Abstract

X-ray scattering has played a key role in non-destructive materials characterization due to the material-specific coherent scattering signatures. In the current energy dispersive coherent scatter imaging systems, including selected volume tomography and coherent scatter computed tomography, each object voxel is measured at a single scatter angle, which suffers from slow acquisition time. The employment of coded apertures in x-ray scatter imaging systems improves the photon collection efficiency, making it promising for real time volumetric imaging and material identification. In this paper, we propose a volumetric x-ray scatter imaging system using a pair of complementary coded apertures: a coded aperture on the detector side introduces multiplexed measurement on an energy-sensitive detector array; a complementary source-side coded aperture selectively illuminates the object to decouple the ambiguity due to the increased parallelization for 4D imaging. The system yields the 1D coherent scattering form factor at each voxel in 3D. We demonstrate tomographic imaging and material identification with the system and achieve a spatial resolution ~1 cm and a normalized momentum transfer resolution, Δq/q, of 0.2.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  3. C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
    [Crossref]
  4. J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
    [Crossref]
  5. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  12. J. A. Greenberg, K. Krishnamurthy, and D. Brady, “Snapshot molecular imaging using coded energy-sensitive detection,” Opt. Express 21(21), 25480–25491 (2013), http://www.opticsexpress.org/abstract.cfm?URI=oe-21-21-25480 .
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. A. Mrozack, D. L. Marks, and D. J. Brady, “Coded aperture spectroscopy with denoising through sparsity,” Opt. Express 20(3), 2297–2309 (2012), http://www.opticsexpress.org/abstract.cfm?URI=oe-20-3-2297 .
    [Crossref] [PubMed]
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    [Crossref]
  18. G. Harding and J. Kosanetzky, “Status and outlook of coherent-x-ray scatter imaging,” J. Opt. Soc. Am. A 4(5), 933–944 (1987), http://www.ncbi.nlm.nih.gov/pubmed/3598745 .
    [Crossref] [PubMed]
  19. D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
    [Crossref] [PubMed]

2014 (2)

J. Greenberg, K. Krishnamurthy, and D. Brady, “Compressive single-pixel snapshot x-ray diffraction imaging,” Opt. Lett. 39(1), 111–114 (2014), http://www.ncbi.nlm.nih.gov/pubmed/24365835 .
[Crossref] [PubMed]

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic X-ray diffraction imaging,” Analyst (Lond.) 139(4), 709–713 (2014), http://www.ncbi.nlm.nih.gov/pubmed/24340351 .
[Crossref] [PubMed]

2013 (3)

2012 (2)

2009 (1)

G. Harding, “X-ray diffraction imaging--a multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009), http://www.ncbi.nlm.nih.gov/pubmed/18805014 .
[Crossref] [PubMed]

2007 (1)

D. J. Brenner and E. J. Hall, “Computed tomography-an increasing source of radiation exposure,” N. Engl. J. Med. 357(22), 2277–2284 (2007), http://www.nejm.org/doi/full/10.1056/nejmra072149 .
[Crossref] [PubMed]

2006 (1)

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

1996 (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

1995 (2)

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

1991 (1)

J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
[Crossref]

1987 (1)

1972 (1)

1959 (1)

P. G. Lale, “The Examination of Internal Tissues, using Gamma-ray Scatter with a Possible Extension to Megavoltage Radiography,” Phys. Med. Biol. 4(2), 159–167 (1959), http://iopscience.iop.org/0031-9155/4/2/305 .
[Crossref] [PubMed]

Babot, D.

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

Batchelar, D. L.

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

Brady, D.

Brady, D. J.

Brenner, D. J.

D. J. Brenner and E. J. Hall, “Computed tomography-an increasing source of radiation exposure,” N. Engl. J. Med. 357(22), 2277–2284 (2007), http://www.nejm.org/doi/full/10.1056/nejmra072149 .
[Crossref] [PubMed]

Brohl, M.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Chawla, A.

Cunningham, I. A.

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

Dabrowski, W.

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

Davidson, M. T. M.

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

Gao, D.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Gonsalves, R. A.

J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
[Crossref]

Greenberg, J.

Greenberg, J. A.

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic X-ray diffraction imaging,” Analyst (Lond.) 139(4), 709–713 (2014), http://www.ncbi.nlm.nih.gov/pubmed/24340351 .
[Crossref] [PubMed]

J. A. Greenberg, K. Krishnamurthy, and D. Brady, “Snapshot molecular imaging using coded energy-sensitive detection,” Opt. Express 21(21), 25480–25491 (2013), http://www.opticsexpress.org/abstract.cfm?URI=oe-21-21-25480 .
[Crossref] [PubMed]

Gureyev, T. E.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Hall, E. J.

D. J. Brenner and E. J. Hall, “Computed tomography-an increasing source of radiation exposure,” N. Engl. J. Med. 357(22), 2277–2284 (2007), http://www.nejm.org/doi/full/10.1056/nejmra072149 .
[Crossref] [PubMed]

Harding, G.

G. Harding, “X-ray diffraction imaging--a multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009), http://www.ncbi.nlm.nih.gov/pubmed/18805014 .
[Crossref] [PubMed]

G. Harding and J. Kosanetzky, “Status and outlook of coherent-x-ray scatter imaging,” J. Opt. Soc. Am. A 4(5), 933–944 (1987), http://www.ncbi.nlm.nih.gov/pubmed/3598745 .
[Crossref] [PubMed]

Hassan, M.

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic X-ray diffraction imaging,” Analyst (Lond.) 139(4), 709–713 (2014), http://www.ncbi.nlm.nih.gov/pubmed/24340351 .
[Crossref] [PubMed]

Hogan, J. P.

J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
[Crossref]

Holmgren, A. D.

Kosanetzky, J.

Krieger, A. S.

J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
[Crossref]

Krishnamurthy, K.

Lagally, M. G.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Lale, P. G.

P. G. Lale, “The Examination of Internal Tissues, using Gamma-ray Scatter with a Possible Extension to Megavoltage Radiography,” Phys. Med. Biol. 4(2), 159–167 (1959), http://iopscience.iop.org/0031-9155/4/2/305 .
[Crossref] [PubMed]

MacCabe, K.

MacCabe, K. P.

MacKay, J. F.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Marks, D.

Marks, D. L.

Mrozack, A.

Muller, J.

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

O’Sullivan, J. A.

Peix, G.

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

Pogany, A.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Richardson, W. H.

Samei, E.

Savage, D. E.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Stevenson, A. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Teichert, C.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Tornai, M. P.

Wagner, P.

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Wilkins, S. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Zhu, P.

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

Analyst (Lond.) (1)

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic X-ray diffraction imaging,” Analyst (Lond.) 139(4), 709–713 (2014), http://www.ncbi.nlm.nih.gov/pubmed/24340351 .
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. Teichert, J. F. MacKay, D. E. Savage, M. G. Lagally, M. Brohl, and P. Wagner, “Comparison of surface roughness of polished silicon wafers measured by light scattering topography, soft-x-ray scattering, and atomic-force microscopy,” Appl. Phys. Lett. 66(18), 2346 (1995), http://scitation.aip.org/content/aip/journal/apl/66/18/10.1063/1.113978 .
[Crossref]

Appl. Radiat. Isot. (1)

G. Harding, “X-ray diffraction imaging--a multi-generational perspective,” Appl. Radiat. Isot. 67(2), 287–295 (2009), http://www.ncbi.nlm.nih.gov/pubmed/18805014 .
[Crossref] [PubMed]

IEEE Trans. Nucl. Sci. (1)

J. P. Hogan, R. A. Gonsalves, and A. S. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nucl. Sci. 38(6), 1721–1727 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

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

Med. Phys. (1)

D. L. Batchelar, M. T. M. Davidson, W. Dabrowski, and I. A. Cunningham, “Bone-composition imaging using coherent-scatter computed tomography: Assessing bone health beyond bone mineral density,” Med. Phys. 33(4), 904–915 (2006), http://scitation.aip.org/content/aapm/journal/medphys/33/4/10.1118/1.2179151 .
[Crossref] [PubMed]

N. Engl. J. Med. (1)

D. J. Brenner and E. J. Hall, “Computed tomography-an increasing source of radiation exposure,” N. Engl. J. Med. 357(22), 2277–2284 (2007), http://www.nejm.org/doi/full/10.1056/nejmra072149 .
[Crossref] [PubMed]

Nature (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

NDT Int. (1)

P. Zhu, G. Peix, D. Babot, and J. Muller, “In-line density measurement system using X-ray Compton scattering,” NDT Int. 28(1), 3–7 (1995), http://www.sciencedirect.com/science/article/pii/0963869594000088 .
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Med. Biol. (1)

P. G. Lale, “The Examination of Internal Tissues, using Gamma-ray Scatter with a Possible Extension to Megavoltage Radiography,” Phys. Med. Biol. 4(2), 159–167 (1959), http://iopscience.iop.org/0031-9155/4/2/305 .
[Crossref] [PubMed]

Other (2)

G. Harding and B. Schreiber, “Coherent X-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem., 56 (1)–(2), 229–245, (1999), URL: http://linkinghub.elsevier.com/retrieve/pii/S0969806X99002832 .
[Crossref]

G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem., 71 (3)–(4), 869–881, (2004), URL: http://linkinghub.elsevier.com/retrieve/pii/S0969806X04003081 .

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Figures (6)

Fig. 1
Fig. 1 Geometric setup for the coded aperture x-ray coherent scatter imaging system.
Fig. 2
Fig. 2 Scatter imaging system setup. (a) System schematics. (b) Photos of the system setup (b1), which includes the detector side mask (b2) and source side mask (b3).
Fig. 3
Fig. 3 Imaging of an object graphite point object. (a) Simulation of one snapshot coherent scattering measurement. (b) The experimental results. (c) The reconstruction of an point graphite cube of 1 cm3 .
Fig. 4
Fig. 4 Comparison between system with and without the illumination masks. (a) Experimental measurement of an aluminum object extended in y direction without structured illumination. (b) Experimental measurement of the same object with structured illumination. (c) Reconstruction of the object without structured illumination in q, z space. (d) Reconstruction of the object with structured illumination.
Fig. 5
Fig. 5 (a) Form factor resolution, Δq, as a function of illumination duty cycle. (b) Cross-correlation coefficients map of the extended object with duty cycles of 50% (b1), and 12.5% (b2).
Fig. 6
Fig. 6 Imaging of 4-dimensional object (a) 3D rendered pseudo-colored image of two object, a Teflon letter “D” and a graphite letter “U”. (b) The photograph of the two objects. (c-d) The interpolated correlation map of the object of the letter “U”(c), and the letter “D” (d). (e-f) the reconstructed form factor of the letter “U” made of graphite (e) and the form factor of the letter “D” made of Teflon (f).

Equations (16)

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

b ( E , r ) = 1 r s c 2 cos θ s c S ( E , E ' ) d Φ s c d E ' ,
  d Φ s c ( E ) = d Φ i n ( E ) T ( r , r ' ) d σ c o h d Ω d z d q ,
β ( z ) ( z l ) / ( z z ) ,
T ( r , r ' ) = t ( x ' β + x ( 1 β ) , y ' β + y ( 1 β ) ) .
T ( r ,   r ' ) = ( 1 cos [ 2 π u ( y ' β + y ( 1 β ) ) ] ) / 2 .
d σ c o h d Ω = r e 2 2 ( 1 + cos 2 θ ) f ( r , q ) = r e 2 2 ( 1 + cos 2 θ ) n ( r ) f 0 ( r , q ) ,
q = E sin θ / 2 h c .
b ( E , y ) = r e 2 4 2 π Δ E I i n ( r , E ) exp ( ( E q h c sin θ 2 ) 2 / 2 Δ E 2 ) | z z | r s c 3 | z | r 3 ( 1 + cos 2 θ )   f ( x , y , z , q ) ( 1 cos [ 2 π u ( y β + y ( 1 β ) ) ] ) d r d q .
g ( E , y , t ) = U ( E , y , r , q ) f ( x + v t , y , z , q ) ( 1 cos [ 2 π u ( y β + y ( 1 β ) ) ] ) d r d q ,
y = m u ( 1 β c ) + y 0 ,     m = 0 ,   ± 1 , ± 2 ,
u s = u ( 1 β c ) d z c .
y n o i s e = Pois ( g + μ b ) ,
f ^ = arg min f ( log P ( y n o i s e | f , y b ) ) ,
Δ q q = ( Δ E E ) 2 + ( Δ θ θ ) 2
Δ z = E m i n 4 h c u q
δ θ θ = [ ( E m i n 2 h c q ) 2 ( ( Δ x z z ' ) 2 + ( Δ y z z ' ) 2 ) + ( Δ z z z ' ) 2 ] 1 / 2

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