# X-ray Ptychography with a Laboratory Source

Darren J. Batey  Diamond Light Source, Harwell Science and Innovation Campus,
Fermi Avenue, Didcot, UK  Frederic Van Assche  Sander Vanheule  Matthieu N.
Boone  UGCT-RP, Department of Physics and Astronomy, Ghent University, Belgium
Andrew J. Parnell  Soft Matter Analytical Laboratory, Department of Chemistry,
University of Sheffield, Sheffield, UK  Oleksandr O. Mykhaylyk  Department of
Physics and Astronomy, University of Sheffield, Sheffield, UK  Christoph Rau
Diamond Light Source, Harwell Science and Innovation Campus, Fermi Avenue,
Didcot, UK  Silvia Cipiccia  Diamond Light Source, Harwell Science and
Innovation Campus, Fermi Avenue, Didcot, UK  Department of Medical Physics and
Biomedical Engineering, University College London, London, UK

###### Abstract

X-ray ptychography has revolutionised nanoscale phase contrast imaging at
large-scale synchrotron sources in recent years. We present here the first
successful demonstration of the technique in a small-scale laboratory setting.
An experiment was conducted with a liquid metal-jet X-ray source and a single
photon-counting detector with a high spectral resolution. The experiment used
a spot size of 5 µm to produce a ptychographic phase image of a Siemens star
test pattern with a sub-micron spatial resolution. The result and methodology
presented show how high-resolution phase contrast imaging can now be performed
at small-scale laboratory sources worldwide.

##  I Introduction

Ptychography is a coherent scanning-diffraction imaging technique that
produces quantitative images at resolutions beyond the imaging performance of
conventional, lens-based, microscopy systems [1]. Ptychography is now
routinely applied at X-ray synchrotron sources across the world, obtaining
highly sensitive, quantitative, images at the highest spatial resolutions,
down to tens of nanometres [2, 3, 4, 5, 6, 7]. Until now, the high level of
coherence required for X-ray ptychography has limited the application of the
technique to high brilliance sources such as synchrotron and, more recently,
FEL facilities [8]. It was recently postulated that the new generation of
X-ray laboratory sources may have sufficient brilliance to conduct a
ptychographic experiment, given the correct experimental setup [9]. We present
here a demonstration of such an experiment and the first proof of concept for
far field X-ray ptychography performed using an X-ray laboratory source.

A ptychography scan consists of recording 2D intensity patterns downstream
from a sample that is irradiated by a localised spot of coherent radiation.
The 4D ptychographic dataset is built up by scanning the sample relative to
the beam to a series of overlapping positions. It is possible to record and
subsequently invert the data to retrieve the complex refractive index of the
object at wavelength limited resolutions across an extended field of view [10,
11, 12, 13, 14]. The success of the inversion step in extracting the phase
relies strongly on the stability of the instrumentation and coherent
properties of the beam. The coherence manifests itself in interference fringes
that hold the relative phase information. The coherent fraction of a beam is
related to the lateral (i.e. spatial) and longitudinal (i.e. temporal)
coherence. The former is determined by the photon energy and the effective
source size - how well confined the source of radiation is laterally in space.
The latter is determined by the source bandwidth - how well confined the
source of radiation is in wavelength, or longitudinally in space. The level of
coherence of an instrument can be described in terms of brilliance. Brilliance
is directly proportional to the spatial and temporal coherence. Typical
brilliance of third generation light sources is of the order of
${10}^{20}\text{\,}\mathrm{photons}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{mm}}^{-2}\text{\,}{\mathrm{mrad}}^{-2}$
0.1% B.W.

In a recent work, we used a detuned synchrotron source and a hyperspectral
X-ray detector to demonstrate the feasibility of broadband spectroscopic X-ray
ptychography [9]. Due to the specific setup, the brilliance of the synchrotron
source was reduced to approximately
$3\text{\times}{10}^{11}\text{\,}\mathrm{photons}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{mm}}^{-2}\text{\,}{\mathrm{mrad}}^{-2}$
0.1% B.W. State of the art high brilliance X-ray laboratory sources based on a
liquid metal-jet (LMJ) approach this level of brilliance [15]. X-ray
ptychography using such a source is therefore feasible, as presented in the
following sections.

##  II Experiment and results

###  II.1 Experimental configuration

The experiment was designed and conducted to explore the possibility of
ptychographic imaging in a laboratory setting. The data were collected at the
University of Sheffield Soft Matter AnalyticaL Laboratory (SMALL) [16, 17],
with the portable ptychography end-station from I13-1 of Diamond Light Source
and a hyperspectral detector from Ghent University [18, 19]. The X-ray source
is an Excillum liquid gallium metal jet (LMJ), which has a brilliance of
approximately of
$5\text{\times}{10}^{11}\text{\,}\mathrm{photons}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{mm}}^{-2}\text{\,}{\mathrm{mrad}}^{-2}$
0.1% B.W. [15], one order of magnitude higher than conventional microfocus
sources [20, 21]. The experimental setup is shown in Figure 1. The spectrum of
the source was characterised using the hyperspectral detector and it shows the
Gallium (Ga) K-alpha and K-beta lines above the Bremsstrahlung background (see
Figure 3 in method section for additional details).

Figure 1: Experimental configuration. Ptychography setup (not to scale)
showing the experimental layout as implemented at SMALL, Sheffield, UK.

The experiment consisted of a ptychographic scan of a Siemens star test
pattern. The ptychographic data was reconstructed through the ePIE operator
[12] in PtyREX [22], where the set of intensity measurements are inverted into
an image of the object.

The detector made it possible to post-process the data for different
bandwidths and exposure times. Two datasets, of bandwidth 200 eV (matching the
detector energy resolution at the Ga K-alpha energy) and 1 keV around the
K-alpha line, were generated. The natural spectral width of the K-alpha lines
is a few electronvolt, and the distance between K-alpha(1) and K-alpha(2) is
17 eV, hence the recorded bandwidth is determined by the detector energy
resolution. Increasing the bandwidth of the data analysed from 200 eV to 1 keV
increases the contribution of the Bremsstrahlung background. The theoretical
resolution achievable for 200 eV and 1 keV bandwidths are 100 nm and 540 nm
respectively [23]. Conversely, the reconstructions of the experimental data
showed a decrease in resolution for the narrower bandwidth (1200 nm for 200 eV
and 930 nm for 1 keV), suggesting that the experiment is photon limited. The
best reconstruction, Figure 2(b), was obtained with 1 keV bandwidth. Both
reconstructions included the correction for the source position and direction.
These corrections were essential to compensate for long-term instabilities of
the source during the acquisition (see method for details). Figure 2(a)
confirms a beam profile of 5 µm in extent. A line profile across the
reconstructed phase image of the object shows that the spokes are well
resolved (Figure 2(c)). The half-bit resolution of the image is 930 nm (Figure
2(d)), a factor of more than 5 beyond the spot size at the sample.

Figure 2: The ptychography reconstruction. a) Modulus of the beam profile at
the sample plane. b) Phase image of the Siemens star test target with a
reconstructed pixel size of 116 nm. c) Line plot from the dashed black line in
(b). The raw data is represented by the solid black line and the 10 pixel
moving average is represented by the solid red line. d) Fourier ring
correlation of the two split exposure reconstructions showing 1.08 µm-1
spatial frequency (corresponding to 930 nm).

###  II.2 Discussion and summary

Performing lab-based X-ray ptychography has required advances in lab-sources
[20] and detector technologies [19]. The high brilliance of the LMJ has
provided the coherent flux required for the ptychography technique. The
hyperspectral detector has been required to characterise spectrally the source
and assess the temporal coherence.

Our analysis of the results suggests that the experiment was limited by the
photon statistics and point-to-point stability of the source. The effect of
the latter was mitigated via the reconstruction algorithm that modelled the
source shift and direction. The use of different or additional optical
components for focussing the X-ray beam to the sample could help to better
harness the coherent flux, increasing the photon statistics and reducing the
sensitivity to long term source instabilities.

We have demonstrated that it is possible to perform X-ray ptychography with a
LMJ source and have shown how to perform ptychography in a laboratory setting,
releasing to the laboratory environment a technique otherwise confined to
synchrotron facilities. The experimental breakthrough achieved with a LMJ is a
first step toward expanding X-ray ptychography to other bright compact light
sources: from inverse Compton scattering [24], to laser-plasma based [25] and
compact storage rings [26].

##  III Methods

###  III.1 Experimental configuration

#### X-ray source

The X-ray beam is generated using a JXS-D2-001 liquid metal-jet laboratory
source modified to a higher power performance (Excillum AB, Kista, Sweden)
with Gallium as anode material. The focal spot size of the source can be
varied within a relatively wide range between 5 µm and more than 50 µm, by
tuning the projection of the electron beam on the Gallium jet stream with a
set of electromagnetic lenses. For this experiment, the focal spot size was
set to a nominal value of 5 µm. A three-dimensional single reflection multi-
layered ellipsoidal mirror (FOX3D 11-600 Ga, Xenocs, Grenoble, France) is used
to focus the X-ray beam. The centre of the mirror is located 11 cm downstream
of the X-ray source, coinciding with the first mirror focus. The resulting
beam is slightly converging, with the second mirror focus located
approximately 5.2 m downstream of the mirror. Due to the chromatic behaviour
of the mirror reflectivity, the mirror also acts as a spectral band-pass
filter, enhancing the relative intensity of the 9.25 keV K-alpha emission line
of Gallium by drastically reducing the Bremsstrahlung continuum spectrum.

#### Scanning system

The portable ptycho-scope end-station developed at the I13-1 branchline of the
Diamond Light Source was used for positioning the sample and the pinhole
(Figure 1). The ptycho-scope consists of two 3-axis SLC2430 piezo stages
(SmarActs GmbH, Oldenburg, Germany), one for the pinhole and one for the
sample. The stages are controlled with a python data collection software
connected to an MCS control box over an RS232 protocol. The software scans the
position point-by-point, triggers the detector through a USB-BNC connection
and uses the detector ready status for synchronising the motion with the
detector readout and beam status.

The instrument was set up with a 5 µm diameter, 50 µm thick, tungsten pinhole
placed 4 m from the source. During the experiment, a flux through the pinhole
of
$\sim$5\text{\times}{10}^{3}\text{\,}\mathrm{photons}\text{\,}{\mathrm{s}}^{-1}$$
was measured. The sample was placed 1 cm downstream of the pinhole and scanned
in the plane perpendicular to the optical axis of the beam on a square grid of
$20\times 20$ steps with step size of 1 µm, following a snake-like trajectory.

#### X-ray detector

The pnCCD based Color X-ray Camera (SLcam) [27] was used to measure the
diffraction patterns. The detector has a physical pixel pitch of 48 µm, and an
active area of $264\times 264$ pixels. The system was operated at a readout
speed of 400 fps. The in-house developed software SpeXiDAQ [28] was used for
camera control and readout as well as raw data processing. The energy
resolution of the SLcam is approximately 144 eV FWHM at the Mn K-alpha peak
and the centre of mass accuracy is better than 10 eV [29]. The detector was
placed downstream of the sample at 9.4 m from the source. Vacuum pipes were
placed between the sample and the detector as well as between the mirror and
the pinhole to reduce the air absorption and scattering. The detector exposure
at each point was 140 s, with a single scan taking 16 hours in total.

#### Sample

The Siemens star is a 500 nm thick gold structure deposited on a silicon
nitride membrane with an outer spoke separation of 4 µm and an inner spoke
separation of 50 nm. An area of 400 µm2 was scanned during the experiment.

###  III.2 Data processing

#### Detector frame processing

The SLcam captures raw frames containing only a few photon events per frame.
The raw frames are subsequently pre-processed into diffractograms for the
ptychography reconstruction, using a cluster-finding algorithm and subsequent
rebinning of the retrieved events into a 3D datacube (two spatial dimensions
and one spectral dimension). Due to this processing method, charge sharing
effects do not deteriorate the spectral response and sub-pixel accuracy can be
achieved [30]. Using SpeXiDAQ [28], the raw frames are stored and afterward
processed and split by time or energy into different datasets. The time-based
splitting was used for assessing the spatial resolution (see post-processing
section below), the energy-based splitting for investigating the spectral
properties. The spectrum has been generated by integrating the photon counts
in each of the 5 eV energy bin datasets. The spectrum recorded is shown in
Figure 3: the escape peak of the K-alpha line in the Silicon bulk and the
double and triple photon pile-up of the K-alpha are visible, beside the main
Ga K-alpha and K-beta peaks. The source spectrum has been retrieved by adding
the counts of the escape peak, those of the double pile-up ($\times 2$) and of
the triple pile-up ($\times 3$) to the K-alpha peak. The energy bandwidth was
investigated and matched to the resolution achievable from the experimental
conditions (flux and geometry). The data shown in Figure 2 was produced using
a single output bin ranging from
$8.75\text{\,}\mathrm{keV}9.75\text{\,}\mathrm{keV}$.

Figure 3: The X-ray source spectrum as recorded with the SLcam. The Ga K-alpha
peak (9.25 keV) along with the double pile-up (18.5 keV) and triple pile-up
peaks (27.75 keV) are shown in blue. The K-alpha escape peak in Si (7.51 keV)
is shown in green and the K-beta (10.26 keV) is shown in red.

###  III.3 Image reconstruction

The image reconstruction process takes a model of the experiment, including
knowledge of the illumination conditions and scanning coordinates along with
the recorded intensity measurements, and applies physical constraints in order
to solve for the unknown sample. Here, the illumination was initially modelled
as a convergent beam of 1 mrad full angle and a defocus of 10 mm. The
convergence angle is calculated from the beam on the detector, and the defocus
was chosen to produce a 5 µm spot creating a balance between the true focal
distance of the mirror and the beam width imposed by the pinhole. The scanning
coordinates are taken from the requested values of the SmarAct motors.

The ptychographic data were processed with 500 iterations of the ePIE operator
[12] available in PtyREX [22]. The reconstruction algorithm is capable of
dealing with source instability, experimental errors and signal degradation
due to noise and decoherence. The beam intensity was monitored during the
acquisition by integrating the flux received on the detector. The intensity
variations, shown in Figure 4(a), are a manifestation of the source
instabilities. The source appears to fluctuate across the first 100 positions,
with a significant sudden drop in intensity at position 131 of the scan. Scan
positions 131 and 132 were removed from the data prior to the reconstruction
(see Figure 4). The source fluctuations translate into point-to-point
instabilities at the sample plane and correspond to either a translation, a
tilt, or a combination of the two in the beam profile. PtyREX employs a scan
correction built on the annealing method of Maiden et al. [31], but is
extended to also accommodate angular variations in the incident beam within
the same update step. The position and tilt correction applied during the
reconstruction are shown Figure 4(b).

Figure 4: Source and illumination stability. a) Fluctuation of total intensity
measured by integrating the total flux on the detector during the scan. The
value is normalised by the mean value. b) Beam position and tilt correction as
recovered during the PtyREX reconstruction. The origin of the arrow represents
the re-calculated position, the direction of the arrow represents the
direction of the tilt correction, and the length of the arrow is proportional
to the modulus of the angular tilt. The colormap of both (a) and (b)
represents the modulus of the angular tilt at each scan position, highlighting
the correlation between intensity fluctuations and angular tilt corrections.
The two points removed during the reconstruction are marked as black dots both
in (a) and (b).

The impact of the source properties, detector readout, and beam-sample
positions on the reconstruction quality, was investigated. In order to
understand the effects of each element and to extract the maximum image
quality, a multidimensional parameter sweep was performed on the HPC cluster
of Diamond Light Source. The parameters included were the number of source
states [32, 33], number of scan correction trials [31], detector threshold
levels, and the bandwidth of the diffraction data. Each parameter permutation
was executed on the split and complete exposure data, allowing for a
quantitative comparison of the resolution.

#### Post-processing

To quantify the attained resolution, the acquired dataset was divided (in
time) into two half datasets to perform a Fourier Ring Correlation (FRC)
analysis. The correlation between the two half datasets was compared to a
half-bit information threshold, using an implementation based on van Heel et
al. [34]. The splitting was done by alternately assigning a camera time-frame
series to the odd or even dataset. Since the frame interval is very short (2.5
ms) compared to the expected timescale of source fluctuations, these half
datasets can be considered to be statistically independent measurements of the
same source-object-camera system, including its fluctuations. The obtained FRC
curve is shown in Figure 2(d), as well as the half-bit threshold curve used to
determine the attained resolution. The crossover point of the two curves lies
at 1.08 µm-1, corresponding to a resolution of 930 nm. The correlation in
Fourier-space was determined over 65 rings. For completeness, a line profile
is provided, taken along an arc centred at the middle of the Siemens star.

###### Acknowledgements.

##  IV Acknowledgements

O.O.M thanks EPSRC for the capital equipment grant (EP/M028437/1) to purchase
the laboratory-based Xenocs Xeuss 2.0/Excillum SAXS beamline used for the data
collection.

The Research Foundation - Flanders (FWO) is acknowledged for the financial
support to this work (Grant number G0A0417N).

The authors acknowledge Dr. Christian David for the design and production of
the Siemens star test pattern.

##  V Contribution

The experiment was conceived by D.J.B. and S.C. and was conducted by D.J.B.,
S.C., F.V.A., S.V., O.O.M and A.J.P.. The portable ptycho-scope was developed
by S.C., D.J.B and C.R.. The raw data were processed by F.V.A., S.V and
M.N.B.. Reconstruction and analysis was performed by D.J.B., S.V. and S.C..
The manuscript was written by D.J.B., S.C., M.N.B., S.V. and F.V.A.. All the
authors reviewed the manuscript.

## References

  * Faulkner and Rodenburg [2004] H. M. L. Faulkner and J. M. Rodenburg, Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm, Physical Review Letters 2, 023903 (2004).
  * Rodenburg  _et al._ [2007] J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Hard-x-ray lensless imaging of extended objects, Physical Review Letters 3, 10.1103/PhysRevLett.98.034801 (2007).
  * Dierolf  _et al._ [2010] M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, Ptychographic X-ray computed tomography at the nanoscale, Nature 7314, 436 (2010).
  * Takahashi  _et al._ [2011] Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, Towards high-resolution ptychographic X-ray diffraction microscopy, Physical Review B - Condensed Matter and Materials Physics 21, 10.1103/PhysRevB.83.214109 (2011).
  * Vila-Comamala  _et al._ [2011] J. Vila-Comamala, A. Diaz, M. Guizar-Sicairos, A. Mantion, C. M. Kewish, A. Menzel, O. Bunk, and C. David, Characterization of high-resolution diffractive X-ray optics by ptychographic coherent diffractive imaging, Optics Express 22, 21333 (2011).
  * Schropp  _et al._ [2012] A. Schropp, R. Hoppe, J. Patommel, D. Samberg, F. Seiboth, S. Stephan, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, Hard X-ray scanning microscopy with coherent radiation: Beyond the resolution of conventional X-ray microscopes, Applied Physics Letter 100, 10.1063/1.4729942 (2012).
  * Holler  _et al._ [2014] M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution, Scientific Reports 1, 3857 (2014).
  * Schropp  _et al._ [2013] A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, Full spatial characterization of a nanofocused X-ray free-electron laser beam by ptychographic imaging, Scientific Reports 1, 1633 (2013).
  * Batey  _et al._ [2019] D. J. Batey, S. Cipiccia, F. Van Assche, S. Vanheule, J. Vanmechelen, M. N. Boone, and C. Rau, Spectroscopic imaging with single acquisition ptychography and a hyperspectral detector, Scientific Reports 9, 10.1038/s41598-019-48642-y (2019).
  * Marchesini  _et al._ [2016] S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, SHARP: a distributed GPU-based ptychographic solver, Journal of Applied Crystallography 4, 1245 (2016).
  * ref [2016] _A computational framework for ptychographic reconstructions_ (Proceeding of the Royal Society A, 2016).
  * Maiden and Rodenburg [2009] A. M. Maiden and J. M. Rodenburg, An improved ptychographical phase retrieval algorithm for diffractive imaging, Ultramicroscopy 10, 1256 (2009).
  * Guizar-Sicairos and Fienup [2008] M. Guizar-Sicairos and J. R. Fienup, Phase retrieval with transverse translation diversity: a nonlinear optimization approach, Optics Express 16, 7264 (2008).
  * Wakonig  _et al._ [2020] K. Wakonig, H.-C. Stadler, M. Odstrcil, E. H. R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, and M. Guizar-Sicairos, PtychoShelves, a versatile high-level framework for high-performance analysis of ptychographic data, Journal of Applied Crystallography 2, 574 (2020).
  * Wansleben  _et al._ [2019] M. Wansleben, C. Zech, C. Streeck, J. Weser, C. Genzel, B. Beckhoff, and R. Mainz, Photon flux determination of a liquid-metal jet X-ray source by means of photon scattering, arXiv 10.1039/C9JA00127A (2019).
  * Derry  _et al._ [2018] M. J. Derry, O. O. Mykhaylyk, A. J. Ryan, and S. P. Armes, Thermoreversible crystallization-driven aggregation of diblock copolymer nanoparticles in mineral oil, Chemical Science 17, 4071 (2018).
  * Thirimanne  _et al._ [2018] H. M. Thirimanne, K. D. G. I. Jayawardena, A. J. Parnell, R. M. I. Bandara, A. Karalasingam, S. Pani, J. E. Huerdler, D. G. Lidzey, S. F. Tedde, A. Nisbet, C. A. Mills, and S. R. P. Silva, High sensitivity organic inorganic hybrid X-ray detectors with direct transduction and broadband response, Nature Communications 9, 10.1038/s41467-018-05301-6 (2018).
  * Bjeoumikhov  _et al._ [2012] A. Bjeoumikhov, G. Buzanich, N. Langhoff, I. Ordavo, M. Radtke, U. Reinholz, H. Riesemeier, O. Scharf, H. Soltau, and R. Wedell, The SLcam: a full-field energy dispersive X-ray camera, Journal of Instrumentation 7 (11), C11008.
  * Scharf  _et al._ [2011] O. Scharf, S. Ihle, I. Ordavo, V. Arkadiev, A. Bjeoumikhov, S. Bjeoumikhova, G. Buzanich, R. Gubzhokov, A. Gunther, R. Hartmann, M. Kuhbacher, M. Lang, N. Langhoff, A. Liebel, M. Radtke, U. Reinholz, H. Riesemeier, H. Soltau, L. Struder, A. F. Thunemann, and R. Wedell, Compact pnCCD-based X-ray camera with high spatial and energy resolution: A color X-ray camera, Analytical Chemistry 7, 2532 (2011).
  * ref [2020] Applications and X-ray techniques, https://web.archive.org/20201204165405/http://www.excillum.com/applications/ (2020), accessed: 2021-02-01.
  * Otendal  _et al._ [2008] M. Otendal, T. Tuohimaa, U. Vogt, and H. M. Hertz, A 9 keV electron-impact liquid-gallium-jet X-ray source, Review of Scientific Instruments 79, 016102 (2008).
  * Batey [2014] D. J. Batey,  _Ptychographic Imaging of Mixed States_ , Thesis, University of Sheffield (2014).
  * Spence  _et al._ [2004] J. C. H. Spence, U. Weierstall, and M. Howells, Coherence and sampling requirements for diffractive imaging, Ultramicroscopy 2, 149 (2004).
  * Gunther  _et al._ [2020] B. Gunther, R. Gradl, C. Jud, E. Eggl, J. Huang, S. Kulpe, K. Achterhold, B. Gleich, M. Dierolf, and F. Pfeiffer, The versatile X-ray beamline of the Munich Compact Light Source: design, instrumentation and applications, Journal of Synchrotron Radiation 5, 1395 (2020).
  * Cipiccia  _et al._ [2011] S. Cipiccia, M. R. Islam, B. Ersfeld, R. P. Shanks, E. Brunetti, G. Vieux, X. Yang, R. C. Issac, S. M. Wiggins, G. H. Welsh, M.-P. Anania, D. Maneuski, R. Montgomery, G. Smith, M. Hoek, D. J. Hamilton, N. R. C. Lemos, D. Symes, P. P. Rajeev, V. O. Shea, J. M. Dias, and D. A. Jaroszynski, Gamma-rays from harmonically resonant betatron oscillations in a plasma wake, Nature Physics 11, 867 (2011).
  * Williams [1988] G. P. Williams, Compact electron storage rings, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1, 59 (1988).
  * Ordavo  _et al._ [2011] I. Ordavo, S. Ihle, V. Arkadiev, O. Scharf, H. Soltau, A. Bjeoumikhov, S. Bjeoumikhova, G. Buzanich, R. Gubzhokov, A. Günther, R. Hartmann, P. Holl, N. Kimmel, M. Kühbacher, M. Lang, N. Langhoff, A. Liebel, M. Radtke, U. Reinholz, H. Riesemeier, G. Schaller, F. Schopper, L. Strüder, C. Thamm, and R. Wedell, A new pnCCD-based color X-ray camera for fast spatial and energy-resolved measurements, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1, 250 (2011).
  * Van Assche  _et al._ [2021] F. Van Assche, S. Vanheule, L. Van Hoorebeke, and M. N. Boone, The spectral X-ray imaging data acquisition (SpeXIDAQ) framework, Sensors 2, 563 (2021).
  * Van Assche  _et al._ [2018] F. Van Assche, S. Vanheule, S. Cipiccia, L. Vincze, L. Van Hoorebeke, and M. N. Boone, Implementation of a hyperspectral x-ray camera control and processing software chain, J. Instrum 13, C11015 (2018).
  * Nowak  _et al._ [2015] S. H. Nowak, A. Bjeoumikhov, J. von Borany, J. Buchriegler, F. Munnik, M. Petric, M. Radtke, A. D. Renno, U. Reinholz, O. Scharf, and R. Wedell, Sub-pixel resolution with a color X-ray camera, Journal of Analytical Atomic Spectrometry 9, 1890 (2015).
  * Maiden  _et al._ [2012] A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, An annealing algorithm to correct positioning errors in ptychography, Ultramicroscopy 120, 64 (2012).
  * Batey  _et al._ [2013] D. J. Batey, D. Claus, and J. Rodenburg, Information multiplexing in ptychography, Ultramicroscopy 138C, 13 (2013).
  * Thibault and Menzel [2013] P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 7435, 68 (2013).
  * van Heel and Schatz [2005] M. van Heel and M. Schatz, Fourier shell correlation threshold criteria, Journal of structural biology 3, 250 (2005).