Abstract

X-ray phase contrast imaging provides additional modes of image contrast compared to conventional attenuation-based x-ray imaging, thus providing additional structural and functional information about the sample. The edge-illumination (EI) technique has been used to provide attenuation, refraction, and scattering contrast in both biological and non-biological samples. However, the retrieval of low scattering signals by fitting a single Gaussian remains problematic, principally due to the inability of the EI system to achieve perfect dark-field illumination. We present a new retrieval method that fits three Gaussians, which successfully overcomes this limitation, and provide examples of the retrieval of such signals in highly absorbing, weakly scattering samples.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
  2. A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
    [Crossref]
  3. A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
    [Crossref]
  4. A. Olivo and R. Speller, Appl. Phys. Lett. 91, 074106 (2007).
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  5. P. R. T. Munro, C. K. Hagen, M. B. Szafraniec, and A. Olivo, Opt. Express 21, 11187 (2013).
    [Crossref]
  6. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
    [Crossref]
  7. L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
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    [Crossref]
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2017 (2)

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

C. J. Maughan Jones and P. R. T. Munro, J. Biomed. Opt. 22, 1 (2017).
[Crossref]

2016 (1)

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

2015 (3)

M. Endrizzi, B. I. S. Murat, P. Fromme, and A. Olivo, Compos. Struct. 134, 895 (2015).
[Crossref]

M. Endrizzi, D. Basta, and A. Olivo, Appl. Phys. Lett. 107, 124103 (2015).
[Crossref]

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

2014 (3)

M. Endrizzi and A. Olivo, J. Phys. D 47, 505102 (2014).
[Crossref]

A. Olivo and E. Castelli, Riv. del Nuovo Cimento 37, 467 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

2013 (2)

2008 (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

2007 (1)

A. Olivo and R. Speller, Appl. Phys. Lett. 91, 074106 (2007).
[Crossref]

2003 (1)

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

2002 (2)

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

M. E. Poletti, O. D. Goncalves, and I. Mazzaro, Phys. Med. Biol. 47, 47 (2002).
[Crossref]

2001 (1)

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Arfelli, F.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Basta, D.

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

M. Endrizzi, D. Basta, and A. Olivo, Appl. Phys. Lett. 107, 124103 (2015).
[Crossref]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Benarafa, C.

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

Besch, H.-J.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[Crossref]

Brönnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Cantatore, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Castelli, E.

A. Olivo and E. Castelli, Riv. del Nuovo Cimento 37, 467 (2014).
[Crossref]

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Coan, P.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[Crossref]

Cremona, T. P.

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

David, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Diemoz, P. C.

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Dreossi, D.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Endrizzi, M.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

M. Endrizzi, D. Basta, and A. Olivo, Appl. Phys. Lett. 107, 124103 (2015).
[Crossref]

M. Endrizzi, B. I. S. Murat, P. Fromme, and A. Olivo, Compos. Struct. 134, 895 (2015).
[Crossref]

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

M. Endrizzi and A. Olivo, J. Phys. D 47, 505102 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Fromme, P.

M. Endrizzi, B. I. S. Murat, P. Fromme, and A. Olivo, Compos. Struct. 134, 895 (2015).
[Crossref]

Goncalves, O. D.

M. E. Poletti, O. D. Goncalves, and I. Mazzaro, Phys. Med. Biol. 47, 47 (2002).
[Crossref]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Hagen, C. K.

Heitner, G.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

Iacoviello, F.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

Kallon, G. K. N.

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Longo, R.

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Louise Jones, J.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Maughan Jones, C. J.

C. J. Maughan Jones and P. R. T. Munro, J. Biomed. Opt. 22, 1 (2017).
[Crossref]

Mazzaro, I.

M. E. Poletti, O. D. Goncalves, and I. Mazzaro, Phys. Med. Biol. 47, 47 (2002).
[Crossref]

Menk, R. H.

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Menk, R.-H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

Millard, T. P.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Modregger, P.

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

Munro, P. R. T.

Murat, B. I. S.

M. Endrizzi, B. I. S. Murat, P. Fromme, and A. Olivo, Compos. Struct. 134, 895 (2015).
[Crossref]

Olivo, A.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

M. Endrizzi, D. Basta, and A. Olivo, Appl. Phys. Lett. 107, 124103 (2015).
[Crossref]

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

M. Endrizzi, B. I. S. Murat, P. Fromme, and A. Olivo, Compos. Struct. 134, 895 (2015).
[Crossref]

A. Olivo and E. Castelli, Riv. del Nuovo Cimento 37, 467 (2014).
[Crossref]

M. Endrizzi and A. Olivo, J. Phys. D 47, 505102 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

P. R. T. Munro, C. K. Hagen, M. B. Szafraniec, and A. Olivo, Opt. Express 21, 11187 (2013).
[Crossref]

A. Olivo and R. Speller, Appl. Phys. Lett. 91, 074106 (2007).
[Crossref]

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Pani, S.

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Methods 7, 134 (2008).
[Crossref]

Plothow-Besch, H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

Poletti, M. E.

M. E. Poletti, O. D. Goncalves, and I. Mazzaro, Phys. Med. Biol. 47, 47 (2002).
[Crossref]

Poropat, P.

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Prest, M.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Rigon, L.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, J. Phys. D 36, A107 (2003).
[Crossref]

A. Olivo, F. Arfelli, D. Dreossi, R. Longo, R. H. Menk, S. Pani, P. Poropat, L. Rigon, F. Zanconati, and E. Castelli, Phys. Med. Biol. 47, 469 (2002).
[Crossref]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Robinson, I. K.

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Schittny, J. C.

P. Modregger, T. P. Cremona, C. Benarafa, J. C. Schittny, A. Olivo, and M. Endrizzi, Sci. Rep. 6, 1 (2016).
[Crossref]

Shearing, P. R.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

Speller, R.

A. Olivo and R. Speller, Appl. Phys. Lett. 91, 074106 (2007).
[Crossref]

Speller, R. D.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[Crossref]

Szafraniec, M. B.

Tromba, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Vallazza, E.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, Med. Phys. 28, 1610 (2001).
[Crossref]

Vittoria, F. A.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, Phys. Rev. Lett. 118, 1 (2017).
[Crossref]

F. A. Vittoria, G. K. N. Kallon, D. Basta, P. C. Diemoz, I. K. Robinson, A. Olivo, and M. Endrizzi, Appl. Phys. Lett. 106, 224102 (2015).
[Crossref]

Zanconati, F.

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Figures (4)

Fig. 1.
Fig. 1. (a) Edge illumination system, including sample mask (SM), sample (S), detector mask (D), and pixel (P). (b) Phantom of TiO 2 concentration 0.77%, mounted on a glass slide, ready for imaging.
Fig. 2.
Fig. 2. Schematic of the “three Gaussian retrieval” on an image ( 7 × 2 pixels), including an example of the fit obtained using experimental data, to gain either the object or flat-field parameters ( t , r , and s ).
Fig. 3.
Fig. 3. s image value calculated for each of the phantoms using both the standard flat-field image and the alternative flat-field image. The value of s image calculated using the standard flat-field image, translated so that 0% scatterer by weight has s image = 0    mm 2 , is also displayed. Error bars are ± 1 standard deviation.
Fig. 4.
Fig. 4. Effect of reducing the number of sample mask positions of both the object and flat-field image to 3 from the original 33. Values displayed were obtained using the standard flat-field method then translated to 0.

Equations (5)

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y IC ( x ) = i = 1 1 a i e ( ( x b i + i Δ ) 2 2 c i 2 ) 2 π ( c i 2 ) ,
y object ( x ) = i = 1 1 t i ( a i e ( ( x b i r i + i Δ ) 2 2 ( c i 2 + s i ) ) 2 π ( c i 2 + s i ) ) ,
t image = t object t flat ( a.u. ) ,
r image = r object r flat ( mm ) ,
s image = s object s flat ( mm 2 ) .

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