Abstract

We demonstrate tomography by measuring a sporadic sequence of ring shaped projections collected during a translational scan. We show that projections using 10% sampling may be used to construct optical sections with peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) of the order of 40 dB and 0.9, respectively. This relatively small degradation in image fidelity was achieved for a 90% potential reduction in X-ray dose coupled with a reduction in scan time. Our approach is scalable in both X-ray energy and inspection volume. A driver for our method is to complement previously reported conical shell beam techniques concerning the measurement of diffracted flux for structural analysis. This work is of great relevance to time critical analytical scanning applications in security screening, process control and diagnostic imaging.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

A. P. Cuadros and G. R. Arce, “Coded aperture optimization in compressive X-ray tomography: a gradient descent approach,” Opt. Express 25(20), 23833–23849 (2017).
[Crossref] [PubMed]

2016 (4)

M. Hassan, J. A. Greenberg, I. Odinaka, and D. J. Brady, “Snapshot fan beam coded aperture coherent scatter tomography,” Opt. Express 24(16), 18277–18289 (2016).
[Crossref] [PubMed]

J. P. O. Evans, S. X. Godber, F. Elarnaut, D. Downes, A. J. Dicken, and K. D. Rogers, “X-ray absorption tomography employing a conical shell beam,” Opt. Express 24(25), 29048–29059 (2016).
[Crossref] [PubMed]

F. Li, Z. Liu, and T. Sun, “Annular beam high-intensity X-ray diffraction based on an ellipsoidal single-bounce monocapillary,” J. Appl. Cryst. 49(2), 627–631 (2016).
[Crossref]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

2015 (4)

2014 (4)

P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22(10), 11930–11944 (2014).
[Crossref] [PubMed]

Y. Kaganovsky, D. Li, A. Holmgren, H. Jeon, K. P. MacCabe, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Compressed sampling strategies for tomography,” J. Opt. Soc. Am. A 31(7), 1369–1394 (2014).
[Crossref] [PubMed]

P. Mohammadi, A. Ebrahimi-Moghadam, and S. Shirani, “Subjective and Objective Quality Assessment of Image,” Survey (Lond.) 41, 6738079 (2014).

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

2013 (1)

D. Prokopiou, K. Rogers, P. Evans, S. Godber, and A. Dicken, “Discrimination of liquids by a focal construct X-ray diffraction geometry,” Appl. Radiat. Isot. 77, 160–165 (2013).
[Crossref] [PubMed]

2012 (3)

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

K. Wells and D. A. Bradley, “A review of X-ray explosives detection techniques for checked baggage,” Appl. Radiat. Isot. 70(8), 1729–1746 (2012).
[Crossref] [PubMed]

F. Xu, L. Helfen, T. Baumbach, and H. Suhonen, “Comparison of image quality in computed laminography and tomography,” Opt. Express 20(2), 794–806 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (2)

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

2009 (1)

G. Harding, “X-ray diffraction imaging-A multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009).
[Crossref] [PubMed]

2006 (1)

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

2002 (1)

J. P. O. Evans and H. W. Hon, “Dynamic stereoscopic X-ray imaging,” NDT Int. 35(5), 337–345 (2002).
[Crossref]

2000 (1)

J. P. O. Evans and M. Robinson, “Design of a stereoscopic X-ray imaging system using a single X-ray source,” NDT Int. 33(5), 325–332 (2000).
[Crossref]

1983 (1)

S. Baumrind, F. H. Moffitt, and S. Curry, “The geometry of three-dimensional measurement from paired coplanar X-ray images,” Am. J. Orthod. 84(4), 313–322 (1983).
[Crossref] [PubMed]

Arce, G. R.

Arguello, H.

Baumbach, T.

Baumrind, S.

S. Baumrind, F. H. Moffitt, and S. Curry, “The geometry of three-dimensional measurement from paired coplanar X-ray images,” Am. J. Orthod. 84(4), 313–322 (1983).
[Crossref] [PubMed]

Beale, A. M.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

Bradley, D. A.

K. Wells and D. A. Bradley, “A review of X-ray explosives detection techniques for checked baggage,” Appl. Radiat. Isot. 70(8), 1729–1746 (2012).
[Crossref] [PubMed]

Brady, D. J.

Carin, L.

Cernik, R. J.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Chan, J.

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

Chan, J. W.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

Clement, J. G.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

Cuadros, A. P.

Curry, S.

S. Baumrind, F. H. Moffitt, and S. Curry, “The geometry of three-dimensional measurement from paired coplanar X-ray images,” Am. J. Orthod. 84(4), 313–322 (1983).
[Crossref] [PubMed]

Di Michiel, M.

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

Dicken, A.

A. Dicken, A. Shevchuk, K. Rogers, S. Godber, and P. Evans, “High energy transmission annular beam X-ray diffraction,” Opt. Express 23(5), 6304–6312 (2015).
[Crossref] [PubMed]

P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22(10), 11930–11944 (2014).
[Crossref] [PubMed]

D. Prokopiou, K. Rogers, P. Evans, S. Godber, and A. Dicken, “Discrimination of liquids by a focal construct X-ray diffraction geometry,” Appl. Radiat. Isot. 77, 160–165 (2013).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

Dicken, A. J.

Dörr, J.

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

Downes, D.

J. P. O. Evans, S. X. Godber, F. Elarnaut, D. Downes, A. J. Dicken, and K. D. Rogers, “X-ray absorption tomography employing a conical shell beam,” Opt. Express 24(25), 29048–29059 (2016).
[Crossref] [PubMed]

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

Ebrahimi-Moghadam, A.

P. Mohammadi, A. Ebrahimi-Moghadam, and S. Shirani, “Subjective and Objective Quality Assessment of Image,” Survey (Lond.) 41, 6738079 (2014).

Egan, C. K.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Elarnaut, F.

Evans, J. P. O.

J. P. O. Evans, S. X. Godber, F. Elarnaut, D. Downes, A. J. Dicken, and K. D. Rogers, “X-ray absorption tomography employing a conical shell beam,” Opt. Express 24(25), 29048–29059 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

J. P. O. Evans and H. W. Hon, “Dynamic stereoscopic X-ray imaging,” NDT Int. 35(5), 337–345 (2002).
[Crossref]

J. P. O. Evans and M. Robinson, “Design of a stereoscopic X-ray imaging system using a single X-ray source,” NDT Int. 33(5), 325–332 (2000).
[Crossref]

Evans, P.

A. Dicken, A. Shevchuk, K. Rogers, S. Godber, and P. Evans, “High energy transmission annular beam X-ray diffraction,” Opt. Express 23(5), 6304–6312 (2015).
[Crossref] [PubMed]

P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22(10), 11930–11944 (2014).
[Crossref] [PubMed]

D. Prokopiou, K. Rogers, P. Evans, S. Godber, and A. Dicken, “Discrimination of liquids by a focal construct X-ray diffraction geometry,” Appl. Radiat. Isot. 77, 160–165 (2013).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

Gibson, E. K.

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

Godber, S.

Godber, S. X.

Greenberg, J. A.

Greenwood, C.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

Harding, G.

G. Harding, “X-ray diffraction imaging-A multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009).
[Crossref] [PubMed]

Hassan, M.

Helfen, L.

Holmgren, A.

Hon, H. W.

J. P. O. Evans and H. W. Hon, “Dynamic stereoscopic X-ray imaging,” NDT Int. 35(5), 337–345 (2002).
[Crossref]

Jacques, S. D. M.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

Jeon, H.

Kaganovsky, Y.

Kandlakunta, P.

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

Khan, R.

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

Li, D.

Li, F.

F. Li, Z. Liu, and T. Sun, “Annular beam high-intensity X-ray diffraction based on an ellipsoidal single-bounce monocapillary,” J. Appl. Cryst. 49(2), 627–631 (2016).
[Crossref]

Liu, Y.

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

Liu, Z.

F. Li, Z. Liu, and T. Sun, “Annular beam high-intensity X-ray diffraction based on an ellipsoidal single-bounce monocapillary,” J. Appl. Cryst. 49(2), 627–631 (2016).
[Crossref]

Lyburn, I.

Lyburn, I. D.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

MacCabe, K. P.

Martin, R. M.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

Moffitt, F. H.

S. Baumrind, F. H. Moffitt, and S. Curry, “The geometry of three-dimensional measurement from paired coplanar X-ray images,” Am. J. Orthod. 84(4), 313–322 (1983).
[Crossref] [PubMed]

Mohammadi, P.

P. Mohammadi, A. Ebrahimi-Moghadam, and S. Shirani, “Subjective and Objective Quality Assessment of Image,” Survey (Lond.) 41, 6738079 (2014).

O’Sullivan, J. A.

Odinaka, I.

Pattrick, R. A. D.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Peitsch, C.

Pham, R.

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

Politte, D. G.

Prokopiou, D.

Robinson, M.

J. P. O. Evans and M. Robinson, “Design of a stereoscopic X-ray imaging system using a single X-ray source,” NDT Int. 33(5), 325–332 (2000).
[Crossref]

Rogers, J.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

Rogers, K.

A. Dicken, A. Shevchuk, K. Rogers, S. Godber, and P. Evans, “High energy transmission annular beam X-ray diffraction,” Opt. Express 23(5), 6304–6312 (2015).
[Crossref] [PubMed]

P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22(10), 11930–11944 (2014).
[Crossref] [PubMed]

D. Prokopiou, K. Rogers, P. Evans, S. Godber, and A. Dicken, “Discrimination of liquids by a focal construct X-ray diffraction geometry,” Appl. Radiat. Isot. 77, 160–165 (2013).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

Rogers, K. D.

Rosenbaum, M.

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

Sauer-Greff, W.

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

Seller, P.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Shevchuk, A.

Shirani, S.

P. Mohammadi, A. Ebrahimi-Moghadam, and S. Shirani, “Subjective and Objective Quality Assessment of Image,” Survey (Lond.) 41, 6738079 (2014).

Stone, N.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

Suhonen, H.

Sun, T.

F. Li, Z. Liu, and T. Sun, “Annular beam high-intensity X-ray diffraction based on an ellipsoidal single-bounce monocapillary,” J. Appl. Cryst. 49(2), 627–631 (2016).
[Crossref]

Urbansky, R.

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

Veale, M. C.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Wells, K.

K. Wells and D. A. Bradley, “A review of X-ray explosives detection techniques for checked baggage,” Appl. Radiat. Isot. 70(8), 1729–1746 (2012).
[Crossref] [PubMed]

Wilson, M. D.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Withers, P. J.

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Xu, F.

Zhang, T.

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

Zioupos, P.

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

Adv. Radio Sci (1)

J. Dörr, M. Rosenbaum, W. Sauer-Greff, and R. Urbansky, “Automatic focus algorithms for TDI X-Ray image reconstruction,” Adv. Radio Sci 10, 145–151 (2012).
[Crossref]

Am. J. Orthod. (1)

S. Baumrind, F. H. Moffitt, and S. Curry, “The geometry of three-dimensional measurement from paired coplanar X-ray images,” Am. J. Orthod. 84(4), 313–322 (1983).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

P. Evans, K. Rogers, J. Chan, J. Rogers, and A. Dicken, “High intensity X-ray diffraction in transmission mode employing an analog of Poisson’s spot,” Appl. Phys. Lett. 97(20), 204101 (2010).
[Crossref]

Appl. Radiat. Isot. (4)

D. Prokopiou, K. Rogers, P. Evans, S. Godber, and A. Dicken, “Discrimination of liquids by a focal construct X-ray diffraction geometry,” Appl. Radiat. Isot. 77, 160–165 (2013).
[Crossref] [PubMed]

K. Wells and D. A. Bradley, “A review of X-ray explosives detection techniques for checked baggage,” Appl. Radiat. Isot. 70(8), 1729–1746 (2012).
[Crossref] [PubMed]

G. Harding, “X-ray diffraction imaging-A multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radiat. Isot. 68(3), 439–443 (2010).
[Crossref] [PubMed]

Coord. Chem. Rev. (1)

A. M. Beale, S. D. M. Jacques, E. K. Gibson, and M. Di Michiel, “Progress towards five dimensional diffraction imaging of functional materials under process conditions,” Coord. Chem. Rev. 277–278, 208–223 (2014).
[Crossref]

J. Appl. Cryst. (1)

F. Li, Z. Liu, and T. Sun, “Annular beam high-intensity X-ray diffraction based on an ellipsoidal single-bounce monocapillary,” J. Appl. Cryst. 49(2), 627–631 (2016).
[Crossref]

J. Opt. Soc. Am. A (1)

NDT Int. (2)

J. P. O. Evans and H. W. Hon, “Dynamic stereoscopic X-ray imaging,” NDT Int. 35(5), 337–345 (2002).
[Crossref]

J. P. O. Evans and M. Robinson, “Design of a stereoscopic X-ray imaging system using a single X-ray source,” NDT Int. 33(5), 325–332 (2000).
[Crossref]

Opt. Express (9)

A. Dicken, A. Shevchuk, K. Rogers, S. Godber, and P. Evans, “High energy transmission annular beam X-ray diffraction,” Opt. Express 23(5), 6304–6312 (2015).
[Crossref] [PubMed]

A. J. Dicken, J. P. O. Evans, K. D. Rogers, C. Greenwood, S. X. Godber, D. Prokopiou, N. Stone, J. G. Clement, I. Lyburn, R. M. Martin, and P. Zioupos, “Energy-dispersive X-ray diffraction using an annular beam,” Opt. Express 23(10), 13443–13454 (2015).
[Crossref] [PubMed]

A. P. Cuadros, C. Peitsch, H. Arguello, and G. R. Arce, “Coded aperture optimization for compressive X-ray tomosynthesis,” Opt. Express 23(25), 32788–32802 (2015).
[Crossref] [PubMed]

M. Hassan, J. A. Greenberg, I. Odinaka, and D. J. Brady, “Snapshot fan beam coded aperture coherent scatter tomography,” Opt. Express 24(16), 18277–18289 (2016).
[Crossref] [PubMed]

J. P. O. Evans, S. X. Godber, F. Elarnaut, D. Downes, A. J. Dicken, and K. D. Rogers, “X-ray absorption tomography employing a conical shell beam,” Opt. Express 24(25), 29048–29059 (2016).
[Crossref] [PubMed]

A. P. Cuadros and G. R. Arce, “Coded aperture optimization in compressive X-ray tomography: a gradient descent approach,” Opt. Express 25(20), 23833–23849 (2017).
[Crossref] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express 19(7), 6406–6413 (2011).
[Crossref] [PubMed]

F. Xu, L. Helfen, T. Baumbach, and H. Suhonen, “Comparison of image quality in computed laminography and tomography,” Opt. Express 20(2), 794–806 (2012).
[Crossref] [PubMed]

P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22(10), 11930–11944 (2014).
[Crossref] [PubMed]

Pattern Recognit. Lett. (1)

J. P. O. Evans, Y. Liu, J. W. Chan, and D. Downes, “View synthesis for depth from motion 3D X-ray imaging,” Pattern Recognit. Lett. 27(15), 1863–1873 (2006).
[Crossref]

Phys. Med. Biol. (1)

P. Kandlakunta, R. Pham, R. Khan, and T. Zhang, “Development of multi-pixel x-ray source using oxide-coated cathodes,” Phys. Med. Biol. 62(13), N320–N336 (2017).
[Crossref] [PubMed]

Sci. Rep. (2)

A. J. Dicken, J. P. O. Evans, K. D. Rogers, N. Stone, C. Greenwood, S. X. Godber, J. G. Clement, I. D. Lyburn, R. M. Martin, and P. Zioupos, “Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter,” Sci. Rep. 6(1), 29011 (2016).
[Crossref] [PubMed]

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref] [PubMed]

Survey (Lond.) (1)

P. Mohammadi, A. Ebrahimi-Moghadam, and S. Shirani, “Subjective and Objective Quality Assessment of Image,” Survey (Lond.) 41, 6738079 (2014).

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S. Singh and M. Singh, “Explosives detection systems (EDS) for aviation security,” Signal Proc. 83(1), 31–55 (2003).

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Supplementary Material (2)

NameDescription
» Visualization 1       Video montage of four tomographic X-ray image sequences produced using a hollow beam.
» Visualization 2       Video montage of four tomographic X-ray image sequences produced using a hollow beam.

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Figures (12)

Fig. 1
Fig. 1 Binary image or map ρ representing the pseudorandom distribution of (annular) image acquisition points with unity pixels and non-acquisitions or nulls with zero pixels. A rectilinear sampling grid of X-ray source positions over the scanned area A is related to ρ by scaling the separation between pixel centers by the scan step size S.
Fig. 2
Fig. 2 Pixels recorded at fixed circumferential locations from each conical shell X-ray projection are composited to form a sporadically sampled oblique projection. The total number of projections are limited by the resolution of the annular sensor (or virtual equivalent). The resolution in pixels of each oblique image equates to the total number of potential acquisition points in the full sampling grid. The relative position of pixels representing nulls (highlighted in black) is identical for every oblique projection as defined by the map ρ.
Fig. 3
Fig. 3 An example radial shift applied to image set M to form a reregistered sequence of oblique images D.
Fig. 4
Fig. 4 Calibrated phantom (~1:4 scale) comprising of 100 mm square, 1 mm thick acrylic sheets supporting flat shapes fabricated from 0.15 mm thick tin. The “knife” and the “scissors” are both on the middle layer with the “phone” and the “gun” on the top and bottom layers, respectively.
Fig. 5
Fig. 5 Luggage core phantom mounted on the carbon fiber translation table in the X-ray inspection chamber. An aggregate of discrete objects, arranged along a ~40 cm component of the z-axis, were supported by polystyrene foam. A mobile phone was positioned nearest the image intensifier input window and a disc of soap together with a paperclip nearest the source. Midway along the core a plastic marker pen (elliptical cross-section) and a medical inhaler containing a pressurized canister (circular cross-section) were arranged with their long axes approximately parallel to the principal phantom axis. Also, two fine gauge wires run from a circular metal contact (initially as a twisted pair) at the center of the soap along the full length of the phantom to the phone.
Fig. 6
Fig. 6 Examples showing (32x32) areas extracted from higher resolution (500x500) pseudorandom maps ρ of sampling levels; left (50%), middle (20%) and right (10%). The black pixels have a one-to-one relationship with nulls in the oblique projections.
Fig. 7
Fig. 7 Fill factor - radial shift characteristics for contribution or normalization maps ω (500x500 pixels) with sampling levels of 50%, 20% and 10%, respectively. The range of r is truncated to illustrate initial growth.
Fig. 8
Fig. 8 Fill factor - radial shift characteristics for contribution or normalization maps ω (700x700 pixels) with sampling of 50%, 25% and 10%, respectively. The range of r is truncated to illustrate initial growth.
Fig. 9
Fig. 9 Optical sections from the calibrated phantom. Row A is 100% sampling or Ground Truth, Row B 50% sampling, and Row C 10% sampling. Column 1 shows the layer (z = 106 mm, r = 46 pixels) nearest the source containing the gun shape, column 2 shows the middle layer (z = 137 mm, r = 59 pixels) containing the knife and scissors, and column 3 the layer nearest the detector (z = 167 mm, r = 72 pixels) containing the phone shape; where the preceding values (z, r) specify the focal plane position and the digital shift radius, respectively. All oblique images and optical sections have a resolution of 500x500 pixels. A direct comparison of optical sections at successive focal plane positions can be seen in (Visualization 1) for; 100%, 50%, 20% and 10% sampling, where a frame-by-frame readout of the corresponding PSNR and SSIM are provided within a video montage.
Fig. 10
Fig. 10 SSIM of optical sections (500x500 pixels) from the calibrated phantom for 50%, 20% and 10% sampling.
Fig. 11
Fig. 11 Optical sections from the luggage phantom. Row A 100% sampling is Ground Truth, Row B 50% sampling, and Row C 10% sampling. Column 1 nearest the source (z = 114mm, r = 36 pixels) shows the disc of soap together with a paperclip, column 2 midway (z = 292 mm, r = 92 pixels) shows a plastic marker pen (elliptical cross-section) and a medical inhaler containing a pressurized canister (circular cross-section), and column 3 nearest the detector (z = 502 mm, r = 158 pixels) the mobile phone; where the preceding values (z, r) specify the focal plane position and the digital shift radius, respectively. All oblique images and optical sections have a resolution of 700x700 pixels. A direct comparison of optical sections at successive focal plane positions can be seen in (Visualization 2) for; 100%, 50%, 25% and 10% sampling, where a frame-by-frame readout of the corresponding PSNR and SSIM are provided within a video montage.
Fig. 12
Fig. 12 SSIM of optical sections (700x700 pixels) from the luggage core phantom for 50%, 25% and 10% sampling.

Tables (2)

Tables Icon

Table 1 Calibrated phantom PSNR and SSIM for rows B and C indexed in Fig. 9 (where row A is Ground Truth). Row B′ provides additional values.

Tables Icon

Table 2 Luggage phantom PSNR and SSIM for rows B and C indexed in Fig. 11 (where row A is Ground Truth). Row B′ provides additional values.

Equations (8)

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

x=S x ρ +lcosγ
y=S y ρ +lsinγ
a= 2π v .
D(γ, x D , y D )=M(γ, x M , y M )
x D = x M +rcosγ+0.5 y D = y M +rsinγ+0.5
ω= i=1 v D ρ ( i )
G= i=1 v D( i ) .
R(x,y)= G(x,y) ω(x,y) .

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