Abstract

We show that a simple (few-element) arrangement for wavelength-multiplexed digital holography allows the measurement of the electric field E(x,y,t) of a femtosecond laser pulse on a single shot. A slightly rotated two-dimensional diffractive optical element and a variable-wavelength filter together generate multiple spectrally resolved digital holograms that are simultaneously captured in a single frame by a digital camera. An additional simultaneous measurement of the spectral phase for a spatially filtered replica of the pulse with frequency-resolved optical gating completes this three-dimensional measurement. An experimental implementation of the technique is presented and its current limitations are discussed.

© 2008 Optical Society of America

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  1. C.-C. Chang, H. P. Sardesai, and A. M. Weiner, “Dispersion-free fiber transmission for femtosecond pulses by use of a dispersion-compensating fiber and programmable pulse shaper,” Opt. Lett. 23, 283-285 (1998).
    [CrossRef]
  2. E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15 fs high-energy pulse generation,” Opt. Lett. 25, 587-589 (2000).
    [CrossRef]
  3. F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, and G. Vdovin, “Wave-front correction of femtosecond terawatt lasers by deformable mirrors,” Opt. Lett. 23, 1043-1045 (1998).
    [CrossRef]
  4. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270-1282 (1985).
    [CrossRef] [PubMed]
  5. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
    [CrossRef]
  6. P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort measurement,” Opt. Lett. 26, 932-934 (2001).
    [CrossRef]
  7. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Cataract Refractive Surg. 17, S573-S577 (2001).
  8. J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack sensor,” J. Opt. Soc. Am. A 11, 1949-1957 (1994).
    [CrossRef]
  9. R. G. Lane and M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31, 6902-6908 (1992).
    [CrossRef] [PubMed]
  10. E. Leith, C. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. C. Sun, J. Valdmanis, and G. Vossler, “Imaging through scattering media with holography,” J. Opt. Soc. Am. A 9, 1148-1153 (1992).
    [CrossRef]
  11. S. Grilli, P. Ferraro, S. De Nicola, A. Finizo, G. Pierattini, and R. Meucci, “Whole optical wavefield reconstruction by digital holography,” Opt. Express 9, 294-302 (2001).
    [CrossRef] [PubMed]
  12. S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
    [CrossRef]
  13. S. Akturk, X. Gu, P. Gabolde, and R. Trebino, “The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams,” Opt. Express 13, 8642-8661 (2005).
    [CrossRef] [PubMed]
  14. S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399-4410 (2004).
    [CrossRef] [PubMed]
  15. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119-121 (1989).
    [CrossRef] [PubMed]
  16. Z. Bor and Z. L. Horvath, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249-258 (1992).
    [CrossRef]
  17. Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
    [CrossRef]
  18. M. Kempe and W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18, 137-139 (1993).
    [CrossRef] [PubMed]
  19. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multipetawatt high-energy laser,” Appl. Opt. 46, 1568-1574 (2007).
    [CrossRef] [PubMed]
  20. G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
    [CrossRef]
  21. T. Tanabe, H. Tanabe, Y. Teramura, and F. Kannari, “Spatiotemporal measurements based on spatial spectral interferometry for ultrashort optical pulses shaped by a Fourier pulse shaper,” J. Opt. Soc. Am. B 19, 2795-2802 (2002).
    [CrossRef]
  22. K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
    [CrossRef]
  23. P. Gabolde and R. Trebino, “Self-referenced measurement of the complete electric field of ultrashort pulses,” Opt. Express 12, 4423-4428 (2004).
    [CrossRef] [PubMed]
  24. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]
  25. P. Gabolde and R. Trebino, “Single-shot measurement of the full spatio-temporal field of ultrashort pulses with multi-spectral digital holography,” Opt. Express 14, 11460-11467 (2006).
    [CrossRef] [PubMed]
  26. Z. Liu, M. Centurion, G. Panotopoulos, J. Hong, and D. Psaltis, “Holographic recording of fast events on a CCD camera,” Opt. Lett. 27, 22-24 (2002).
    [CrossRef]
  27. P. H. Lissberger, “Properties of all-dielectric interference filters. I. A new method of calculation,” J. Opt. Soc. Am. 49, 121-125 (1959).
    [CrossRef]
  28. M. Bass, Handbook of Optics, 2nd ed. (Optical Society of America, 1995), pp. 4289-4290.
  29. P. H. Lissberger and W. L. Wilcock, “Properties of all-dielectric interference filters. II. Filters in parallel beams of light incident obliquely and in convergent beams,” J. Opt. Soc. Am. 29, 126-130 (1959).
    [CrossRef]
  30. P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, “Practical issues in ultra-short-pulse measurements with 'GRENOUILLE',” Appl. Phys. B 79, 683-691 (2004).
    [CrossRef]
  31. K. Naganuma, K. Mogi, and H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393-395 (1990).
    [CrossRef] [PubMed]
  32. A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16, 637-649 (1999).
    [CrossRef]
  33. D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of continuum,” J. Opt. Soc. Am. B, doc. ID 89269 (posted 4 March 2008, in press).
  34. P. Gabolde, D. Lee, S. Akturk, and R. Trebino, “Describing first-order spatio-temporal distortions in ultrashort pulses using normalized parameters,” Opt. Express 15, 242-251 (2007).
    [CrossRef] [PubMed]
  35. J. P. Uyemura, Introduction to VLSI Circuits and Systems (Wiley, 2001).
  36. C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
    [CrossRef]

2007 (2)

2006 (1)

2005 (1)

2004 (3)

2002 (3)

2001 (4)

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizo, G. Pierattini, and R. Meucci, “Whole optical wavefield reconstruction by digital holography,” Opt. Express 9, 294-302 (2001).
[CrossRef] [PubMed]

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort measurement,” Opt. Lett. 26, 932-934 (2001).
[CrossRef]

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Cataract Refractive Surg. 17, S573-S577 (2001).

2000 (3)

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15 fs high-energy pulse generation,” Opt. Lett. 25, 587-589 (2000).
[CrossRef]

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
[CrossRef]

1999 (1)

1998 (2)

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

1994 (1)

1993 (2)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

M. Kempe and W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18, 137-139 (1993).
[CrossRef] [PubMed]

1992 (3)

1990 (1)

1989 (1)

1985 (1)

1982 (1)

1959 (2)

P. H. Lissberger, “Properties of all-dielectric interference filters. I. A new method of calculation,” J. Opt. Soc. Am. 49, 121-125 (1959).
[CrossRef]

P. H. Lissberger and W. L. Wilcock, “Properties of all-dielectric interference filters. II. Filters in parallel beams of light incident obliquely and in convergent beams,” J. Opt. Soc. Am. 29, 126-130 (1959).
[CrossRef]

Akturk, S.

Backus, S.

Bartels, R.

Bass, M.

M. Bass, Handbook of Optics, 2nd ed. (Optical Society of America, 1995), pp. 4289-4290.

Bhan, C.

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

Bille, J. F.

Blanchot, N.

Bor, Z.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Z. Bor and Z. L. Horvath, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249-258 (1992).
[CrossRef]

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119-121 (1989).
[CrossRef] [PubMed]

Brodeur, A.

Centurion, M.

Chang, C.-C.

Chanteloup, J.-C.

Chen, C.

Chen, Y.

Chériaux, G.

Chin, S. L.

De Nicola, S.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Diels, J.-C. M.

Dilworth, D.

Druon, F.

Faure, J.

Ferraro, P.

Finizo, A.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Fontaine, J. J.

Gabolde, P.

Goelz, S.

Grilli, S.

Grimm, B.

Gu, X.

Gupta, A. K.

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

Hazim, H. A.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Hilbert, M.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Hong, J.

Horvath, Z. L.

Z. Bor and Z. L. Horvath, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249-258 (1992).
[CrossRef]

Ina, H.

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Kannari, F.

Kapteyn, H. C.

Kasper, A.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
[CrossRef]

Kempe, M.

Kimmel, M.

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, “Practical issues in ultra-short-pulse measurements with 'GRENOUILLE',” Appl. Phys. B 79, 683-691 (2004).
[CrossRef]

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort measurement,” Opt. Lett. 26, 932-934 (2001).
[CrossRef]

King, B.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Kobayashi, S.

Kovacs, A. P.

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
[CrossRef]

Krumbuegel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Kurdi, G.

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
[CrossRef]

Lai, S.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Lane, R. G.

Lee, D.

P. Gabolde, D. Lee, S. Akturk, and R. Trebino, “Describing first-order spatio-temporal distortions in ultrashort pulses using normalized parameters,” Opt. Express 15, 242-251 (2007).
[CrossRef] [PubMed]

D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of continuum,” J. Opt. Soc. Am. B, doc. ID 89269 (posted 4 March 2008, in press).

Leith, E.

Liang, J.

Lissberger, P. H.

P. H. Lissberger and W. L. Wilcock, “Properties of all-dielectric interference filters. II. Filters in parallel beams of light incident obliquely and in convergent beams,” J. Opt. Soc. Am. 29, 126-130 (1959).
[CrossRef]

P. H. Lissberger, “Properties of all-dielectric interference filters. I. A new method of calculation,” J. Opt. Soc. Am. 49, 121-125 (1959).
[CrossRef]

Liu, Z.

Lopez, J.

Mainali, L.

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

Maksimchuk, A.

McMichael, I. C.

Meucci, R.

Mogi, K.

Mohan, D.

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

Mourou, G.

Murnane, M. M.

Naganuma, K.

Nantel, M.

Néauport, J.

Nees, J.

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

O'Shea, P.

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, “Practical issues in ultra-short-pulse measurements with 'GRENOUILLE',” Appl. Phys. B 79, 683-691 (2004).
[CrossRef]

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort measurement,” Opt. Lett. 26, 932-934 (2001).
[CrossRef]

Osvay, K.

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
[CrossRef]

Panotopoulos, G.

Pierattini, G.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Cataract Refractive Surg. 17, S573-S577 (2001).

Pretzler, G.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
[CrossRef]

Psaltis, D.

Racz, B.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Rouyer, C.

Rudd, J.

Rudolph, W.

Sardesai, H. P.

Sauteret, C.

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Cataract Refractive Surg. 17, S573-S577 (2001).

Simoni, F.

Sun, P. C.

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Szabo, G.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Takeda, M.

Tallon, M.

Tanabe, H.

Tanabe, T.

Teramura, Y.

Trebino, R.

P. Gabolde, D. Lee, S. Akturk, and R. Trebino, “Describing first-order spatio-temporal distortions in ultrashort pulses using normalized parameters,” Opt. Express 15, 242-251 (2007).
[CrossRef] [PubMed]

P. Gabolde and R. Trebino, “Single-shot measurement of the full spatio-temporal field of ultrashort pulses with multi-spectral digital holography,” Opt. Express 14, 11460-11467 (2006).
[CrossRef] [PubMed]

S. Akturk, X. Gu, P. Gabolde, and R. Trebino, “The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams,” Opt. Express 13, 8642-8661 (2005).
[CrossRef] [PubMed]

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399-4410 (2004).
[CrossRef] [PubMed]

P. Gabolde and R. Trebino, “Self-referenced measurement of the complete electric field of ultrashort pulses,” Opt. Express 12, 4423-4428 (2004).
[CrossRef] [PubMed]

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, “Practical issues in ultra-short-pulse measurements with 'GRENOUILLE',” Appl. Phys. B 79, 683-691 (2004).
[CrossRef]

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort measurement,” Opt. Lett. 26, 932-934 (2001).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of continuum,” J. Opt. Soc. Am. B, doc. ID 89269 (posted 4 March 2008, in press).

Uyemura, J. P.

J. P. Uyemura, Introduction to VLSI Circuits and Systems (Wiley, 2001).

Valdmanis, J.

Varju, K.

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
[CrossRef]

Vdovin, G.

Vossler, G.

Weiner, A. M.

Wilcock, W. L.

P. H. Lissberger and W. L. Wilcock, “Properties of all-dielectric interference filters. II. Filters in parallel beams of light incident obliquely and in convergent beams,” J. Opt. Soc. Am. 29, 126-130 (1959).
[CrossRef]

Witte, K. J.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
[CrossRef]

Yamada, H.

Zeek, E.

Appl. Opt. (3)

Appl. Phys. B (3)

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1-9 (2000).
[CrossRef]

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a CPA laser,” Appl. Phys. B 74, 259-263 (2002).
[CrossRef]

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, “Practical issues in ultra-short-pulse measurements with 'GRENOUILLE',” Appl. Phys. B 79, 683-691 (2004).
[CrossRef]

J. Cataract Refractive Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Cataract Refractive Surg. 17, S573-S577 (2001).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

Z. Bor and Z. L. Horvath, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249-258 (1992).
[CrossRef]

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Opt. Eng. (1)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32, 2501-2504 (1993).
[CrossRef]

Opt. Express (6)

Opt. Lasers Eng. (1)

C. Bhan, L. Mainali, D. Mohan, and A. K. Gupta, “Recycling of undiffracted laser light for reconstruction of holograms,” Opt. Lasers Eng. 35, 355-360 (2001).
[CrossRef]

Opt. Lett. (8)

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Other (3)

M. Bass, Handbook of Optics, 2nd ed. (Optical Society of America, 1995), pp. 4289-4290.

D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of continuum,” J. Opt. Soc. Am. B, doc. ID 89269 (posted 4 March 2008, in press).

J. P. Uyemura, Introduction to VLSI Circuits and Systems (Wiley, 2001).

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Figures (9)

Fig. 1
Fig. 1

Three-dimensional view of STRIPED FISH. The signal and reference pulses are crossed at a small vertical angle α. The DOE is rotated by an angle φ about the z axis, and the IBPF is rotated by an angle β about the y axis. The inset shows one of the spatial interferograms (digital holograms) captured by the digital camera.

Fig. 2
Fig. 2

(Top) Side view ( y z plane) showing the signal and reference beams crossing at an angle α. (Bottom) Top view ( x z plane) showing how the frequencies transmitted by the IBPF increase with position x.

Fig. 3
Fig. 3

Algorithm used to reconstruct the three-dimensional electric field from a single camera frame. (a) A two-dimensional fast Fourier transform is applied to a simulated STRIPED FISH trace. (b) The interferometric terms are selected in the Fourier plane, and (c) transformed back to the original x y plane. The resulting image contains both the spatial amplitude and phase, at the expense of a loss of vertical spatial resolution. (d) A registration step is applied to center all the spatial distributions and to assign the calibrated wavelengths in order to obtain the multispectral complex data E ( x , y , ω ) .

Fig. 4
Fig. 4

Mach–Zehnder interferometer used to implement our STRIPED FISH device, drawn in the x z plane. BS, beam splitter. The optical paths of both arms are matched using the delay stage, and a small vertical angle is introduced between the signal and reference pulses so that horizontal fringes are obtained on the digital camera. (b) Setup used for a fully self-referenced STRIPED FISH. L 1 , 2 , achromatic doublets arranged as a telescope; Comp, compensating plate. In these top views, the signal and the reference pulses are displaced vertically and overlap on the drawing. The interferometer is dispersion compensated over 200 nm .

Fig. 5
Fig. 5

Typical experimental STRIPED FISH trace ( 2208 × 3000   pixels ) obtained with a 5   megapixel CMOS camera. The central digital hologram is saturated because of the absence of antireflection coating on the DOE substrate used away from Brewster’s angle. (b) Experimental STRIPED FISH trace recorded at Brewster’s angle to remove the bright central spot.

Fig. 6
Fig. 6

Encoding of the spectral phase in a STRIPED FISH trace. The lower left image is a STRIPED FISH trace. Two profiles are recorded along the gray lines and graphed on the upper right plot. The insets show the profile of two holograms (a) and (b) recorded at two different wavelengths. Gray curves, zero delay. Black curves, group delay introduced in the signal pulse.

Fig. 7
Fig. 7

Fringe shift in each digital hologram as a function of frequency, showing a linear phase due to group delay. Open circles, measurement; dotted line, linear fit. (b) Fringe shift in each digital hologram as a function of frequency, showing a quadratic phase due to group-delay dispersion. Open circles, measurement; dotted curve, quadratic fit.

Fig. 8
Fig. 8

(a) x t slice of the measured electric field E ( x , y , t ) of a pulse with spatial chirp. The vertical axis shows the electric field intensity E ( x , t ) 2 and the color shows the instantaneous wavelength derived from the phase ϕ ( x , t ) . The spatial gradient of color shows the spatial chirp along the x direction. (b) y t slice of the same measured electric field. No spatial chirp is present along the y direction, as expected.

Fig. 9
Fig. 9

STRIPED FISH trace recorded with a self-referenced broadband STRIPED FISH obtained with white-light continuum generated in bulk fused silica

Equations (10)

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E ( x , y , t ) 1 2 π ω k E ( x , y ; ω k ) exp ( i ω k t ) δ ω .
I ( x , y ) = E s ( x , y ) 2 + E r ( x , y ) 2 + E s ( x , y ) * E r ( x , y ) exp ( i k y sin α ) + E s ( x , y ) E r ( x , y ) * exp ( + i k y sin α ) .
λ t = λ n [ 1 ( β θ ) 2 2 μ 2 ] .
b w λ 0 z w 2 λ 0 .
( d θ d λ ) IBPF μ 2 λ n β .
( d θ d λ ) IBPF μ 2 λ n ( λ n λ 0 ) .
ρ x λ 2 m Δ λ F λ 0 .
ρ x λ b a Δ λ F λ 0 .
Δ λ range = λ 0 μ a 2 λ n ( λ n λ 0 ) .
δ λ 2 λ 0 a μ b 2 2 λ n ( λ n λ 0 ) .

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