## Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact

Optics Express, Vol. 17, Issue 19, pp. 16820-16833 (2009)

http://dx.doi.org/10.1364/OE.17.016820

Acrobat PDF (1348 KB)

### 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

## 1. Introduction

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]

2. 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]

3. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express **11**(8), 889–894 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-8-889. [CrossRef] [PubMed]

4. 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]

5. 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]

6. J. T. Oh and B.-M. Kim, “Artifact removal in complex frequency domain optical coherence tomography with an iterative least-squares phase-shifting algorithm,” Appl. Opt. **45**(17), 4157–4164 (2006). [CrossRef] [PubMed]

7. 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]

8. M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers,” Opt. Express **13**(3), 957–967 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-957. [CrossRef] [PubMed]

9. 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]

10. A. Bachmann, R. Leitgeb, and T. Lasser, “Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution,” Opt. Express **14**(4), 1487–1496 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1487. [CrossRef] [PubMed]

11. 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]

12. 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]

13. A. B. Vakhtin, K. A. Peterson, and D. J. Kane, “Demonstration of complex-conjugate-resolved harmonic Fourier-domain optical coherence tomography imaging of biological samples,” Appl. Opt. **46**(18), 3870–3877 (2007). [CrossRef] [PubMed]

14. B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express **17**(1), 7–24 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-1-7. [CrossRef] [PubMed]

15. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. **45**(8), 1861–1865 (2006). [CrossRef] [PubMed]

*π/2*. This phase-shifting introduces a linear carrier to the detected interference signal versus transversal position. Complex spectral interferograms can be obtained by band-pass filtering or Hilbert transformation along transversal direction. Methods implemented to introduce linear spatial carrier include reference mirror mounted on the PZT driven by saw-tooth or triangular waveforms [16], piezoelectric fiber stretcher (PFS) [17

17. 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]

18. 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]

*π/2*introduced between successive A-scans in the linear B-M method results in accumulated OPD for case with large transverse scanning range. The OPD between reference arm and sample arm caused by linear phase modulation results in sensitivity fall-off along transverse direction, contradicting our pursued target of increasing the imaging depth range. Moreover, linear phase modulation places high demand on the phase-shifting actuator, typically a PZT, which is mainly limited by its slow linear response. An alternative to linear phase modulation is sinusoidal phase modulation, in which the actuator is driven by a sinusoidal waveform. High frequency sinusoidal phase modulation by sine waveform is easier to realize than linear phase modulation by ramp or saw tooth waveforms.

## 2. Principle

### 2.1. Sinusoidal B-M method

### 2.2. Criterion for transverse over-sampling factor and modulation frequency

*N*A-scans covering a transverse range of

*X*, there are

*N*sampling points in the transverse direction of the image and the sampling interval is

*X/N*. So the maximum retrievable spatial frequency according to Nyquist theory is

*ν*. For coherent imaging, we assume a characteristic width of the detected spatial frequency spectrum which is determined by the inverse speckle size as

_{x}= N/2X*ν*1

_{σ}=*/σ*[18

18. 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]

*σ = 4λf/πd*with

*λ*being the central wavelength,

*f*representing the focal length of the object lens in sample arm, and

*d*denoting the collimated beam diameter at the aperture of the object lens. If the phase change between successive A-scans is

*ΔΦ*, the spatial frequency spectrum of the detected signal is shifted by

*± ν*. If

_{Φ}= ± (ΔΦ/2π)(N/X)*ν*and

_{Φ}>>ν_{σ}*ν*, the spatial frequency spectrum can be separated completely, otherwise, the negative part of the spatial spectrum will leak into the positive part leading to a overlapping region and hence unresolved complex ambiguity.

_{Φ}<ν_{x}*ϕ(t) = 2πf*, where

_{m}t*f*is the modulation frequency. Corresponding phase shift

_{m}*ΔΦ*between successive A-scans is

*2πf*, here

_{m}T*T*represents the time interval between successive A-scans, i.e. the integration time of line-scan CCD in SD-OCT system. The resulting spatial carrier is

*ν*, then the condition for complete separation of spatial spectrum of sample as shown in Fig. 2(b) is We define the ratio between the transverse resolution

_{Φ}= f_{m}T(N/X)*σ*and the transverse step size (

*X/N*) as transverse over-sampling factor, i.e.,

*ρ = σ/(X/N)*. With the relationship of

17. 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]

18. 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]

*ϕ(t) = a*, where

_{m}(ω)sin2πf_{m}t*a*is the phase-modulation amplitude,

_{m}(ω)*f*is the modulation frequency. Then Eq. (1) can be expressed with respect to time

_{m}*t*and expanded as:

*ν*, it’s evident that frequency separation between harmonics can be guaranteed if separation between negative and positive first-order harmonic pairs is assured, i.e.

_{Φ}*ν*. Thus, similar to the criterion described by Eq. (4) in the linear B-M method, the modulation frequency in sinusoidal B-M method must obey the following criterion:here

_{Φ}>>ν_{σ}*n*is the order of the harmonics term. Thus, with a given A-scan rate, the over-sampling factor

*ρ*must be large enough to satisfy Eq. (6), which means that the transverse step must be small enough for effective artifact removal.

### 2.3. Digital synchronous demodulation

*sin2πf*:

_{m}t*t*. Then the resulting spectral interference signal at each spectral point is integrated over the interval of

*nT*to obtain the first harmonic term, here

*T*is the period of modulation signal which equals to

*1/f*,

_{m}*n*is the number of the modulation period. Larger

*n*is helpful in increasing the signal-to-noise ratio by averaging the signal over multiple modulation periods. Similarly, the second and third harmonic terms can be extracted by multiplying the spectral interference signal at each spectral point by

*sin(*2

*×*2

*πf*and

_{m}t)*sin(*3

*×*2

*πf*, respectively. Hence, the extracted harmonic terms are: It can be seen that

_{m}t)*H*and

_{1}*H*represent the imaginary and real parts of the complex spectral interferogram, respectively. In order to construct the complex interferogram, an additional scaling coefficient

_{2}*β*must be applied to equalize the amplitude of

*H*and that of

_{1}*H*:The scaling coefficient

_{2}*β*depends on the modulation amplitude

*a*.

_{m}(ω)*a*is wavelength dependent, and can be extracted fromOnce the modulation amplitude is determined, the scaling coefficient is obtained. Then the complex interferogram can be constructed. Its Fourier transform is free from complex-conjugate ambiguity and removal of the DC and autocorrelation terms, as shown in Eq. (11):

_{m}(ω)## 3. Experiments and results

19. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express **17**(14), 12121–12131 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-14-12121. [CrossRef] [PubMed]

20. 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]

### 3.1 Calculation of the scaling coefficient β

*β*is essential for reconstruction of the complex spectral interferograms. Actually,

*β*is dependent on the peak-to-peak voltage amplitude (

*V*) of the sinusoidal waveform applied to PZT and the wavelength distribution on CCD. In order to determine

_{pp}*β*, firstly the wavelength distribution on CCD in the spectrometer is firstly determined by a commercial available mercury argon lamp which is illustrated in Fig. 6(a) . Herein, seven characteristic spectral lines from the lamp are dispersed and then detected by the CCD in the spectrometer. The indexed pixel numbers of all characteristic spectral lines are recorded and a third-order polynomial fitting is performed to them. It can be seen that wavelength versus CCD pixel number is not linear due to residual aberrations and perhaps misalignment of the spectrometer. Then spectral interferograms are obtained with a mirror used as the sample when the integration time of CCD is set to be 100 µs (corresponding A-scan rate is 10 KHz), the initial phase and the frequency of sinusoidal signal is 0 and 1250 Hz, respectively. With a stationary sample arm, a 2048 (pixel) × 1024 (point) 2D spectral interferogram is acquired for different

*V*of the sinusoidal signal, where the two dimensions of the matrix can be specified as wavelength axis and time axis, respectively. Then the 2D spectral interferograms are digitally 1D Fourier transformed along the time axis to retrieve the harmonic terms. After harmonics analysis of the acquired 2D spectral interferogram with different

_{pp}*V*, we find that when the

_{pp}*V*is set to be 1.0 V, the power spectrum of the time dependent spectral interferogram is mainly concentrated in the first- and second-order harmonic terms which are illustrated in Fig. 6(b), herein the wavelength is 849.7 nm. Since the first- and second-order harmonic terms are used for complex spectral interferogram reconstruction, higher complex conjugate rejection ratio can be realized due to the better utilization of total power under this condition. Thus, the

_{pp}*V*of the sinusoidal signal applied to PZT is set to be 1.0 V for following imaging on biological sample.

_{pp}*a*(

_{m}*ω*) by minimizing the least square differences Δ

*U*, i.e.,Here,

*a*

_{m}^{0}is the modulation amplitude at central wavelength,

*λ*

_{0}is the central wavelength, and

*ω*

_{0}is the central optical frequency. The choice of fitting range from 805nm to 885nm is due to the spectral distribution of the source implemented in the system, outside above range the spectrum intensity is very weak and can be disregarded. The smoothed ratio of the amplitude of the first- and third-order harmonic terms at different wavelength and its corresponding least square fitting are illustrated in Fig. 7(b), herein the

*a*

_{m}^{0}is about 2.19. It should be mentioned that the fitting curve and corresponding

*a*(

_{m}*ω*) are extended to the wavelength range from about 770nm to 910nm covering the whole pixel range on the CCD array. Such extension makes no difference because of the negligible contribution from outside wavelength range from 805nm to 885nm.

### 3.2 Determination of the transverse over-sampling factor and modulation frequency

*t*are illustrated in Figs. 9(a) -9(c). It can be seen that with a fixed modulation frequency, larger transverse over-sampling factor is better for separation of the transverse spatial spectrum. Secondly, the transverse over-sampling factor is fixed at 16, and the modulation frequency of the sinusoidal waveform is set to be 500Hz, 800Hz and 1250Hz, respectively. The results of the transverse Fourier transform with respect to time

*t*are illustrated in Figs. 9(d)-9(f). It is clear that with higher modulation frequency, the transverse spatial spectrum can be well separated without overlap, which is helpful for complex conjugate rejection.

### 3.3 Imaging on biological sample

*V*and the frequency of sinusoidal signal is 1.0 V and 1250 Hz, respectively, which means that exactly eight spectral interferograms are collected during one phase modulation period. In order to meet the condition described by the inequality of Eq. (6) and obtain the maximum complex conjugate rejection ratio, the transverse over-sampling factor is firstly chosen to be 32. Thus in the digital synchronous demodulation procedure, integration is performed over 32 data points i.e. 4 phase modulation periods. With the extracted first and second harmonic terms and the pre-calculated scaling coefficient

_{pp}*β*demonstrated in Fig. 8(b), the complex spectral interferograms can be constructed whose inverse Fourier transform is free from complex conjugate ambiguous. Figure 10 shows the cross-sectional images of the fresh shrimp and corresponding A-scan signals (indicated by arrows) obtained by conventional SD-OCT system and full range complex SD-OCT system using the proposed method with the transverse over-sampling factor of 32, respectively. The image size is about 2mm × 4.5mm formed by 4800 A-scans. And the resulting typical complex conjugate rejection ratio is about 45 dB. With the transverse over-sampling factor of 8 comparable to that adopted in the linear B-M method [17

17. 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]

**32**(23), 3453–3455 (2007). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgements

## References and links

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 |

2. | 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. |

3. | R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express |

4. | M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. |

5. | 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. |

6. | J. T. Oh and B.-M. Kim, “Artifact removal in complex frequency domain optical coherence tomography with an iterative least-squares phase-shifting algorithm,” Appl. Opt. |

7. | 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. |

8. | M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers,” Opt. Express |

9. | 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. |

10. | A. Bachmann, R. Leitgeb, and T. Lasser, “Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution,” Opt. Express |

11. | 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. |

12. | 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. |

13. | A. B. Vakhtin, K. A. Peterson, and D. J. Kane, “Demonstration of complex-conjugate-resolved harmonic Fourier-domain optical coherence tomography imaging of biological samples,” Appl. Opt. |

14. | B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express |

15. | Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. |

16. | R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. |

17. | S. Vergnole, G. Lamouche, and M. L. Dufour, “Artifact removal in Fourier-domain optical coherence tomography with a piezoelectric fiber stretcher,” Opt. Lett. |

18. | R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett. |

19. | K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express |

20. | Y. Zhang, X. Li, L. Wei, K. Wang, Z. Ding, and G. Shi, “Time-domain interpolation for Fourier-domain optical coherence tomography,” Opt. Lett. |

**OCIS Codes**

(100.2650) Image processing : Fringe analysis

(110.4500) Imaging systems : Optical coherence tomography

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: July 24, 2009

Revised Manuscript: August 19, 2009

Manuscript Accepted: August 25, 2009

Published: September 4, 2009

**Virtual Issues**

Vol. 4, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Kai Wang, Zhihua Ding, Yan Zeng, Jie Meng, and Minghui Chen, "Sinusoidal B-M method based spectral domain optical coherence tomography for the elimination of complex-conjugate artifact," Opt. Express **17**, 16820-16833 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-19-16820

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### References

- 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]
- 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. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-8-889 . [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]
- 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. T. Oh and B.-M. Kim, “Artifact removal in complex frequency domain optical coherence tomography with an iterative least-squares phase-shifting algorithm,” Appl. Opt. 45(17), 4157–4164 (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]
- M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers,” Opt. Express 13(3), 957–967 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-957 . [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]
- A. Bachmann, R. Leitgeb, and T. Lasser, “Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution,” Opt. Express 14(4), 1487–1496 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1487 . [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]
- 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]
- A. B. Vakhtin, K. A. Peterson, and D. J. Kane, “Demonstration of complex-conjugate-resolved harmonic Fourier-domain optical coherence tomography imaging of biological samples,” Appl. Opt. 46(18), 3870–3877 (2007). [CrossRef] [PubMed]
- B. Hofer, B. Považay, B. Hermann, A. Unterhuber, G. Matz, and W. Drexler, “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express 17(1), 7–24 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-1-7 . [CrossRef] [PubMed]
- Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef] [PubMed]
- R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90, 054103–1-054103–3 (2007).
- 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]
- 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]
- K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express 17(14), 12121–12131 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-14-12121 . [CrossRef] [PubMed]
- 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]

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