Abstract

Scanning X-ray fluorescence microscopy (XFM) is a particularly useful method for studying the spatial distribution of trace metals in biological samples. Here we demonstrate the utility of combining coherent diffractive imaging (CDI) with XFM for imaging biological samples to simultaneously produce high-resolution and high-contrast transmission images and quantitative elemental maps. The reconstructed transmission function yields morphological details which contextualise the elemental maps. We report enhancement of the spatial resolution in both the transmission and fluorescence images beyond that of the X-ray optics. The freshwater diatom Cyclotella meneghiniana was imaged to demonstrate the benefits of combining these techniques that have complementary contrast mechanisms.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
  30. M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
    [CrossRef]
  31. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  32. J. Fienup, T. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. A 72, 610–624 (1982).
    [CrossRef]
  33. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lens transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [CrossRef] [PubMed]
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2011 (1)

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

2010 (5)

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[CrossRef]

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010).
[CrossRef]

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with x-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

2009 (2)

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

2008 (3)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
[CrossRef]

2007 (3)

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

2006 (2)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502 (2006).
[CrossRef] [PubMed]

2005 (1)

H. M. L. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for movable illumination microscopy,” Ultramicroscopy 103, 153–164 (2005).
[CrossRef] [PubMed]

2004 (1)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lens transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

2003 (2)

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

K. H. Thompson and C. Orvig, “Boon and bane of metal ions in medicine,” Science 300, 936–939 (2003).
[CrossRef] [PubMed]

2002 (2)

X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti, “Medipix2: A 64-k pixel readout chip with 55 μm square elements working in single photon counting mode,” IEEE T. Nucl. Sci. 49, 2279–2283 (2002).
[CrossRef]

R. A. Armstrong, C. Lee, J. I. Hedges, S. Honjo, and S. G. Wakeham, “A new, mechanistic model for organic carbon fluxes in the ocean based on the quantitative association of POC with ballast minerals,” Deep-Sea Res.Pt. 2 49, 219–236 (2002).
[CrossRef]

2001 (1)

I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

2000 (1)

J. Nagy and Z. Strakos, “Enforcing nonnegativity in image reconstruction algorithms,” in Proc. SPIE 4121 (2000).
[CrossRef]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

1998 (3)

K. O. Buesseler, “The decoupling of production and particulate export in the surface ocean,” Global Biogeochem. Cy. 12, 297–310 (1998).
[CrossRef]

C. B. Field, M. J. Behrenfeld, J. T. Randerson, and P. Falkowski, “Primary production of the biosphere: Integrating terrestrial and oceanic components,” Science 281, 237–240 (1998).
[CrossRef] [PubMed]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

1995 (1)

A. A. Snigirev, I. I. Snigreva, V. G. Kohn, S. Kuznetsov, and I. A. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

1992 (1)

L. Hare, “Aquatic insects and trace metals: Bioavailability, bioaccumulation, and toxicity,” Crc. Cr. Rev. Toxicol. 22, 327–369 (1992).
[CrossRef]

1982 (1)

J. Fienup, T. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. A 72, 610–624 (1982).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Abbey, B.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

Allin, M.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Armstrong, R. A.

R. A. Armstrong, C. Lee, J. I. Hedges, S. Honjo, and S. G. Wakeham, “A new, mechanistic model for organic carbon fluxes in the ocean based on the quantitative association of POC with ballast minerals,” Deep-Sea Res.Pt. 2 49, 219–236 (2002).
[CrossRef]

Augustine, F.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Baines, S. B.

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with x-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

Behrenfeld, M. J.

C. B. Field, M. J. Behrenfeld, J. T. Randerson, and P. Falkowski, “Primary production of the biosphere: Integrating terrestrial and oceanic components,” Science 281, 237–240 (1998).
[CrossRef] [PubMed]

Boye, P.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Buesseler, K. O.

K. O. Buesseler, “The decoupling of production and particulate export in the surface ocean,” Global Biogeochem. Cy. 12, 297–310 (1998).
[CrossRef]

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Burghammer, M.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Campbell, M.

X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti, “Medipix2: A 64-k pixel readout chip with 55 μm square elements working in single photon counting mode,” IEEE T. Nucl. Sci. 49, 2279–2283 (2002).
[CrossRef]

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Clark, J. N.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

Cleverley, J.

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

Cowley, J. M.

J. M. Cowley, Diffraction Physics, 3rd ed. (North-Holland Publishing Company, Amsterdam, 1995).

Crimmins, T.

J. Fienup, T. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. A 72, 610–624 (1982).
[CrossRef]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

De Geronimo, G.

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

de Jonge, M.

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

de Jonge, M. D.

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

Dempsey, G. T.

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

Dhal, B. B.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

Diaz, J.

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Dinapoli, R.

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M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
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M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
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G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
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A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
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T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502 (2006).
[CrossRef] [PubMed]

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D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
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G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
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X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti, “Medipix2: A 64-k pixel readout chip with 55 μm square elements working in single photon counting mode,” IEEE T. Nucl. Sci. 49, 2279–2283 (2002).
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D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
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B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
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I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
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C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
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A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
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X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti, “Medipix2: A 64-k pixel readout chip with 55 μm square elements working in single photon counting mode,” IEEE T. Nucl. Sci. 49, 2279–2283 (2002).
[CrossRef]

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B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
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R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

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J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Schelokov, I. A.

A. A. Snigirev, I. I. Snigreva, V. G. Kohn, S. Kuznetsov, and I. A. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Schröder, S.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Schroer, C.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Schropp, A.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Schuette, D. R.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Siddons, D.

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

Snigirev, A. A.

A. A. Snigirev, I. I. Snigreva, V. G. Kohn, S. Kuznetsov, and I. A. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Snigreva, I. I.

A. A. Snigirev, I. I. Snigreva, V. G. Kohn, S. Kuznetsov, and I. A. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Stephan, S.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Strakos, Z.

J. Nagy and Z. Strakos, “Enforcing nonnegativity in image reconstruction algorithms,” in Proc. SPIE 4121 (2000).
[CrossRef]

Struder, L.

B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
[CrossRef]

Tate, M. W.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Thompson, K. H.

K. H. Thompson and C. Orvig, “Boon and bane of metal ions in medicine,” Science 300, 936–939 (2003).
[CrossRef] [PubMed]

Tovar-Sanchez, A.

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

Tran, C. Q.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

Twining, B. S.

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

Vartanyants, I. A.

I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Vernon, W.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Vine, D. J.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

Vogt, S.

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with x-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
[CrossRef]

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502 (2006).
[CrossRef] [PubMed]

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

Wakeham, S. G.

R. A. Armstrong, C. Lee, J. I. Hedges, S. Honjo, and S. G. Wakeham, “A new, mechanistic model for organic carbon fluxes in the ocean based on the quantitative association of POC with ballast minerals,” Deep-Sea Res.Pt. 2 49, 219–236 (2002).
[CrossRef]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Williams, G. J.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Woloschak, G.

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502 (2006).
[CrossRef] [PubMed]

Xuong, N. H.

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

Adv. Phys. (1)

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[CrossRef]

Anal. Chem. (1)

B. S. Twining, S. B. Baines, N. S. Fisher, J. Maser, S. Vogt, C. Jacobsen, A. Tovar-Sanchez, and S. A. San̅udo-Wilhelmy, “Quantifying trace elements in individual aquatic protist cells with a synchrotron x-ray fluorescence microprobe,” Anal. Chem. 75, 3806–3816 (2003).
[CrossRef] [PubMed]

Crc. Cr. Rev. Toxicol. (1)

L. Hare, “Aquatic insects and trace metals: Bioavailability, bioaccumulation, and toxicity,” Crc. Cr. Rev. Toxicol. 22, 327–369 (1992).
[CrossRef]

Deep-Sea Res.Pt. 2 (1)

R. A. Armstrong, C. Lee, J. I. Hedges, S. Honjo, and S. G. Wakeham, “A new, mechanistic model for organic carbon fluxes in the ocean based on the quantitative association of POC with ballast minerals,” Deep-Sea Res.Pt. 2 49, 219–236 (2002).
[CrossRef]

Global Biogeochem. Cy. (1)

K. O. Buesseler, “The decoupling of production and particulate export in the surface ocean,” Global Biogeochem. Cy. 12, 297–310 (1998).
[CrossRef]

IEEE T. Nucl. Sci. (1)

X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti, “Medipix2: A 64-k pixel readout chip with 55 μm square elements working in single photon counting mode,” IEEE T. Nucl. Sci. 49, 2279–2283 (2002).
[CrossRef]

J. Cell Biochem. (1)

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502 (2006).
[CrossRef] [PubMed]

J. Microsc. (1)

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schröder, M. Burghammer, and C. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Fienup, T. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. A 72, 610–624 (1982).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

J. Synch. Rad. (1)

B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Jacobsen, D. Legnini, P. Rehak, L. Struder, and S. Vogt, “Differential phase contrast with a segmented detector in a scanning x-ray microprobe,” J. Synch. Rad. 15, 355–362 (2008).
[CrossRef]

Nat. Photonics (1)

H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010).
[CrossRef]

Nat. Phys. (1)

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with x-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Nature (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Nucl. Instrum. Meth. A (1)

C. Ryan, R. Kirkham, R. Hough, G. Moorhead, D. Siddons, M. de Jonge, D. Paterson, G. De Geronimo, D. Howard, and J. Cleverley, “Elemental x-ray imaging using the maia detector array: The benefits and challenges of large solid-angle,” Nucl. Instrum. Meth. A 619, 37–43 (2010).
[CrossRef]

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

P. Natl. Acad. Sci. USA (1)

M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli, I. McNulty, C. J. Jacobsen, and S. Vogt, “Quantitative 3D elemental microtomography of cyclotella meneghiniana at 400-nm resolution,” P. Natl. Acad. Sci. USA 107, 15676–15680 (2010).
[CrossRef]

Phys. Rev. A (1)

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. De Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lens transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Proc. SPIE (2)

W. Vernon, M. Allin, R. Hamlin, T. Hontz, D. Nguyen, F. Augustine, S. M. Gruner, N. H. Xuong, D. R. Schuette, M. W. Tate, and L. J. Koerner, “First results from the 128x128 pixel mixed-mode Si x-ray detector chip,” Proc. SPIE 6706, 67060U (2007).
[CrossRef]

J. Nagy and Z. Strakos, “Enforcing nonnegativity in image reconstruction algorithms,” in Proc. SPIE 4121 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

A. A. Snigirev, I. I. Snigreva, V. G. Kohn, S. Kuznetsov, and I. A. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Science (6)

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

C. B. Field, M. J. Behrenfeld, J. T. Randerson, and P. Falkowski, “Primary production of the biosphere: Integrating terrestrial and oceanic components,” Science 281, 237–240 (1998).
[CrossRef] [PubMed]

K. H. Thompson and C. Orvig, “Boon and bane of metal ions in medicine,” Science 300, 936–939 (2003).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High resolution scanning x-ray diffrction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Ultramicroscopy (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for movable illumination microscopy,” Ultramicroscopy 103, 153–164 (2005).
[CrossRef] [PubMed]

Other (3)

Factorising the exit surface wave into the product of the incident beam multiplied by the sample transmission function requires assuming the sample is sufficiently thin for the projection approximation to hold [14, 34, 35].

J. M. Cowley, Diffraction Physics, 3rd ed. (North-Holland Publishing Company, Amsterdam, 1995).

D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Simultaneous ptychographic and fluorescence microscopy. A focused X-ray beam is scanned across a sample whilst simultaneously recording the X-ray fluorescence spectra and coherent diffraction pattern.

Fig. 2
Fig. 2

Imaging below the lens resolution. (Rows: Top, Bottom) Two different areas of a gold spoked resolution target, (Columns Left-Right): the scanning transmission image (a,d), the gold M-edge fluorescence (b, e) and the sample exit surface intensity reconstructed using ptychography (c, f). The spacing of the inner ring of spokes in (c) is 30nm. (a) Inset shows the reconstructed probe intensity (log scale).

Fig. 3
Fig. 3

Morphological structure and elemental composition of a freshwater diatom. (a) & (b) the reconstructed amplitude (arb. units) and phase (rad) of the sample exit surface wave respectively, (c) the X-ray absorption contrast and fluorescence maps (inset text describes element and image minimum, maximum). The reconstructed transmission images clearly show features not easily resolved in the fluorescence maps such as the diatom wall thickness and a low density cavity surrounded by a much more dense wall.

Fig. 4
Fig. 4

CDI-enhanced X-ray fluorescence microscopy. The reconstructed X-ray probe in the sample plane and the overlap between probe positions allow imaging beyond the resolution of the X-ray optics. The reconstructed transmission function amplitude (a) & phase (b), (c–i) the X-ray fluorescence map upsampled to the probe resolution (left column) and after iterative deconvolution (right). (i) a plot of the line profile indicated in (g,h) and the derivative (dashed line) demonstrates the resolution improvement is a factor of two.

Fig. 5
Fig. 5

Determining the reconstruction plane. By propagating the reconstructed X-ray probe intensity through focus we can quantify the distance of the sample from the focal plane. Line profiles through the focal waist (log scale) (a) and through focal series with optical axis running left to right (b), (c). The reconstructed probe in the sample plane (d).

Equations (1)

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I 1 ( u Δ x 1 ) = v | P ( u Δ x 1 v Δ x 2 ) | 2 I 2 ( v Δ x 2 ) ,

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