Abstract

The superior resolution of optical coherence tomography (OCT) with respect to alternative imaging modalities makes it highly attractive, and some of its applications are already in extensive clinical use. However, one of the major limitations of OCT is that the tomographic picture it generates is depth-limited to approximately 1 mm in most biological tissues. This is mainly due to the spatially turbulent nature of the tissue, which leads to scattering. Moreover, this technique is extremely sensitive to temporal variations in the medium. We show that insensitivity to temporal and spatial turbulence may be gained by replacing the linear detector with an ultrasensitive two-photon detector. These results have striking implications on the attainable penetration depth of optical imaging and on its sensitivity to sample motion.

© 2013 Optical Society of America

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2012 (1)

T. Michaeli and Y. C. Eldar, “Xampling at the rate of innovation,” IEEE Trans. Signal Process. 60, 1121–1133 (2012).
[CrossRef]

2011 (5)

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol. 95, 171–177 (2011).
[CrossRef]

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

2010 (3)

T. Kubo and T. Asakura, “Optical coherence tomography imaging: current status and future perspectives,” Cardiovasc. Interv. Ther. 25, 2–10 (2010).
[CrossRef]

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Quantitatively characterizing fluctuations of dielectric susceptibility of tissue with Fourier domain optical coherence tomography,” J. Opt. Soc. Am. A 27, 2588–2592 (2010).
[CrossRef]

2009 (3)

2008 (1)

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2, 238–241 (2008).
[CrossRef]

2007 (2)

A. Pe’er, Y. Bromberg, B. Dayan, Y. Silberberg, and A. A. Friesem, “Broadband sum-frequency generation as an efficient two-photon detector for optical tomography,” Opt. Express 15, 8760–8769 (2007).
[CrossRef]

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

2005 (1)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

2004 (4)

2003 (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

2002 (2)

J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. 27, 2076–2078 (2002).
[CrossRef]

J. F. de Boer, and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

2001 (1)

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

1999 (2)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

1998 (2)

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

M. J. Everett, K. Schoenenberger, B. W. Colston, and L. B. Da Silva, “Birefringence characterization of biological tissue by use of optical coherence tomography,” Opt. Lett. 23, 228–230 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (1)

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

1994 (1)

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

1993 (1)

M. S. Handcock and M. L. Stein, “A Bayesian analysis of kriging,” Technometrics 35, 403–410 (1993).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

1989 (1)

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

1987 (1)

1956 (1)

R. Hanbury-Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 177, 1046–1048 (1956).
[CrossRef]

Adler, D. C.

Akasaka, T.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Allemann, Y.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Arbustini, E.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Asakura, T.

T. Kubo and T. Asakura, “Optical coherence tomography imaging: current status and future perspectives,” Cardiovasc. Interv. Ther. 25, 2–10 (2010).
[CrossRef]

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Beaud, P.

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Boitier, F.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[CrossRef]

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Brambilla, E.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Brezinski, M. E.

M. E. Brezinski, Optical Coherence Tomography: Principles and Applications (Academic, 2006).

Bromberg, Y.

Carr, S.

Cense, B.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Colston, B. W.

Costa, M.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Da Silva, L. B.

Davies, D. E. N.

Dayan, B.

de Boer, J.

de Boer, J. F.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[CrossRef]

J. F. de Boer, and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef]

Deacon, K. S.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Delaye, P.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

Di Mario, C.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Dubreuil, N.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

Eckhaus, M. A.

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

Eldar, Y. C.

T. Michaeli and Y. C. Eldar, “Xampling at the rate of innovation,” IEEE Trans. Signal Process. 60, 1121–1133 (2012).
[CrossRef]

El-Zaiat, S. Y.

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

Everett, M. J.

Fabre, C.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[CrossRef]

Fercher, A. F.

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

Ferri, F.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Friberg, A. T.

Friesem, A. A.

Fujimoto, J. G.

T. H. Ko, D. C. Adler, J. G. Fujimoto, D. Mamedov, V. Prokhorov, V. Shidlovski, and S. Yakubovich, “Ultrahigh resolution optical coherence tomography imaging with a broadband superluminescent diode light source,” Opt. Express 12, 2112–2119 (2004).
[CrossRef]

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

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Geitzenauer, W.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol. 95, 171–177 (2011).
[CrossRef]

Gilgen, H. H.

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Ginzburg, P.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2, 238–241 (2008).
[CrossRef]

Godard, A.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Grube, E.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Guagliumi, G.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Hanbury-Brown, R.

R. Hanbury-Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 177, 1046–1048 (1956).
[CrossRef]

Handcock, M. S.

M. S. Handcock and M. L. Stein, “A Bayesian analysis of kriging,” Technometrics 35, 403–410 (1993).
[CrossRef]

Hausler, G.

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

Hayat, A.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2, 238–241 (2008).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Hitzenberger, C. K.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol. 95, 171–177 (2011).
[CrossRef]

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

Hodel, W.

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Jang, I.-K.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Kaltenbaek, R.

Kamp, G.

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

Knuttel, A.

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

Ko, T. H.

Kubo, T.

T. Kubo and T. Asakura, “Optical coherence tomography imaging: current status and future perspectives,” Cardiovasc. Interv. Ther. 25, 2–10 (2010).
[CrossRef]

Kucher, N.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Kumar, G.

Lajunen, H.

Lancis, J.

Lavoie, J.

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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Lindner, M. W.

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

Lipp, E.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

Lugiato, L. A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Mamedov, D.

Meyers, R. E.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Michaeli, T.

T. Michaeli and Y. C. Eldar, “Xampling at the rate of innovation,” IEEE Trans. Signal Process. 60, 1121–1133 (2012).
[CrossRef]

Milner, T. E.

J. F. de Boer, and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef]

Mintz, G. S.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Mohacsi, P.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Murphy, T. E.

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

Nelson, J. S.

Nevet, A.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

Novak, R. P.

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Orenstein, M.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2, 238–241 (2008).
[CrossRef]

Ozaki, Y.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Park, B. H.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[CrossRef]

Pe’er, A.

Pierce, M. C.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[CrossRef]

Pinto, F.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Prati, F.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Prokhorov, V.

Puliafato, C.

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

Regar, E.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Resch, K. J.

Rosencher, E.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[CrossRef]

Roth, J. M.

Salathé, R. P.

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

Salem, R.

Schmidt-Erfurth, U. M.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol. 95, 171–177 (2011).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Quantitatively characterizing fluctuations of dielectric susceptibility of tissue with Fourier domain optical coherence tomography,” J. Opt. Soc. Am. A 27, 2588–2592 (2010).
[CrossRef]

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996).
[CrossRef]

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

Schoenenberger, K.

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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Seiler, C.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Sergienko, A. V.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

Serruys, P. W. J.

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Shidlovski, V.

Shih, Y.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Silberberg, Y.

Stein, M. L.

M. S. Handcock and M. L. Stein, “A Bayesian analysis of kriging,” Technometrics 35, 403–410 (1993).
[CrossRef]

Stengel, S. M.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Stifter, D.

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Strasswimmer, J.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[CrossRef]

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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Tearney, G.

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Teich, M. C.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

Torres-Company, V.

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Twiss, R. Q.

R. Hanbury-Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 177, 1046–1048 (1956).
[CrossRef]

van der Zee, P.

P. van der Zee, “Measurement and modelling of the optical properties of human tissue in the near infrared,” Ph. D. dissertation (Department of Medical Physics and Bioengineering, University College London, 1993).

van Gemert, M. J. C.

Xiang, S. H.

Xu, C.

Yadlowsky, M.

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Yakubovich, S.

Youngquist, R. C.

Yun, S. H.

Yung, K. M.

Zimmerli, M.

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

Appl. Phys. B (1)

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Br. J. Ophthalmol. (1)

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol. 95, 171–177 (2011).
[CrossRef]

Cardiovasc. Interv. Ther. (1)

T. Kubo and T. Asakura, “Optical coherence tomography imaging: current status and future perspectives,” Cardiovasc. Interv. Ther. 25, 2–10 (2010).
[CrossRef]

Eur. Heart J. (1)

F. Prati, E. Regar, G. S. Mintz, E. Arbustini, C. Di Mario, I.-K. Jang, T. Akasaka, M. Costa, G. Guagliumi, E. Grube, Y. Ozaki, F. Pinto, and P. W. J. Serruys, “Expert review document on methodology, terminology and clinical applications of optical coherence tomography: physical principles, methodology of image acquisition and clinical application for assessment of coronary arteries and atherosclerosis,” Eur. Heart J. 31, 401–415 (2010).
[CrossRef]

Heart (1)

S. M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart 86, 432–437 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

IEEE Trans. Signal Process. (1)

T. Michaeli and Y. C. Eldar, “Xampling at the rate of innovation,” IEEE Trans. Signal Process. 60, 1121–1133 (2012).
[CrossRef]

J. Biomed. Opt. (3)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef]

J. F. de Boer, and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

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

J. Invest. Dermatol. (1)

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” J. Invest. Dermatol. 123, 458–463 (2004).
[CrossRef]

J. Lightwave Technol. (1)

H. H. Gilgen, R. P. Novak, R. P. Salathé, W. Hodel, and P. Beaud, “Submillimeter optical reflectometry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nat. Commun. (1)

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425 (2011).
[CrossRef]

Nat. 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 micro-optical coherence tomography,” Nat. Med. 17, 1010–1014 (2011).
[CrossRef]

Nat. Photonics (1)

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics 2, 238–241 (2008).
[CrossRef]

Nat. Phys. (1)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[CrossRef]

Nature (1)

R. Hanbury-Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 177, 1046–1048 (1956).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Lett. (6)

Phys. Med. Biol. (1)

J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett. 107, 253601 (2011).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[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. Puliafato, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Technometrics (1)

M. S. Handcock and M. L. Stein, “A Bayesian analysis of kriging,” Technometrics 35, 403–410 (1993).
[CrossRef]

Other (4)

P. van der Zee, “Measurement and modelling of the optical properties of human tissue in the near infrared,” Ph. D. dissertation (Department of Medical Physics and Bioengineering, University College London, 1993).

M. E. Brezinski, Optical Coherence Tomography: Principles and Applications (Academic, 2006).

W. Drexler and J. G. Fujimoto, eds., Optical Coherence Tomography: Technology and Applications (Springer, 2008).

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematics of TPA in a semiconductor direct-bandgap material (CB, conduction band; VB, valence band). (b) SO-OCT setup: a chaotic NIR source enters a Michelson interferometer through a λ>1μm filter and is detected at the output by TPA in a GaAs PMT. A phase modulator located before the sample generates temporal phase variations.

Fig. 2.
Fig. 2.

(a) First-order OCT measurement (blue) of a single reflector resulting in a high-frequency carrier multiplied by an exponentially decaying envelope, in addition to a constant background (green). (b) SO-OCT measurement of a single reflector resulting in frequency content around DC (green) in addition to high-frequency terms. The inset is the spectrum of the source. (c) Standard first-order OCT through temporally variant phase. The inset is a schematic of one-photon absorption. (d) SO-OCT through temporally variant phase. The inset is a schematic of TPA.

Fig. 3.
Fig. 3.

Sparsely sampled interferogram measured through temporally variant phase. The deliberate turbulence erases the high frequencies of the interferogram, enabling an ultralow sampling rate.

Fig. 4.
Fig. 4.

SO-OCT through spatially variant phase implemented using a phase-only SLM. The inset is a schematic of the setup.

Fig. 5.
Fig. 5.

SO-OCT measurement of a single reflector with a λ/4 waveplate located before the sample, generating nearly orthogonal polarizations and therefore reduced visibility of the fringes only. The inset is a schematic of the setup.

Fig. 6.
Fig. 6.

Value of the peak of the interferogram’s envelope in first- and second-order OCT for imaging through turbid media as a function of depth [Eqs. (4) and (5)] for L0=4μm, δn2=0.012, and a source of wavelength 1.3 μm and coherence time τc=100fs. The inset visualizes the frequency content of the two modalities along with the frequency response of the low-pass filter (LPF) caused by the phase variations.

Equations (11)

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S(1)(τ)=C1+kakg(1)(τtk),
S˜(1)(τ)=A0TS(1)(τΔτ(x,y,t))dxdydt,
SLF(2)(τ)=C2+kak2exp[2|τtk|τc]+klkakalcos(ω0(tktl))exp[|τtk|+|τtl|τc],
α1=τcτ˜cexp{τc2ω02Δτ22τ˜c2},
α2=τcτc+2πΔτ2.
S(2)(τ)=|E(tτ)+kakE(ttk)|4=3|E(tτ)+kakE(ttk)|22=3(S(1)(τ))2.
4πδn2L0(m1)(1+L02ω2)m,
Δτ2=(1c0Lδn(0,0,z)dz)2=1c20L0LRδn(z1z2)dz1dz2=2L0δn2c(LL0(1eLL0)),
S˜(1)(τ)=αexp[πτ22τ˜c,12]cos(ω˜0τ).
α1=τcτ˜c,1exp{τc2ω0Δτ22τ˜c,12}.
S˜(2)(τ)=1+α2exp[πτ2τ˜c,22],

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