Abstract

The two previously reported calculations of the amplitude distribution of speckles in optical coherence tomography, each based on a different mathematical formulation, yield different results. We show that a modification of an initial assumption in one of the formulations leads to equivalent results.

© 2005 Optical Society of America

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References

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  1. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.
  2. A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
    [CrossRef]
  3. J. M. Schmitt, A. Knuettel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A 14, 1231–1242 (1997).
    [CrossRef]
  4. J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
    [CrossRef] [PubMed]
  5. J. M. Schmitt, “Array detection for speckle reduction in optical coherence tomography,” Phys. Med. Biol. 42, 2307–2320 (1997).
    [CrossRef]
  6. M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
    [CrossRef] [PubMed]
  7. N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
    [CrossRef] [PubMed]
  8. K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
    [CrossRef]
  9. K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
    [CrossRef] [PubMed]
  10. D. A. Zimnyakov, V. V. Tuchin, A. A. Mishin, “Spatial speckle correlometry in applications to tissue structure monitoring,” Appl. Opt. 36, 5594–5607 (1997).
    [CrossRef] [PubMed]
  11. M. Bashkansky, J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25, 545–547 (2000).
    [CrossRef]
  12. J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 1985), Chap. 2.
  13. H. H. Arsenault, G. April, “Properties of speckle integrated with a finite aperture and logarithmically transformed,” J. Opt. Soc. Am. 66, 1160–1163 (1976).
    [CrossRef]

2003 (4)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
[CrossRef] [PubMed]

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

2000 (1)

1999 (2)

K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef]

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

1997 (3)

1976 (1)

April, G.

Arsenault, H. H.

Barton, J. K.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

Bashkansky, M.

Bouma, B. E.

N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
[CrossRef] [PubMed]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

Goetzinger, E.

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 1985), Chap. 2.

Gossage, K. W.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

Hitzenberger, C. K.

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Iftimia, N.

N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
[CrossRef] [PubMed]

Jung, K. M.

K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef]

Knuettel, A.

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Lee, S. L.

K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef]

Leitgeb, R.

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

Mishin, A. A.

Pircher, M.

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

Reintjes, J.

Rodriguez, J. J.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

Schmitt, J. M.

K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef]

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knuettel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A 14, 1231–1242 (1997).
[CrossRef]

J. M. Schmitt, “Array detection for speckle reduction in optical coherence tomography,” Phys. Med. Biol. 42, 2307–2320 (1997).
[CrossRef]

Tearney, G. J.

N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
[CrossRef] [PubMed]

Tkaczyk, T. S.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

Tuchin, V. V.

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

Yung, K. M.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

Zimnyakov, D. A.

Appl. Opt. (1)

J. Biomed. Opt. (5)

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

M. Pircher, E. Goetzinger, R. Leitgeb, A. F. Fercher, C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003).
[CrossRef] [PubMed]

N. Iftimia, B. E. Bouma, G. J. Tearney, “Speckle reduction in optical coherence tomography by path length encoded angular compounding,” J. Biomed. Opt. 8, 260–263 (2003).
[CrossRef] [PubMed]

K. M. Jung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef]

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt. 8, 570–575 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

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

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. M. Schmitt, “Array detection for speckle reduction in optical coherence tomography,” Phys. Med. Biol. 42, 2307–2320 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Other (2)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 1985), Chap. 2.

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Figures (1)

Fig. 1
Fig. 1

Summation of phasors in OCT represented in the real (Re) and imaginary (Im) dimension. UR is the reference field, US the random sample field, and UT = UR + US.

Equations (22)

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I t = ( U R + U S ) ( U R + U S ) * = A R 2 + A S 2 - 2 A R A S cos ϕ ,
S M = 2 A R A S cos ϕ .
S OCT = 2 A R A S .
p ( A S ) = A S σ 2 exp ( - A S 2 2 σ 2 )
p ( S OCT ) = S OCT 4 A R 2 σ 2 exp ( - S OCT 2 8 A R 2 σ 2 ) .
C = ( 4 / π - 1 ) 1 / 2 0.52.
C = ( π / 2 - 1 ) 1 / 2 0.75.
p ( A T ) A T 2 π σ 2 exp [ - ( A T - A R ) 2 2 σ 2 ] .
p ( A T , θ ) = A T 2 π σ 2 exp [ - ( A T cos θ - A R ) 2 + ( A T sin θ ) 2 2 σ 2 ] .
p ( S OCT ) = p ( S M ϕ = 0 ) = p ( S M , ϕ = 0 ) p ( ϕ = 0 ) .
p ( S M ϕ = 0 ) = 2 π p ( S M , ϕ = 0 ) .
p ( S OCT ) = p [ A T ( S M , ϕ = 0 ) , θ ( S M , ϕ = 0 ) ] J ( S M , ϕ = 0 ) ,
J = A T ( S M , ϕ ) S M θ ( S M , ϕ ) ϕ - A T ( S M , ϕ ) ϕ θ ( S M , ϕ ) S M .
A T ( S M , ϕ ) = [ A R 2 + ( S M 2 A R cos ϕ ) 2 + S M ] 1 / 2 ,
θ ( S M , ϕ ) = arcsin [ S M 2 A R A T ( S M , ϕ ) tan ϕ ] .
A T S M | ϕ = 0 = 1 2 A R ,
θ ϕ | ϕ = 0 = S OCT 2 A R ( A R + S OCT / 2 A R ) .
A T ϕ | ϕ = 0 = 0.
J ϕ = 0 = S OCT 4 A R 3 + 2 A R S OCT .
A T ( S M , ϕ = 0 ) = A R + S OCT 2 A R ,
p [ A T ( S M , ϕ = 0 ) , θ ( S M , ϕ = 0 ) ] = 1 2 π σ 2 ( A R + S OCT 2 A R ) exp ( S OCT 2 8 A R 2 σ 2 ) .
p ( S OCT ) = 2 π p [ A T ( S M , ϕ = 0 ) , θ ( S M , ϕ = 0 ) ] J ϕ = 0 = S OCT 4 A R 2 σ 2 exp ( - S OCT 2 8 A R 2 σ 2 ) ,

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