Abstract

In this study, we propose a generic speckle simulation for optical coherence tomography (OCT) signal, by convolving the point-spread function (PSF) of the OCT system with the numerically synthesized random sample field. We validate our model and use the simulation method to study the statistical properties of cross-correlation coefficients between A-scans, which have been recently applied in transverse motion analysis by our group. The results of simulation show that oversampling is essential for accurate motion tracking; exponential decay of OCT signal leads to an underestimate of motion that can be corrected; lateral heterogeneity of sample leads to an overestimate of motion for a few pixels corresponding to the structural boundary.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2012

2011

2010

2009

2008

2007

2006

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

2005

2004

2003

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

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

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11, 2183–2189 (2003).
[CrossRef]

2001

P. C. Li, C. J. Cheng, and C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[CrossRef]

2000

1999

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

1997

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

1995

J. Meunier and M. Bertrand, “Ultrasonic texture motion analysis: theory and simulation,” IEEE Trans. Med. Imaging 14, 293–300 (1995).
[CrossRef]

1976

Adie, S. G.

Adler, D. C.

Ahmad, A.

Barton, J.

Barton, J. K.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

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

Bashkansky, M.

Bertrand, M.

J. Meunier and M. Bertrand, “Ultrasonic texture motion analysis: theory and simulation,” IEEE Trans. Med. Imaging 14, 293–300 (1995).
[CrossRef]

Bilenca, A.

Boppart, S. A.

Bouma, B. E.

Cable, A.

Cadotte, A.

Cadotte, D. W.

Carson, P. L.

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

Chaney, E. J.

Chen, J.-F.

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

Chen, Z.

Cheng, C. J.

P. C. Li, C. J. Cheng, and C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[CrossRef]

Choma, M.

Curatolo, A.

Desjardins, A. E.

Duncan, D. D.

Fehlings, M. G.

Fercher, A. F.

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

Fowlkes, J. B.

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

Fraser, S.

Fujimoto, J. G.

Goodman, J. W.

Gossage, K. W.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

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

Götzinger, E.

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

Hariri, L. P.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Hassler, K.

Hillman, T. R.

Hinds, M. T.

Hitzenberger, C. K.

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

Huang, Y.

Izatt, J.

Jarvi, M.

Jian, Z.

Jiang, J.

Kang, J. U.

Kanter, E. M.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Karamata, B.

Kasaragod, D. K.

D. K. Kasaragod, Z. Lu, L. E. Smith, and S. J. Matcher, “Speckle texture analysis of optical coherence tomography images,” Proc. SPIE 7387, 73871V (2010).
[CrossRef]

Kennedy, B. F.

Khurana, M.

Kiehl, T.

Kirkpatrick, S. J.

Ko, T. H.

Lasser, T.

Laubscher, M.

Lee, K.

Lee, K. K. C.

Leitgeb, R.

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

Leung, M. K. K.

Li, P. C.

P. C. Li, C. J. Cheng, and C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[CrossRef]

Liu, X.

Lu, Z.

D. K. Kasaragod, Z. Lu, L. E. Smith, and S. J. Matcher, “Speckle texture analysis of optical coherence tomography images,” Proc. SPIE 7387, 73871V (2010).
[CrossRef]

Mariampillai, A.

Marks, D. L.

Matcher, S. J.

D. K. Kasaragod, Z. Lu, L. E. Smith, and S. J. Matcher, “Speckle texture analysis of optical coherence tomography images,” Proc. SPIE 7387, 73871V (2010).
[CrossRef]

Meunier, J.

J. Meunier and M. Bertrand, “Ultrasonic texture motion analysis: theory and simulation,” IEEE Trans. Med. Imaging 14, 293–300 (1995).
[CrossRef]

Moriyama, E. H.

Motaghiannezam, R.

Motaghiannezam, S. M.

Munce, N. R.

Oh, W. Y.

Ozcan, A.

Pircher, M.

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

Ralston, T. S.

Rao, B.

Reintjes, J.

Rodriguez, J. J.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

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

Rubin, J. M.

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

Sampson, D. D.

Sarunic, M.

Schmitt, J. M.

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

Sharma, U.

Smith, C. M.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Smith, L. E.

D. K. Kasaragod, Z. Lu, L. E. Smith, and S. J. Matcher, “Speckle texture analysis of optical coherence tomography images,” Proc. SPIE 7387, 73871V (2010).
[CrossRef]

Standish, B. A.

Stone, A. L.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Stromski, S.

Tearney, G. J.

Tkaczyk, T. S.

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

Tromberg, B. J.

Vakoc, B. J.

Vitkin, A.

Vitkin, I. A.

Wang, R. K.

Williams, S. K.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Wilson, B. C.

Xiang, S. H.

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

Yang, C.

Yang, V. X. D.

Yeh, C. K.

P. C. Li, C. J. Cheng, and C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[CrossRef]

Yu, L.

Yung, K. M.

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

Zhang, K.

Biomed. Opt. Express

IEEE Trans. Med. Imaging

J. Meunier and M. Bertrand, “Ultrasonic texture motion analysis: theory and simulation,” IEEE Trans. Med. Imaging 14, 293–300 (1995).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

P. C. Li, C. J. Cheng, and C. K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[CrossRef]

Int. J. Imaging Syst. Technol.

J.-F. Chen, J. B. Fowlkes, P. L. Carson, and J. M. Rubin, “Determination of scan-plane motion using speckle decorrelation: theoretical considerations and initial test,” Int. J. Imaging Syst. Technol. 8, 38–44 (1997).

J. Biomed. Opt.

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

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

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Med. Biol.

K. W. Gossage, C. M. Smith, E. M. Kanter, L. P. Hariri, A. L. Stone, J. J. Rodriguez, S. K. Williams, and J. K. Barton, “Texture analysis of speckle in optical coherence tomography images of tissue phantoms,” Phys. Med. Biol. 51, 1563–1575 (2006).
[CrossRef]

Proc. SPIE

D. K. Kasaragod, Z. Lu, L. E. Smith, and S. J. Matcher, “Speckle texture analysis of optical coherence tomography images,” Proc. SPIE 7387, 73871V (2010).
[CrossRef]

Other

J. W. Goodman, Statistical Optics (Wiley, 1985).

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Figures (6)

Fig. 1.
Fig. 1.

(a) hz(z), the axial PSF of OCT system (blue thick curve, magnitude; red thin curve, real part; black and thin curve, imaginary part). (b) hx(x), Lateral PSF of OCT system; (c) hx,z(x,z), 2D PSF; (d) synthesized OCT speckle pattern from spatial-domain simulation; (e) axial MTF; (f) lateral MTF; (g) 2D MTF; and (h) synthesized OCT speckle pattern from frequency-domain simulation.

Fig. 2.
Fig. 2.

(a) PDF of OCT speckle pattern obtained from SD simulation. (b) PSD of OCT speckle pattern obtained from SD simulation. (c) PDF of OCT speckle pattern obtained from FD simulation. (d) PSD of OCT speckle pattern obtained from FD simulation.

Fig. 3.
Fig. 3.

(a) Probability for ρΔx to take different values; (b) mean value of ρΔx from simulation (black circles) as compared with the expectation of ρΔx from theoretical calculation (red curve); and (c) variance of ρΔx at different displacement.

Fig. 4.
Fig. 4.

(a) OCT signal with exponential decay (green) and after exponential decay correction (black); (b) XCC calculated using OCT signal with exponential decay (green circles with larger values); XCC calculated using OCT signal after exponential decay correction (black circles with smaller values); and theoretical XCC values (red curve).

Fig. 5.
Fig. 5.

(a) Speckle pattern with lateral heterogeneity generated from Gaussian random matrices M1 and M2; the variance of M1 is four times larger than that of M2. (b) XCC calculated from the speckle pattern shown in Fig. 5(a) using adjacent A-scans at different lateral locations. (c) Speckle pattern with lateral heterogeneity generated using Gaussian random matrices M1 and M2; the variance of M1 is 16 times larger than that of M2. (d) XCC calculated from the speckle pattern shown in Fig. 5(c) using adjacent A-scans at different lateral locations.

Fig. 6.
Fig. 6.

(a) Speckle pattern with axial heterogeneity generated using Gaussian random matrices M1 and M2; the variance of M1 is four times larger than that of M2. (b) XCC calculated from the speckle pattern shown in Fig. 6(a) using adjacent A-scans in different lateral locations.

Equations (15)

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

ra(z)=hx,y(x,y)*rs(x,y,z)|y=0.
S(x,k)=αrrS0(k)Re[ra(z)ej2kzdz].
Ns(x,z)=+hy(y)rs(x,y,z)dy.
S(x,z)=k0δk2k0+δk2αrrS0(k)[hx(x)*Ns(x,z)ej2kzdz]ej2kzdk.
S(x,z)=δk2δk2αrrs0e4ln2k2Δk2{[hx(x)*Ns(x,z)]ej2kzdz}ej2kzdkαrrs0[hx(x)*Ns(x,z)]ej2k0(zz)[+ej2k(zz)e4ln2k2Δk2dk]dz.
+ej2k(zz)e4ln2k2Δk2dk=Δk2π8ln2e4ln2(zz)2wz2.
S(x,z)β[hx(x)*Ns(x,z)]ej2k0(zz)e4ln2(zz)2/wz2dz.
S(x,z)β[hx(x)*Ns(x,z)]hz(zz)dz=β[hx(x)hz(z)]*Ns(x,z).
Ns(x,z)=nanδ(xxn,zzn).
SP(x,z)=S(x,z)*rect(xΔx,zΔz)=β[hx(x)hz(z)]*[Ns(x,z)*rect(xΔx,zΔz)]=βhx,z(x,z)*NP(x,z).
NP(x,z)=nan[xΔx2x+Δx2zΔz2z+Δz2δ(xxn,zzn)dxdz]=n=1man.
PR(S)=Sσ2eS2/2σ2.
ρΔx=[Ix(z)Ix(z)][Ix+Δx(z)Ix+Δx(z)]σIx(z)σIx+Δx(z).
E(ρΔx)=exp[(Δx)2wx2].
Δx=wxln(1ρΔx).

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