Abstract

We present a method for realizing snapshot, depth-resolved material identification using only a single, energy-sensitive pixel. To achieve this result, we employ a coded aperture with subpixel features to modulate the energy spectrum of coherently scattered photons and recover the object properties using an iterative inversion algorithm based on compressed sensing theory. We demonstrate high-fidelity object estimation at x-ray wavelengths for a variety of compression ratios exceeding unity.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013

P. Stallforth and J. Clardy, Nature 495, 456 (2013).
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, and D. Brady, Opt. Express 21, 25480 (2013).
[CrossRef]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, Opt. Lett. 38, 2524 (2013).
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

2012

2011

2009

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

I. Robinson and R. Harder, Nat. Mater. 8, 291 (2009).
[CrossRef]

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

2008

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

2006

J. Delfs and J.-P. Schlomka, Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

1999

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

1990

G. Harding, M. Newton, and J. Kosanetzky, Phys. Med. Biol. 35, 33 (1990).
[CrossRef]

1974

1949

Andrés, P.

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Barnes, P.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Brady, D.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, and D. Brady, Opt. Express 21, 25480 (2013).
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, Opt. Express 20, 16310 (2012).
[CrossRef]

Brady, D. J.

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2008).

Candes, E.

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

Chan, J. W.

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, 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, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Chawla, A.

Chikkatur, A. P.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Clardy, J.

P. Stallforth and J. Clardy, Nature 495, 456 (2013).
[CrossRef]

Clemente, P.

Climent, V.

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Delfs, J.

J. Delfs and J.-P. Schlomka, Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

Dicken, A.

Driscoll, T.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Durán, V.

Edgar, M. P.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Evans, P.

Fellgett, P. B.

Fernández-Alonso, M.

Godber, S.

Gordon, J.

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

Greenberg, J. A.

J. A. Greenberg, K. Krishnamurthy, and D. Brady, Opt. Express 21, 25480 (2013).
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

Harder, R.

I. Robinson and R. Harder, Nat. Mater. 8, 291 (2009).
[CrossRef]

Harding, G.

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

G. Harding, M. Newton, and J. Kosanetzky, Phys. Med. Biol. 35, 33 (1990).
[CrossRef]

Hunt, J.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Inouye, S.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Jacques, S.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

Kapadia, A.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Ketterle, W.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Kosanetzky, J.

G. Harding, M. Newton, and J. Kosanetzky, Phys. Med. Biol. 35, 33 (1990).
[CrossRef]

Kosciesza, D.

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

Krishnamurthy, K.

Lakshmanan, M.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

Lancis, J.

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Lazzari, O.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

Lipworth, G.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

MacCabe, K.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, Opt. Express 20, 16310 (2012).
[CrossRef]

Marks, D.

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Mrozack, A.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Newton, M.

G. Harding, M. Newton, and J. Kosanetzky, Phys. Med. Biol. 35, 33 (1990).
[CrossRef]

Oliver, C. J.

Padgett, M. J.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Pike, E. R.

Pritchard, D. E.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Reynolds, M.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Robinson, I.

I. Robinson and R. Harder, Nat. Mater. 8, 291 (2009).
[CrossRef]

Rogers, J.

Rogers, K.

Samei, E.

Schlomka, J.-P.

J. Delfs and J.-P. Schlomka, Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

Smith, D. R.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Sochi, T.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

Stallforth, P.

P. Stallforth and J. Clardy, Nature 495, 456 (2013).
[CrossRef]

Stamper-Kurn, D. M.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Stenger, J.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Strecker, H.

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

Sun, B.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Tajahuerce, E.

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Wakin, M.

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Wolter, S.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

Analyst

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, Analyst 134, 1802 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. Delfs and J.-P. Schlomka, Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

IEEE Signal Process. Mag.

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

J. Opt. Soc. Am.

Nat. Mater.

I. Robinson and R. Harder, Nat. Mater. 8, 291 (2009).
[CrossRef]

Nature

P. Stallforth and J. Clardy, Nature 495, 456 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

G. Harding, M. Newton, and J. Kosanetzky, Phys. Med. Biol. 35, 33 (1990).
[CrossRef]

Phys. Rev. Lett.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 82, 4569 (1999).
[CrossRef]

Proc. SPIE

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, Proc. SPIE 8858, 885813 (2013).
[CrossRef]

G. Harding, H. Strecker, D. Kosciesza, and J. Gordon, Proc. SPIE 7306, 730619 (2009).

Science

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, Science 339, 310 (2013).
[CrossRef]

Other

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2008).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of setup showing the pencil beam illumination, object, coded aperture, and single pixel detector. (b) Simulated and (c) measured scatter spectrum at the detector with (solid blue line) and without (dashed red line) a coded aperture for a 10 mm diameter vial of graphite powder at z=157mm.

Fig. 2.
Fig. 2.

Object reconstruction results for a 10 mm wide vial of graphite placed at z=157mm. (a) The ground truth and (b) estimated two-dimensional object in qz space for CR=1. (c) Correlation r(z) along the range dimension. (d) Coherent scatter form factors obtained via conventional XRD (blue and green curves correspond to reference data at fine q sampling and interpolated at δq=0.2Å1) and SP-CACSSI (red).

Fig. 3.
Fig. 3.

Estimated object for compression ratios of (a) 4.5, (b) 13, and (c) 34. (d) Correlation between the true and estimated objects as a function of the compression ratio.

Equations (3)

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

q12d=Ehcsin(θ/2),
h(E,x;q,z)fΦ(E)t[x(1zmz)].
y(E,xd)fΦ(E)t[2hcq(zzm)E]rect[xd2hcqzEΔx].

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