Abstract

We address numerical dispersion compensation based on the use of the fractional Fourier transform (FrFT). The FrFT provides a new fundamental perspective on the nature and role of group-velocity dispersion in Fourier domain OCT. The dispersion induced by a 26 mm long water cell was compensated for a spectral bandwidth of 110 nm, allowing the theoretical axial resolution in air of 3.6 μm to be recovered from the dispersion degraded point spread function. Additionally, we present a new approach for depth dependent dispersion compensation based on numerical simulations. Finally, we show how the optimized fractional Fourier transform order parameter can be used to extract the group velocity dispersion coefficient of a material.

© 2012 OSA

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2011 (4)

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011).
[CrossRef]

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express19, 12141–12155 (2011).
[CrossRef] [PubMed]

2010 (2)

L. Durak and S. Aldirmaz, “Adaptive fractional Fourier domain filtering,” Sig. Proc.90, 1188–1196 (2010).
[CrossRef]

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (3)

2007 (1)

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt.12(4), 041205 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (1)

2004 (4)

2003 (5)

2002 (2)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

2001 (3)

2000 (1)

1999 (2)

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett.24, 1221–1223 (1999).
[CrossRef]

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

1998 (2)

G. Häusler and M. W. Lindner, “Coherence radar and spectral radar — New tools for dermatological diagnosis,” J. Biomed. Opt.3, 21–31 (1998).
[CrossRef]

A. G. Van Engen, S. A. Diddams, and T. S. Clement, “Dispersion measurements of water with white-light interferometry,” Appl. Opt.37, 5679–5686 (1998).
[CrossRef]

1997 (3)

1996 (1)

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

1995 (2)

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]

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995).
[CrossRef] [PubMed]

1994 (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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

1989 (1)

L. Cohen, “Time-frequency distributions — A review,” Proc. of the IEEE77, 941–981 (1989).
[CrossRef]

1980 (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” IMA J. Appl. Math.25, 241–265 (1980).
[CrossRef]

Aldirmaz, S.

L. Durak and S. Aldirmaz, “Adaptive fractional Fourier domain filtering,” Sig. Proc.90, 1188–1196 (2010).
[CrossRef]

Arikan, O.

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

Bachmann, A. H.

Bajraszewski, T.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

Barr, H.

J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008).
[CrossRef]

Baumgartner, A.

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

Bazant-Hegemark, F.

J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008).
[CrossRef]

Belabas, N.

Biedermann, B. R.

Blatter, C.

Boppart, S. A.

Bouma, B.

Bouma, B. E.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express12, 2435–2447 (2004).
[CrossRef] [PubMed]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express12, 367–376 (2004).
[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, 2067–2069 (2003).
[CrossRef] [PubMed]

S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express11, 2953–2963 (2003).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett.22, 1811–1813 (1997).
[CrossRef]

B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+: forsterite laser,” Opt. Lett.22, 1704–1706 (1997).
[CrossRef]

Bozdagi, G.

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

Brckner, C.

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

Brezinski, M. E.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography system,” Phys. Med. Biol.49, 923–930 (2004).
[CrossRef] [PubMed]

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, N.

Chen, T. C.

Chinn, S. R.

Choma, M. A.

Clement, T. S.

Coen, S.

Cohen, L.

L. Cohen, “Time-frequency distributions — A review,” Proc. of the IEEE77, 941–981 (1989).
[CrossRef]

de Boer, J. F.

Diaz, F.

Diddams, S. A.

Dorrer, C.

Drexler, W.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

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

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett.24, 1221–1223 (1999).
[CrossRef]

Duker, J. S.

Durak, L.

L. Durak and S. Aldirmaz, “Adaptive fractional Fourier domain filtering,” Sig. Proc.90, 1188–1196 (2010).
[CrossRef]

Eigenwillig, C. M.

El-Zaiat, S. Y.

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]

Fercher, A. F.

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001).
[CrossRef] [PubMed]

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

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]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Froehly, L.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011).
[CrossRef]

Fujimoto, J. G.

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. Express14, 3225–3237 (2006).
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express12, 2404–2422 (2004).
[CrossRef] [PubMed]

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett.24, 1221–1223 (1999).
[CrossRef]

B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+: forsterite laser,” Opt. Lett.22, 1704–1706 (1997).
[CrossRef]

G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett.22, 1811–1813 (1997).
[CrossRef]

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett.22, 340–342 (1997).
[CrossRef] [PubMed]

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gardecki, J. A.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

Ghanta, R. K.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

Golubovic, B.

Grajciar, B.

C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express19, 12141–12155 (2011).
[CrossRef] [PubMed]

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hattersley, S.

J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008).
[CrossRef]

Haueisen, J.

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

Häusler, G.

G. Häusler and M. W. Lindner, “Coherence radar and spectral radar — New tools for dermatological diagnosis,” J. Biomed. Opt.3, 21–31 (1998).
[CrossRef]

Hee, M. R.

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hillman, T. R.

Hitzenberger, C. K.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001).
[CrossRef] [PubMed]

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

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]

Holmes, J.

J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008).
[CrossRef]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huber, R.

Huignard, J.-P.

Iftimia, N.

Ippen, E. P.

Iyer, S.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011).
[CrossRef]

S. Iyer, S. Coen, and F. Vanholsbeeck, “Dual-fiber stretcher as a tunable dispersion compensator for an all-fiber optical coherence tomography system,” Opt. Lett.34, 2903–2905 (2009).
[CrossRef] [PubMed]

Izatt, J. A.

Joffre, M.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

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]

Karamata, B.

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001).
[CrossRef] [PubMed]

Kartner, F. X.

Ko, T. H.

Kowalczyk, A.

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express12, 2404–2422 (2004).
[CrossRef] [PubMed]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

Krtner, F. X.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

Kutay, M. A.

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

Lasser, T.

Lee, K. K. C.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Lee, K.-S.

Leitgeb, R.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003).
[CrossRef] [PubMed]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

Leitgeb, R. A.

Leung, M. K. K.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Li, X. D.

Liebermann, J.

J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011).
[CrossRef]

Likforman, J. P.

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Lindner, M. W.

G. Häusler and M. W. Lindner, “Coherence radar and spectral radar — New tools for dermatological diagnosis,” J. Biomed. Opt.3, 21–31 (1998).
[CrossRef]

Liu, B.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography system,” Phys. Med. Biol.49, 923–930 (2004).
[CrossRef] [PubMed]

Liu, L.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
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L. Liu, F. Diaz, L. Wang, B. Loiseaux, J.-P. Huignard, C. J. R. Sheppard, and N. Chen, “Superresolution along extended depth of focus with binary-phase filters for the Gaussian beam,” J. Opt. Soc. Am. A25, 2095–2101 (2008).
[CrossRef]

Lohmann, A. W.

Loiseaux, B.

Macdonald, E. A.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography system,” Phys. Med. Biol.49, 923–930 (2004).
[CrossRef] [PubMed]

Mariampillai, A.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Marks, D. L.

Mendlovic, D.

Morgner, U.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett.24, 1221–1223 (1999).
[CrossRef]

Mujat, M.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt.12(4), 041205 (2007).
[CrossRef] [PubMed]

Munce, N. R.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Nadkarni, S. K.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

Namias, V.

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” IMA J. Appl. Math.25, 241–265 (1980).
[CrossRef]

Nassif, N. A.

Nelson, J. S.

Oldenburg, A. L.

Ozaktas, H. M.

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt.33, 6188–6193 (1994).
[CrossRef] [PubMed]

Park, B. H.

Pierce, M. C.

Pitris, C.

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Reynolds, J. J.

Rolland, J. P.

Sampson, D. D.

Sarunic, M. V.

Saxer, C. E.

Schuman, J. S.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

Srinivasan, V. J.

Stamper, D. L.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography system,” Phys. Med. Biol.49, 923–930 (2004).
[CrossRef] [PubMed]

Standish, B. A.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Steinmann, L.

Sticker, M.

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stone, N.

J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008).
[CrossRef]

Swanson, E. A.

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett.22, 340–342 (1997).
[CrossRef] [PubMed]

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 J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express12, 367–376 (2004).
[CrossRef] [PubMed]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express12, 2435–2447 (2004).
[CrossRef] [PubMed]

S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express11, 2953–2963 (2003).
[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, 2067–2069 (2003).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett.22, 1811–1813 (1997).
[CrossRef]

B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+: forsterite laser,” Opt. Lett.22, 1704–1706 (1997).
[CrossRef]

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995).
[CrossRef] [PubMed]

Toussaint, J. D.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

Van Engen, A. G.

Vanholsbeeck, F.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011).
[CrossRef]

S. Iyer, S. Coen, and F. Vanholsbeeck, “Dual-fiber stretcher as a tunable dispersion compensator for an all-fiber optical coherence tomography system,” Opt. Lett.34, 2903–2905 (2009).
[CrossRef] [PubMed]

Villiger, M.

Vitkin, I. A.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Wang, L.

Wieser, W.

Wojtkowski, M.

Yagi, Y.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

Yang, C.

Yang, V. X. D.

B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010).
[CrossRef] [PubMed]

Yun, S. H.

Yun, S.-H.

Zawadzki, R.

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001).
[CrossRef] [PubMed]

Appl. Opt. (4)

IEEE Trans. Sig. Proc. (1)

H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996).
[CrossRef]

IMA J. Appl. Math. (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” IMA J. Appl. Math.25, 241–265 (1980).
[CrossRef]

J. Biomed. Opt. (2)

G. Häusler and M. W. Lindner, “Coherence radar and spectral radar — New tools for dermatological diagnosis,” J. Biomed. Opt.3, 21–31 (1998).
[CrossRef]

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt.12(4), 041205 (2007).
[CrossRef] [PubMed]

J. of 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. of Biomed. Opt., 144–151 (1999).
[CrossRef]

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

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

Journal of Biomedical Optics (1)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002).
[CrossRef] [PubMed]

Nature Med. (1)

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011).
[CrossRef] [PubMed]

Nature Medicine (1)

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001).
[CrossRef] [PubMed]

Opt. Comm. (1)

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002).
[CrossRef]

Opt. Commun. (2)

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011).
[CrossRef]

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 (10)

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Figures (11)

Fig. 1
Fig. 1

Wigner distribution of a chirped signal in the time-frequency plane (u1, u). It illustrates how 2nd-order dispersion affects a spectral interferogram and how the continuum of domains of the FrFT can be interpreted geometrically by the rotated frame (ua, ua+1). The order parameter a chosen for the plot is optimal for the signal considered here, i.e., it leads to a dispersion-compensated OCT depth signal after FrFT.

Fig. 2
Fig. 2

SD OCT configuration used to demonstrate FrFT-based dispersion compensation. A 26 mm water cell induces a dispersion imbalance between the interferometer arms. M: mirror, L: lens, PC: polarization controller, FC: fiber collimator, GM: galvo mirror, S: sample, SLD: superluminescent diode, Disp: dispersion matching material, G: grating, LSC: line scan camera.

Fig. 3
Fig. 3

PSF of our OCT system after coarse physical dispersion compensation (dotted red) compared with the theoretical one (solid blue). Inset: corresponding source spectrum.

Fig. 4
Fig. 4

(a) The dotted red curve is the PSF of our OCT system (3.8 μm FWHM) using only BK7 coarse physical dispersion compensation and the traditional FT (same as in Fig.3). The two other curves are obtained with an additional 26 mm long dispersive water cell. Using the traditional FT (solid blue curve), the PSF broadens to 49 μm FWHM, while the FrFT with optimized order aopt = 1.0555 numerically compensates dispersion, leading to a 3.65 μm FWHM PSF (dashed black curve). (b) Sharpness function as a function of fractional Fourier transform order, a.

Fig. 5
Fig. 5

(a) Spectral phase and (b) instantaneous spectral fringe frequency without (dotted red) and with the water cell (solid blue), and with the water cell plus FrFT dispersion compensation (dashed black). (c) and (d) shows the Wigner distribution of the spectrum acquired with the water cell before and after FrFT dispersion compensation.

Fig. 6
Fig. 6

Measured PSF for different delays for matched dispersion (dots) and FrFT compensated dispersion (cross).

Fig. 7
Fig. 7

OCT depth scan and intensity image of two cover slides (a) using the traditional FT and (b) using FrFT numerical dispersion compensation with the optimized order parameter. The 26 mm-long dispersive water cell is present in the setup in both cases.

Fig. 8
Fig. 8

(a) Radon transform of the spectrogram of one A-scan of a grape. (b) B-scan of the grape using the traditional FT (orange line). (c) B-scan of the grape using the optimized FrFT (aopt = 1.04, green line). The same FrFT order was used for all A-scans. The white bars correspond to 500 μm. Note that the x-axis of (a) only corresponds strictly to depth for the optimized FrFT so is labeled in terms of the pixels of the projections (or Radon bins).

Fig. 9
Fig. 9

(a) Sharpness function at each interface of a simulated sample made up five identical 100 μm-thick cover slides as a function of FrFT order. (b) Corresponding optimal FrFT order as a function of imaging depth.

Fig. 10
Fig. 10

(a) Color plot of OCT depth scans obtained for a range of FrFT orders for a simulated sample made up five identical 100 μm-thick cover slides. Three cross-sections are highlighted: (b) traditional FT (a = 1, solid green line), (c) average sample dispersion compensation (dotted red line), and (d) depth-dependent dispersion compensation (dashed yellow line).

Fig. 11
Fig. 11

Same as in Fig. 10 but for a simulated sample which presents linearly increasing normal dispersion in a first 150 μm-thick layer, followed by a second layer with uniform anomalous dispersion. (b) is obtained with the traditional FT (solid green line), while (c) comes from the optimized cross-section of the Radon plot (dashed yellow line).

Tables (1)

Tables Icon

Table 1 FrFT-based measurements of the group velocity dispersion coefficient β2 of a single mode fiber and of distilled water. All the measurements have been done at 843 nm but the reference value for water is for a 840 nm wavelength. N = 1001, = 34.5×1010 rad/s.

Equations (13)

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f a ( u a ) = F a [ f ( u ) ] = A ϕ exp [ i π [ u a 2 cot ( ϕ ) 2 u u a csc ( ϕ ) + u 2 cot ( ϕ ) ] ] f ( u ) d u ,
A ϕ = exp { i π sign [ sin ( ϕ ) ] 4 + i ϕ 2 } | sin ( ϕ ) | 1 / 2 and ϕ = a π 2 .
W f a ( u a , u a + 1 ) = W f ( u a cos ϕ u a + 1 sin ϕ , u a sin ϕ + u a + 1 cos ϕ ) .
W f a ( u a , u a + 1 ) d u a + 1 = | f a ( u a ) | 2 .
S ( ω ) = Re { I ( ω ) exp [ j ( ω τ + β 2 l ( ω ω c ) 2 ) ] } .
S ( u ) = Re { I ( u ) exp [ j ( 2 π u u 1 + ( 2 π η ) 2 β 2 l ( u u c ) 2 ) ] } = Re { I ( u ) exp [ j φ ] } .
η = Δ ν Δ τ = d ν N ,
1 2 π φ u = u 1 + ( 2 π η ) 2 β 2 l π ( u u c ) ,
φ FrFT = arg { F 1 { F a opt { S ( u ) + i S ^ ( u ) } } } .
σ PSF = 1 + ( π 2 c 2 2 ln ( 2 ) l β 2 Δ λ FWHM 2 λ c 4 ) 2 .
tan ( π ϕ ) = π l β 2 ( 2 π η ) 2 ,
β 2 = π l N d ω 2 tan ( a opt π / 2 ) ,
β 2 ( sample ) = 1 l sample [ ( l β 2 ) ( total ) ( l β 2 ) ( setup ) ] .

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