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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 9 — Aug. 28, 2012
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Simultaneous X-ray fluorescence and ptychographic microscopy of Cyclotella meneghiniana

D. J. Vine, D. Pelliccia, C. Holzner, S. B. Baines, A. Berry, I. McNulty, S. Vogt, A. G. Peele, and K. A. Nugent  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 18287-18296 (2012)
http://dx.doi.org/10.1364/OE.20.018287


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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

Scanning hard X-ray fluorescence microscopy (XFM) is an increasingly important tool for studying the role of trace elements in biological and biomedical research [1

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]

]. It is known that trace metals are involved in most intracellular processes however there has been a dearth of tools with the sensitivity required to quantify them at the nanoscale. XFM allows cells and organisms to be studied in close to their natural state, permitting the detection of just a few thousand atoms [2

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]

] and so obviating the need for tags or dyes. Coherent diffractive imaging (CDI) is a type of microscopy that is able to form images without the need for lenses and therefore with a spatial resolution which is, in principle, limited only by the wavelength of the incident light [3

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

]. Here we demonstrate the utility of combining CDI and XFM for imaging biological samples to 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. Unlike optical super-resolution methods [4

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

6

6. 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]

] this approach is not limited to imaging samples which express fluorescent proteins. For the transmission images the resolution is 30 nm, a factor of eight smaller than the focused beam diameter. In addition, we show that the reconstructed X-ray beam amplitude can be used to gain a factor of two improvement in the spatial resolution of the elemental maps to 155 nm. We image the freshwater diatom Cyclotella meneghiniana to demonstrate the benefits of combining these techniques that have complementary contrast mechanisms.

Scanning X-ray microprobes form images by raster-scanning a focused X-ray beam over a sample while the transmitted beam and secondary emission are recorded. In X-ray fluorescence microscopy the secondary fluorescence signal is used to quantify the elemental concentration while the transmitted beam carries information about the projected electron density. The transmitted X-ray beam carries a significant amount of information that is complementary to the fluorescence signal. Light elements in the sample such as C, N and O that are much more difficult to map by their fluorescence can still be detected from the phase shift they impart to the incident X-rays.

Since the initial demonstration experiments [7

7. 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]

] phase contrast X-ray imaging has found widespread use because refraction can be the dominant contrast mechanism for hard X-rays. The traditional approach to measuring a phase contrast signal in a scanning microscope involves measuring the average refraction over the focal spot [8

8. 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]

] but this method under-utilizes the scattering information available. A recent demonstration of Zernike phase contrast in the scanning geometry more fully utilizes the scattered signal [9

9. 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]

]. Coherent diffractive imaging is a new technique that provides the full complex exit surface wave from the object without the use of an image-forming objective lens. Imaging by CDI involves recording the coherent diffraction pattern of the object then reconstructing its image on a computer using an iterative algorithm to retrieve the missing phases from the diffraction data through the imposition of known constraints on the sample transmission function [10

10. 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]

14

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

]. The reconstructed exit surface wave gives a quantitative measure of the attenuation and phase shift at a spatial resolution determined by the numerical aperture (NA) of the detector which can easily be much larger than that of the highest resolution X-ray optics currently available.

Recent developments in scanning CDI make the approach entirely compatible with XFM. In scanning CDI, diffraction patterns are recorded with some overlap of the incident X-ray probe between adjacent measurement points [15

15. 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]

17

17. 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]

]. By constraining the reconstructions to be mutually consistent in the overlap region one can reconstruct an unlimited field of view without any a priori information about the sample [18

18. 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].

]. The set of diffraction patterns may also be analysed to extract the complex wavefield describing the probe in the sample plane simultaneously [19

19. 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]

]. Recording a far-field diffraction pattern at every scan point in an XFM experiment allows a high-resolution and phase sensitive image to be reconstructed with little additional experimental overhead.

The benefit of this approach, scanning multi-modal X-ray microscopy (SMXM), derives from the complementary contrast mechanisms of the two techniques. The soft X-ray fluorescence from low-Z biomass elements (C,N,O) are difficult to detect due to low fluorescence yields and strong absorption by the sample itself. The transmitted X-rays however are sensitive to the electron density so that even though these elements interact weakly they are present in sufficient quantity to be detected using phase contrast. Trace metals can then be associated with specific cellular functions by correlating spatial distributions of trace metals with cell structures that perform specific cellular processes. The ability to determine the location of metals with respect to cell structure in high resolution is a significant new capability. The applications for such an advance range from studying the uptake and subsequent transfer of metals within natural food webs [20

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

] to evaluating the effectiveness of designer drugs which contain metals as active agents [21

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

]. Earlier work has also demonstrated the benefits of combining ptychography and fluorescence mapping for materials science applications [22

22. 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]

].

An SMXM experiment was performed at beamline 2-ID-E of the Advanced Photon Source using the experimental geometry sketched in Fig. 1 (for details see Appendix). SMXM uses a similar setup to XFM - the only notable difference is the introduction of a pixellated area detector to record the transmitted X-rays. A 7.7 keV X-ray beam was focused by a 160 μm-diameter zone plate lens with an outermost zone width of 100 nm. A 50 μm aperture was placed 0.5 m upstream of the zone plate to ensure it was coherently illuminated. The coherence selecting aperture apodized the lens so that the focused beam size, 250nm as measured by a knife edge scan, was much larger than the outermost zone width. The focused beam was then scanned across the sample and at each point in the scan a photon counting pixel array detector [23

23. 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]

] (2562 55 μm pixels) located 1.34 m downstream of the focus recorded a far-field diffraction pattern as an energy dispersive silicon drift diode measured the fluorescence spectrum.

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.

To explore the improvement in spatial resolution of the transmitted image using SMXM we imaged several regions of a gold spoked “star” resolution pattern, Fig. 2. The sample was raster scanned through a 31×31 grid using a step size of 100 nm and exposure times of 100 ms (transmitted) and 1 s (fluorescence). The data were reconstructed (see Appendix) and the results are shown in Fig. 2. The first column (Figs. 2(a) and 2(d)) show the transmitted image. The second column (Figs. 2(b) and 2(e)) show the fluorescence image. There is little structure visible in either of these data sets consistent with the expected resolution of the zone plate. The third column (Figs. 2(c) and 2(e)) shows the reconstructed intensity in the sample plane; the dramatic improvement in resolution (in this data a factor of 8 increase) is obvious. The inset shows the reconstruction of the probe beam (see Appendix). The 30 nm features at the center of the star pattern are resolved, however the bifurcation of some spokes in the inner ring are artifacts which we believe are caused by the sample positioning system. The evident skew distortion of the circular features is due to a slight misalignment between the horizontal and vertical travel of the scan stages.

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).

We then imaged the diatom Cyclotella meneghiniana, a common siliceous freshwater microalgae. Diatoms play an important role in global material and energy cycles. For example, marine diatoms account for 40% of the photosynthesis in the ocean and 20% of that on earth [24

24. 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]

]. Due to their dense silica cell walls, they also facilitate the movement of organic material to depth via sinking particles [25

25. 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]

, 26

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

]. Where trace concentrations of Fe and Mn localize and their role in the life-cycle of Cyclotella m. are key questions determining how these microalgae sequester and organize the silica and thus their propensity to sink. Scanning XFM can determine the locations of these important transition metals within the diatom, but in order to quantify their concentrations the remainder of the diatom mass (principally made of light elements) must be determined. The data in Fig. 3 shows the concentrations of major biomass constituents including Si, P, S and K, trace amounts of F and Mn, and the complex transmission function. The SMXM scan consisted of 121 × 101 points with 100 nm step size and 130 ms (transmission) and 1 s (fluorescence) exposure times. The attenuation image in Fig. 3(a) shows poor contrast because this sample is almost transparent to hard X-rays. The phase is more sensitive to the internal structure of the diatom as expected at this energy. The Fresnel fringing evident in Fig. 3(a) is due to the plane of the reconstruction being in the near field of some of the small or sharp features. That the sample is in the focal waist of the zone plate can be verified by propagating the reconstructed probe through focus (see Appendix).

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.

In XFM the spatial resolution is limited by the size of the probe beam used to map the specimen. In this work we show that the spatial resolution of the elemental maps obtained by XFM may be significantly improved by deconvolving the reconstructed probe beam. The point spread function (PSF) of the X-ray fluorescence microscope can be estimated from the squared magnitude of the incident X-ray probe and the overlap between scan positions required for the CDI reconstruction. Figure 4 presents an almost twofold improvement in the spatial resolution of the elemental maps that was achieved by deconvolution to remove the blur caused by the finite extent of the incident probe. Figures 4(c), 4(e) and 4(f) have been rescaled from the step scan resolution of 101×121 100 nm pixels to the pixel size of the transmission image (15 nm) using bilinear interpolation. The interpolation step does not add any new information and as such does not increase the spatial resolution. The point spread function was then deconvolved [27

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

] from the interpolated images to give Fig. 4(d), 4(f) and 4(h). The resolution improvement estimated from the diatom wall is approximately 40% or 155 nm. Barely visible features such as the banding in the diatom frustule are clearly visible post-deconvolution. Agreement between the size of features visible in the deconvolved XFM data and the independently measured transmission function attest to the accuracy of the deconvolution.

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.

We have demonstrated the benefits of multi-modal imaging for biological samples. SMXM combines XFM and ptychography to yield nanoscale phase sensitive maps with elemental specificity. The high resolution transmission images reveal sample structure which provides context for the elemental maps. The reconstructed X-ray probe can be used to super resolve the elemental maps significantly better than the size of the focused probe, and hence the diffraction limit of the imaging system. Because this measurement requires no additional time overhead to a typical XFM measurement and involves only the adoption of an area detector to record the coherently diffracted signal we anticipate it may find widespread adoption on X-ray fluorescence microscopes.

The resolution is limited only by the diffracted signal and precision of the specimen scan stage, thus we envision further improvements will be made due to the rapid advances in x-ray dispersive detector, area detector, and nanopositioning technology underway [28

28. 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]

, 29

29. 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]

]. Finally, we observe that the interior complexity of biological cells and sub-cellular organelles is just beginning to be understood. Extension of this methodology to three-dimensional imaging by tomographic methods [30

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]

] is straightforward, opening the door to understanding the compartmentalization and function of metals and other trace elements in biology.

Appendix

Experimental apparatus

All experiments were carried out at beamline 2-ID-E of the Advanced Photon Source. X-rays from a 3.3 cm period undulator were reflected from a mirror to remove high orders contributions to the energy spectrum and a 7.7 keV monochromatic beam was selected using a single reflection from a Si(111) single crystal.

A 50 μm aperture was used to select partially coherent illumination of a zone plate lens used to focus the beam to approximately 250 μm at a distance of 0.5 m. The coherence selecting aperture was located a distance of 57 m from the source with dimensions of approximately 270(h)×11(v) μm. The zone plate diameter was 160 μm with an outermost zone width of 100 nm. A 40 μm central stop and 20 μm order sorting aperture were used to select the first diffraction order from the zone plate for the experiment.

A Medipix2 pixel array detector with 256×256 55 μm pixels and a dynamic range of 11800 counts was used to measure the coherent diffraction patterns. A low energy threshhold setting on the detector was used to discriminate thermal noise. The detector was placed 1.34 metres from the focal plane. The resulting NA of 5.3×10−3 corresponds to a pixel size in the sample plane of 15.4 nm.

The sample was placed in a He filled chamber and scanned through the focal waist of the X-ray beam while the fluorescence and diffraction data were recorded. The complex wavefield describing the X-ray probe has been computationally propagated through focus as in Fig. 5 to verify that we were in the focal plane as expected. From that measurement we determined the sample plane was with the 110μm focal depth of this lens. The fluorescence spectra were measured using a single element Vortex EX-60 silicon drift diode detector. The sample was rotated by 15° from perpendicular to the beam axis to increase the solid angle of the fluorescence detector as viewed from the sample. The step size in all scans was 100 nm and the scan dimensions varied as reported with the data. A 100 nm step size corresponds to approximately 60% overlap between adjacent scan points.

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).

A whitefield (no sample) measurement was made at the beginning and end of each scan for 500 exposures at the same exposure time as the sample exposures. The whitefield data were averaged for use in the phase retrieval algorithm.

Phase retrieval

Phase retrieval was performed using a modified version of the algorithm outlined in [16

16. 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]

]. In the modified algorithm, alternating iterations of difference map and an error reduction (ER) algorithm [31

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

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]

] were applied. The real space finite support constraint of ER was replaced with the ptychographic overlap constraint [33

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]

].

Each reconstruction presented in this manuscript ran for 1000 iterations with the probe iteratively updated beginning the 30-th iteration. The 31 × 31 reconstructions took on average 4 hours on a single core processor using code written in Python. The 121 × 101 scans took approximately 24 hours to complete. The reconstruction was easily identifiable at the conclusion of the second iteration and convergence was achieved after just a few hundred iterations.

No additional constraints were used on the amplitude or phase of any of the wavefields.

Iterative deconvolution of the point spread function of X-ray fluorescence data

The forward problem of image formation in the X-ray fluorescence microscope can be formulated as a discrete convolution with two native length scales, Δx1 the pixel size of the step scan and Δx2 the pixel size of the reconstructed probe,
I1(uΔx1)=v|P(uΔx1vΔx2)|2I2(vΔx2),
(1)
where Ip is the intensity measured with resolution p and P is the probe amplitude.

The deconvolution process involves first resampling the elemental maps from the step scan resolution to the resolution of the probe and finally deconvolving the probe. Resampling the data was done using bilinear interpolation after low pass filtering the data. The bilinear interpolation does not increase the spatial resolution of the images but rather ensures smooth variation between pixels in the rescaled image.

The probe was then deconvolved using the modified residual norm steepest descent algorithm (MRNSDA) [27

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

] as implemented in the “Parallel Iterative Deconvolution” ImageJ plugin written by Piotr Wendykier.

Deconvolution attempts to solve an ill-posed problem and as such our deconvolved images were treated with cautious skepticism. We are confident that the features resolved by the deconvolution process are not artifacts because they are in agreement with the independently reconstructed CDI images.

Acknowledgments

Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.

References and links

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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]

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]

3.

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

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

5.

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]

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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]

7.

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]

8.

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]

9.

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]

10.

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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). [CrossRef] [PubMed]

14.

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

15.

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]

16.

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]

17.

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]

18.

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].

19.

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]

20.

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

21.

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

22.

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]

23.

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]

24.

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]

25.

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]

26.

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

27.

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

28.

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]

29.

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]

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]

34.

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

35.

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

OCIS Codes
(180.5810) Microscopy : Scanning microscopy
(180.7460) Microscopy : X-ray microscopy
(300.6560) Spectroscopy : Spectroscopy, x-ray
(340.7440) X-ray optics : X-ray imaging
(340.7460) X-ray optics : X-ray microscopy

ToC Category:
Microscopy

History
Original Manuscript: May 14, 2012
Revised Manuscript: June 21, 2012
Manuscript Accepted: June 22, 2012
Published: July 25, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Citation
D. J. Vine, D. Pelliccia, C. Holzner, S. B. Baines, A. Berry, I. McNulty, S. Vogt, A. G. Peele, and K. A. Nugent, "Simultaneous X-ray fluorescence and ptychographic microscopy of Cyclotella meneghiniana," Opt. Express 20, 18287-18296 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-16-18287


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References

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  25. 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. 249, 219–236 (2002). [CrossRef]
  26. K. O. Buesseler, “The decoupling of production and particulate export in the surface ocean,” Global Biogeochem. Cy.12, 297–310 (1998). [CrossRef]
  27. J. Nagy and Z. Strakos, “Enforcing nonnegativity in image reconstruction algorithms,” in Proc. SPIE4121 (2000). [CrossRef]
  28. 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. A619, 37–43 (2010). [CrossRef]
  29. 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. SPIE6706, 67060U (2007). [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. USA107, 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,” Optik35, 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. A72, 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]
  34. J. M. Cowley, Diffraction Physics, 3rd ed. (North-Holland Publishing Company, Amsterdam, 1995).
  35. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006). [CrossRef]

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