Abstract

We propose a framework for Compressive Multi-heterodyne Optical Spectroscopy [CMOS], based on multiple heterodyne measurements of an optical signal mixed with a dynamically encoded frequency comb. The sparsity of optical spectra of interest is exploited by using the compressive sensing strategy to significantly reduce the number of heterodyne measurements. Numerical results are presented to demonstrate retrieval of coherent and incoherent hypothetical singly resonant sparse spectra over a 2 THz-wide bandwidth, sampled every 100 MHz, by using less than 50% measurements.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
    [CrossRef]
  2. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express11(20), 2549–2554 (2003).
    [CrossRef] [PubMed]
  3. A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
    [CrossRef]
  4. P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
    [CrossRef]
  5. T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).
  6. J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
    [CrossRef] [PubMed]
  7. M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
    [CrossRef] [PubMed]
  8. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
    [CrossRef] [PubMed]
  9. R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
    [CrossRef] [PubMed]
  10. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
    [CrossRef] [PubMed]
  11. I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
    [CrossRef]
  12. T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
    [CrossRef]
  13. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett.29(13), 1542–1544 (2004).
    [CrossRef] [PubMed]
  14. J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
    [CrossRef]
  15. F. Adler, P. Masłowski, A. Foltynowicz, K. C. Cossel, T. C. Briles, I. Hartl, and J. Ye, “Mid-infrared fourier transform spectroscopy with a broadband frequency comb,” Opt. Express18(21), 21861–21872 (2010).
    [CrossRef] [PubMed]
  16. T. Ideguchi, B. Bernhardt, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Raman-induced Kerr-effect dual-comb spectroscopy,” Opt. Lett.37(21), 4498–4500 (2012).
    [CrossRef] [PubMed]
  17. A. Schliesser, M. Brehm, F. Keilmann, and D. van der Weide, “Frequency-comb infrared spectrometer for rapid, remote chemical sensing,” Opt. Express13(22), 9029–9038 (2005).
    [CrossRef] [PubMed]
  18. S. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B27(11), B51–B62 (2010).
    [CrossRef]
  19. E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag.25(2), 21–30 (2008).
    [CrossRef]
  20. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
    [CrossRef]
  21. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express17(15), 13040–13049 (2009).
    [CrossRef] [PubMed]
  22. See Fig, 18.4 in A. Yariv and P. Yeh, in Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007)
  23. A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
    [CrossRef]
  24. C. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
  25. E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
    [CrossRef]
  26. D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
    [CrossRef]
  27. E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians: Madrid, August 22–30, 1433–1452 (2006).
  28. J. H. Reed, in Software radio: a modern approach to radio engineering (Prentice Hall Professional, 2002).
  29. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
    [CrossRef]
  30. See §2.4 in L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  31. J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process.16(12), 2992–3004 (2007).
    [CrossRef] [PubMed]
  32. A. Maleki and D. Donoho, “Optimally tuned iterative reconstruction algorithms for compressed sensing,” IEEE J. Sel. Top. Sig. Proc.4(2), 330–341 (2010).
    [CrossRef]

2012 (1)

2010 (3)

2009 (4)

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
[CrossRef]

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express17(15), 13040–13049 (2009).
[CrossRef] [PubMed]

2008 (3)

I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
[CrossRef]

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag.25(2), 21–30 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

2007 (1)

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process.16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

2006 (3)

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
[CrossRef]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

2005 (1)

2004 (2)

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett.29(13), 1542–1544 (2004).
[CrossRef] [PubMed]

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

2000 (5)

A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

1998 (1)

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
[CrossRef]

Adler, F.

Araki, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Arcizet, O.

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Baraniuk, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Bernhardt, B.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process.16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

Brady, D. J.

Brehm, M.

Briles, T. C.

Candes, E.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag.25(2), 21–30 (2008).
[CrossRef]

Candès, E.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
[CrossRef]

Choi, K.

Coddington, I.

I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
[CrossRef]

Cossel, K. C.

Cundiff, S. T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Del'Haye, P.

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Diddams, S.

Diddams, S. A.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Donoho, D.

A. Maleki and D. Donoho, “Optimally tuned iterative reconstruction algorithms for compressed sensing,” IEEE J. Sel. Top. Sig. Proc.4(2), 330–341 (2010).
[CrossRef]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Figueiredo, M. A.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process.16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

Fischer, M.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Foltynowicz, A.

Gohle, C.

Gorodetsky, M.

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Guelachvili, G.

T. Ideguchi, B. Bernhardt, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Raman-induced Kerr-effect dual-comb spectroscopy,” Opt. Lett.37(21), 4498–4500 (2012).
[CrossRef] [PubMed]

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
[CrossRef]

Haas, M.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Hansch, T.

T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).

Hansch, T. W.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

T. Ideguchi, B. Bernhardt, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Raman-induced Kerr-effect dual-comb spectroscopy,” Opt. Lett.37(21), 4498–4500 (2012).
[CrossRef] [PubMed]

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Hartl, I.

Heilweil, E.

A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
[CrossRef]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett.29(13), 1542–1544 (2004).
[CrossRef] [PubMed]

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Horisaki, R.

Ideguchi, T.

Inoue, H.

Jacobsen, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Jentschura, U. D.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Kabetani, Y.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Kawase, K.

Keilmann, F.

Keitel, C. H.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Kelly,

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
[CrossRef]

Kippenberg, T.

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Knight, J. C.

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

Kolachevsky, N.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Lim, S.

Maleki, A.

A. Maleki and D. Donoho, “Optimally tuned iterative reconstruction algorithms for compressed sensing,” IEEE J. Sel. Top. Sig. Proc.4(2), 330–341 (2010).
[CrossRef]

Mandon, J.

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
[CrossRef]

Markelz, A.

A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
[CrossRef]

Marks, D. L.

Maslowski, P.

Mittleman, D.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
[CrossRef]

Neelamani, R.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Newbury, N.

I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
[CrossRef]

Niering, M.

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

Nuss, M.

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Ogawa, Y.

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
[CrossRef]

Picqué, N.

T. Ideguchi, B. Bernhardt, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Raman-induced Kerr-effect dual-comb spectroscopy,” Opt. Lett.37(21), 4498–4500 (2012).
[CrossRef] [PubMed]

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
[CrossRef]

Ranka, J. K.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Reichert, J.

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

Roitberg, A.

A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
[CrossRef]

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
[CrossRef]

Russell, P. S.

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

Saneyoshi, E.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Schliesser, A.

Swann, W.

I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
[CrossRef]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Tao, T.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
[CrossRef]

Ting Sun, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

Udem, T.

T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

van der Weide, D.

Wadsworth, W. J.

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

Wakin, M.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag.25(2), 21–30 (2008).
[CrossRef]

Watanabe, Y.

Weiner, A.

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Weitz, M.

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

Windeler, R. S.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Yasui, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Ye, J.

F. Adler, P. Masłowski, A. Foltynowicz, K. C. Cossel, T. C. Briles, I. Hartl, and J. Ye, “Mid-infrared fourier transform spectroscopy with a broadband frequency comb,” Opt. Express18(21), 21861–21872 (2010).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

Yokoyama, S.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Zimmermann, M.

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (1)

D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B67(3), 379–390 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett.88(24), 241104 (2006).
[CrossRef]

Chem. Phys. Lett. (1)

A. Markelz, A. Roitberg, and E. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett.320(1-2), 42–48 (2000).
[CrossRef]

Commun. Pure Appl. Math. (1)

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006).
[CrossRef]

Elec. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Elec. Lett.16(16), 630–631 (1980).
[CrossRef]

Eur. Phys. J. (1)

T. Udem, R. Holzwarth, and T. Hansch, “Femtosecond optical frequency combs,” Eur. Phys. J.172, 69–79 (2009).

IEEE J. Sel. Top. Sig. Proc. (1)

A. Maleki and D. Donoho, “Optimally tuned iterative reconstruction algorithms for compressed sensing,” IEEE J. Sel. Top. Sig. Proc.4(2), 330–341 (2010).
[CrossRef]

IEEE Sig. Proc. Mag. (2)

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag.25(2), 21–30 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Sig. Proc. Mag.25(2), 83–91 (2008).
[CrossRef]

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process.16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

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

Nat. Photonics (2)

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics3(2), 99–102 (2009).
[CrossRef]

P. Del'Haye, O. Arcizet, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (5)

I. Coddington, W. Swann, and N. Newbury, “Coherent multi-heterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008).
[CrossRef]

J. Reichert, M. Niering, R. Holzwarth, M. Weitz, T. Udem, and T. W. Hansch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett.84(15), 3232–3235 (2000).
[CrossRef] [PubMed]

M. Fischer, N. Kolachevsky, M. Zimmermann, R. Holzwarth, T. Udem, T. W. Hänsch, M. Haas, U. D. Jentschura, and C. H. Keitel, “New limits on the drift of fundamental constants from laboratory measurements,” Phys. Rev. Lett.92(23), 230802 (2004).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84(22), 5102–5105 (2000).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Other (5)

C. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).

See §2.4 in L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

See Fig, 18.4 in A. Yariv and P. Yeh, in Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007)

E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians: Madrid, August 22–30, 1433–1452 (2006).

J. H. Reed, in Software radio: a modern approach to radio engineering (Prentice Hall Professional, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Illustrative schematic for CMOS. The frequency comb is first filtered by weighting its comb modes with a digitally controlled Spatial Light Modulator [SLM] and then combined with the signal from the sample. The balanced detector measures the RF beat signal between the reference comb and signal. The RF signal is further filtered by a Low Pass Filter [LPF] and detected by a spectrum analyzer or a D-FFT block. The broadband quadrature phase-shifter is used to generate a π/2 phase shifted copy of the comb for the coherent case. (b) Frequency axis indicating relative value of frequency variables. τ D is the characteristic response time of the fast detector. (Diagram is not to scale).

Fig. 2
Fig. 2

(a) Error norm of estimated amplitude spectrum as a function of regularization parameter λ. Shaded area highlights minimum error norm and corresponding λ= 0.01. (b) Error norm of estimated spectral density as a function of λ. Shaded area highlights minimum error norm and corresponding to λ= 3e-4.

Fig. 3
Fig. 3

Coherent Spectrum Estimation: Estimated complex spectrum for (a), (b) K = 150; and (c), (d) K = 250.

Fig. 4
Fig. 4

Incoherent Spectrum Estimation: Estimated power spectrum for (a) K = 150 and (b) K = 250. The dotted red lines in inset mark σ th level.

Tables (2)

Tables Icon

Table 1 Coherent Spectrum Estimation: Comparision between theoretical and numerical results of TwIST applied to Eq. (5)

Tables Icon

Table 2 Incoherent Spectrum Estimation: Comparison between theoretical and numerical results of TwIST applied to Eq. (7)

Equations (9)

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

m(t)=s(t) n ( c n e j ω n t + c n * e j ω n t ) = 1 2π n 0 S * ( ω n Ω) c n e jΩt dΩ+ 0 S ( ω n +Ω) c n * e jΩt dΩ+c.c.
M(Ω)= n [ S * ( ω n Ω) c n +S( ω n +Ω) c n * ] ;Ω Ω LPF
f(s)= argmin s 1 2 ||mFs| | 2 2 +λ||s| | 1 ,
M π/2 (Ω)=j( n S * ( ω n Ω) c n S( ω n +Ω) c n * )
M c (Ω)= n S( ω n +Ω) c n * ;Ω Ω LPF
M c[K×1] = F [K×N] S [N×1] Ω Ω LPF
M P (Ω)= n f n (k) (P( ω n +Ω)+P( ω n Ω));Ω Ω LPF
[ M P (Ω) M P ( Ω ) ] [2K×1] = F [2K×2N] P P [2N×1]
F P =[ f 1 (1) f 2 (1) f 2 (1) f N (1) f N (1) f N+1 (1) f 1 (K) f 2 (K) f 2 (K) f N (K) f N (K) f N+1 (K) f 2 (1) f 1 (1) f 3 (1) f N1 (1) f N+1 (1) f N (1) f 2 (K) f 1 (K) f 3 (K) f N1 (K) f N+1 (K) f N (K) ]

Metrics