Abstract

We demonstrate the efficiency of the convolution using an optimized Kaiser–Bessel window to resample nonlinear data in wavenumber for Fourier-domain optical coherence tomography (OCT). We extend our previous experimental demonstration that was performed with a specific swept-source nonlinearity. The method is now applied to swept-source OCT data obtained for various simulated swept-source nonlinearities as well as spectral-domain OCT data obtained from both simulations and experiments. Results show that the new optimized method is the most efficient for handling all the different types of nonlinearities in the wavenumber domain that one can encounter in normal practice. The efficiency of the method is evaluated through comparison with common methods using resampling through interpolation prior to performing a fast-Fourier transform and with the accurate but time-consuming discrete Fourier transform for unequally spaced data, which involves Vandermonde matrices.

© 2012 Optical Society of America

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References

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  1. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
    [CrossRef]
  2. M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
    [CrossRef]
  3. Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. 32, 3525–3527 (2007).
    [CrossRef]
  4. S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express 18, 10446–10461 (2010).
    [CrossRef]
  5. D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009).
    [CrossRef]
  6. P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
    [CrossRef]
  7. P. N. Swarztrauber, Vectorizing the FFTs, G. Rodrigue, ed. (Academic, 1982), pp. 51–83.
  8. P. Puvanathasan, P. Forbes, Z. Ren, D. Malchow, S. Boyd, and K. Bizheva, “High-speed, high-resolution Fourier-domain optical coherence tomography system for retinal imaging in the 1060 nm wavelength region,” Opt. Lett. 33, 2479–2481 (2008).
    [CrossRef]
  9. S. Hariri, A. A. Moayed, A. Dracopolos, C. Hyun, S. Boyd, and K. Bizheva, “Limiting factors to the OCT axial resolution for in-vivo imaging of human and rodent retina in the 1060 nm wavelength range,” Opt. Express 17, 24304–24316 (2009).
    [CrossRef]

2010 (1)

2009 (2)

2008 (1)

2007 (1)

2005 (2)

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
[CrossRef]

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
[CrossRef]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Beatty, P. J.

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
[CrossRef]

Bizheva, K.

Boyd, S.

Choma, M. A.

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
[CrossRef]

Dracopolos, A.

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Forbes, P.

Hariri, S.

Hillmann, D.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Hsu, K.

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
[CrossRef]

Hu, Z.

Huttmann, G.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009).
[CrossRef]

Hyun, C.

Izatt, J. A.

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
[CrossRef]

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Koch, P.

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009).
[CrossRef]

Lamouche, G.

Lévesque, D.

Malchow, D.

Moayed, A. A.

Nishimura, D. G.

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
[CrossRef]

Pauly, J. M.

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
[CrossRef]

Puvanathasan, P.

Ren, Z.

Rollins, A. M.

Swarztrauber, P. N.

P. N. Swarztrauber, Vectorizing the FFTs, G. Rodrigue, ed. (Academic, 1982), pp. 51–83.

Vergnole, S.

Zaiat, S. Y. El

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

IEEE Trans. Med. Imag. (1)

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imag. 24, 799–808 (2005).
[CrossRef]

J. Biomed. Opt. (1)

M. A. Choma, K. Hsu, and J. A. Izatt, “Swept source optical coherence tomography using an all-fiber 1300 nm ring laser source,” J. Biomed. Opt. 10, 044009 (2005).
[CrossRef]

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (1)

D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009).
[CrossRef]

Other (1)

P. N. Swarztrauber, Vectorizing the FFTs, G. Rodrigue, ed. (Academic, 1982), pp. 51–83.

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Figures (6)

Fig. 1.
Fig. 1.

Plot of the Fourier transform of the Kaiser–Bessel window [cn in Eq. (5)] with (a), (c) nonoptimal and (b), (d) optimal values of β, for the case (a), (b) M=5 and α=2 and (c), (d) α=1.2. PB denotes the passband zone, and SB is the first stop band zone.

Fig. 2.
Fig. 2.

Example of an error calculation: (a) PSF at 3 mm processed with the Vandermonde method (green curve) and the LIFFT1 method (red curve) and (b) error evaluated from the subtraction of the two PSFs over the whole A-scan.

Fig. 3.
Fig. 3.

Simulated nonlinearities [first row, (a)–(d)]. Error evaluated from comparison to the Vandermonde method: LIFFTα processing [second row (e)–(h)], SIFFTα processing [third row (i)–(l)], and KBFFTM,α processing [fourth row (m)–(p)]. Error bars correspond to 2σ. The pink shaded area in SD-OCT correspond to depths that have been, up to now, rarely reached with SD-OCT systems.

Fig. 4.
Fig. 4.

Processing time ratio evaluated by comparison to our optimized proposed method (KBFFT5,1.2). Based on the previous analysis of Fig. 3, green identifies good-quality imaging methods, while red identifies bad-quality imaging methods. Pink identifies a method that is efficient for low-depth imaging.

Fig. 5.
Fig. 5.

(a) Experimental nonlinearity of the spectrometer used in our setup. Error evaluation for (b) LIFFT, (c) SIFFT, and (d) KBFFT methods.

Fig. 6.
Fig. 6.

Example of imaging in SD-OCT processed with (a) SIFFT1.0 and (b) KBFFT5,1.2. Tic marks are 0.5 mm spaced in the X direction and 0.2 mm spaced in the Y direction. Gray scale is log scale. The dynamic range is 30 dB.

Equations (9)

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δk=kmaxkminNα=2πNδz,δz=2πkmaxkmin,
Sk=j=1MSjCkj,
Ckj=I0(β1(2κ/M)2)/M,κ=|kkjδk|M2,
β=πM2α2(α12)20.8.
1cn=(nπM/N)2β2sin((nπM/N)2β2),
S(t)S0(t)cos[2πcν(t)·2δz],
ν(t)=cλ0+Δλ2+inai·ti,
ν(t)=3·1081300+1002·1012+inai·ti=222.22+inai·ti.
error=PSFmethod,XmmPSFVDM,Xmm,

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