Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Dispersive Fourier transformation for fast continuous single-shot measurements

Abstract

Dispersive Fourier transformation is an emerging measurement technique that overcomes the speed limitations of traditional optical instruments and enables fast continuous single-shot measurements in optical sensing, spectroscopy and imaging. Using chromatic dispersion, dispersive Fourier transformation maps the spectrum of an optical pulse to a temporal waveform whose intensity mimics the spectrum, thus allowing a single-pixel photodetector to capture the spectrum at a scan rate significantly beyond what is possible with conventional space-domain spectrometers. Over the past decade, this method has brought us a new class of real-time instruments that permit the capture of rare events such as optical rogue waves and rare cancer cells in blood, which would otherwise be missed using conventional instruments. In this Review, we discuss the principle of dispersive Fourier transformation and its implementation across a wide range of diverse applications.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Dispersive Fourier transformer.
Figure 2: Methods for DFT.
Figure 3: Spectroscopy with DFT.
Figure 4: Imaging with DFT.
Figure 5: Laser scanning with DFT.
Figure 6: Analog-to-digital conversion with DFT.

Similar content being viewed by others

References

  1. Jalali, B., Solli, D. R., Goda, K., Tsia, K. & Ropers, C. Real-time measurements, rare events, and photon economics. Eur. J. Phys. Spec. Top. 185, 145–157 (2010).

    Article  Google Scholar 

  2. Donati, S. Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, 2004).

    Google Scholar 

  3. Brady, D. J. Optical Imaging and Spectroscopy (Wiley-OSA, 2009).

    Book  Google Scholar 

  4. Fujii, T. & Fukuchi, T. Laser Remote Sensing (CRC Press, 2005).

    Book  Google Scholar 

  5. Hollas, J. M. Modern Spectroscopy Ch. 9 (Wiley, 2004).

    Google Scholar 

  6. Pavia, D. L., Lampman, G. M., Kriz, G. S. & Vyvyan, J. A. Introduction to Spectroscopy Ch. 2 (Brooks Cole, 2008).

    Google Scholar 

  7. Grigoryan, G. V., Lima, I. T. Jr, Yu, T., Grigoryan, V. S. & Menyuk, C. R. Using color to understand light transmission. Opt. Photon. News 11, 44–50 (2000).

    Article  ADS  Google Scholar 

  8. Trebino, R. & Kane, D. J. Using phase retrieval to measure the intensity and phase of ultrashort pulses: Frequency-resolved optical gating. J. Opt. Soc. Am. A 10, 1101–1111 (1993).

    Article  ADS  Google Scholar 

  9. Kane, D. J. & Trebino, R. Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating. Opt. Lett. 18, 823–825 (1993).

    Article  ADS  Google Scholar 

  10. Clement, T. S., Taylor, A. J. & Kane, D. J. Single-shot measurement of the amplitude and phase of ultrashort laser pulses in the violet. Opt. Lett. 20, 70–72 (1995).

    Article  ADS  Google Scholar 

  11. Gu, X. et al. Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum. Opt. Lett. 27, 1174–1176 (2002).

    Article  ADS  Google Scholar 

  12. Trebino, R. et al. Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating. Rev. Sci. Instr. 69, 3277–3295 (1997).

    Article  ADS  Google Scholar 

  13. O'Shea, P., Kimmel, M., Gu, X. & Trebino, R. Highly simplified device for ultrashort-pulse measurement. Opt. Lett. 26, 932–934 (2001).

    Article  ADS  Google Scholar 

  14. Iaconis, C. & Walmsley, I. A. Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses. Opt. Lett. 23, 792–794 (1998).

    Article  ADS  Google Scholar 

  15. French, D., Dorrer, C. & Jovanovic, I. Two-beam SPIDER for dual-phase single-shot characterization. Opt. Lett. 34, 3415–3417 (2009).

    Article  ADS  Google Scholar 

  16. Zewail, A. H. Laser femtochemistry. Science 242, 1645–1653 (1988).

    Article  ADS  Google Scholar 

  17. Zewail, A. H. Femtochemistry: Atomic-scale dynamics of the chemical bond. J. Phys. Chem. A 104, 5660–5694 (2000).

    Article  Google Scholar 

  18. Woutersen, S., Emmerichs, U. & Bakker, H. J. Femtosecond mid-IR pump-probe spectroscopy of liquid water: Evidence for a two-component structure. Science 278, 658–660 (1997).

    Article  ADS  Google Scholar 

  19. Woutersen, S. & Bakker, H. J. Resonant intermolecular transfer of vibrational energy in liquid water. Nature 402, 507–509 (1999).

    Article  ADS  Google Scholar 

  20. Tong, Y. C., Chan, L. Y. & Tsang, H. K. Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope. Electron. Lett. 33, 983–985 (1997).

    Article  Google Scholar 

  21. Kelkar, P. V., Coppinger, F., Bhushan, A. S. & Jalali, B. Time-domain optical sensing. Electron. Lett. 35, 1661–1662 (1999).

    Article  Google Scholar 

  22. Goda, K., Solli, D. R., Tsia, K. K. & Jalali, B. Theory of amplified dispersive Fourier transformation. Phys. Rev. A 80, 043821 (2009).

    Article  ADS  Google Scholar 

  23. Solli, D. R., Chou, J. & Jalali, B. Amplified wavelength-time transformation for real-time spectroscopy. Nature Photon. 2, 48–51 (2008).

    Article  ADS  Google Scholar 

  24. Jannson, T. Real-time Fourier transformation in dispersive optical fibers. Opt. Lett. 8, 232–234 (1983).

    Article  ADS  Google Scholar 

  25. Anaza, J., Chen, L. R., Muriel, M. A. & Smith, P. W. E. Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings. Electron. Lett. 35, 2223–2224 (1999).

    Article  Google Scholar 

  26. Muriel, M. A., Azana, J. & Carballar, A. Real-time Fourier transformer based on fiber gratings. Opt. Lett. 24, 1–3 (1999).

    Article  ADS  Google Scholar 

  27. Azana, J. & Muriel, M. A. Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings. IEEE J. Quant. Electron. 36, 517–526 (2000).

    Article  ADS  Google Scholar 

  28. Akhmanov, S. A. et al. Nonstationary nonlinear optical effects and ultrafast light pulse formation. IEEE J. Quant. Electron. QE-4, 598–605 (1968).

    Article  ADS  Google Scholar 

  29. Caputi, W. J. Stretch: A time-transformation technique. IEEE Trans. Aerosp. Electron. Syst. AES-7, 269–278 (1971).

    Article  ADS  Google Scholar 

  30. Goodman, J. Introduction to Fourier Optics Ch. 3 & 4 (Roberts and Company, 2004).

    Google Scholar 

  31. Steward, E. G. Fourier Optics: An Introduction Ch. 2 (Dover, 2011).

    Google Scholar 

  32. Kolner, B. H. & Nazarathy, M. Temporal imaging with a time lens. Opt. Lett. 14, 630–632 (1989).

    Article  ADS  Google Scholar 

  33. Kolner, B. H. Space-time duality and the theory of temporal imaging. IEEE J. Quant. Electron. 30, 1951–1963 (1994).

    Article  ADS  Google Scholar 

  34. Bennett, C. V. & Kolner, B. H. Upconversion time microscope demonstrating 103× magnification of femtosecond waveforms. Opt. Lett. 24, 783–785 (1999).

    Article  ADS  Google Scholar 

  35. Bennett, C. V. & Kolner, B. H. Principles of parametric temporal imaging. I. System configurations. IEEE J. Quant. Electron. 36, 430–437 (2000).

    Article  ADS  Google Scholar 

  36. Foster, M. A. et al. Silicon-chip-based ultrafast optical oscilloscope. Nature 456, 81–84 (2008).

    Article  ADS  Google Scholar 

  37. Jalali, B., Solli, D. R. & Gupta, S. Silicon's time lens. Nature Photon. 3, 8–10 (2009).

    Article  ADS  Google Scholar 

  38. Salem, R. et al. Optical time lens based on four-wave mixing on a silicon chip. Opt. Lett. 33, 1047–1049 (2008).

    Article  ADS  Google Scholar 

  39. Okawachi, Y. et al. Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier. Opt. Lett. 37, 4892–4894 (2012).

    Article  ADS  Google Scholar 

  40. Foster, M. A. et al. Ultrafast waveform compression using a time-domain telescope. Nature Photon. 3, 581–585 (2009).

    Article  ADS  Google Scholar 

  41. Friedman, M., Farsi, A., Okawachi, Y. & Gaeta, A. L. Demonstration of temporal cloaking. Nature 481, 62–65 (2012).

    Article  ADS  Google Scholar 

  42. Chou, J., Han, Y. & Jalali, B. Time-wavelength spectroscopy for chemical sensing. IEEE Photon. Tech. Lett. 16, 1140–1141 (2004).

    Article  ADS  Google Scholar 

  43. Hult, J., Watt, R. S. & Kaminski, C. F. High bandwidth absorption spectroscopy with a dispersed supercontinuum source. Opt. Express 15, 11385–11395 (2007).

    Article  ADS  Google Scholar 

  44. Chou, J., Solli, D. R. & Jalali, B. Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation. Appl. Phys. Lett. 92, 111102 (2008).

    Article  ADS  Google Scholar 

  45. Sych, Y. et al. Broadband time-domain absorption spectroscopy with a ns-pulse supercontinuum source. Opt. Express 18, 22762–22771 (2010).

    Article  ADS  Google Scholar 

  46. Solli, D. R., Roper, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).

    Article  ADS  Google Scholar 

  47. Solli, D. R., Herink, G., Jalali, B. & Ropers, C. Fluctuations and correlations in modulation instability. Nature Photon. 6, 463–468 (2012).

    Article  ADS  Google Scholar 

  48. Wetzel, B. et al. Real-time full bandwidth measurement of spectral noise in supercontinuum generation. Sci. Rep. 2, 882; 10.1038/srep00882 (2012).

    Article  Google Scholar 

  49. Solli, D. R., Ropers, C. & Jalali, B. Active control of rogue waves for stimulated supercontinuum generation. Phys. Rev. Lett. 101, 233902 (2008).

    Article  ADS  Google Scholar 

  50. Solli, D. R., Ropers, C. & Jalali, B. Rare frustration of optical supercontinuum generation. Appl. Phys. Lett. 96, 151108 (2010).

    Article  ADS  Google Scholar 

  51. Goda, K., Tsia, K. K. & Jalali, B. Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena. Nature 458, 1145–1149 (2009).

    Article  ADS  Google Scholar 

  52. Tsia, K. K., Goda, K., Capewell, D. & Jalali, B. Performance of serial time-encoded amplified microscope. Opt. Express 18, 10016–10028 (2010).

    Article  ADS  Google Scholar 

  53. Goda, K., Tsia, K. K. & Jalali, B. Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading. Appl. Phys. Lett. 93, 131109 (2008).

    Article  ADS  Google Scholar 

  54. Fard, A. et al. Nomarski serial time-encoded amplified microscopy for high-speed contrast-enhanced imaging of transparent media. Biomed. Opt. Express 2, 3387–3392 (2011).

    Article  Google Scholar 

  55. Mahjoubfar, A. et al. High-speed nanometer-resolved imaging vibrometer and velocimeter. Appl. Phys. Lett. 98, 101107 (2011).

    Article  ADS  Google Scholar 

  56. Kim, S. H., Goda, K., Fard, A. & Jalali, B. An optical time-domain analog pattern correlator for high-speed image recognition. Opt. Lett. 36, 220–222 (2011).

    Article  ADS  Google Scholar 

  57. Goda, K. et al. High-throughput single-microparticle imaging flow analyzer. Proc. Natl Acad. Sci. USA 109, 11630–11635 (2012).

    Article  ADS  Google Scholar 

  58. Qian, F., Song, Q., Tien, E. K., Kalyoncu, S. K. & Boyraz, O. Real-time optical imaging and tracking of micron-sized particles. Opt. Commun. 282, 4672–4675 (2009).

    Article  ADS  Google Scholar 

  59. Wong, T. T. W., Lau, A. K. S., Wong, K. K. Y. & Tsia, K. K. Optical time-stretch confocal microscopy at 1 mm. Opt. Lett. 37, 3330–3332 (2012).

    Article  ADS  Google Scholar 

  60. Goda, K. et al. Hybrid dispersion laser scanner. Sci. Rep. 2, 445; 10.1038/srep00445 (2012).

    Article  Google Scholar 

  61. Moon, S. & Kim, D. Y. Ultra-high-speed optical coherence tomography with a stretched pulse supercontinuum source. Opt. Express 14, 11575–11584 (2006).

    Article  ADS  Google Scholar 

  62. Park, Y., Ahn, T. J., Kieffer, J. C. & Azana, J. Optical frequency domain reflectometry based on real-time Fourier transformation. Opt. Express 15, 4598–4617 (2007).

    ADS  Google Scholar 

  63. Saperstein, R. E. et al. Processing advantages of linear chirped fiber Bragg gratings in the time domain realization of optical frequency-domain reflectometry. Opt. Express 15, 15464–15479 (2007).

    Article  ADS  Google Scholar 

  64. Goda, K., Solli, D. R. & Jalali, B. Real-time optical reflectometry enabled by amplified dispersive Fourier transformation. Appl. Phys. Lett. 93, 031106 (2008).

    Article  ADS  Google Scholar 

  65. Goda, K. et al. High-throughput optical coherence tomography at 800 nm. Opt. Express 20, 19612–19617 (2012).

    Article  ADS  Google Scholar 

  66. Bhushan, A. S., Coppinger, F. & Jalali, B. Time-stretched analog-to-digital conversion. Electron. Lett. 34, 839–841 (1998).

    Article  Google Scholar 

  67. Bhushan, A. S., Han, Y. & Jalali, B. Time stretched ADC arrays. J. Trans. Circ. Sys. 49, 521–524 (2002).

    Google Scholar 

  68. Han, Y. & Jalali, B. Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations. J. Lightwave Tech. 21, 3085–3103 (2003).

    Article  ADS  Google Scholar 

  69. Chou, J., Boyraz, O., Solli, D. & Jalali, B. Femtosecond real-time single-shot digitizer. Appl. Phys. Lett. 91, 161105 (2007).

    Article  ADS  Google Scholar 

  70. Valley, G. C. Photonic analog-to-digital converters. Opt. Express 15, 1955–1982 (2007).

    Article  ADS  Google Scholar 

  71. Fard, A. M. et al. All-optical time-stretch digitizer. Appl. Phys. Lett. 101, 051113 (2012).

    Article  ADS  Google Scholar 

  72. Islam, M. N. Raman amplifiers for telecommunications. IEEE J. Sel. Top. Quant. Electron. 8, 548–559 (2002).

    Article  ADS  Google Scholar 

  73. Agrawal, G. P. Nonlinear Fiber Optics Ch. 2, 3 & 8 (Academic, 2006).

    MATH  Google Scholar 

  74. Goda, K., Mahjoubfar, A. & Jalali, B. Demonstration of Raman gain at 800 nm in single-mode fiber and its potential application to biological sensing and imaging. Appl. Phys. Lett. 95, 251101 (2009).

    Article  ADS  Google Scholar 

  75. Agrawal, G. P. Fiber-Optic Communication Systems Ch. 7 (Wiley, 2002).

    Book  Google Scholar 

  76. Goda, K. & Jalali, B. Noise figure of amplified dispersive Fourier transformation. Phys. Rev. A 82, 033827 (2010).

    Article  ADS  Google Scholar 

  77. Gupta, S. & Jalali, B. Time-warp correction and calibration in photonic time-stretch ADC. Opt. Lett. 33, 2674–2676 (2008).

    Article  ADS  Google Scholar 

  78. Saperstein, R. E., Panasenko, D. & Fainman, Y. Demonstration of a microwave spectrum analyzer based on time-domain optical processing in fiber. Opt. Lett. 29, 501–503 (2004).

    Article  ADS  Google Scholar 

  79. Saperstein, R. E., Alic, N., Panasenko, D., Rokitski, R. & Fainman, Y. Time-domain waveform processing using chromatic dispersion for temporal shaping of optical pulses. J. Opt. Soc. Am. B 22, 2427–2436 (2005).

    Article  ADS  Google Scholar 

  80. Liu, W., Li, W. & Yao, J. Real-time interrogation of a linearly chirped fiber Bragg grating sensor for simultaneous measurement of strain and temperature. IEEE Photon. Tech. Lett. 23, 1340–1342 (2011).

    Article  ADS  Google Scholar 

  81. Fork, R. L., Martinez, O. E. & Gordon, J. P. Negative dispersion using pairs of prisms. Opt. Lett. 9, 150–152 (1984).

    Article  ADS  Google Scholar 

  82. Gu, X., Akturk, S. & Trebino, R. Spatial chirp in ultrafast optics. Opt. Commun. 242, 599–604 (2004).

    Article  ADS  Google Scholar 

  83. Weiner, A. Ultrafast Optics Ch. 8 (Wiley, 2011).

    Google Scholar 

  84. Diebold, E. D. et al. Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide. Opt. Express 19, 23809–23817 (2011).

    Article  ADS  Google Scholar 

  85. Tan, Z., Wang, C., Diebold, E. D., Hon, N. K. & Jalali, B. Real-time wavelength and bandwidth-independent optical integrator based on modal dispersion. Opt. Express 20, 14109–14116 (2012).

    Article  ADS  Google Scholar 

  86. http://www.corning.com/opticalfiber/products/SMF-28_ULL_fiber.aspx.

  87. Asghari, M. H., Park, Y. & Azaña, J. Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry. Opt. Express 18, 16526–16538 (2010).

    Article  ADS  Google Scholar 

  88. Wang, C. & Yao, J. Complete characterization of an optical pulse based on temporal interferometry using an unbalanced temporal pulse shaping system. J. Lightwave Tech. 29, 789–800 (2011).

    Article  ADS  Google Scholar 

  89. Asghari, M. H. & Jalali, B. Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS). IEEE Photon. J. 4, 1693–1701 (2012).

    Article  ADS  Google Scholar 

  90. Holst, G. C. & Lomheim, T. S. CMOS/CCD Sensors and Camera Systems (SPIE, 2011).

    Book  Google Scholar 

  91. Janesick, J. R. Scientific Charge-Coupled Devices (SPIE, 2001).

    Book  Google Scholar 

  92. Ohta, J. Smart CMOS Image Sensors and Applications Ch. 2 (CRC, 2007).

    Google Scholar 

  93. Velten, A. et al. Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging. Nature Commun. 3, 745 (2012).

    Article  ADS  Google Scholar 

  94. Terada, Y., Yoshida, S., Takeuchi, O. & Shigekawa, H. Real-space imaging of transient carrier dynamics by nanoscale pump-probe microscopy. Nature Photon. 4, 869–874 (2010).

    Article  ADS  Google Scholar 

  95. Dixit, G., Vendrell, O. & Santra, R. Imaging electronic quantum motion with light. Proc. Natl Acad. Sci. USA 109, 11636–11640 (2012).

    Article  ADS  Google Scholar 

  96. Hockett, P., Bisgaard, C. Z., Clarkin, O. J. & Stolow, A. Time-resolved imaging of purely valence-electron dynamics during a chemical reaction. Nature Phys. 7, 612–615 (2011).

    Article  ADS  Google Scholar 

  97. Haessler, S. et al. Attosecond imaging of molecular electronic wavepackets. Nature Phys. 6, 200–206 (2010).

    Article  ADS  Google Scholar 

  98. Drescher, M. et al. Time-resolved atomic inner-shell spectroscopy. Nature 419, 803–807 (2002).

    Article  ADS  Google Scholar 

  99. Durbin, S. M., Clevenger, T., Graber, T. & Henning, R. X-ray pump optical probe cross-correlation study of GaAs. Nature Photon. 6, 111–114 (2012).

    Article  ADS  Google Scholar 

  100. Schwartz, B. LIDAR: Mapping the world in 3D. Nature Photon. 4, 429–430 (2010).

    Article  ADS  Google Scholar 

  101. Pelesko, J. A. Modeling MEMS and NEMS Ch. 5 (CRC, 2002).

    Book  MATH  Google Scholar 

  102. Marshall, G. F. Handbook of Optical and Laser Scanning Ch. 2 (Dekker, 2009).

    Google Scholar 

  103. Dotson, C. L. Fundamentals of Dimensional Metrology Ch. 8 & 12 (Delmar Cengage Learning, 2006).

    Google Scholar 

  104. Osten, W. Optical Inspection of Microsystems Ch. 1, 5 & 9 (CRC, 2006).

    Google Scholar 

  105. Gobel, W., Kampa, B. M. & Helmchen, F. Imaging cellular network dynamics in three dimensions using fast 3D laser scanning. Nat. Methods 4, 73–79 (2007).

    Article  Google Scholar 

  106. Denk, W., Strickler, J. H. & Webb, W. W. Two-photon laser scanning fluorescence microscopy. Science 248, 73–76 (1990).

    Article  ADS  Google Scholar 

  107. Stigwall, J. & Galt, S. Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems. J. Lightwave Tech. 25, 3017–3027 (2007).

    Article  ADS  Google Scholar 

  108. Fard, A. M., Gupta, S. & Jalali, B. Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging, Laser & Photon. Rev. DOI 10.1002/lpor.201200015 (2013).

Download references

Acknowledgements

The authors acknowledge support from the US Defense Advanced Research Projects Agency, the National Science Foundation, the National Institutes of Health and Congressionally Directed Medical Research Programs. K.G. is supported by the Burroughs Wellcome Fund Career Award at the Scientific Interface. The authors also thank C. Kaminski, D. Solli, A. Fard and E. Diebold for permission to use their figures.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Goda.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goda, K., Jalali, B. Dispersive Fourier transformation for fast continuous single-shot measurements. Nature Photon 7, 102–112 (2013). https://doi.org/10.1038/nphoton.2012.359

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2012.359

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing