Abstract

A high speed spectral domain optical coherence tomography based on the spatial sinusoidal phase modulation for the elimination of complex-conjugate artifact is presented, where sinusoidal phase modulation of reference arm (M scan) and transverse scanning of sample arm (B scan) are performed simultaneously (sinusoidal B-M method). Herein, the linear phase modulation of the reference arm in conventional linear B-M method is modified to sinusoidal phase modulation. The proposed sinusoidal B-M method relaxes the requirements on the phase-shifting mechanical system and avoids sensitivity fall-off along the transverse direction in contrast to the linear B-M method. A criterion for the relation between transverse over-sampling factor and modulation frequency for optimal complex conjugate rejection is deduced and verified by experiments. Under this criterion, the complex spectral interferogram is reconstructed by harmonic analysis and digital synchronous demodulation. Double imaging depth range on fresh shrimp at A-scan rate of 10 kHz with complex conjugate rejection ratio up to 45dB is achieved.

© 2009 OSA

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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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (3)

2008 (1)

2007 (4)

2006 (5)

2005 (2)

2003 (3)

2002 (1)

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Aoki, G.

Bachmann, A.

Bajraszewski, T.

Bouma, B. E.

Cense, B.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, M.

Chen, Z.

Choma, M. A.

de Boer, J. F.

Ding, Z.

Drexler, W.

Dufour, M. L.

Endo, T.

et,

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fercher, A.

Fercher, A. F.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hitzenberger, C.

Hitzenberger, C. K.

Hofer, B.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Itoh, M.

Izatt, J. A.

Kane, D. J.

Kim, B.-M.

Kowalczyk, A.

Lamouche, G.

Lasser, T.

Leitgeb, R.

Leitgeb, R. A.

Li, X.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Makita, S.

Matz, G.

Meng, J.

Michaely, R.

Nelson, J. S.

Oh, J. T.

Park, B. H.

Peterson, K. A.

Pierce, M. C.

Považay, B.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sarunic, M.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sekhar, S. C.

Shi, G.

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. 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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tao, Y. K.

Tearney, G. J.

Unterhuber, A.

Vakhtin, A. B.

Vakoc, B. J.

Vergnole, S.

Wang, C.

Wang, K.

Wang, R. K.

R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90, 054103–1-054103–3 (2007).

Wei, L.

Wojtkowski, M.

Wu, T.

Xu, L.

Yang, C.

Yasuno, Y.

Yatagai, T.

Yun, S. H.

Zhang, J.

Zhang, Y.

Zhao, M.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90, 054103–1-054103–3 (2007).

Opt. Express (5)

Opt. Lett. (10)

Y. Zhang, X. Li, L. Wei, K. Wang, Z. Ding, and G. Shi, “Time-domain interpolation for Fourier-domain optical coherence tomography,” Opt. Lett. 34(12), 1849–1851 (2009).
[CrossRef] [PubMed]

A. B. Vakhtin, K. A. Peterson, and D. J. Kane, “Resolving the complex conjugate ambiguity in Fourier-domain OCT by harmonic lock-in detection of the spectral interferogram,” Opt. Lett. 31(9), 1271–1273 (2006).
[CrossRef] [PubMed]

Y. K. Tao, M. Zhao, and J. A. Izatt, “High-speed complex conjugate resolved retinal spectral domain optical coherence tomography using sinusoidal phase modulation,” Opt. Lett. 32(20), 2918–2920 (2007).
[CrossRef] [PubMed]

R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett. 32(23), 3453–3455 (2007).
[CrossRef] [PubMed]

S. Vergnole, G. Lamouche, and M. L. Dufour, “Artifact removal in Fourier-domain optical coherence tomography with a piezoelectric fiber stretcher,” Opt. Lett. 33(7), 732–734 (2008).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett. 28(22), 2201–2203 (2003).
[CrossRef] [PubMed]

J. Zhang, J. S. Nelson, and Z. Chen, “Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator,” Opt. Lett. 30(2), 147–149 (2005).
[CrossRef] [PubMed]

B. J. Vakoc, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Elimination of depth degeneracy in optical frequency-domain imaging through polarization-based optical demodulation,” Opt. Lett. 31(3), 362–364 (2006).
[CrossRef] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27(16), 1415–1417 (2002).
[CrossRef]

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, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Time sequences for B-M scans in (a) conventional phase-shifting method, (b) linear B-M method, and (c) sinusoidal B-M method.

Fig. 2
Fig. 2

(a) Saw-tooth waveform for phase modulation in the reference arm and (b) spatial frequency spectrum from the detected signal versus transverse scanning in the linear B-M method.

Fig. 3
Fig. 3

(a) Sinusoidal waveform for phase modulation in the reference arm and (b) spatial frequency spectrum from detected interference signal versus transverse scanning in the sinusoidal B-M method.

Fig. 4
Fig. 4

Schematic diagram of the established SD-OCT system, where OI is the optical isolator, FC is the 3dB fiber coupler, PC is the polarization controller, DG is the diffraction grating, and NDF is the neutral density filter.

Fig. 5
Fig. 5

Block diagram of the processing procedure in the sinusoidal B-M method

Fig. 6
Fig. 6

(a) The calibration curve of wavelength distribution on the CCD array. (b) Fourier transform of interference signal at 849.7nm when the Vpp of sinusoidal signal is set to be 1.0V.

Fig. 7
Fig. 7

(a) Calculated ratio of the amplitude of the first- and third-order harmonic term (H1/ H3) with respect to wavelength and (b) smoothed curve after low-pass filtering and corresponding least square fitting with am 0 of 2.19.

Fig. 8
Fig. 8

(a) Calculated wavelength dependent phase-modulation amplitude am (ω) under the least square fitting and (b) corresponding calculated scaling coefficient β with respect to wavelength.

Fig. 9
Fig. 9

Transverse Fourier transformation spectra with respect to time t under different conditions: (a)-(c) with a fixed modulation frequency of the sinusoidal waveform at 1250Hz and different transverse over-sampling factor corresponding to 4, 18 and 32, respectively. (d)-(f) with a fixed transverse over-sampling factor of 16 and different modulation frequency of the sinusoidal waveform corresponding to 500 Hz, 800Hz, 1250Hz, respectively.

Fig. 10
Fig. 10

(a) Picture of the fresh shrimp under imaging; Tomogram of dorsal part of the fresh shrimp denoted by the line segment in (a) with (b) standard and (c) complex reconstruction with the transverse over-sampling factor of 32; and the corresponding A-scans (d) and (e) indicated by the arrows.

Fig. 11
Fig. 11

(a) Picture of the fresh shrimp under imaging; Tomogram of dorsal part of the fresh shrimp denoted by the line segment in (a) with (b) standard and (c) complex reconstruction with the transverse over-sampling factor of 8; and the corresponding A-scans (d) and (e) indicated by the arrows.

Equations (14)

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Isignal(ω,x)=IR(ω)+IS(ω,x)+2[IR(ω)IS(ω,x)]12cos[ΔφS(ω,x)+φ(x)],
fmT(N/X)>>1/σfmT>>(X/N)/σ,
fmT(N/X)<N/2XfmT<12.
1ρfAscan<<fm<12fAscan.
Isignal(ω,t)=IR(ω)+IS(ω,t)                                 +2[IR(ω)IS(ω,t)]12×{J0[am(ω)]                                 2J1[am(ω)]sin(2πfmt)sin(ΔϕS(ω,t))                                 +2J2[am(ω)]cos(2×2πfmt)cos(ΔϕS(ω,t))                                 2J3[am(ω)]sin(3×2πfmt)sin(ΔϕS(ω,t))                                 +2J4[am(ω)]cos(4×2πfmt)cos(ΔϕS(ω,t))}.
1ρfAscan<<fm<1nfAscan,
Isignal(ω,t)sin(2πfmt)=IR(ω)sin(2πfmt)+IS(ω,t)sin(2πfmt)                                 +2[IR(ω)IS(ω,t)]12×{J0[am(ω)]sin(2πfmt)                                 J1[am(ω)]sin(ΔϕS(ω,t))(12cos(2×2πfmt))                                 +J2[am(ω)]cos(ΔϕS(ω,t))(sin(3×2πfmt)sin(2πfmt))                                 J3[am(ω)]sin(ΔϕS(ω,t))(cos(2×2πfmt)cos(4×2πfmt))+}.
H1[ω,ΔϕS(ω,t)]=4J1[am(ω)][IR(ω)IS(ω,t)]12sin(ΔϕS(ω,t)),
H2[ω,ΔϕS(ω,t)]=4J2[am(ω)][IR(ω)IS(ω,t)]12cos(ΔϕS(ω,t)),
H3[ω,ΔϕS(ω,t)]=4J3[am(ω)][IR(ω)IS(ω,t)]12sin(ΔϕS(ω,t)).
β=J1[am(ω)]J2[am(ω)].
J1[am(ω)]J3[am(ω)]=H1/H3.
f(z)=F1{βH2[ω,ΔϕS(ω)]iH1[ω,ΔϕS(ω)]}.
ΔU=ω[ratio(ω)(J1[am0ω/ω0]/J3[am0ω/ω0])]2

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