Abstract

Synthesis of a coherence function by manipulation of the spectral phase of low-coherent light with a segmented liquid-crystal phase modulator and its application in a low-coherence interferometry are described. Effects of space–time coupling caused at diffractive gratings and second-order dispersion at the spatial light modulator on the coherence function synthesis are theoretically and experimentally verified. Various coherence functions can be shaped with phase-only masks designed by simulated annealing optimization algorithm. We utilized this technique for a novel optical low-coherence reflectometry without any mechanical movement for scanning optical delay.

© 1999 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
    [CrossRef] [PubMed]
  3. A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
    [CrossRef]
  4. A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
    [CrossRef]
  5. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, W. S. Warren, “Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses,” Opt. Lett. 19, 737–739 (1994).
    [CrossRef] [PubMed]
  6. J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
    [CrossRef]
  7. P. C. Sun, Y. T. Mazurenko, W. S. C. Chang, P. K. L. Yu, Y. Fainman, “All-optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding,” Opt. Lett. 20, 1728–1730 (1995).
    [CrossRef] [PubMed]
  8. D. Meshulach, D. Yelin, Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
    [CrossRef]
  9. V. Binjrajka, C.-C. Chang, A. W. R. Emanuel, D. E. Leaird, A. M. Weiner, “Pulse shaping of incoherent light by use of a liquid-crystal modulator array,” Opt. Lett. 21, 1756–1758 (1996).
    [CrossRef] [PubMed]
  10. R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” IEEE J. Lightwave Technol. 13, 1826–1837 (1995).
    [CrossRef]
  11. Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
    [CrossRef]
  12. K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
    [CrossRef]
  13. M. M. Wefers, K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
    [CrossRef]
  14. M. M. Wefers, K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
    [CrossRef]
  15. G. S. Agarwal, E. Wolf, “Correlation-induced spectral changes and energy conservation,” Phys. Rev. A 54, 4424–4427 (1996).
    [CrossRef] [PubMed]

1998 (1)

1997 (1)

Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
[CrossRef]

1996 (4)

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

V. Binjrajka, C.-C. Chang, A. W. R. Emanuel, D. E. Leaird, A. M. Weiner, “Pulse shaping of incoherent light by use of a liquid-crystal modulator array,” Opt. Lett. 21, 1756–1758 (1996).
[CrossRef] [PubMed]

M. M. Wefers, K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

G. S. Agarwal, E. Wolf, “Correlation-induced spectral changes and energy conservation,” Phys. Rev. A 54, 4424–4427 (1996).
[CrossRef] [PubMed]

1995 (4)

1994 (1)

1991 (1)

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

1990 (2)

B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
[CrossRef] [PubMed]

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
[CrossRef]

1988 (1)

Agarwal, G. S.

G. S. Agarwal, E. Wolf, “Correlation-induced spectral changes and energy conservation,” Phys. Rev. A 54, 4424–4427 (1996).
[CrossRef] [PubMed]

Binjrajka, V.

Chang, C.-C.

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

Chang, W. S. C.

Emanuel, A. W. R.

Fainman, Y.

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

Goswami, D.

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

Griffin, R. A.

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” IEEE J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

He, Z.

Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Heritage, J. P.

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
[CrossRef]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

Hillegas, C. W.

Hotate, K.

Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
[CrossRef]

Huang, D.

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

Itoh, T.

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Jackson, D. A.

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” IEEE J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

Kannari, F.

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Kirschner, E. M.

Leaird, D. E.

Lee, B. S.

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

Mazurenko, Y. T.

Meshulach, D.

Mukohzaka, N.

Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
[CrossRef]

Nelson, K. A.

M. M. Wefers, K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

M. M. Wefers, K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Salehi, J. A.

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
[CrossRef]

Sampson, D. D.

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” IEEE J. Lightwave Technol. 13, 1826–1837 (1995).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Silberberg, Y.

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

Strand, T. C.

Strickland, D.

Sun, P. C.

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

Takasago, K.

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Takekawa, M.

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Tull, J. X.

Uto, K.

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Warren, W. S.

Wefers, M. M.

M. M. Wefers, K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

M. M. Wefers, K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[CrossRef]

Weiner, A. M.

V. Binjrajka, C.-C. Chang, A. W. R. Emanuel, D. E. Leaird, A. M. Weiner, “Pulse shaping of incoherent light by use of a liquid-crystal modulator array,” Opt. Lett. 21, 1756–1758 (1996).
[CrossRef] [PubMed]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
[CrossRef]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

Wolf, E.

G. S. Agarwal, E. Wolf, “Correlation-induced spectral changes and energy conservation,” Phys. Rev. A 54, 4424–4427 (1996).
[CrossRef] [PubMed]

Yelin, D.

Yu, P. K. L.

Appl. Opt. (1)

IEEE J. Lightwave Technol. (2)

J. A. Salehi, A. M. Weiner, J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” IEEE J. Lightwave Technol. 8, 478–491 (1990).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” IEEE J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Wefers, K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. He, N. Mukohzaka, K. Hotate, “Selective image extraction by synthesis of the coherence function using two-dimensional optical lock-in amplifier with microchannel spatial light modulator,” IEEE Photon. Technol. Lett. 9, 514–516 (1997).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

K. Takasago, T. Itoh, M. Takekawa, K. Uto, F. Kannari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys. 35, 624–629 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

G. S. Agarwal, E. Wolf, “Correlation-induced spectral changes and energy conservation,” Phys. Rev. A 54, 4424–4427 (1996).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic setup of the coherence function synthesis. BS, beam splitter.

Fig. 2
Fig. 2

Power spectrum of the SLD used in our experiments. Broken lines indicate the low and upper limits of the SLM bandwidth.

Fig. 3
Fig. 3

Measured autocorrelation function of the SLD.

Fig. 4
Fig. 4

Experimental results of the coherence function shifted in OPD by 0.6 mm (upper), 1.2 mm (middle), and 1.8 mm by use of an alternative π-shift mask (bottom).

Fig. 5
Fig. 5

(a) Measured coherence function shaped by an alternative π-shift mask. Calculated coherence functions: (b) ignoring both second-order dispersion and space–time coupling, (c) with second-order dispersion, (d) with space–time coupling, (e) with both terms.

Fig. 6
Fig. 6

(a) Measured spatial beam profile of a SLD light shaped by an alternative π-shift mask. (b) Measured spatial beam profile of a original SLD light.

Fig. 7
Fig. 7

Calculated coherence functions indicating the space–time coupling: (a) unshaped original light, (b) shifted by 0.6 mm, (c) shifted by 1.2 mm, (d) shifted by 1.8 mm with an alternative π-shift mask.

Fig. 8
Fig. 8

Comparison of calculated and measured coherence functions shaped (a) to a rectangular envelope, (b) three equal peaks, (c) three peaks with different heights.

Fig. 9
Fig. 9

Schematic of an object consisting of three glass plates piled up like stairs, which is used to measure the individual plane by the coherence function shaping in interferometry. The numbers are painted on each glass plate to absorb light.

Fig. 10
Fig. 10

Experimental results of synthesized coherence functions (left) and corresponding CCD images of interferometry (right) with the object shown in Fig. 9: (a) only the second glass plate surface is imaged with an original SLD light by adjustment of the optical delay; (b) both the second and the third glass plate surfaces are simultaneously imaged with a dual-peak coherence function; (c) similar image for the first and the third planes; (d) all the three planes are imaged with a triple-peak coherence function.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

eobjt=e1t+e2t-τ.
I=eobjteobj*t=e1te1*t-τ+e2te2*t-τ+e1te2*t-τ+e1*te2t-τ.
Γτ=e1te2*t-τ=limT12-TT e1te2*t-τdt.
γτ=ΓτI1I21/2|γτ|exp+iϕτ.
I=I1+I2+2I1I21/2|γτ|cos ϕτ.
Γˆω=γτ=E1ωE2ω,
E2ω=MωE1ω.
ΓMτ=-1MωE1ωE1*ω=-1MωIω.
Γτ-t=-Γωexp-i2πωtexp-i2πωτdω.
δx=λ022πdϕdλ.
U=sinccΔλ2λ02 t,
λ=sin θi+sin θdG,
x=f tanθd-θd0,
dλdx=cos θd0fG.
x=fθdωω=ω0(ωω0)+122θdω2ω=ω0(ωω0)2+ =α1ω¯+α2ω¯2+,
α1=-1ω0Gλ0fcos θd0,
α2=-12ω02Gλ0fcos θd01+πcGωtan θd0cos θd0.
einx, t=esxett.
Einξ, ω=EsξEtω.
x=α1ω+βξ,
β=λ0f2πcos θicos θd0.
Esynξ, ω=Mα1ω+βξEsξEtω.
Γx, τ=esynx, tein*x, t-τ=t-1Esynx, ωEin*x, ω=t-1x-1Mα1ω+βξEsξEtωes*xEt*ω=t-1x-1Mα1ω+βξEsξes*xItω.

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