Abstract

The far infrared region of the electromagnetic spectrum often necessitates the use of thermal detectors that, by nature, typically have poor response times and diminished sensitivities, at least compared to adjacent bands. However, many signals of interest contain frequency components far too fast to be reliably measured with such detectors, and hence expensive and inefficient alternatives are brought to bear. Here we propose and experimentally validate a new method leveraging the speed and scalability of dynamic metamaterial modulators to encode high-frequency signal components at a lower frequency, making them reliably measurable with thermal detectors that would otherwise be too slow. An optimal weighing scheme design in the time domain is realized, the result being an imaging system whose time resolution is independent of detector speed and is rather limited only by the speed of the modulator and the reproducibility of the signal of interest.

© 2017 Optical Society of America

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References

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2017 (2)

2016 (2)

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. Photon. 8, 605 (2014).
[Crossref]

2013 (1)

Y. Shen, “Algorithm of Walsh-Hadamard Transform with Optical Approach,” J. Inf. Comput. Sci. 10, 4427–4434 (2013).
[Crossref]

2012 (1)

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

2011 (1)

2009 (1)

W. de Launey, “On the asymptotic existence of Hadamard matrices,” J. Comb. Theory. Ser. A 116, 1002–1008 (2009).
[Crossref]

1994 (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. 76, 1–24 (1994).

1991 (1)

1949 (1)

Azad, A. K.

Becker, A.

Bell, R.

R. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

Bernhard, M.

M. Bernhard and J. Speidel, “Multicarrier Transmission using Hadamard Transform for Optical Communications,” in “2013 ITG Symposium Proceedings - Photonic Networks,” (Leipzig, Germany, 2013), pp. 1–5.

Budzier, H.

H. Budzier and G. Gerlach, Thermal Infrared Sensors (Wiley, 2011).
[Crossref]

Chang, C.-C.

Chen, H. T.

Choi, C. G.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Choi, H. K.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Choi, M.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Choi, S. Y.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

de Launey, W.

W. de Launey, “On the asymptotic existence of Hadamard matrices,” J. Comb. Theory. Ser. A 116, 1002–1008 (2009).
[Crossref]

Dyer, B.

Fan, K.

Fellgett, P. B.

Gerlach, G.

H. Budzier and G. Gerlach, Thermal Infrared Sensors (Wiley, 2011).
[Crossref]

Harwit, M.

M. Harwit, Hadamard Transform Optics (Academic, 1979).

Hodges, S. E.

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

Huang, L.

Huber, P. J.

P. J. Huber, Robust Statistical Procedures (Society for Industrial and Applied Mathematics, 1977).

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. Photon. 8, 605 (2014).
[Crossref]

Khan, O. U.

O. U. Khan and D. D. Wentzloff, “1.2 GS / s Hadamard Transform Front-End For Compressive Sensing in 65nm CMOS,” in “Radio and Wireless Symposium (RWS), 2013 IEEE,” (2013), pp. 181–183.

Kim, T. T.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Kinch, M. A.

M. A. Kinch, Fundamentals of Infrared Detector Materials, vol. 285 (SPIE, 2007).
[Crossref]

Krishna, S.

C. M. Watts, C. C. Nadell, J. Montoya, S. Krishna, and W. J. Padilla, “Frequency-division-multiplexed single-pixel imaging with metamaterials,” Optica 3, 133 (2016).
[Crossref]

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. Photon. 8, 605 (2014).
[Crossref]

Lee, S.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Lee, S. H.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Lee, S. S.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

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. Photon. 8, 605 (2014).
[Crossref]

Liu, M.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Liu, X.

Luo, S.-N.

Magana, D.

Marshall, A. G.

A. G. Marshall, Fourier, Hadamard, and Hilbert Transforms in Chemistry (Springer Science & Business Media, 1982).
[Crossref]

Min, B.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Montoya, J.

C. M. Watts, C. C. Nadell, J. Montoya, S. Krishna, and W. J. Padilla, “Frequency-division-multiplexed single-pixel imaging with metamaterials,” Optica 3, 133 (2016).
[Crossref]

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. Photon. 8, 605 (2014).
[Crossref]

Nadell, C. C.

Nogan, J.

Padilla, W. J.

Parul, D.

Pierce, G.

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

Richards, P. L.

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. 76, 1–24 (1994).

Shen, Y.

Y. Shen, “Algorithm of Walsh-Hadamard Transform with Optical Approach,” J. Inf. Comput. Sci. 10, 4427–4434 (2013).
[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. Photon. 8, 605 (2014).
[Crossref]

Shreve, A. P.

Siebert, F.

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. Photon. 8, 605 (2014).
[Crossref]

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. Photon. 8, 605 (2014).
[Crossref]

Speidel, J.

M. Bernhard and J. Speidel, “Multicarrier Transmission using Hadamard Transform for Optical Communications,” in “2013 ITG Symposium Proceedings - Photonic Networks,” (Leipzig, Germany, 2013), pp. 1–5.

Stegall, M.

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

Suen, J.

Suen, J. Y.

Taran, C.

Taylor, A. J.

Uhmann, W.

Vampola, J.

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

Vincent, J. D.

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

Watts, C. M.

C. M. Watts, C. C. Nadell, J. Montoya, S. Krishna, and W. J. Padilla, “Frequency-division-multiplexed single-pixel imaging with metamaterials,” Optica 3, 133 (2016).
[Crossref]

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. Photon. 8, 605 (2014).
[Crossref]

Wentzloff, D. D.

O. U. Khan and D. D. Wentzloff, “1.2 GS / s Hadamard Transform Front-End For Compressive Sensing in 65nm CMOS,” in “Radio and Wireless Symposium (RWS), 2013 IEEE,” (2013), pp. 181–183.

Wu, X.

Yin, X.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Zeng, B.-B.

Zhang, X.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Appl. Spectrosc. (2)

J. (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. 76, 1–24 (1994).

J. Comb. Theory. Ser. A (1)

W. de Launey, “On the asymptotic existence of Hadamard matrices,” J. Comb. Theory. Ser. A 116, 1002–1008 (2009).
[Crossref]

J. Inf. Comput. Sci. (1)

Y. Shen, “Algorithm of Walsh-Hadamard Transform with Optical Approach,” J. Inf. Comput. Sci. 10, 4427–4434 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

Nat. Photon. (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. Photon. 8, 605 (2014).
[Crossref]

Opt. Express (1)

Optica (3)

Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 (1)

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials at terahertz frequencies,” Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012 11, 582–583 (2012).

Other (9)

P. J. Huber, Robust Statistical Procedures (Society for Industrial and Applied Mathematics, 1977).

A. G. Marshall, Fourier, Hadamard, and Hilbert Transforms in Chemistry (Springer Science & Business Media, 1982).
[Crossref]

J. D. Vincent, S. E. Hodges, J. Vampola, M. Stegall, and G. Pierce, Fundamentals of Infrared and Visible Detector Operation and Testing (John Wiley & Sons, Inc., 2016).

H. Budzier and G. Gerlach, Thermal Infrared Sensors (Wiley, 2011).
[Crossref]

M. Harwit, Hadamard Transform Optics (Academic, 1979).

R. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

O. U. Khan and D. D. Wentzloff, “1.2 GS / s Hadamard Transform Front-End For Compressive Sensing in 65nm CMOS,” in “Radio and Wireless Symposium (RWS), 2013 IEEE,” (2013), pp. 181–183.

M. Bernhard and J. Speidel, “Multicarrier Transmission using Hadamard Transform for Optical Communications,” in “2013 ITG Symposium Proceedings - Photonic Networks,” (Leipzig, Germany, 2013), pp. 1–5.

M. A. Kinch, Fundamentals of Infrared Detector Materials, vol. 285 (SPIE, 2007).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) schematic of the experimental setup with and image representation of a size 152 S-matrix. (b) and (c) respectively show the difference between the standard raster approach and the multiplexed approach, where many elements of the object vector x are sampled simultaneously in different combinations according to the measurement matrix. (d) shows the implementation of the modulation scheme, where some row is repeated many times and chopped in order to allow lock-in amplification, which is proportional to a single y value.
Fig. 2
Fig. 2 Plot of simulated absorption curves for 0.09 eV (10 volts applied bias) Fermi energy and 0.4 eV (−10 volts applied bias) Fermi energy, while (b) shows an illustration of the metamaterial unit cell with the various geometric parameters.
Fig. 3
Fig. 3 Block diagram illustrating measured signal components. Frequency response spectra are also shown.
Fig. 4
Fig. 4 Blue curves show measured results at 614GHz, while red curves show ground truth objects; the width of the blue shading is proportional to 2 standard deviations of the waveform images. (a) and (b) show direct measurements of a 108Hz square wave and arbitrary waveform respectively. (c) and (d) depict N = 63 identity matrix reconstructions of the waveforms, while (e) and (f) depict s matrix reconstructions; the corresponding time resolution for a single point in is 0.147ms. Error ribbons have a width of 2 standard deviations.
Fig. 5
Fig. 5 (a) Plot of the SNR metric from Eq. (13) for N = 31 measurements of square waves of increasing frequency. Additionally, the SNR of direct measurements is plotted given the metric defined in Eq. (14) and normalized by the modulator insertion loss. (b) shows the SNR improvement factor for S matrix over raster scan (identity), with the predicted n / 2 improvement illustrated with a dashed line.
Fig. 6
Fig. 6 The strength of lock-in amplification response to the various rows (masks) of the N = 63 S matrix, along with the response renormalized by the maximum. Inset is an image representation of a size 63 S matrix with {0 → black, 1→ white}.
Fig. 7
Fig. 7 The strength of lock-in amplification response to the various rows (masks) of the N = 63 S matrix, along with the response renormalized by the maximum. Inset is a gray scale image representation of the corrected identity matrix with {0 → black, 1→ white}.

Equations (14)

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

y = Hx ,
E f = ν f π | n |
n = n 0 2 + ( α Δ V ) 2
α = d 0 e t
a n ( t ) = m n ( t ) o ( t )
A n ( f ) = ( M n * O ) ( f ) .
b n ( t ) = h det ( t ) * a n ( t )
B n ( f ) = H det ( f ) A n ( f ) = H det ( f ) ( M n * O ) ( f ) .
C n ( f ) = H int ( f ) B n ( f ) = J int ( f ) H det ( f ) ( M n * O ) ( f ) .
C n ( 0 ) = H int ( 0 ) H det ( 0 ) ( M n * O ) ( 0 ) ,
c n = H int ( 0 ) H det ( 0 ) M n ( ν ) O ( ν ) d ν .
P ( f ) = T sinc ( π f T ) e j 2 π f t 0 ,
m = Mean [ x ^ ] x x ^ 2
SNR RMS = 1 2 Δ t π 2 Mean [ x ] n x 2 + n y 2

Metrics