Abstract

We present a sparse synthetic-aperture, active imaging system at W-band (75 – 110 GHz), which uses sub-harmonic mixer modules. The system employs mechanical scanning of the receiver module position, and a fixed transmitter module. A vector network analyzer provides the back end detection. A full-wave forward model allows accurate construction of the image transfer matrix. We solve the inverse problem to reconstruct scenes using the least squares technique. We demonstrate far-field, diffraction limited imaging of 2D and 3D objects and achieve a cross-range resolution of 3 mm and a depth-range resolution of 4 mm, respectively. Furthermore, we develop an information-based metric to evaluate the performance of a given image transfer matrix for noise-limited, computational imaging systems. We use this metric to find the optimal gain of the radiating element for a given range, both theoretically and experimentally in our system.

© 2016 Optical Society of America

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References

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  1. A. Wootten and A. R. Thompson, “The Atacama Large Millimeter/Submillimeter Array,” Proceedings of the IEEE 97, 1463–1471 (2009).
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    [Crossref]
  7. E. Ojefors, B. Heinemann, and U. R. Pfeiffer, “Active 220- and 325-GHz Frequency Multiplier Chains in an SiGe HBT Technology,” IEEE Trans. Microwave Theory Tech. 59, 1311–1318 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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2015 (1)

G. Charvat, A. Temme, M. Feigin, and R. Raskar, “Time-of-Flight Microwave Camera,” Scientific Reports 5, 14709 (2015).
[Crossref] [PubMed]

2014 (3)

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 (2014).
[Crossref]

J. Hunt, J. Gollub, T. Driscoll, G. Lipworth, A. Mrozack, M. Reynolds, D. Brady, and D. Smith, “Metamaterial microwave holographic imaging system,” J. Opt. Soc. Am. A 31, 2109–2119 (2014).
[Crossref]

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

2013 (2)

2012 (1)

R. Appleby and C. Cameron, “Seeing hidden objects with millimetre waves,” Physics World 25, 35 (2012).
[Crossref]

2011 (1)

E. Ojefors, B. Heinemann, and U. R. Pfeiffer, “Active 220- and 325-GHz Frequency Multiplier Chains in an SiGe HBT Technology,” IEEE Trans. Microwave Theory Tech. 59, 1311–1318 (2011).
[Crossref]

2010 (3)

2009 (1)

A. Wootten and A. R. Thompson, “The Atacama Large Millimeter/Submillimeter Array,” Proceedings of the IEEE 97, 1463–1471 (2009).
[Crossref]

2006 (3)

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution,” Comm. on Pure and Applied Math. 59, 797–829 (2006).
[Crossref]

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

2005 (1)

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

2004 (1)

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[Crossref] [PubMed]

2001 (1)

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49, 1581–1592 (2001).
[Crossref]

1990 (1)

G. M. Rebeiz, D. P. Kasilingam, Y. Guo, P. A. Stimson, and D. B. Rutledge, “Monolithic millimeter-wave two-dimensional horn imaging arrays,” IEEE Trans. Antennas Propag. 38, 1473–1482 (1990).
[Crossref]

Allan, G.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Alvarez, Y.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Appleby, R.

R. Appleby and C. Cameron, “Seeing hidden objects with millimetre waves,” Physics World 25, 35 (2012).
[Crossref]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Berkowitz, B.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Beukema, T.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).
[Crossref]

Brady, D.

Briese, G.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Cameron, C.

R. Appleby and C. Cameron, “Seeing hidden objects with millimetre waves,” Physics World 25, 35 (2012).
[Crossref]

Candes, E. J.

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

Canterakis, N.

S. Rahmann and N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 149–155.

Carin, L.

Cetin, M.

L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, “Sparsity and Compressed Sensing in Radar Imaging,” Proceedings of the IEEE 98, 1006–1020 (2010).
[Crossref]

Charvat, G.

G. Charvat, A. Temme, M. Feigin, and R. Raskar, “Time-of-Flight Microwave Camera,” Scientific Reports 5, 14709 (2015).
[Crossref] [PubMed]

Cull, C.

Donoho, D. L.

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution,” Comm. on Pure and Applied Math. 59, 797–829 (2006).
[Crossref]

Driscoll, T.

Ertin, E.

L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, “Sparsity and Compressed Sensing in Radar Imaging,” Proceedings of the IEEE 98, 1006–1020 (2010).
[Crossref]

Erukulla, S.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Essen, H.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Feigin, M.

G. Charvat, A. Temme, M. Feigin, and R. Raskar, “Time-of-Flight Microwave Camera,” Scientific Reports 5, 14709 (2015).
[Crossref] [PubMed]

Floyd, B. A.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

Fuchs, H.-H.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Gaucher, B.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

Gollub, J.

Gonzalez-Valdes, B.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Gregor, A.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Guo, Y.

G. M. Rebeiz, D. P. Kasilingam, Y. Guo, P. A. Stimson, and D. B. Rutledge, “Monolithic millimeter-wave two-dimensional horn imaging arrays,” IEEE Trans. Antennas Propag. 38, 1473–1482 (1990).
[Crossref]

Hagelen, M.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Hall, T. E.

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Near-field three-dimensional radar imaging techniques and applications,” Appl. Opt. 49, E83–E93 (2010).
[Crossref] [PubMed]

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49, 1581–1592 (2001).
[Crossref]

Heinemann, B.

E. Ojefors, B. Heinemann, and U. R. Pfeiffer, “Active 220- and 325-GHz Frequency Multiplier Chains in an SiGe HBT Technology,” IEEE Trans. Microwave Theory Tech. 59, 1311–1318 (2011).
[Crossref]

Huck, J.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Hunt, J.

Kasilingam, D. P.

G. M. Rebeiz, D. P. Kasilingam, Y. Guo, P. A. Stimson, and D. B. Rutledge, “Monolithic millimeter-wave two-dimensional horn imaging arrays,” IEEE Trans. Antennas Propag. 38, 1473–1482 (1990).
[Crossref]

Kittle, D.

Kloppel, F.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[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 (2014).
[Crossref]

Las-Heras, F.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Liao, X.

Lipworth, G.

Liu, Q. H.

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[Crossref] [PubMed]

Llull, P.

Mait, J.

Mantzavinos, S.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Marks, D.

Martinez-Lorenzo, J. A.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Mattheiss, M.

McMakin, D. L.

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Near-field three-dimensional radar imaging techniques and applications,” Appl. Opt. 49, E83–E93 (2010).
[Crossref] [PubMed]

D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49, 1581–1592 (2001).
[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 (2014).
[Crossref]

Mrozack, A.

Nickerson, M.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Notel, D.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Ojefors, E.

E. Ojefors, B. Heinemann, and U. R. Pfeiffer, “Active 220- and 325-GHz Frequency Multiplier Chains in an SiGe HBT Technology,” IEEE Trans. Microwave Theory Tech. 59, 1311–1318 (2011).
[Crossref]

E. Ojefors and U. R. Pfeiffer, “A 650GHz SiGe receiver front-end for terahertz imaging arrays,” Solid-State Circuits Conference Digest of Technical Papers (ISSCC), 2010 IEEE International, 430–431, Feb. 2010.

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 (2014).
[Crossref]

Pagels, A.

S. Stanko, F. Kloppel, J. Huck, D. Notel, M. Hagelen, G. Briese, A. Gregor, S. Erukulla, H.-H. Fuchs, H. Essen, and A. Pagels, “Remote concealed weapon detection in millimeter-wave region: active and passive,” Proc. SPIE 6396, 639606, Oct2006.
[Crossref]

Parker, J. T.

L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, “Sparsity and Compressed Sensing in Radar Imaging,” Proceedings of the IEEE 98, 1006–1020 (2010).
[Crossref]

Pfeiffer, U. R.

E. Ojefors, B. Heinemann, and U. R. Pfeiffer, “Active 220- and 325-GHz Frequency Multiplier Chains in an SiGe HBT Technology,” IEEE Trans. Microwave Theory Tech. 59, 1311–1318 (2011).
[Crossref]

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

E. Ojefors and U. R. Pfeiffer, “A 650GHz SiGe receiver front-end for terahertz imaging arrays,” Solid-State Circuits Conference Digest of Technical Papers (ISSCC), 2010 IEEE International, 430–431, Feb. 2010.

Potter, L. C.

L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, “Sparsity and Compressed Sensing in Radar Imaging,” Proceedings of the IEEE 98, 1006–1020 (2010).
[Crossref]

Rahmann, S.

S. Rahmann and N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 149–155.

Rappaport, C. M.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Raskar, R.

G. Charvat, A. Temme, M. Feigin, and R. Raskar, “Time-of-Flight Microwave Camera,” Scientific Reports 5, 14709 (2015).
[Crossref] [PubMed]

Rebeiz, G. M.

G. M. Rebeiz, D. P. Kasilingam, Y. Guo, P. A. Stimson, and D. B. Rutledge, “Monolithic millimeter-wave two-dimensional horn imaging arrays,” IEEE Trans. Antennas Propag. 38, 1473–1482 (1990).
[Crossref]

Reynolds, M.

Reynolds, S. K.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE Journal of Solid-State Circuits 40, 156–167 (2005).
[Crossref]

Rodriguez-Vaqueiro, Y.

B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
[Crossref]

Romberg, J.

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B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. A. Martinez-Lorenzo, F. Las-Heras, and C. M. Rappaport, “Sparse Array Optimization Using Simulated Annealing and Compressed Sensing for Near-Field Millimeter Wave Imaging,” IEEE Trans. Antennas Propag. 62, 1716–1722 (2014).
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Figures (10)

Fig. 1
Fig. 1 W-band setup showing Tx and Rx modules. Tx is at a fixed location and Rx is on a x–y scanning stage.
Fig. 2
Fig. 2 Forward Model setup showing the stationary Tx and scanned Rx grid on the source/measurement aperture along with target voxels on the scene plane.
Fig. 3
Fig. 3 a). Shows the optical image of 3mm resolution target made of copper strips. b). Shows the W-band reconstructed image of the target from both simulation and measurement at a standoff distance of 15 cm. c). Shows the Rx grid and Tx locations relative to the target.
Fig. 4
Fig. 4 a). Shows the optical image of 5mm resolution target made of copper strips. b). Shows the W-band reconstructed image of the target from both simulation and measurement at a standoff distance of 30 cm.
Fig. 5
Fig. 5 a). Shows the optical image of 4mm depth resolution target made of copper strips. b). Shows the W-band reconstructed image (perspective and side view) of the target from both simulation and measurement at a standoff distance of 30 cm.
Fig. 6
Fig. 6 a). Shows the Tx and Rx modules with brass wire as the target. b) Shows the plot of normalized total information metric, Q, as a function of Tx/Rx aperture gain and standoff range distance. Points (1), (3) and (5) correspond to WR10 open ended waveguide element-apertures (low gain) for both Tx and Rx. Points (2), (4) and (6) correspond to WR10 standard pyramidal horn element-apertures (high gain) for both Tx and Rx.
Fig. 7
Fig. 7 Image reconstructions of a 1 mm wire target at a stand-off distance of 4 cm with WR10 open-ended waveguide and standard gain pyramidal horn on Tx/Rx. The line plots correspond to the dashed line region in the 2D measured plots. The corresponding information metric Q for these two cases corresponds to marked points (1) and (2) in Fig. 6.
Fig. 8
Fig. 8 Image reconstructions of a 1 mm wire target at a stand-off distance of 20 cm with WR10 open-ended waveguide and standard gain pyramidal horn on Tx/Rx. The line plots correspond to the dashed line region in the 2D measured plots. The corresponding information metric Q for these two cases corresponds to marked points (3) and (4) in Fig. 6.
Fig. 9
Fig. 9 Image reconstructions of a 1 mm wire target at a stand-off distance of 50 cm with WR10 open-ended waveguide and standard gain pyramidal horn on Tx/Rx. The line plots correspond to the dashed line region in the 2D measured plots. The corresponding information metric Q for these two cases corresponds to marked points (5) and (6) in Fig. 6.
Fig. 10
Fig. 10 Shows the effect of reducing the bandwidth on our frequency diverse computational imaging system. Shown are the experimental image reconstructions for the 3 mm resolution target.

Equations (20)

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g [ M × 1 ] = H [ M × N ] f [ N × 1 ]
f e = min f Hf g 2 2 + ϒ f 1 1
H ( { r T , r R , ω } , { r S } ) = α ( ω ) E ( r S ; r T , ω ) E ( r S ; r R , ω )
H m n = H ( { r T , r R , ω } m , { r S } n )
E = E 0 cos ( π y a ) x ^
E = E 0 cos ( π y a ) exp [ j ω 2 ( x 2 R 1 + y 2 R 2 ) ] x ^
M s = 2 n ^ × E
m p = ( j Δ x Δ y ω μ 0 ) M s
E ( r S ; r R or r T , ω ) = j ω μ 0 4 π Σ p [ ( m p × r S | r S | ) ( j k R p 1 R p 2 ) exp ( j k R p ) ]
Δ c r = λ R 2 D
Δ d r = c 2 B
Σ f = Δ f 2 I
Σ g = H Σ f H
Σ g = H Σ f H = US V Δ f 2 I ( US V ) = Δ f 2 US S U
σ g = δ g 2 I
γ = U g
σ γ = U σ g ( U ) = U δ g 2 I ( U ) = δ g 2 I
Σ γ = U Σ g ( U ) = U Δ f 2 US S U ( U ) = Δ f 2 S S
Q m = Δ t B log 2 [ Σ γ m m σ γ m m + 1 ] = Δ t B log 2 [ ( Δ f δ g S m m ) 2 + 1 ]
Q = m = 1 M Q m

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