Abstract

Optical coherence tomography (OCT) reconstruction by using frequency measurements in the wavelength domain is presented in this paper. The method directly recovers the axial scan by formulating the frequency domain OCT (FD-OCT) into an algebraic reconstruction problem. In this way, the need for interpolation is removed. Then by solving the problem with ℓ1 optimization, the computational load is significantly reduced. It is demonstrated by experiment and simulation that the proposed method can achieve high resolution and longer imaging depth compared to the FD-OCT method.

© 2011 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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    [CrossRef] [PubMed]
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2010 (2)

S. Vergnole, D. Lvesque, 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] [PubMed]

W. Qiu, and E. Skafidas, “Robust estimation of GCD with sparse coefficients,” Signal Process. 90, 972–976 (2010).
[CrossRef]

2009 (2)

M. S. Muller, and J. M. Fraser, “Contrast improvement in Fourier-domain optical coherence tomography through time gating,” J. Opt. Soc. Am. A 26, 969–976 (2009).
[CrossRef]

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, 12121–12131 (2009).
[CrossRef] [PubMed]

2008 (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

2007 (1)

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[CrossRef]

2005 (2)

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

E. J. Candès, and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

2004 (1)

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

2003 (1)

O. P. Bruno, and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28, 2049–2051 (2003).
[CrossRef] [PubMed]

2000 (1)

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

1998 (1)

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

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Andersen, P. E.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Belabas, N.

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

Boppart, S. A.

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

Bruno, O. P.

O. P. Bruno, and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28, 2049–2051 (2003).
[CrossRef] [PubMed]

Candès, E. J.

E. J. Candès, and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chaubell, J.

O. P. Bruno, and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28, 2049–2051 (2003).
[CrossRef] [PubMed]

Chen, M.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Ding, Z.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

Dorrer, C.

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

Dufour, M.

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fraser, J. M.

M. S. Muller, and J. M. Fraser, “Contrast improvement in Fourier-domain optical coherence tomography through time gating,” J. Opt. Soc. Am. A 26, 969–976 (2009).
[CrossRef]

Frosz, M. H.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Fujimoto, J. 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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gauthier, B.

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

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.

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Joffre, M.

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

Jørgensen, T. M.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Lamouche, G.

S. Vergnole, D. Lvesque, 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] [PubMed]

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[CrossRef]

Levesque, D.

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[CrossRef]

Likforman, J.

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

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,” Science 254, 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]

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

Lvesque, D.

S. Vergnole, D. Lvesque, 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] [PubMed]

Marks, D. L.

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

Meng, J.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Muller, M. S.

M. S. Muller, and J. M. Fraser, “Contrast improvement in Fourier-domain optical coherence tomography through time gating,” J. Opt. Soc. Am. A 26, 969–976 (2009).
[CrossRef]

Oldenburg, A. L.

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Qiu, W.

W. Qiu, and E. Skafidas, “Robust estimation of GCD with sparse coefficients,” Signal Process. 90, 972–976 (2010).
[CrossRef]

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Skafidas, E.

W. Qiu, and E. Skafidas, “Robust estimation of GCD with sparse coefficients,” Signal Process. 90, 972–976 (2010).
[CrossRef]

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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tao, T.

E. J. Candès, and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

Thrane, L.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Tycho, A.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Vergnole, S.

S. Vergnole, D. Lvesque, 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] [PubMed]

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[CrossRef]

Wang, C.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Wang, K.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Wu, T.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Xu, C.

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

Xu, L.

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, 12121–12131 (2009).
[CrossRef] [PubMed]

Yura, H. T.

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

IEEE Signal Process. Mag. (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (1)

E. J. Candès, and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[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]

S. A. Boppart, A. L. Oldenburg, C. Xu, and D. L. Marks, “Optical probes and techniques for molecular contrast enhancement in coherence imaging,” J. Biomed. Opt. 10, 041208 (2005).
[CrossRef]

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

M. S. Muller, and J. M. Fraser, “Contrast improvement in Fourier-domain optical coherence tomography through time gating,” J. Opt. Soc. Am. A 26, 969–976 (2009).
[CrossRef]

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

C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
[CrossRef]

Opt. Express (2)

S. Vergnole, D. Lvesque, 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] [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, 12121–12131 (2009).
[CrossRef] [PubMed]

Opt. Lett. (1)

O. P. Bruno, and J. Chaubell, “Inverse scattering problem for optical coherence tomography,” Opt. Lett. 28, 2049–2051 (2003).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, “Advanced modelling of optical coherence tomography systems,” Phys. Med. Biol. 49, 1307–1327 (2004).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. Vergnole, D. Levesque, G. Lamouche, M. Dufour, and B. Gauthier, “Characterization of thin layered structures using deconvolution techniques in time-domain and Fourier-domain optical coherence tomography,” Proc. SPIE 6796, 67961 (2007).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Signal Process. (1)

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Figures (5)

Fig. 1
Fig. 1

Fourier domain OCT setup.

Fig. 2
Fig. 2

Simulated imaging range of the proposed method.

Fig. 3
Fig. 3

Experiment results on the imaging depth of various OCT methods.

Fig. 4
Fig. 4

The reconstruction error as a function of SNR.

Fig. 5
Fig. 5

Cross-section images obtained by various methods using an OSA spectral resolution of 0.4 nm (The arrow in the figures indicates the imaging depth determined by Eq. (7); the vertical axis represents the depth and the range shown is 1 mm; the horizon axis represents lateral position and the range is 1 mm; the intensity in all the images is in logarithmic scale). (a) The proposed method; (b) The conventional FD-OCT method; (c) The non-uniform Fourier transform method [19]; (d) The conventional ART method.

Tables (1)

Tables Icon

Table 1 Comparison of computational time among the proposed method, the conventional ART method, and the conventional FD-OCT method

Equations (7)

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S ( λ ) = R r G ( λ ) + G ( λ ) 0 z m a x 0 z o a ( z ) a ( z ) e i 2 ( z z ) 2 π λ d z d z + G ( λ ) 0 z max a ( z ) cos ( 2 z π λ ) d z ,
Ax = b ,
A = ( G ( λ 1 ) e i 4 π λ 1 z 1 G ( λ 1 ) e i 4 π λ 1 z 2 G ( λ 1 ) e i 4 π λ 1 z M 1 G ( λ 1 ) e i 4 π λ 1 z M G ( λ 2 ) e i 4 π λ 2 z 1 G ( λ 2 ) e i 4 π λ 2 z 2 G ( λ 2 ) e i 4 π λ 2 z M 1 G ( λ 2 ) e i 4 π λ 2 z M G ( λ N ) e i 4 π λ N z 1 G ( λ N ) e i 4 π λ N z 2 G ( λ N ) e i 4 π λ N z M 1 G ( λ N ) e i 4 π λ N z M ) , x = ( a ( z 1 ) a ( z 2 ) a ( z M ) ) ,
b = ( S ( λ 1 ) S ( λ 2 ) S ( λ N ) ) R r ( G ( λ 1 ) G ( λ 2 ) G ( λ N ) ) .
min x x 1 subject to Ax = b .
min x x 1 subject to Ax b 2 < ɛ ,
z max = 1 4 n λ 2 δ λ ,

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