Abstract

Adaptive optical-coherence-domain reflectometry (OCDR) is performed by use of an adaptive interferometer and homodyne detection. The adaptive element of the interferometer is a photorefractive quantum-well device in a two-wave mixing geometry. The mixing self-adaptively maintains constant relative phase between the signal and reference waves and dynamically compensates gross movements of the sample or optical components as well as image speckle. The application described here is used for laser ranging into and through turbid media. Adaptive OCDR is a bridge between conventional optical coherence tomography and adaptive holographic optical coherence imaging. The insertion loss for the adaptive performance is -15 dB, but adaptive OCDR has potential applications for coherence tomography under conditions of large target motion and low background. We also demonstrate its potential application for optoacoustics and laser-based ultrasound detection.

© 2004 Optical Society of America

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2003

P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
[CrossRef]

L. Peng, P. Yu, D. D. Nolte, and M. R. Melloch, “High-speed adaptive interferometer for optical coherence-domain reflectometry through turbid media,” Opt. Lett. 26, 396–398 (2003).
[CrossRef]

P. Yu, L. Peng, D. D. Nolte, and M. R. Melloch, “Ultrasound detection through turbid media,” Opt. Lett. 28, 819–821 (2003).
[CrossRef] [PubMed]

2002

2001

2000

A. Lev, Z. Kolter, and B. G. Sfez, “Ultrasound tagged light imaging in turbid media in a reflectance geometry,” Opt. Lett. 25, 378–380 (2000).
[CrossRef]

R. Jones, D. D. Nolte, and M. R. Melloch, “Adaptive femtosecond optical pulse combining,” Appl. Phys. Lett. 77, 3692–3694 (2000).
[CrossRef]

1999

D. D. Nolte, “Semi-insulating semiconductor heterostructures: optoelectronic properties and applications,” J. Appl. Phys. 85, 6259–6289 (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] [PubMed]

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

1998

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Y. Ding, I. Lahiri, D. D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive-force detector,” J. Opt. Soc. Am. B 15, 2013–2017 (1998).
[CrossRef]

1997

L. Wang and X. Zhao, “Ultrasound-modulated optical tomography of absorbing objects buries in dense tissue-simulating turbid media,” Appl. Opt. 36, 7727–7782 (1997).
[CrossRef]

1996

R. M. Brubaker, Q. N. Wang, and D. D. Nolte, “Nonlocal photorefractive screening from hot electron velocity saturation on semiconductors,” Phys. Rev. Lett. 77, 4249–4252 (1996).
[CrossRef] [PubMed]

1995

1994

1993

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location on tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. (USA) 90, 3423 (1993).
[CrossRef]

1992

1991

J. Khoury, V. Ryan, C. Woods, and M. Cronin-Golomb, “Photorefractive optical lock-in detector,” Opt. Lett. 16, 1442–1444 (1991).
[CrossRef] [PubMed]

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

I. Rossomakhin and S. I. Stepanov, “Linear adaptive interferometers via diffusion recording in cubic photorefractive crystals,” Opt. Commun. 86, 199–204 (1991).
[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. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990

F. M. Davidson and L. Boutsikaris, “Homodyne detection using photorefractive materials as beamsplitters,” Opt. Eng. 29, 369–377 (1990).
[CrossRef]

1987

Bacher, G. D.

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Balasubramanian, S.

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

Boutsikaris, L.

F. M. Davidson and L. Boutsikaris, “Homodyne detection using photorefractive materials as beamsplitters,” Opt. Eng. 29, 369–377 (1990).
[CrossRef]

Brubaker, R. M.

R. M. Brubaker, Q. N. Wang, and D. D. Nolte, “Nonlocal photorefractive screening from hot electron velocity saturation on semiconductors,” Phys. Rev. Lett. 77, 4249–4252 (1996).
[CrossRef] [PubMed]

R. M. Brubaker, Q. N. Wang, D. D. Nolte, E. S. Harmon, and M. R. Melloch, “Steady-state four-wave mixing in photorefractive quantum wells with femtosecond pulses,” J. Opt. Soc. Am. B 11, 1038–1044 (1994).
[CrossRef]

Carr, S.

Carrasco, L. A.

Chance, B.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location on tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. (USA) 90, 3423 (1993).
[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]

Cheriaux, G.

Cronin-Golomb, M.

Cubel, T.

Davidson, F. M.

F. M. Davidson and L. Boutsikaris, “Homodyne detection using photorefractive materials as beamsplitters,” Opt. Eng. 29, 369–377 (1990).
[CrossRef]

Davies, D. E. N.

Ding, Y.

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

Y. Ding, I. Lahiri, D. D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive-force detector,” J. Opt. Soc. Am. B 15, 2013–2017 (1998).
[CrossRef]

Dobre, G.

Dunning, G. J.

Fitzke, F. W.

Flores, M. A. C.

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]

Frech, P. M. W.

P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
[CrossRef]

Fujimoto, J. G.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

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]

Harmon, E. S.

He, L.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location on tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. (USA) 90, 3423 (1993).
[CrossRef]

Hee, M. R.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hisaka, M.

Huang, D.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ing, R. K.

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Jackson, D. A.

Joffre, M.

Jones, R.

R. Jones, D. D. Nolte, and M. R. Melloch, “Adaptive femtosecond optical pulse combining,” Appl. Phys. Lett. 77, 3692–3694 (2000).
[CrossRef]

Kang, K.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, “Highly sensitive object location on tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. (USA) 90, 3423 (1993).
[CrossRef]

Kawata, S.

Khoury, J.

Klein, M. B.

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Kolter, Z.

Kruger, R. A.

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Lahiri, I.

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Y. Ding, I. Lahiri, D. D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive-force detector,” J. Opt. Soc. Am. B 15, 2013–2017 (1998).
[CrossRef]

Lepetit, L.

Lev, A.

Lin, C. P.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

López, A. A.

Melloch, M. R.

P. Yu, L. Peng, D. D. Nolte, and M. R. Melloch, “Ultrasound detection through turbid media,” Opt. Lett. 28, 819–821 (2003).
[CrossRef] [PubMed]

P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
[CrossRef]

L. Peng, P. Yu, D. D. Nolte, and M. R. Melloch, “High-speed adaptive interferometer for optical coherence-domain reflectometry through turbid media,” Opt. Lett. 26, 396–398 (2003).
[CrossRef]

D. D. Nolte, T. Cubel, L. J. Pyrak-Nolte, and M. R. Melloch, “Adaptive beam combining and interferometry using photorefractive quantum wells,” J. Opt. Soc. Am. B 18, 195–205 (2001).
[CrossRef]

R. Jones, D. D. Nolte, and M. R. Melloch, “Adaptive femtosecond optical pulse combining,” Appl. Phys. Lett. 77, 3692–3694 (2000).
[CrossRef]

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

R. M. Brubaker, Q. N. Wang, D. D. Nolte, E. S. Harmon, and M. R. Melloch, “Steady-state four-wave mixing in photorefractive quantum wells with femtosecond pulses,” J. Opt. Soc. Am. B 11, 1038–1044 (1994).
[CrossRef]

Mixcoatl, J. C.

Monchalin, J.-P.

R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Montero, P. R.

Mustata, M.

P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
[CrossRef]

Nolte, D. D.

P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
[CrossRef]

L. Peng, P. Yu, D. D. Nolte, and M. R. Melloch, “High-speed adaptive interferometer for optical coherence-domain reflectometry through turbid media,” Opt. Lett. 26, 396–398 (2003).
[CrossRef]

P. Yu, L. Peng, D. D. Nolte, and M. R. Melloch, “Ultrasound detection through turbid media,” Opt. Lett. 28, 819–821 (2003).
[CrossRef] [PubMed]

D. D. Nolte, T. Cubel, L. J. Pyrak-Nolte, and M. R. Melloch, “Adaptive beam combining and interferometry using photorefractive quantum wells,” J. Opt. Soc. Am. B 18, 195–205 (2001).
[CrossRef]

R. Jones, D. D. Nolte, and M. R. Melloch, “Adaptive femtosecond optical pulse combining,” Appl. Phys. Lett. 77, 3692–3694 (2000).
[CrossRef]

S. Balasubramanian, I. Lahiri, Y. Ding, M. R. Melloch, and D. D. Nolte, “Two-wave mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68, 863–869 (1999).
[CrossRef]

D. D. Nolte, “Semi-insulating semiconductor heterostructures: optoelectronic properties and applications,” J. Appl. Phys. 85, 6259–6289 (1999).
[CrossRef]

I. Lahiri, L. J. Pyrak-Nolte, D. D. Nolte, M. R. Melloch, R. A. Kruger, G. D. Bacher, and M. B. Klein, “Laser-based ultrasound detection using photorefractive quantum wells,” Appl. Phys. Lett. 73, 1041–1043 (1998).
[CrossRef]

Y. Ding, I. Lahiri, D. D. Nolte, G. J. Dunning, and D. M. Pepper, “Electric-field correlation of femtosecond pulses by use of a photoelectromotive-force detector,” J. Opt. Soc. Am. B 15, 2013–2017 (1998).
[CrossRef]

R. M. Brubaker, Q. N. Wang, and D. D. Nolte, “Nonlocal photorefractive screening from hot electron velocity saturation on semiconductors,” Phys. Rev. Lett. 77, 4249–4252 (1996).
[CrossRef] [PubMed]

R. M. Brubaker, Q. N. Wang, D. D. Nolte, E. S. Harmon, and M. R. Melloch, “Steady-state four-wave mixing in photorefractive quantum wells with femtosecond pulses,” J. Opt. Soc. Am. B 11, 1038–1044 (1994).
[CrossRef]

Peng, L.

P. Yu, L. Peng, D. D. Nolte, and M. R. Melloch, “Ultrasound detection through turbid media,” Opt. Lett. 28, 819–821 (2003).
[CrossRef] [PubMed]

L. Peng, P. Yu, D. D. Nolte, and M. R. Melloch, “High-speed adaptive interferometer for optical coherence-domain reflectometry through turbid media,” Opt. Lett. 26, 396–398 (2003).
[CrossRef]

Pepper, D. M.

Podoleanu, A. G.

Puliafito, C. A.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
[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,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Pyrak-Nolte, L. J.

D. D. Nolte, T. Cubel, L. J. Pyrak-Nolte, and M. R. Melloch, “Adaptive beam combining and interferometry using photorefractive quantum wells,” J. Opt. Soc. Am. B 18, 195–205 (2001).
[CrossRef]

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I. Rossomakhin and S. I. Stepanov, “Linear adaptive interferometers via diffusion recording in cubic photorefractive crystals,” Opt. Commun. 86, 199–204 (1991).
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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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P. Yu, M. Mustata, J. J. Turek, P. M. W. Frech, M. R. Melloch, and D. D. Nolte, “Holographic optical coherence imaging of tumor spheroids,” Appl. Phys. Lett. 83, 575–577 (2003).
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J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
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Yu, P.

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

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[CrossRef]

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[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. (USA)

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[CrossRef]

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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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Figures (11)

Fig. 1
Fig. 1

Schematic drawing of adaptive homodyne interferometry. Signal and reference fields from the same source S(ω-ωs) are mixed by a PRQW device with a complex transfer function of Q(ω-ωq). The reference is phase modulated by ϕ(t), and by being reflected back from a sample, the signal has a delay τ in time. Homodyne signals from the mixed fields are detected through a spectrometer with a transfer function of D(ω-ωd). A lock-in amplifier is used to readout the homodyne signal with ϕ(t) as synchronization.

Fig. 2
Fig. 2

Adaptive OCDR experimental setup.

Fig. 3
Fig. 3

Pulse-characterization results: (a) Spectrum and second-harmonic intensity autocorrelation of 5-nm-bandwidth nominal pulses. (b) Spectrum, second-harmonic intensity autocorrelation, and electric field autocorrelation of 12-nm-band width pulses. The electric field correlation function gives a FWHM of 180 fs, corresponding to a 27-µm depth resolution in reflectometry.

Fig. 4
Fig. 4

Depth resolution of adaptive OCDR (solid curve) and conventional OCDR (dashed curve) for θ=0.01 rad and W=1, 0.5, 0.25 mm. The minimum distinguishable pulse duration in this case is 20 fs for the 1-mm window. The lower limit of adaptive OCDR depth resolution is 10 µm for the 1-mm window.

Fig. 5
Fig. 5

(a) Effective modulation index m versus phase-modulation amplitude. (b) Homodyne signal versus phase-modulation amplitude, experiment results (data points), and theoretical curve (solid curve). Both show a maximum at Δϕπ/3.

Fig. 6
Fig. 6

Adaptive OCDR delay-line traces by narrow-band homodyne detection. The wavelengths are the detection wavelengths. (a) Experiment results with 0.5-nm detection bandwidth. (b) Simulation results under the same experimental conditions.

Fig. 7
Fig. 7

Homodyne signal with increasing detection bandwidth. The homodyne signals with broadband pulses were detected at 0.5-, 1-, 2.5-, 4-, and 5-nm detection bandwidths.

Fig. 8
Fig. 8

Adaptive OCDR delay scan trace by broadband homodyne detection: (a) Experimental results with 5-nm-bandwidth laser pulses centered at 833 nm. (b) Simulations for the same conditions.

Fig. 9
Fig. 9

Adaptive OCDR delay scan traces by broadband homodyne detection: (a) Experimental result with 12-nm-bandwidth laser pulses centered at 833 nm. (b) Simulation under nominally the same conditions, but assuming transform-limited pulses.

Fig. 10
Fig. 10

Adaptive OCDR traces of a single reflection behind a turbid medium with total travel lengths from 0 to 16.4 MFPs (redrawn from Ref. 27). Data for 0–9.8 MFPs were measured with 200-µW incident power, and for 9.8–16.4 MFPs were measured with 200-mW incident power.

Fig. 11
Fig. 11

Laser-based ultrasound (LBU) signal versus increasing optical thickness from 0.59 MFP to 11 MFP (redrawn from Ref. 28). The signal was detected at the quadrature wavelength with 1-nm detection bandwidth at zero relative time delay. Beam-intensity ratio β at the PRQW devices was maintained at a value of 3 by decreasing the reference intensity while increasing the optical thickness of the turbid medium.

Equations (38)

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Es(ω)=Iss(ω-ωs)exp(iωτ),
Er(ω)=Irs(ω-ωs),
n˜(x, ωs)=n˜(ωs)+δn˜(ωs)m(τ)cos(Kx+ϕP+ωsτ),
n˜(ω)=n(ω)+iα(ω)2k,δn˜(ω)=δn(ω)+iδα(ω)2k,
x0(τ)=cτ2 sin(θ).
|δId(ω, τ)|1W-W/2W/2m(x, τ)dx.
|δId(ω, τ)|erf[4 ln(2)]1/2[W/2+x0(τ)]Δx+erf[4 ln(2)]1/2[W/2-x0(τ)]Δx,
m(x, τ)=2IsIrIs+IrΓ[τ-2x sin(θ)/c],
Δτ=ξ1Δω,
Δx=cΔτ2 sin(θ)=c2 sin(θ)ξ1Δω.
ϕ(t)=Δϕ sin(Ωt),
m=m(τ)Ωπ0π/Ω cos[Δϕ sin(Ωt)]dt=m(τ)J0(Δϕ),
δPd(t)sin(Δϕ)J0(Δϕ).
γ(ω-ωq)=δn(ω)kL/cos(θ)+iδα(ω)L/2 cos(θ)=2η(ω-ωq)exp[iψ(ω)],
ψ(ω)=tan-1δα(ω)2δn(ω)k,
q0(ω)=exp[in(ω)kL/cos(θ)]exp[-α(ω)L/2]
q1(ω-ωq)=q1(ω-ωq)exp{i[ψ(ω)+ϕP+π/2+ωsτ]},
q1(ω-ωq)=q0(ω)m(τ)η(ω-ωq).
Es(ω, L)=q0(ω)Iss(ω-ωs)exp(iωτ),
Er(ω, L)=q1(ω-ωq)Irs(ω-ωs)×exp{i[ψ(ω)+ϕP+π/2+ωsτ]},
Ed(ω)=q0(ω)Iss(ω-ωs)exp(iωτ)+q1(ω-ωq)Irs(ω-ωs)×exp{i[ψ(ω)+ϕP+π/2+iωsτ]}.
Pd(ω)=IsQ0(ω)S(ω-ωs)+Q0(ω-ω0)IrIsS(ω-ωs)cos[ψ(ω)+ϕP+π/2-(ω-ωs)τ],
Q0(ω)=|q0(ω)|2,
Q0(ω-ω0)=2|q1(ω-ωq)||q0(ω)|,
S(ω-ωs)=|s(ω-ωs)|2.
PΩ(ω; ωs, ωq)=2IrIs|q1(ω-ωq)||q0(ω)|S(ω-ωs)×sin[ψ(ω)+ϕP-(ω-ωs)τ+Δϕ cos Ωt].
PΩ=0PΩ(ω; ωs, ωq)D(ω-ωd)dω.
PΩ=2IrIs|q1(ωd-ωq)||q0(ωd)|S(ωd-ωs)sin[ψ(ωd)+ϕP-(ωd-ωs)τ+Δϕ cos Ωt]Δωd,
ψ(ωd)+ϕP=0,π±π/2.
SNconv=2PrPsPr+PsηdhνB,
SN=exp(-αL)4PrPr+Psη(ω)[J0(Δϕ)sin(Δϕ)]2SNconv.
δPdexp(-αL)η(ω0)mPrPcorPcor,
(δPd)convPrPcorPcor.
Pdexp(-αL)η(ω0)m2PrPs,
δPd(ωq, τ; t)=2 exp[-α(ωd)L]×m(τ)η(ωd)Is(ωd)Ir(ωd)Δωd×sin[-(ωd-ωs)τ+ϕ(t)],
δPd(ωd, 0; t)=2 exp[-α(ωd)L]m(0)η(ωd)×Is(ωd)Ir(ωd)Δωd sin4πλd(t).
Δdmin=λ4πexp[α(ωd)L/2]hνB2mη(ωd)ηdIr(ωd)Δωd.
Δdmin=λ4πexp[α(ωq, F)L/2]hν2mη(ωq)ηd×1ηΔω,

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