomed. Opt. 4, 144 (1999).
[CrossRef] [PubMed]

B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, J. Biomed. Opt. 3, 76 (1998), and references therein.
[CrossRef] [PubMed]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. A (2)

A. Wax and J. E. Thomas, J. Opt. Soc. A 15, 1896 (1998).
[CrossRef]

M. J. Bastiaans, J. Opt. Soc. A 3, 1227 (1986).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

A. Wax and J. E. Thomas, Proc. SPIE 3598, 2 (1999).
[CrossRef]

A. Wax and J. E. Thomas, Proc. SPIE 3726, 494 (1999).
[CrossRef]

Other (4)

G. A. Alphonse, N. Morris, M. G. Harvey, D. B. Gilbert, and J. C. Connolly, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 107.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995), Chap. 5.
[CrossRef]

A. Wax, S. Bali, G. A. Alphonse, and J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. (to be published).

A. Wax, “Optical phase space distributions for Coherence Tomography,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).

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Figures (3)

Fig. 1
Fig. 1

Heterodyne scheme for measurement of optical phase-space contours for low-coherence light. A sample can be introduced into the signal arm for study of the scattered light in transmission or reflection. PC, personal computer; BS1, beam splitter. See text for other definitions.

Fig. 2
Fig. 2

Phase-space contour plot: mean-square heterodyne signal as function of transverse position x and transverse momentum px for an extended-bandwidth SLD. Each dx step is 50 µm, and each θ=px/k0 step is 0.083 mrad.

Fig. 3
Fig. 3

Mean-square heterodyne signal as a function of effective path delay Δl between the signal and the LO arms for the Sarnoff SLD while we hold dx=0 and dp=0.

Equations (4)

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

VBdxELO*x,zD+ΔlESx,zD,
VBdxdΩkELOk*x-dx,z=0ESkx,z=0×expikΔl-dpfx+dp22f.
ELOk*xESkxexp-Ωk-Ωk02ΔΩk2×expik2Rx2-x2×exp-x2+x24σs2×exp-x-x22σg2.
VBdx,dp,dc2exp-dx214σs2+1σg2×exp-k02σs2dpf+dxR2×exp-ΔlΔlB2,

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