Abstract

We propose and experimentally realize the concept of frequency-division-multiplexed single-pixel imaging. Our technique relies entirely on metamaterial spatial light modulators, the advent of which has permitted advanced modulation techniques difficult to achieve with alternative approaches. So far, implementations of single-pixel imaging have used a single encoding frequency, making them sensitive to narrowband noise. Here, we implement frequency-division methods to parallelize the single-pixel imaging process at 3.2 THz. Our technique enables a trade-off between signal-to-noise ratio and acquisition speed—without altering detector integration time—thus realizing a key development due to the limitations imposed by slow thermal detectors in terahertz and far IR. In addition, our technique yields high image fidelity and marries communications concepts to single-pixel imaging, opening a new path forward for future imaging systems.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Graphene metamaterial spatial light modulator for infrared single pixel imaging

Kebin Fan, Jonathan Y. Suen, and Willie J. Padilla
Opt. Express 25(21) 25318-25325 (2017)

Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator

David Shrekenhamer, Claire M. Watts, and Willie J. Padilla
Opt. Express 21(10) 12507-12518 (2013)

Programmable single-pixel-based broadband stimulated Raman scattering

Pascal Berto, Camille Scotté, Frédéric Galland, Hervè Rigneault, and Hilton B. de Aguiar
Opt. Lett. 42(9) 1696-1699 (2017)

References

  • View by:
  • |
  • |
  • |

  1. M. J. E. Golay, “Static multislit spectrometry and its application to the panoramic display of infrared spectra,” J. Opt. Soc. Am. 41, 468–472 (1951).
    [Crossref]
  2. M. J. E. Golay, “Multi-slit spectrometry,” J. Opt. Soc. Am. 39, 437–444 (1949).
  3. 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]
  4. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [Crossref]
  5. T. Strohmer, “Measure what should be measured: progress and challenges in compressive sensing,” IEEE Signal Process. Lett. 19, 887–893 (2012).
    [Crossref]
  6. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
    [Crossref]
  7. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003).
    [Crossref]
  8. N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
    [Crossref]
  9. D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
    [Crossref]
  10. P. B. Fellgett, “On the ultimate sensitivity and practical performance of radiation detectors,” J. Opt. Soc. Am. 39, 970–976 (1949).
    [Crossref]
  11. C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
    [Crossref]
  12. W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).
  13. T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Antennas Wireless Propag. Lett. 6, 401–404 (2007).
    [Crossref]
  14. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
  15. D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
    [Crossref]
  16. H. T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
    [Crossref]
  17. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).
  18. A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 1320–1322 (1978).
    [Crossref]
  19. N. J. A. Sloane, “Hadamard and other discrete transforms in spectroscopy,” in Fourier, Hadamard, and Hilbert Transforms in Chemistry (Plenum, 1982), pp. 45–67.
  20. J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), Vol. 6.
  21. R. Prasad, OFDM for Wireless Communications Systems (Artech House, 2004).
  22. J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inform. Theory 45, 2397–2417 (1998).
  23. T. May and H. Rohling, “Reducing the peak-to-average power ratio in OFDM radio transmission systems,” in 48th IEEE Vehicular Technology Conference (IEEE, 1998), pp. 2474–2478.
  24. M. Pauli and H. P. Kuchenbecker, “Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal,” Wireless Personal Commun. 4, 93–101 (1997).
    [Crossref]
  25. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
    [Crossref]
  26. S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
    [Crossref]
  27. P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).
  28. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [Crossref]
  29. R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).
  30. J. Almodovar-Faria and J. McNair, “Optimal integration time for energy-detection PPM UWB systems,” in IEEE Global Communications Conference (GLOBECOM) (IEEE, 2012), pp. 4054–4059.
  31. S. Haykin, Communication Systems (Wiley, 2001).
  32. P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).
  33. K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
    [Crossref]
  34. R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
    [Crossref]
  35. T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004).
    [Crossref]
  36. C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

2014 (1)

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

2013 (3)

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
[Crossref]

2012 (1)

T. Strohmer, “Measure what should be measured: progress and challenges in compressive sensing,” IEEE Signal Process. Lett. 19, 887–893 (2012).
[Crossref]

2011 (1)

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

2009 (2)

R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

2008 (2)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

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]

2007 (2)

2006 (2)

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

2005 (1)

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

2004 (1)

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004).
[Crossref]

2003 (2)

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003).
[Crossref]

1998 (1)

J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inform. Theory 45, 2397–2417 (1998).

1997 (1)

M. Pauli and H. P. Kuchenbecker, “Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal,” Wireless Personal Commun. 4, 93–101 (1997).
[Crossref]

1993 (1)

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

1978 (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 1320–1322 (1978).
[Crossref]

1966 (1)

1951 (1)

1949 (2)

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Almodovar-Faria, J.

J. Almodovar-Faria and J. McNair, “Optimal integration time for energy-detection PPM UWB systems,” in IEEE Global Communications Conference (GLOBECOM) (IEEE, 2012), pp. 4054–4059.

Anitha, G.

R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).

Arnone, D. D.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 1320–1322 (1978).
[Crossref]

Averitt, R. D.

Bank, S. R.

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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Brener, I.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Chan, W. L.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Chattopadhyay, G.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Chen, H. T.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

H. T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
[Crossref]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).

Cich, M. J.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

Cole, B. E.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Cooper, K. B.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Cummer, S.

T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Antennas Wireless Propag. Lett. 6, 401–404 (2007).
[Crossref]

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]

Davis, J. A.

J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inform. Theory 45, 2397–2417 (1998).

De Haseth, J. A.

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Dengler, R. J.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Denny, S. P. P.

S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
[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]

Fellgett, P. B.

Fried, D. L.

Golay, M. J. E.

Goldsmith, P. F.

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

Gossard, A. C.

Griffiths, P. R.

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Hand, T.

T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Antennas Wireless Propag. Lett. 6, 401–404 (2007).
[Crossref]

Harwit, M.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Haykin, S.

S. Haykin, Communication Systems (Wiley, 2001).

Hsieh, C.-T.

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

Huguenin, G. R.

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

Hunt, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Hwang, J. S.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Inoue, H.

Jedwab, J.

J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inform. Theory 45, 2397–2417 (1998).

Kapitzky, J.

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

Karpowicz, N.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Kawase, K.

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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Korter, T. M.

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004).
[Crossref]

Krishna, S.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

Kuchenbecker, H. P.

M. Pauli and H. P. Kuchenbecker, “Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal,” Wireless Personal Commun. 4, 93–101 (1997).
[Crossref]

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]

Lin, K. I.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Linfield, E. H.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Lipworth, G.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Llombart, N.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Lubin, P. M. M.

S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
[Crossref]

May, T.

T. May and H. Rohling, “Reducing the peak-to-average power ratio in OFDM radio transmission systems,” in 48th IEEE Vehicular Technology Conference (IEEE, 1998), pp. 2474–2478.

McNair, J.

J. Almodovar-Faria and J. McNair, “Optimal integration time for energy-detection PPM UWB systems,” in IEEE Global Communications Conference (GLOBECOM) (IEEE, 2012), pp. 4054–4059.

Mittleman, D. M.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Montoya, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

Montoya, J. A.

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

Moore, E. L.

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

Nadell, C. C.

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

Ogawa, Y.

Padilla, W. J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

H. T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
[Crossref]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

Pauli, M.

M. Pauli and H. P. Kuchenbecker, “Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal,” Wireless Personal Commun. 4, 93–101 (1997).
[Crossref]

Pepper, M.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Plusquellic, D. F.

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004).
[Crossref]

Prasad, R.

R. Prasad, OFDM for Wireless Communications Systems (Artech House, 2004).

Proakis, J.

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), Vol. 6.

Pye, R. J.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Ramalingam, R.

R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).

Rohling, H.

T. May and H. Rohling, “Reducing the peak-to-average power ratio in OFDM radio transmission systems,” in 48th IEEE Vehicular Technology Conference (IEEE, 1998), pp. 2474–2478.

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Salehi, M.

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), Vol. 6.

Shanmugam, J.

R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Shrekenhamer, D.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

Siegel, P. H.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Sleasman, T.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Sloane, N. J. A.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

N. J. A. Sloane, “Hadamard and other discrete transforms in spectroscopy,” in Fourier, Hadamard, and Hilbert Transforms in Chemistry (Plenum, 1982), pp. 45–67.

Smith, D. R.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Strohmer, T.

T. Strohmer, “Measure what should be measured: progress and challenges in compressive sensing,” IEEE Signal Process. Lett. 19, 887–893 (2012).
[Crossref]

Suen, J. Y. Y.

S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
[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]

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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Taylor, A. J.

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

H. T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
[Crossref]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).

Thomas, B.

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

Tikhonov, A. N.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 1320–1322 (1978).
[Crossref]

Wallace, V. P.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Watanabe, Y.

Watts, C. M.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

Woodward, R. M.

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

Xu, J.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Zhang, C.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Zhang, X. C.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Zhong, H.

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

Zide, J. M. O.

Adv. Opt. Mater. (1)

D. Shrekenhamer, J. Montoya, S. Krishna, and W. J. Padilla, “Four-color metamaterial absorber THz spatial light modulator,” Adv. Opt. Mater. 1, 905–909 (2013).
[Crossref]

Appl. Phys. Lett. (3)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

N. Karpowicz, H. Zhong, C. Zhang, K. I. Lin, J. S. Hwang, J. Xu, and X. C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[Crossref]

W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 3–5 (2009).

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[Crossref]

Chem. Phys. Lett. (1)

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004).
[Crossref]

Defence Sci. J. (1)

R. Ramalingam, G. Anitha, and J. Shanmugam, “Microelectromechnical systems inertial measurement unit error modelling and error analysis for low-cost strapdown inertial navigation system,” Defence Sci. J. 59, 650–658 (2009).

IEEE Antennas Wireless Propag. Lett. (1)

T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Antennas Wireless Propag. Lett. 6, 401–404 (2007).
[Crossref]

IEEE Signal Process. Lett. (1)

T. Strohmer, “Measure what should be measured: progress and challenges in compressive sensing,” IEEE Signal Process. Lett. 19, 887–893 (2012).
[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. Inf. Theory (1)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

IEEE Trans. Inform. Theory (1)

J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inform. Theory 45, 2397–2417 (1998).

IEEE Trans. Microwave Theory Tech. (1)

P. F. Goldsmith, C.-T. Hsieh, G. R. Huguenin, J. Kapitzky, and E. L. Moore, “Focal plane imaging systems for millimeter wavelengths,” IEEE Trans. Microwave Theory Tech. 41, 1664–1675 (1993).

IEEE Trans. Terahertz Sci. Technol. (1)

K. B. Cooper, R. J. Dengler, N. Llombart, B. Thomas, G. Chattopadhyay, and P. H. Siegel, “THz imaging radar for standoff personnel screening,” IEEE Trans. Terahertz Sci. Technol. 1, 169–182 (2011).
[Crossref]

J. Invest. Dermatol. (1)

R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120, 72–78 (2003).
[Crossref]

J. Opt. Soc. Am. (4)

Math. Comput. (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 1320–1322 (1978).
[Crossref]

Nat. Photonics (1)

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Nature (1)

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).

New Astron. (1)

S. P. P. Denny, J. Y. Y. Suen, and P. M. M. Lubin, “Fundamental limits of detection in the far infrared,” New Astron. 25, 114–129 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Wireless Personal Commun. (1)

M. Pauli and H. P. Kuchenbecker, “Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal,” Wireless Personal Commun. 4, 93–101 (1997).
[Crossref]

Other (9)

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

T. May and H. Rohling, “Reducing the peak-to-average power ratio in OFDM radio transmission systems,” in 48th IEEE Vehicular Technology Conference (IEEE, 1998), pp. 2474–2478.

C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, “Single pixel quadrature imaging with metamaterials,” Adv. Opt. Mater., doi: 10.1002/adom.201500435 (to be published).

J. Almodovar-Faria and J. McNair, “Optimal integration time for energy-detection PPM UWB systems,” in IEEE Global Communications Conference (GLOBECOM) (IEEE, 2012), pp. 4054–4059.

S. Haykin, Communication Systems (Wiley, 2001).

N. J. A. Sloane, “Hadamard and other discrete transforms in spectroscopy,” in Fourier, Hadamard, and Hilbert Transforms in Chemistry (Plenum, 1982), pp. 45–67.

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), Vol. 6.

R. Prasad, OFDM for Wireless Communications Systems (Artech House, 2004).

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 (5)

Fig. 1.
Fig. 1.

(a) Illustration of the simultaneous orthogonal carrier frequencies that transfer information. The maxima of one carrier align with the zero-crossing points of the others, which corresponds to the orthogonality condition in Eq. (3). (b) The time domain of the same carriers, separated on the y axis for clarity, and (c) a simplified schematic of p parallel masks encoded on the SLM and spatially multiplexed into the detector, to be processed by the LIA.

Fig. 2.
Fig. 2.

Experimental constellation diagrams for (a) single-frequency modulation (scaled for illustration), (b) simultaneous four-frequency modulation, and (c) time domain data for different state combinations, with the average signal power remaining constant; the vectors show the encoded 1 or 1 for each frequency, i.e., { f 1 , f 2 , f 3 , f 4 } , for the first three aggregate states.

Fig. 3.
Fig. 3.

Images at approximately 3.2 THz acquired with varying amounts of different modulation frequencies. Image color is on a normalized scale. Inset is an image of the original object.

Fig. 4.
Fig. 4.

Quantitative comparison using the 2 norm of images obtained with two and four subcarrier frequencies, with averages of 2.3% and 13.0%, respectively. Differences are normalized by maximum pixel value. Results show that the two-frequency image is closer to the one-frequency image.

Fig. 5.
Fig. 5.

(a) LIA time domain data for steady BPSK states, with subcarriers added in piecemeal, and (b) fit curves for the measured average power values. The 1 n curve is fit only to the first point and is intended as a guide to the eye.

Equations (3)

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

Y = Φ X .
X = Φ 1 Y .
0 τ g 1 ( t ) g 2 ( t ) d t = 0 ,

Metrics