Abstract

Many Fourier-domain optical coherence tomography (FD-OCT) systems sample the interference fringes with a non-uniform wavenumber (k) interval, introducing a chirp to the signal that depends on the path length difference underlying each fringe. A dispersion imbalance between sample and reference arms also generates a chirp in the fringe signal which, in contrast, is independent of depth. Fringe interpolation to obtain a signal linear in k and compensate dispersion imbalance is critical to achieving bandwidth-limited axial resolution. In this work, we propose an optimization-based algorithm to perform robust and automated calibration of FD-OCT systems, recovering both the interpolation function and the dispersion imbalance. Our technique relies on the fact that the unique function that correctly linearizes the fringe data in k space produces a depth-independent chirp. The calibration procedure requires experimental data corresponding to a single reflector at various depth locations, which can easily be obtained by acquiring data while moving a sample mirror in depth. We have tested both spectral domain OCT and swept source OCT systems with various nonlinearities. Results indicate that the proposed calibration method has excellent performance on a wide range of data sets and enables nearly constant resolution at all imaging depths. An implementation of the algorithm is available online.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
    [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. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
    [Crossref] [PubMed]
  4. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
    [Crossref] [PubMed]
  5. S. Yun, G. Tearney, J. de Boer, N. Iftimia, and B. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11(22), 2953–2963 (2003).
    [Crossref] [PubMed]
  6. E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. 26(6), 413–414 (1990).
    [Crossref]
  7. C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
    [Crossref] [PubMed]
  8. V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
    [Crossref]
  9. E. Brinkmeyer and U. Glombitza, “High-resolution coherent frequency-domain reflectrometry using continuously tuned laser diodes,” in Optical Fiber Communication Conference, Vol. 4 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), paper WN2.
  10. K. Takada, “Fiber-optic frequency encoder for high-resolution OFDR,” IEEE Photonics Technol. Lett. 4(10), 1174–1177 (1992).
    [Crossref]
  11. S. Yun, G. Tearney, J. de Boer, and B. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12(20), 4822–4828 (2004).
    [Crossref] [PubMed]
  12. C. S. Cheung, M. Spring, and H. Liang, “Ultra-high resolution Fourier domain optical coherence tomography for old master paintings,” Opt. Express 23(8), 10145–10157 (2015).
    [Crossref] [PubMed]
  13. M. Szkulmowski, S. Tamborski, and M. Wojtkowski, “Spectrometer calibration for spectroscopic Fourier domain optical coherence tomography,” Biomed. Opt. Express 7(12), 5042–5054 (2016).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  16. Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  18. R. Huber, M. Wojtkowski, K. Taira, J. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
    [Crossref] [PubMed]
  19. K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
    [Crossref]
  20. M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
    [Crossref] [PubMed]
  21. M. J. Todd, “The many facets of linear programming,” Math. Program. 91(3), 417–436 (2002).
    [Crossref]
  22. T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45(3), 385–482 (2003).
    [Crossref]
  23. C. Jun, M. Villiger, W.-Y. Oh, and B. E. Bouma, “All-fiber wavelength swept ring laser based on Fabry-Perot filter for optical frequency domain imaging,” Opt. Express 22(21), 25805–25814 (2014).
    [Crossref] [PubMed]
  24. K. Totsuka, K. Isamoto, T. Sakai, A. Morosawa, and C. Chong, “MEMS scanner based swept source laser for optical coherence tomography,” Proc. SPIE 7554, 75542Q1 (2010)
  25. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier domain mode locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006).
    [Crossref] [PubMed]
  26. N. Uribe-Patarroyo, S. H. Kassani, M. Villiger, and B. E. Bouma, “Robust wavenumber and dispersion calibration for Fourier-domain optical coherence tomography,” figshare (2018) [retrieved 15 Jan 2018], https://doi.org/10.6084/m9.figshare.5787840 .

2018 (1)

K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
[Crossref]

2016 (1)

2015 (1)

2014 (1)

2012 (1)

2010 (1)

K. Totsuka, K. Isamoto, T. Sakai, A. Morosawa, and C. Chong, “MEMS scanner based swept source laser for optical coherence tomography,” Proc. SPIE 7554, 75542Q1 (2010)

2009 (1)

V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
[Crossref]

2006 (1)

2005 (2)

2004 (4)

2003 (5)

2002 (1)

M. J. Todd, “The many facets of linear programming,” Math. Program. 91(3), 417–436 (2002).
[Crossref]

2000 (1)

1999 (1)

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

1992 (1)

K. Takada, “Fiber-optic frequency encoder for high-resolution OFDR,” IEEE Photonics Technol. Lett. 4(10), 1174–1177 (1992).
[Crossref]

1990 (1)

E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. 26(6), 413–414 (1990).
[Crossref]

Akiba, M.

Bajraszewski, T.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Baumgartner, A.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

Belabas, N.

Bizheva, K.

Bouma, B.

Bouma, B. E.

Brinkmeyer, E.

E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. 26(6), 413–414 (1990).
[Crossref]

Cense, B.

Chan, K.-P.

Chen, T.

Cheung, C. S.

Choma, M.

Chong, C.

de Boer, J.

de Boer, J. F.

Dorrer, C.

Drexler, W.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

Duker, J.

Fercher, A.

Fercher, A. F.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

Fujimoto, J.

Fujimoto, J. G.

Gelikonov, G. V.

V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
[Crossref]

Gelikonov, V. M.

V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
[Crossref]

Gorczynska, I.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Hitzenberger, C.

Hitzenberger, C. K.

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

Hsu, K.

Huber, R.

Iftimia, N.

Isamoto, K.

K. Totsuka, K. Isamoto, T. Sakai, A. Morosawa, and C. Chong, “MEMS scanner based swept source laser for optical coherence tomography,” Proc. SPIE 7554, 75542Q1 (2010)

Itoh, M.

Izatt, J.

Joffre, M.

Jun, C.

Ko, T.

Kolda, T. G.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45(3), 385–482 (2003).
[Crossref]

Kowalczyk, A.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

Lamouche, G.

Leitgeb, R.

Lévesque, D.

Lewis, R. M.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45(3), 385–482 (2003).
[Crossref]

Liang, H.

Likforman, J.-P.

Madjarova, V. D.

Makita, S.

Morosawa, A.

Nassif, N.

Oh, W.-Y.

Park, B.

Park, B. H.

Pierce, M.

Pierce, M. C.

Radzewicz, C.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Sakai, T.

Sarunic, M.

Sharma, G.

K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
[Crossref]

Shilyagin, P. A.

V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
[Crossref]

Singh, K.

K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
[Crossref]

Spring, M.

Srinivasan, V.

Szkulmowski, M.

Taira, K.

Takada, K.

K. Takada, “Fiber-optic frequency encoder for high-resolution OFDR,” IEEE Photonics Technol. Lett. 4(10), 1174–1177 (1992).
[Crossref]

Tamborski, S.

Targowski, P.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Tearney, G.

Tearney, G. J.

K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
[Crossref]

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]

Todd, M. J.

M. J. Todd, “The many facets of linear programming,” Math. Program. 91(3), 417–436 (2002).
[Crossref]

Torczon, V.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45(3), 385–482 (2003).
[Crossref]

Totsuka, K.

K. Totsuka, K. Isamoto, T. Sakai, A. Morosawa, and C. Chong, “MEMS scanner based swept source laser for optical coherence tomography,” Proc. SPIE 7554, 75542Q1 (2010)

Ulrich, R.

E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. 26(6), 413–414 (1990).
[Crossref]

Vergnole, S.

Villiger, M.

Wasilewski, W.

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Wojtkowski, M.

Yang, C.

Yasuno, Y.

Yatagai, T.

Yun, S.

Yun, S.-H.

Am. J. Ophthalmol. (1)

M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, A. Kowalczyk, W. Wasilewski, and C. Radzewicz, “Ophthalmic imaging by spectral optical coherence tomography,” Am. J. Ophthalmol. 138(3), 412–419 (2004).
[Crossref] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Electron. Lett. (1)

E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. 26(6), 413–414 (1990).
[Crossref]

IEEE Photonics Technol. Lett. (1)

K. Takada, “Fiber-optic frequency encoder for high-resolution OFDR,” IEEE Photonics Technol. Lett. 4(10), 1174–1177 (1992).
[Crossref]

J. Biomed. Opt. (1)

C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. 4(1), 144–151 (1999).
[Crossref] [PubMed]

J. Opt. (1)

K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” J. Opt. 20(2), 025301 (2018).
[Crossref]

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

Math. Program. (1)

M. J. Todd, “The many facets of linear programming,” Math. Program. 91(3), 417–436 (2002).
[Crossref]

Opt. Express (11)

C. Jun, M. Villiger, W.-Y. Oh, and B. E. Bouma, “All-fiber wavelength swept ring laser based on Fabry-Perot filter for optical frequency domain imaging,” Opt. Express 22(21), 25805–25814 (2014).
[Crossref] [PubMed]

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier domain mode locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006).
[Crossref] [PubMed]

B. Cense, N. Nassif, T. Chen, M. Pierce, S.-H. Yun, B. Park, B. Bouma, G. Tearney, and J. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12(11), 2435–2447 (2004).
[Crossref] [PubMed]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

S. Yun, G. Tearney, J. de Boer, and B. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12(20), 4822–4828 (2004).
[Crossref] [PubMed]

C. S. Cheung, M. Spring, and H. Liang, “Ultra-high resolution Fourier domain optical coherence tomography for old master paintings,” Opt. Express 23(8), 10145–10157 (2015).
[Crossref] [PubMed]

R. Huber, M. Wojtkowski, K. Taira, J. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13(9), 3513–3528 (2005).
[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).
[Crossref] [PubMed]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[Crossref] [PubMed]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

S. Yun, G. Tearney, J. de Boer, N. Iftimia, and B. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11(22), 2953–2963 (2003).
[Crossref] [PubMed]

Opt. Lett. (1)

Opt. Spectrosc. (1)

V. M. Gelikonov, G. V. Gelikonov, and P. A. Shilyagin, “Linear-wavenumber spectrometer for high-speed spectral-domain optical coherence tomography,” Opt. Spectrosc. 106(3), 459–465 (2009).
[Crossref]

Proc. SPIE (1)

K. Totsuka, K. Isamoto, T. Sakai, A. Morosawa, and C. Chong, “MEMS scanner based swept source laser for optical coherence tomography,” Proc. SPIE 7554, 75542Q1 (2010)

SIAM Rev. (1)

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45(3), 385–482 (2003).
[Crossref]

Other (2)

N. Uribe-Patarroyo, S. H. Kassani, M. Villiger, and B. E. Bouma, “Robust wavenumber and dispersion calibration for Fourier-domain optical coherence tomography,” figshare (2018) [retrieved 15 Jan 2018], https://doi.org/10.6084/m9.figshare.5787840 .

E. Brinkmeyer and U. Glombitza, “High-resolution coherent frequency-domain reflectrometry using continuously tuned laser diodes,” in Optical Fiber Communication Conference, Vol. 4 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), paper WN2.

Supplementary Material (1)

NameDescription
» Code 1       This is a MATLAB implementation of the technique described in "Robust Wavenumber and Dispersion Calibration for Fourier-Domain Optical Coherence Tomography" by Uribe-Patarroyo et al. Core functions, exemplary usage and calibration data are supplied.

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Figures (6)

Fig. 1
Fig. 1 Typical configuration of an SS-OCT (a) and SD-OCT (b) system. Image of a mirror at different optical path differences (c), broadening of the peaks due to nonlinearity and dispersion artifacts (d), full width at half maximum (e) of the peaks, and uncorrected, chirped fringe signal (f).
Fig. 2
Fig. 2 Flowchart showing optimization algorithm procedure.
Fig. 3
Fig. 3 (a) Initial fk seed function and its derivative, (b) mapping function and its derivative (c) associated residual chirp at different depths, (d) mean square error of dispersion, (e) optimized fk and its derivative (f) mapping function for optimized fk function and its derivative, (g) associated dispersion at different depths after optimization, (h) mean square error of the residual chirp.
Fig. 4
Fig. 4 (a) Corrected image of a mirror at different OPDs, (d) PSF at different OPDs, (e) flat FWHM, (f) corrected fringe signal.
Fig. 5
Fig. 5 Uncorrected mirror image at different OPDs, corrected mirror image at different OPDs and FWHM respectively for (a)-(c) an FP-based wavelength-swept laser with 25% duty cycle, (d)-(f) an FP-based wavelength-swept laser with 45% duty cycle, (g)-(i) a MEMS scanner-based wavelength-swept laser and (j)-(l) an SD-OCT system.
Fig. 6
Fig. 6 (a) Nonlinearity of different wavelength-swept lasers: (top) the k sampling function of a FP-based wavelength-swept laser with 25% duty cycle (FP25), a FP-based wavelength-swept laser with 45% duty cycle (FP45), a MEMS scanner-based wavelength-swept laser and a spectral-domain (SD) OCT system. (bottom) The derivative of the k sampling function for the same systems, which more clearly shows the nonlinear behavior. (b) Final p for the different systems. Bar height shows the absolute value of each term, light shaded bars correspond to negative terms.

Equations (16)

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

I int (q,z)=S(q) R R +S(q) R s +2S(q) R R R S cos[ 2 f k (q)z+g(q) ],
I i nt (q,z)=S(q) R R R S exp[ iφ(q,z) ],
φ(q,z)=2 f k (q)z+g(q).
φ 1 (q, z 1 )=2 f k (q) z 1 +g(q)
φ 2 (q, z 2 )=2 f k (q) z 2 +g(q).
φ ^ 1 (k, z 1 )=2 f k [ f k 1 (k) ] z 1 +g[ f k 1 (k) ]=2k z 1 + g ^ (k),
φ ^ 2 (k, z 2 )=2 f k [ f k 1 (k) ] z 2 +g[ f k 1 (k) ]=2k z 2 + g ^ (k),
φ ˜ 1 ( k ˜ , z 1 )=2 f k [ f ˜ k 1 (k) ] z 1 +g[ f ˜ k 1 (k) ],
φ ˜ 2 (k, z 2 )=2 f k [ f ˜ k 1 (k) ] z 2 +g[ f ˜ k 1 (k) ],
f k [ f ˜ k 1 (k) ]z=α k ˜ z+βO( k ˜ n )z=α k ˜ z+ γ ˜ ( k ˜ ,z),
ψ ˜ ( k ˜ ,z)= γ ˜ ( k ˜ ,z)+ g ˜ ( k ˜ ),
f k ( q j , p )=( N s 1 )γ[ c+( 2 q j N s 1 1 )+ p 2 2 ( 2 q j N s 1 1 ) 2 + p 3 3 ( 2 q j N s 1 1 ) 3 +... ],
γ= 1 2+ l=2 n p l l [ 1 (1) l ] ,
c=1 l=2 n (1) l p l l .
MSE( k ˜ j , p )= 1 N z 1 l=1 N z ( ψ ˜ ( k ˜ j , z l , p ) ψ ˜ ¯ ( k ˜ j , p ) ) 2 ,
AMSE( p )= 1 N s 1 j=1 N s 1 N z 1 l=1 N z ( ψ ˜ ( k ˜ j , z l , p ) ψ ˜ ¯ ( k ˜ j , p ) ) 2 .

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