Abstract

Quantum optical coherence tomography (QOCT) makes use of an entangled twin-photon light source to carry out axial optical sectioning. We have probed the longitudinal structure of a sample comprising multiple surfaces in a dispersion-cancelled manner while simultaneously measuring the group-velocity dispersion of the interstitial media between the reflecting surfaces. The results of the QOCT experiments are compared with those obtained from conventional optical coherence tomography (OCT).

© 2004 Optical Society of America

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References

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  4. 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]
  5. J. M. Schmitt, �??Optical coherence tomography (OCT): A review,�?? IEEE J. Sel. Topics Quantum Electron. 5, 1205�??1215 (1999)
    [CrossRef]
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    [CrossRef]
  7. A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, �??Quantum-optical coherence tomography with dispersion cancellation,�?? Phys. Rev. A 65, 053817 (2002)
    [CrossRef]
  8. M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, �??Demonstration of dispersion-canceled quantumoptical coherence tomography,�?? Phys. Rev. Lett. 91, 083601 (2003)
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. T. S. Larchuk, M. C. Teich, and B. E. A. Saleh, �??Nonlocal cancellation of dispersive broadening in Mach-Zehnder interferometers�?? Phys. Rev. A 52, 4145�??4154 (1995)
    [CrossRef] [PubMed]
  13. L. Mandel and E.Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995), ch. 22
  14. C. K. Hong, Z. Y. Ou, and L. Mandel, �??Measurement of subpicosecond time intervals between two photons by interference,�?? Phys. Rev. Lett. 59, 2044�??2046 (1987)
    [CrossRef] [PubMed]
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991)
    [CrossRef]
  16. 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. Commun. 204, 67�??74 (2002)
    [CrossRef]
  17. M. Bass, Ed., Handbook of Optics, Vol. II, 2nd ed. (McGraw�??Hill, New York, 1995), ch. 33, p. 67
  18. <a href="http://www.cvdmaterials.com/pdf/Zinc%20Selenide.pdf">http://www.cvdmaterials.com/pdf/Zinc%20Selenide.pdf</a>

Appl. Opt. (1)

IEEE J. Sel. Topics Quantum Electron (1)

J. M. Schmitt, �??Optical coherence tomography (OCT): A review,�?? IEEE J. Sel. Topics Quantum Electron. 5, 1205�??1215 (1999)
[CrossRef]

Opt. Commun. (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. Commun. 204, 67�??74 (2002)
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

T. S. Larchuk, M. C. Teich, and B. E. A. Saleh, �??Nonlocal cancellation of dispersive broadening in Mach-Zehnder interferometers�?? Phys. Rev. A 52, 4145�??4154 (1995)
[CrossRef] [PubMed]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, �??Quantum-optical coherence tomography with dispersion cancellation,�?? Phys. Rev. A 65, 053817 (2002)
[CrossRef]

J. D. Franson, �??Nonlocal cancellation of dispersion,�?? Phys. Rev. A 45, 3126�??3132 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, �??Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,�?? Phys. Rev. A 45, 6659�??6665 (1992)
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, �??Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,�?? Phys. Rev. Lett. 68, 2421�??2424 (1992)
[CrossRef] [PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, �??Demonstration of dispersion-canceled quantumoptical coherence tomography,�?? Phys. Rev. Lett. 91, 083601 (2003)
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, �??Measurement of subpicosecond time intervals between two photons by interference,�?? Phys. Rev. Lett. 59, 2044�??2046 (1987)
[CrossRef] [PubMed]

Proc. SPIE (1)

A. F. Fercher and E. Roth, �??Ophthalmic laser interferometry,�?? Proc. SPIE 658, 48�??51 (1986)
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, �??Optical coherence tomography�??principles and applications,�?? Rep. Prog. Phys. 66, 239�??303 (2003).
[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]

Other (4)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991)
[CrossRef]

L. Mandel and E.Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995), ch. 22

M. Bass, Ed., Handbook of Optics, Vol. II, 2nd ed. (McGraw�??Hill, New York, 1995), ch. 33, p. 67

<a href="http://www.cvdmaterials.com/pdf/Zinc%20Selenide.pdf">http://www.cvdmaterials.com/pdf/Zinc%20Selenide.pdf</a>

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of quantum optical coherence tomography (QOCT). A monochromatic laser of angular frequency ωp pumps a nonlinear crystal (NLC), generating pairs of entangled photons. BS stands for beam splitter and τ is an adjustable temporal delay. D1 and D2 are single-photon-counting detectors that feed a coincidence circuit indicated by the symbol ⊗. The outcome of an experiment is the coincidence rate C(τ).

Fig. 2.
Fig. 2.

Experimental arrangement for quantum/classical optical coherence tomography (QOCT/OCT). A monochromatic Kr+-ion laser operated at λ p =406 nm pumps an 8-mm-thick type-I LiIO3 nonlinear crystal (NLC) after passage through a prism, P, and an aperture (not shown), which remove the spontaneous glow of the laser tube. BD stands for beam dump (to block the pump), BS for beam splitter, M for mirror, A for 2.2-mm aperture, F for long-pass filter with cutoff at 725 nm, and D for single-photon-counting detector (EG&G, SPCM-AQR-15). The quantity τ represents a temporal delay. For QOCT scans, the dotted components M1, M2 and D3 are removed, the delay τ at the top of the figure is swept, and the coincidence rate C(τ) is measured within a 3.5-nsec time window. For OCT scans, beam 1 is discarded (beam 2 serves as the short-coherence-time light source), mirror M1 is scanned thereby sweeping the delay τ at the bottom of the figure, and the singles rate I(τ) is recorded.

Fig. 3.
Fig. 3.

QOCT and OCT normalized interferograms for two d=90-µm fused-silica (FS) windows separated by D=4.5 mm of air. The four surfaces that comprise the sample are numbered, as shown at the top of the figure. The abscissa is the scaled temporal delay /2, which represents the displacement of the delay line for both experiments (OCT and QOCT). (a) Coincidence rate C(τ) normalized to the constant background Λ0 (the normalized QOCT interferogram). Features labelled (j, j) correspond to reflections from the jth surface whereas those labelled (j, k), jk, correspond to cross-interference between pairs of surfaces. The outermost clusters of features, labelled ΛF and ΛB, correspond to the triplets of terms appearing in Eq. (9). The center cluster, labelled ΛFB, corresponds to the terms appearing in Eq. (10), in which (1,4) and (2,3) overlap. The power of the pump laser was 7 mW, which resulted in a power in each of the downconverted beams of 43 pW. (b) Singles rate I(τ) normalized to constant background (the normalized OCT interferogram). The power of the pump laser was 13 mW, resulting in a downconverted-beam power of 80 pW.

Fig. 4.
Fig. 4.

QOCT and OCT normalized interferograms for two d=90-µm fused-silica (FS) windows sandwiching an L=12-mm window of highly dispersive ZnSe. As shown at the top of the figure, the ZnSe is slightly canted with respect to the incident beam (arrow) to divert back-reflections. The four surfaces that comprise the sample are numbered, as shown at the top of the figure. The abscissa is the scaled temporal delay /2, which represents displacement of the delay line for both experiments (OCT and QOCT). (a) Coincidence rateC(τ) normalized to the constant background Λ0 (the QOCT normalized interferogram). Features labelled (j, j) correspond to reflections from the jth surface whereas those labelled (j, k), jk, correspond to cross-interference between pairs of surfaces. The outermost clusters of features, labelled ΛF and ΛB, correspond to the features appearing in the first and second terms of Eq. (13), respectively. The center cluster, labelled ΛFBdisp, corresponds to the terms appearing in Eq. (14), in which (1,4) and (2,3) overlap. The power of the pump laser was 120 mW, which resulted in a power in each of the downconverted beams of 685 pW. (b) Singles rate I(τ) normalized to constant background (the normalized OCT interferogram). The power of the pump laser was 120 mW, resulting in a downconverted-beam power of 685 pW.

Equations (20)

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ψ = d Ω ζ ( Ω ) | ω 0 + Ω 1 ω 0 Ω 2 ,
H ( ω ) = 0 d z r ( z , ω ) e i 2 ϕ ( z , ω ) .
C ( τ ) Λ 0 Re { Λ ( 2 τ ) } ,
Λ 0 = d Ω H ( ω 0 + Ω ) 2 S ( Ω )
Λ ( τ ) = d Ω H ( ω 0 + Ω ) H * ( ω 0 Ω ) S ( Ω ) e i Ω τ
H ( ω ) = H F ( ω ) + H B ( ω ) e i ω τ d e i ω τ D ,
Λ 0 = j = 1 4 r j 2
Λ ( τ ) = Λ F ( τ ) + Λ B ( τ 2 τ 0 ) + Λ F B ( τ τ 0 ) ,
Λ F ( τ ) = r 1 2 s ( τ ) + r 2 2 s ( τ 2 τ d )
+ 2 Re { r 1 r 2 * s ( τ τ d ) e i ω 0 τ d } ,
Λ B ( τ ) = r 3 2 s ( τ ) + r 4 2 s ( τ 2 τ d )
+ 2 Re { r 3 r 4 * s ( τ τ d ) e i ω 0 τ d } ,
Λ FB ( τ ) = 2 Re { [ r 1 r 3 * s ( τ ) + ( r 1 r 4 * e i ω 0 τ d + r 2 r 3 * e i ω 0 τ d ) s ( τ τ d )
+ r 2 r 4 * s ( τ 2 τ d ) e i ω 0 τ 0 ] ,
H disp ( ω ) = H F ( ω ) + α H B ( ω ) e i ω τ d e i 2 β ( ω ) L ,
Λ 0 = j = 1 2 r j 2 + α 2 j = 3 4 r j 2 ,
Λ ( τ ) = Λ F ( τ ) + α 2 Λ B ( τ 2 τ 1 ) + Λ FB disp ( τ τ 1 ) ,
Λ FB disp ( τ ) = 2 Re { α * [ r 1 r 3 * s disp ( τ ) + ( r 1 r 4 * e i ω 0 τ d + r 2 r 3 * e i ω 0 τ d ) s disp ( τ τ d )
+ r 2 r 4 * s disp ( τ 2 τ d ) ] e i ( ω 0 τ d + 2 β 0 L ) } ,
s disp ( τ ) = d Ω S ( Ω ) e i 2 β " Ω 2 L e i Ω τ .

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