Chemical composition mapping with nanometre resolution … · SUPPLEMENTARY INFORMATION DOI:...

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHOTON.2014.207

NATURE PHOTONICS | www.nature.com/naturephotonics 1

Mapping Chemical Composition with Nanometer Resolution by Soft X-rayMicroscopy

David A. Shapiroa, Young-Sang Yub,g, Tolek Tyliszczaka, Jordi Cabanab,c, Rich Celestrea, Weilun Chaod,Konstantin Kaznatcheeve, A.L. David Kilcoynea, Filipe Maiaf, Stefano Marchesinia, Y. Shirley Mengg,Tony Warwicka, Lee Lisheng Yanga, and Howard A. Padmorea

a Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720b Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720c Department of Chemistry, University of Illinois at Chicago, Chicago, IL 60607d Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA 94720e NSLS-II, Brookhaven National Laboratory, Upton, NY 11973f Laboratory of Molecular Biophysics, Uppsala University, SE-751 24 Uppsala, Swedeng Department of NanoEngineering, University of California at San Diego, San Diego, CA 92093

Supplementary Information

The ALS has implemented ptychography in two of the three standard STXMs, all of which use

a similar configuration of motor stages for sample scanning. The foundation of the scanning

mechanism is an XY pair of stepper motors while the precision scanning is performed by an XY piezo

flexure stage, mounted on top of the stepper motor base, which is stabilized with respect to the x-ray

focusing optic by a laser interferometer. The closed loop operation of the piezo motors allows for long

term stability, scan step precision, and vibrational amplitudes in the 1-5 nm (RMS) range depending on

the particular system mechanics and environmental conditions on any given day. Since these values

are already approaching the wavelength of the radiation used for imaging, and will ultimately set the

resolution limit, it is not generally necessary to implement any numerical optimization of the scan

positions during post-processing as has been done in previous work.

During normal user operations, the STXMs use a 25 nm outer zone width zone plate but

ptychographic data can be generated with a larger spot, in this case using a 60 nm outer zone width

optic, in order to reduce the number of scan points needed for a given field of view and to increase the

scattering contrast in each illuminated sample position. The limited dynamic range of soft x-ray pixel

detectors necessarily implies that there is a relationship between the size of the probe and the

achievable spatial resolution which is more complicated than a standard point spread function. As the

spot size increases, the dynamic range of the signal between the minimum spatial frequency present

and the desired resolution increases as well. At soft x-ray energies, CCD detectors can only span 2-3

Chemical composition mapping with nanometre resolution by soft X-ray microscopy

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orders of magnitude in intensity, due to the limited electron well depth, which corresponds to a range

of length scales spanning only a factor of 5 at maximum, assuming the inverse fourth power

dependence of the cross-section for coherent scattering on voxel size and that we can phase reliably

to a scattered intensity with average signal-to-noise ratio of 11,2. Thus, a 60 nm zone plate should

achieve 12.7 nm resolution when imaging in two dimensions. However, the facets of the LiFePO4

crystals scattered so strongly that the scattered intensity was significant at the edge of the detector NA

which is equivalent to a half period spatial resolution of 4.1 nm. In order to avoid aliasing effects in the

reconstruction, the data were truncated with a Gaussian filter with a full-width at half maximum

(FWHM) of 10 nm in real space though the real space pixel size of the reconstructions was set at 4.0

nm in order to have an integer number of pixels per scan step.

We have implemented a merging technique which expands the dynamic range of our

measurement by combining long and short exposures at each sample position and improves the

achievable spatial resolution by more than a factor of 2. This requires saturation of the detector during

the long exposure times (since a beamstop is not used) and is practically limited to roughly a factor of

10-20 difference between long and short exposures because of charge blooming in the sensor which

contaminates non-saturated pixels. The two exposure times are merged during pre-reconstruction

processing according to:

where s is a saturation mask which is 0 for pixels near or beyond saturation and 1 otherwise. The

diffraction patterns Ilong and Ishort are the background subtracted exposures, with exposure times tshort

and tlong, which are also thresholded to remove readout noise which is not time dependent. After

merging and filtering the data, they are zero padded so as to give a real space pixel size which results

in an integer number of pixels between scan steps, and then finally downsampled to 128 pixels across

the field of view. Figure SI-1 shows details of the merging and downsampling.

The background refinement determines an offset which is common to all frames but which is

variable across a single frame. The background refinement is particularly important to this work as the


interferometer lasers and order sorting aperture can introduce significant stray light which is common

to all diffraction patterns. This stray light is iteratively determined and subtracted from the

measurements thus improving the convergence. Figure SI-1 shows the average of all diffraction

frames from the test sample before and after the iterative background refinement. Stray reflections

and a faint halo around the STXM brightfield annulus are apparently incoherent signal which are

removed during the reconstruction. Figure SI-2 shows a comparison of the reconstructed phase

image with (a) and without (b) background refinement. The finest lines in the test object are only

resolved for the former case. The probe refinement allows for determination of a probe function which

is not precisely known but we have found that the end result does not differ significantly from the initial

estimate which is well defined in a diffraction-limited STXM as the Fourier transform of the zone plate

pupil with flat phase (Supplementary Figure 1 (c)-(d)). Since the zone plate focus in a STXM is filtered

by an order sorting aperture (OSA) which removes all but the positive first diffraction order, the

diffraction pattern of the probe is localized to an annulus. This lack of high spatial frequency content in

the probe can be enforced during reconstruction via a mask applied in reciprocal space and

suppresses the emergence of grid pathologies which have prohibited the use of square scan grids in

previous work3.

The chemical compositions of the reconstructions where analyzed by first registering the

images using the StackReg4 plugin to ImageJ5 (image shifts are found using the absorption signal)

then calculating a complex-valued principal component analysis, expectation-maximization clustering

of the second and third component (ignoring the first component to minimize mass effects), followed

finally by singular value decomposition to obtain the target spectra of the end members. The

composition maps are calculated as a dot product of the three dimensional energy image stack with

the target spectra. The components in the composition maps are interpreted as FePO4 and LiFePO4

because of qualitative agreement with the reference spectra. However, the maps do not represent

quantitative fractions of the end members as they are determined from the ptychographic spectra

rather than the reference spectra. All computations, except image registration, used code available in

the SciPy6 Python package. The analysis is automated and parameter free except for the choice of


the number of clusters. For this system, which is expected to be two phase, the number of clusters is

necessary three. The same automated analysis was performed on the STXM absorption images.

Supplemental References

1. Howells, M. R. et al. An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy. J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).

2. Chapman, H. N. et al. High-resolution ab initio three-dimensional x-ray diffraction microscopy. J Opt Soc Am Opt Image Sci Vis 23, 1179–1200 (2006).

3. Thibault, P., Dierolf, M., Bunk, O., Menzel, A. & Pfeiffer, F. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109, 338–343 (2009).

4 Thevenaz, P., Ruttimann, U. E. & Unser, M. A pyramid approach to subpixel registration based on intensity. IEEE Trans. Image Process. 7, 27–41 (1998).

5. Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).

6. Jones, E., Oliphant, T. & Peterson, P. SciPy: Open Source Scientific Tools for Python. (2001). at

<http://www.scipy.org


http://www.scipy.org/

Supplementary Figure Legends


Supplementary Figure 1 Details of the data processing and ptychographic reconstruction. Raw

diffraction data for the short (a) and long (b) exposures. The long exposure is saturated and the

saturated pixels have bloomed slightly into neighboring pixels. The red arrows point to spurious x-ray

signal which does not originate from the sample but which has comparable intensity to the sample

scattering. Central portions of the average diffraction data (after merging and downsampling) before

(c) and after (d) background retrieval. Outside of the central annulus (the image of the zone plate

pupil) spurious x-ray scattering spots (red arrow) and a faint halo of incoherent light can be seen.

These features are determined by the algorithm and subtracted during the reconstruction process. (e)

Shows the ratio of the recovered background intensity to that of the average diffraction pattern. The x-

ray probe function before (f) and after (g) the probe retrieval process. The initial probe is calculated as

the Fourier transform of the zone plate pupil assuming flat phase. The recovered probe shows minor

differences from the original, indicating the high quality of the STXM focus. These HSV images

represent the probe intensity on a log scale as Value and phase as Hue.


Supplementary Figure 2 Comparison of the reconstructed phase images with (a) and without (b) the

background refinement step. The inset images show a red arrow pointing at an isolated line with 5 nm

width. The line is only resolved for the case with background refinement showing clearly enhanced

spatial resolution. (c) Power spectral densities (PSD) of the reconstructed phase images under various

conditions. The PSD for the actual sequences are calculated from a single line while that of the x-ray

images is the average PSD of all lines in the image.


Supplementary Figure 3 Comparison of the chemical composition maps obtained by ptychography

(a) and (c) and normal STXM, (b) and (d). The blue lines indicate the regions used for estimating the

spatial resolution while the red lines indicate the regions used for comparing the achieved chemical

contrast.


Supplementary Figure 4: Comparison with SEM and standard spectra. (a) LiFePO4 and (b)

Li0.55FePO4. Surface cracks appear along the c-axis as a result of delithiation. (c) Comparison of the

reference absorption spectra for LiFePO4 and FePO4 with those calculated from the ptychographic

reconstructions showing qualitative agreement though possible saturation at the energies of maximum

absorption. The reference spectra are the dotted lines.


Chemical composition mapping with nanometre resolution … · SUPPLEMENTARY INFORMATION DOI:...

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