Abstract

We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system’s resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Ptychographic reconstruction algorithm for frequency-resolved optical gating: super-resolution and supreme robustness

Pavel Sidorenko, Oren Lahav, Zohar Avnat, and Oren Cohen
Optica 3(12) 1320-1330 (2016)

Deep learning reconstruction of ultrashort pulses

Tom Zahavy, Alex Dikopoltsev, Daniel Moss, Gil Ilan Haham, Oren Cohen, Shie Mannor, and Mordechai Segev
Optica 5(5) 666-673 (2018)

Multiplexed FROG

Gil Ilan Haham, Pavel Sidorenko, Oren Lahav, and Oren Cohen
Opt. Express 25(26) 33007-33017 (2017)

References

  • View by:
  • |
  • |
  • |

  1. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [Crossref]
  2. A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
    [Crossref] [PubMed]
  3. P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
    [Crossref] [PubMed]
  4. S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
    [Crossref] [PubMed]
  5. Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
    [Crossref]
  6. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
    [Crossref]
  7. L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
    [Crossref] [PubMed]
  8. J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
    [Crossref] [PubMed]
  9. M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
    [Crossref] [PubMed]
  10. Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, 1st ed. (Cambridge University, 2012).
  11. S. Gleichman and Y. C. Eldar, “Blind compressed sensing,” IEEE Trans. Inf. Theory (2011).
  12. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
    [Crossref] [PubMed]
  13. T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).
  14. P.A. Janamagi, “Breaking the 100-fs barrier with a streak camera,” Proc. SPIE 5194, Fourth-Generation X-Ray Sources and Ultrafast X-Ray Detectors.171–183 (2004).
  15. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
  16. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
    [Crossref] [PubMed]
  17. M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
    [Crossref] [PubMed]
  18. S. M. Riad, “The deconvolution problem: An overview,” Proc. IEEE 74(1), 82–85 (1986).
    [Crossref]
  19. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
    [Crossref]
  20. J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10(1), 16–18 (1967).
    [Crossref]
  21. I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308 (2009).
    [Crossref]
  22. J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001).
    [Crossref]
  23. V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4(2), 445–448 (1998).
    [Crossref]
  24. Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
    [Crossref]

2015 (2)

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

2014 (1)

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
[Crossref]

2012 (4)

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

2010 (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

2009 (4)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308 (2009).
[Crossref]

2008 (1)

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

2001 (2)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
[Crossref]

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001).
[Crossref]

1998 (2)

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4(2), 445–448 (1998).
[Crossref]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
[Crossref] [PubMed]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

1994 (1)

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

1986 (1)

S. M. Riad, “The deconvolution problem: An overview,” Proc. IEEE 74(1), 82–85 (1986).
[Crossref]

1967 (1)

J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10(1), 16–18 (1967).
[Crossref]

Alonso, B.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Armstrong, J. A.

J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10(1), 16–18 (1967).
[Crossref]

Arnold, C. L.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Bagnoud, V.

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4(2), 445–448 (1998).
[Crossref]

Baraniuk, R. G.

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

Barbastathis, G.

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

Beck, A.

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
[Crossref]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
[Crossref]

Chung, J.-H.

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001).
[Crossref]

Cohen, O.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Crespo, H.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Davenport, M. A.

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

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Donoho, D. L.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
[Crossref]

Dorrer, C.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308 (2009).
[Crossref]

Duarte, M. F.

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

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Eldar, Y. C.

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
[Crossref]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Fleischer, A.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

Fordell, T.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

Iaconis, C.

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
[Crossref] [PubMed]

Iwasuki, K.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Janamagi, P.A.

P.A. Janamagi, “Breaking the 100-fs barrier with a streak camera,” Proc. SPIE 5194, Fourth-Generation X-Ray Sources and Ultrafast X-Ray Detectors.171–183 (2004).

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Kato, K.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Kelly, K. F.

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

Kfir, O.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

Kley, E. B.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Kozen, A.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

L’Huillier, A.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Laska, J. N.

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

Lee, H.-N.

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

Lee, J.

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

Lee, W.

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

Miranda, M.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Mutzafi, M.

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

Nagatsuma, T.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Oh, S. B.

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

Oliver, J.

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

Osherovich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Park, S.

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

Riad, S. M.

S. M. Riad, “The deconvolution problem: An overview,” Proc. IEEE 74(1), 82–85 (1986).
[Crossref]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Salin, F.

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4(2), 445–448 (1998).
[Crossref]

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
[Crossref]

Segev, M.

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

Shechtman, Y.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
[Crossref]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Shinagawa, M.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Shoham, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Sidorenko, P.

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Silva, F.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Steiner, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Sun, T.

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

Suzuki, K.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

Takhar, D.

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

Tian, L.

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

Walmsley, I. A.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308 (2009).
[Crossref]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
[Crossref] [PubMed]

Weigand, R.

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Weiner, A. M.

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001).
[Crossref]

Yaita, M.

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

Yavneh, I.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308 (2009).
[Crossref]

Appl. Phys. Lett. (2)

J. A. Armstrong, “Measurement of picosecond laser pulse widths,” Appl. Phys. Lett. 10(1), 16–18 (1967).
[Crossref]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Electronics Letters. (1)

T. Nagatsuma, M. Yaita, M. Shinagawa, K. Kato, A. Kozen, K. Iwasuki, and K. Suzuki, “Electro-optic characterization of ultrafast photodetectors using adiabatically compressed soliton pulses,” Electronics Letters. 30(10), 814–816 (1994).

IEEE J. Sel. Top. Quantum Electron. (2)

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001).
[Crossref]

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4(2), 445–448 (1998).
[Crossref]

IEEE Signal Process. Mag. (1)

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

IEEE Trans. Image Process. (1)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

IEEE Trans. Signal Process. (1)

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” IEEE Trans. Signal Process. 62(4), 928–938 (2014).
[Crossref]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Nat. Commun. (2)

P. Sidorenko, O. Kfir, Y. Shechtman, A. Fleischer, Y. C. Eldar, M. Segev, and O. Cohen, “Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects,” Nat. Commun. 6(1), 8209 (2015).
[Crossref] [PubMed]

M. Mutzafi, Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity,” Nat. Commun. 6(1), 7950 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Opt. Express (4)

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

L. Tian, J. Lee, S. B. Oh, and G. Barbastathis, “Experimental compressive phase space tomography,” Opt. Express 20(8), 8296–8308 (2012).
[Crossref] [PubMed]

J. Oliver, W. Lee, S. Park, and H.-N. Lee, “Improving resolution of miniature spectrometers by exploiting sparse nature of signals,” Opt. Express 20(3), 2613–2625 (2012).
[Crossref] [PubMed]

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20(17), 18732–18743 (2012).
[Crossref] [PubMed]

Opt. Lett. (1)

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
[Crossref] [PubMed]

Proc. IEEE (1)

S. M. Riad, “The deconvolution problem: An overview,” Proc. IEEE 74(1), 82–85 (1986).
[Crossref]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).

SIAM J. Sci. Comput. (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (2001).
[Crossref]

Other (3)

P.A. Janamagi, “Breaking the 100-fs barrier with a streak camera,” Proc. SPIE 5194, Fourth-Generation X-Ray Sources and Ultrafast X-Ray Detectors.171–183 (2004).

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, 1st ed. (Cambridge University, 2012).

S. Gleichman and Y. C. Eldar, “Blind compressed sensing,” IEEE Trans. Inf. Theory (2011).

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 (10)

Fig. 1
Fig. 1 Experimental setup: a laser pulse is probed by slow (1000 ps rise-time) and fast (175 ps rise-time) photodiodes and an oscilloscope with 6 GHz bandwidth. Impulse response functions (b) and corresponding spectra (c) of the slow (red) and fast (blue) photodiodes.
Fig. 2
Fig. 2 Direct signals (a) and corresponding spectra (b) when the laser pulse is probed by the slow (red) and fast (blue) photodiodes. (c) Reconstructed pulse-shapes by implementing Wiener de-convolution. (d) The number of non-zero elements in each sparsity-based reconstruction (see text above). (e) The sparsity-based reconstructions with the slow (solid black) and the fast (solid blue) photodiodes as well as the Wiener de-convolution with a fast photodiode (dashed red) are all quite similar: the three-peak waveform is well captured, and their spectra (f) nicely match up to 5 GHz. On the other hand, without utilizing sparsity, the Wiener de-convolution with the slow photodiode ((c) (dash red) does not capture the peaks of the waveform and its associated spectrum starts to deviate from the other spectra at 1 GHz. In these experiments, the sparsity-based reconstruction with the slow photodiode exhibits super-resolution of up to 5 times relative to the Wiener de-convolution.
Fig. 3
Fig. 3 Calculated sparsity-based reconstruction of electric field profiles from their autocorrelations using GESPAR under the assumption that the pulse is sparse in the GH frame. (a) Original (blue solid) and reconstructed (dashed red curve) electric field profiles. The original electric field profile is comprised of 16 GH functions. The inset shows the autocorrelation signal of the original pulse. (b) Reliable recovery probability using the sparsity-based method versus sparsity level, i.e. the minimum number of GH functions that can represent the electric field profile of the pulse. The recovery is certain (~100%) for s≤17.
Fig. 4
Fig. 4 A demonstration that pulses with low-order polynomial spectral chirps can be represented compactly in our GH frame. (a) Gaussian power spectrum used in the current simulation (blue curve) and a specific example of a 5th-order polynomial spectral phase (green curve). (b) Waveform (pulse intensity profile in time) that corresponds to the spectrum and spectral phase in (a). (c) Sparsity level of pulses - all with the same power spectrum shown in (a), and all with 5th-order polynomial spectral chirps, as a function of sparsity, for three AC support lengths (see text). (d) The fraction of pulses with s≤17 as a function of AC support length. As shown here, correct reconstruction of all pulses with AC support length ≤ 500 fs has almost 100% certainty.
Fig. 5
Fig. 5 Experimental demonstration of reconstructing the laser intensity profile from its autocorrelation trace. For comparison, we also characterize the pulse using SHG FROG. (a) Measured intensity autocorrelation trace. (b) Measured SHG FROG interferogram. (c) Reconstructed interferogram (NMSE is 8.3x10-6). (d) Reconstructed pulse (blue curve) and spectral phase (green curve) - using the standard (singular value decomposition) FROG recovery algorithm. (e) The reconstructed intensity profiles using the sparsity-based algorithm from the measured intensity AC trace (blue dashed line) and the FROG method (solid red line), clearly showing that the sparsity-based reconstruction is very good (the NMSE between the intensity profiles is 2%). (f) The population of the reconstructed pulses in the GH basis (g) The distribution of pulses with power spectrum in plot (d), 5th-order polynomial spectral phase and intensity autocorrelation support length of 600 fs as a function of sparsity-level.
Fig. 6
Fig. 6 Compactness of ultrashort laser pulses in the Von-Neumann (VN) representation. (a) Normalized cumulative histogram for obtaining good representations of pulses as a function of the minimal number of non-zero coefficients using VN basis (solid lines) and time basis (dash lines) for sets of pulses with pulse duration in the range 150-300 fs (blue lines), 70-150 fs (green lines) and 40-70 fs (red lines). (b-j) examples of three pulses with significantly different pulse durations showing: (b,e,h) time-varying intensities (blue line) and phases (red line), (c,f,i) VN representations in the VN basis and (d,g,j) representations in the STFT basis. St, SVN and SSTFT correspond to the sparsity levels in the time, VN and STFT bases.
Fig. 7
Fig. 7 Numerical demonstration of sparsity-based XFROG reconstruction when 20 coefficients describe the unknown pulse in VN basis, SVN = 20. (A) XFROG trace (B) the gate pulse, amplitude (blue) and phase (red). (c)-(f) reconstructions of the unknown pulse, amplitude (blue) and phase (red), under different values of SNR and incompleteness, compared to the original pulse, amplitude and phase (black curves). The SNR, incompleteness parameter η, and reconstruction error, δ1, are denoted in each plot.
Fig. 8
Fig. 8 Numerical demonstration of sparsity-based XFROG reconstruction when 25 coefficients describe the unknown pulse in VN basis, SVN = 25. (a) XFROG trace (b) the gate pulse, amplitude (blue) and phase (red). (c)-(f) reconstructions of the unknown pulse, amplitude (blue) and phase (red), under different values of SNR and incompleteness, compared to the original pulse, amplitude, and phase (black curves). The SNR, incompleteness parameter, η, and reconstruction error, δ1, are denoted in each plot.
Fig. 9
Fig. 9 Numerical investigation of sparsity-based XFROG reconstruction versus incompleteness, η, SNR values 30, 40 and 50 and VN sparsity levels 20, 25, and 30.
Fig. 10
Fig. 10 Experimental demonstration of sparsity-based XFROG reconstruction using an incomplete XFROG trace. (a) amplitude (blue) and phase (red) of the gate pulse. (b) Measured XFROG trace with η = 0.25, (i.e., 16 frequencies out of 64 in the complete XFROG trace shown in the inset). (c) Recovered XFROG trace using the spectrally filtered XFROG trace and the sparsity-based reconstruction algorithm. (d) The recovered unknown pulse (amplitude in blue and phase in red) on top of the amplitude and phase curves measured through FROG. The error between the reconstructions is 0.19.

Equations (2)

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

α ˜ ω n , t m ( ω )= ( 2α π ) 1 4 exp{ α ( ω ω n ) 2 i t m ( ω ω n ) }
ν ^ =arg min ν { i=1 N 2 ( | F i r ν | 2 y i ) 2 } s.t. | ν | 0 s,supp( ν ){ 1,2,...,n }.

Metrics