Coherent Tabletop EUV Ptychography of Nanopatterns

Abstract

Coherent diffraction imaging (CDI) or lensless X-ray microscopy has become of great interest for high spatial resolution imaging of, e.g., nanostructures and biological specimens. There is no optics required in between an object and a detector, because the object can be fully recovered from its far-field diffraction pattern with an iterative phase retrieval algorithm. Hence, in principle, a sub-wavelength spatial resolution could be achieved in a high-numerical aperture configuration. With the advances of ultrafast laser technology, high photon flux tabletop Extreme Ultraviolet (EUV) sources based on the high-order harmonic generation (HHG) have become available to small-scale laboratories. In this study, we report on a newly established high photon flux and highly monochromatic 30 nm HHG beamline. Furthermore, we applied ptychography, a scanning CDI version, to probe a nearly periodic nanopattern with the tabletop EUV source. A wide-field view of about 15 × 15 μm was probed with a 2.5 μm−diameter illumination beam at 30 nm. From a set of hundreds of far-field diffraction patterns recorded for different adjacent positions of the object, both the object and the illumination beams were successfully reconstructed with the extended ptychographical iterative engine. By investigating the phase retrieval transfer function, a diffraction-limited resolution of reconstruction of about 32 nm is obtained.

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Coherent Tabletop EUV
Ptychography of Nanopatterns
Nguyen Xuan Truong
1,2, Reza Safaei3, Vincent Cardin3, Scott M. Lewis1, Xiang Li Zhong4,
François Légaré
3 & Melissa A. Denecke1,2
Coherent diraction imaging (CDI) or lensless X-ray microscopy has become of great interest for
high spatial resolution imaging of, e.g., nanostructures and biological specimens. There is no optics
required in between an object and a detector, because the object can be fully recovered from its far-eld
diraction pattern with an iterative phase retrieval algorithm. Hence, in principle, a sub-wavelength
spatial resolution could be achieved in a high-numerical aperture conguration. With the advances
of ultrafast laser technology, high photon ux tabletop Extreme Ultraviolet (EUV) sources based
on the high-order harmonic generation (HHG) have become available to small-scale laboratories. In
this study, we report on a newly established high photon ux and highly monochromatic 30 nm HHG
beamline. Furthermore, we applied ptychography, a scanning CDI version, to probe a nearly periodic
nanopattern with the tabletop EUV source. A wide-eld view of about 15 × 15 μm was probed with a
2.5 μm−diameter illumination beam at 30 nm. From a set of hundreds of far-eld diraction patterns
recorded for dierent adjacent positions of the object, both the object and the illumination beams were
successfully reconstructed with the extended ptychographical iterative engine. By investigating the
phase retrieval transfer function, a diraction-limited resolution of reconstruction of about 32 nm is
obtained.
Since the last three decades, coherent diraction imaging (CDI), also named as lensless X-ray microscopy, has
been of great interest as an alternative to the current state-of-the-art microscopy to achieve the atomic-level
resolution. Conventional X-ray microscopy oen requires multiple extremely precise and pricy optical condens-
ers and deectors, e.g., Fresnel zone plates or multilayer mirrors, which might introduce optical aberrations or
signicantly absorb X-rays. Nevertheless, the highest image resolution achieved with X-ray microscopy is about
10 nm1,2, which is well far away from the diraction-limited resolution. As a simple version of X-ray micros-
copy, CDI is the most ecient way of using photons with the spatial resolution essentially depending only on
the wavelength and the highest scattering angle (numerical aperture). In CDI, the exit-surface wave (ESW) dif-
fracted from an object can be fully recovered in both amplitude and phase from a single diraction pattern
(DP) measured in the far-eld. According to Sayre3, if an experimental DP is suciently oversampled, i.e., at
least twice the Nyquist frequency, the ESW can be reconstructed with the iterative phase retrieval (IPR) algo-
rithms, giving the physical image of the object. A number of IPR algorithms have been introduced to solve the
phase problem for a single experimental DP, such as the error reduction (ER)4, hybrid input-output (HIO)5, and
their modied versions. Basically, an IPR algorithm computes the ESW back and forth between the object- and
Fourier-domains, applying certain known constraints such as the Fourier modulus, support, and non-negativity
constraints5,6. Both ER and HIO algorithms have been widely used in numerous situations7–15, but they oen
suer from stagnation and trapping in local minima for noisy diraction patterns16,17. Intensive eorts have been
made to improve their performance, leading to the introduction of the noise-robust frameworks, e.g., the relaxed
averaged alternating reections (RAAR)18, noise-robust HIO19, dierence-map20, oversampling smoothness
(OSS)21, and optimisation-based IPR algorithms16,22–24. Still, CDI works well only for isolated objects. A scanning
version of CDI, termed as ptychography, has been proposed for wide-eld imaging. In ptychography, multiple
well-overlapping areas of an object are sequentially probed with a probe beam and the corresponding (far-eld)
diraction patterns are measured. With the additional overlap constraint, ptychography is hence more robust
and reliable compared to the conventional CDI, resulting in a higher resolution of reconstruction. Since the rst
1School of Chemistry, The University of Manchester, M13 9PL, Manchester, UK. 2Dalton Nuclear Institute, The
University of Manchester, M13 9PL, Manchester, UK. 3INRS, Energie, Matériaux et Télécommunications, 1650 Bld.
Lionel Boulet, Varennes, Québec, J3X 1S2, Canada. 4School of Materials, The University of Manchester, M13 9PL,
Manchester, UK. Correspondence and requests for materials should be addressed to N.X.T. (email: xuantruong.
nguyen@manchester.ac.uk)
Received: 4 May 2018
Accepted: 17 September 2018
Published: xx xx xxxx
OPEN
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demonstrations in the 1990s25–28, ptychography has been increasingly applied to study various kinds of samples
including nanostructures and biological cells29–33. Recently, for instance, electron ptychographical microscopy has
achieved a sub-nm resolution for 3D-imaging of carbon nanotubes34. A number of iterative phase retrieval frame-
works have been introduced to recover both the object and illumination beam from a ptychographical data set,
including the basic and extended ptychographical iterative engines (PIE35 and ePIE36) and the dierence map30,37.
ere exist a few ptychographical solvers such as ptypy38, PyNX.Ptycho39, and SHARP40.
Due to the demand of a great number of coherent X-ray photons, high-resolution ptychography has been
oen demonstrated at large facilities such as synchrotrons and free electron lasers41,42. anks to the recent
advances in the ultrafast laser technology, coherent tabletop EUV to so X-ray sources based on the high-order
harmonic generation have become achievable in many small-scale laboratories. Future high photon ux and
long-term stable HHG sources might oer a unique tool for developing novel phase retrieval algorithms and
time-resolved CDI, among other things, in laboratories. So far, only a few groups have been able to demonstrate
Figure 1. Schematic view of the tabletop EUV source for high-numerical aperture ptychography. An 1 kHz
Ti:sa amplier delivers 35 fs–FWHM optical pulses with up to 8 mJ pulse energy and at an 800 nm central
wavelength. e IR beam was focused with a 500 mm focal length lens into an 8 mm long gas cell fed with argon
gas through a piezo-driven valve at a backing pressure of 1.5 bars. e resulting HHG beam passed from the
source through an 1 mm–inner diameter dierential pumping tube to the characterisation chamber, and then
was characterised with a at-eld EUV spectrometer. To separate the IR beam, a 300 nm–thick Al foil was used
as a spectral lter. At about 80 cm downstream from the HHG source, an 1 mm–diameter aperture was inserted
as a spatial lter, resulting in a desired illumination prole for ptychography. A single harmonic at 30 nm was
selected and focused with a pair of multilayer mirrors in a z-conguration to minimise astigmatism, including
a at bending mirror (M1) and an f2 = 110 mm spherical mirror (M2). A sample with lithographed nanopatterns
was mounted on an xyz-translation stage and located at the focus of the 30 nm probe beam. An SEM image of
the sample is provided in Fig.2a. Diraction patterns of the adjacent areas on the sample were recorded with
an in-vacuum X-ray CCD camera at a distance z = 16.5 mm. A second 200 nm–thick Al lter was installed
in front of the CCD camera to block the residual stray light. e lateral positioning and data recording were
synchronised with a home-built LabVIEW program. Image reconstruction was performed with the extended
ptychographical iterative engine (ePIE) on an NVIDIA Tesla K40 computing processor.
Figure 2. (a) An SEM image of the nanopatterned sample. (b) A representative diraction pattern of the
sample aer binning 2 × 2 pixels into 1 pixel and performing curvature correction. An almost six orders of
magnitude high dynamic range image was obtained without the use of a beamstop.
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ptychographical imaging with tabletop EUV sources, mostly at around 30 nm43–46 and 13 nm47,48. In an attempt
to achieve a 100 μm–wide eld of view within a single ePIE reconstruction, a polychromatic EUV beam around
29 nm was employed to provide a sucient photon ux44. A breakthrough has been recently made by Gardner et
al.47 in achieving a sub-wavelength spatial resolution for a periodic sample with a 13 nm HHG beam. However,
the experimental far-eld intensity of the probe beam was required for the image reconstruction47, termed as the
modulus enforced probe (MEP) approach.
In this study, we demonstrate the preparation of a nanostructured sample by means of the state-of-the-art
electron-beam lithography. We then introduce a high photon ux and highly monochromatic tabletop 30 nm
beamline, newly established at the Photon Science Institute of the University of Manchester. Finally, we present
the rst EUV ptychographical imaging of the nearly periodic nanopattern, reconstructed with a modied ePIE
without a prior knowledge of the probe.
Materials and Methods
Tabletop EUV source. e EUV beamline used for ptychography is shown in Fig.1, including an HHG, a
characterisation, and an imaging stage. Great details of the beamline have been given in our recent reports16,49.
In brief, a femtosecond infrared (IR) Ti:sa laser system provides laser pulses with pulse energy up to 8 mJ, a
full-width at half maximum (FWHM) duration of 35 fs and a central wavelength of 800 nm at 1 kHz repetition
rate. e IR beam was focused with an f1 = 500 mm lens into an 8 mm–long gas cell located in the HHG vacuum
chamber. Argon gas was fed into the gas cell with a piezo-driven jet (Attotech) at a backing pressure of 1.5 bars.
e gas jet operated at 1 kHz with a typical 250 μs opening time driven by a high-voltage controller. e temporal
delay between the IR laser pulses and the gas jet was varied to maximize the HHG yield. e position of the gas
cell could be precisely tuned with an xyz-translation and rotation stage. e HHG chamber was separated from
the dierential pumping chamber by a 100 mm long tube with an 1 mm inner diameter, reducing the gas load in
the successive vacuum chambers. e vacuum pressure was ~4 × 10−3 mbar in the HHG chamber, and ~10−6
mbar in the dierential pumping and the experimental chambers. Aer passing the dierential pumping stage,
the HHG beam entered the experimental chamber, where it was characterised with a home-built at-eld EUV
spectrometer49. e IR beam was ltered out with a 300 nm–thick aluminium foil. At about 80 cm downstream
from the HHG source, an 1 mm–diameter aperture was inserted as a spatial lter, resulting in a desired EUV
beam prole for ptychography.
For ptychographical imaging, a single harmonic at λ = 30 nm was selected using a pair of multilayer mirrors
(optiX fab) in a z-conguration, containing a at mirror and an f2 = 110 mm mirror. Each mirror has a reectivity
>33% and a FWHM bandwidth of ~1 nm. e fold angles were kept <5° to minimize the astigmatism of the
30 nm probe beam. e spectral bandwidth (λ/∆λ) is about 200, which is sucient to perform coherent imaging
in this work16,50,51. A sample with lithographed nanopatterns was mounted on a sub-nm xyz-translation stage
(SmarAct) at the focus of the concave multilayer mirror M2, perpendicular to the 30 nm probe beam. e light
diracted from the sample was detected with an in-vacuum X-ray CCD camera (Andor iKon-M 934, 1024 × 1024
pixels, and p0 = 13 µm pixel-size) placed at a distance z = 16.5 mm downstream. e CCD’s sensor was cooled
down to −95 °C to enhance the signal-to-noise ratio. e camera was rotated an angle θ ≈ 45° relative to the sam-
ple so that the strongest diracted signals go along the diagonal of the sensor, optimizing the use of the sensor. A
second 200 nm-thick aluminium foil was installed in between the sample and camera to block the residual stray
light. By measuring the 30 nm beam prole, a photon ux of ∼7 × 107 photons/s on the detector was obtained.
It corresponds to a photon ux of ∼1.1 × 108 photons/s impinging on the sample when taking the absorption
of the second Al foil into account. e FWHM-diameter of the focal area of the probe was about wp = 2.5 µm,
determined by xyz-scanning of a 2 µm–diameter iris and recording the probe beam with the X-ray CCD camera.
Sample Preparation. Nanopatterns were prepared on a 10 nm thick silicon nitride (Si3N4) membrane,
which acts as an EUV-transmitting window (~15 µm × 15 µm), on a silicon frame (5 mm × 5 mm × 200 µm) by
means of the electron beam lithography. To apply the resist to the Si3N4 window via a spinning process, poly(me-
thyl methacrylate) (PMMA) was used as a bonding agent. e spinning process requires the sample to be held on
by a vacuum, which might damage the Si3N4 membrane. To support the Si3N4 membrane sample, we rst applied
a mixture of 8% wt. of anisole and PMMA to the surface of a 10 mm × 10 mm silicon wafer and then placed the
sample onto the PMMA. e whole unit was baked on a hot plate at a temperature of 180 °C for 20 minutes, allow-
ing the anisole to evaporate and leaving the PMMA behind. Next, the resist/solvent material was applied to the
sample by spin-coating with a speed of 8000 rpm and duration of 40 s. e sample with resist/solvent was then so
baked at a temperature of 100 °C for 2 minutes, resulting in an 100 nm thick resist evenly coated on the sample.
Further details are given elsewhere52.
e nanopatterns were written using an FEI scanning electron microscope that was driven by a Raith Elphy
Quantum 6 MHz pattern generator. e pattern consisted of boxes that were 50 µm in length and their widths
varied from 1 µm to 100 nm, and the line space varied to match the width of the box. e pattern was exposed
onto the Si3N4 window using an acceleration voltage of 30 keV, a current of 50 pA, and a 4 nm step-size. Once the
exposure was completed, the sample was developed in hexane for 10 s and the result is shown in Fig.2a. e nal
step was to remove the silicon wafer from the sample by dissolving the PMMA bonding agent in an acetone bath
for a period of ten hours.
Image Reconstructions. Image reconstruction was performed with the extended ptychographical iterative
engine36, including the lateral translation correction53. In brief, at the mth iteration, a complex-valued probe beam
Pm(r) illuminates an object Om(r, Rj), coordinated by Rj as the lateral translation of the object relative to the probe
beam. e exit surface wave at the object-plane is given as,
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=⋅ .fPOrR rrR(, )()(,) (1)
m
jm mj
At the detector-plane in the far-eld, the waveeld is computed as the Fourier transform of the ESW,
=.FT fFk rR() {(,)}(2)
mmj
e modulus constraint replaces the calculated amplitude (|Fm(K)|) with the experimental one while main-
taining the phase,
=⋅ .
IFk kFkFk
() () ()/()
(3)
m,j
mod
jmm
By back-propagating to the object-plane, the modied ESW is then updated as
Figure 3. (Top) Typical normalised error as a function of the number of iteration (Eq. (7)). e ePIE algorithm
performed 500 iterations with probe updates aer 120 iterations and translation renement aer 250 iterations.
(Top, insets) e reconstructed images illustrate the visual quality of the object without probe updates (a),
with probe updates (b), and with translation correction (c), taken at the iteration marked by vertical arrows.
(Bottom) e nal reconstructed amplitude and phase of the object (d,e) and probe (f,g), respectively.
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=.
−
{}
fFTrR Fk(, )()
(4)
m
mod
j
1
m,j
mod
Here, the support constraint might be applied5,54. Furthermore, probe and object updates are obtained by
applying the overlap constraint, namely,
α=+
||


−


+
⁎
OO
P
P
ffrR rR
r
r
rR rR(, )(,)
()
()
(, )(,)
(5)
m1 jmjm
mmax
2m
modjmj
β=+
||


−


+
⁎
PP
O
Offrr
rR
rR rR rR() ()
(, )
(, )(, )(,),
(6)
m1 mmj
mjmax
2m
modjmj
where the empirical parameters (α, β) are set to unity in this study. e above steps are sequentially repeated for
all available scan positions {Rj} to form a single ePIE-iteration. Aer each complete iteration, to monitor the ePIE
progress the normalised error is measured as36
σ=
∑∑ −
∑∑ .
I
I
kFk
k
() ()
()
(7)
m
k
k
jjm
2
jj
Oen, the initial probe guess is unity and only updated aer a few tens of iterations. Translation correction for
each scan position Rj was performed by calculating the relative shi δj(δjx, δjy) between the object’s estimates of the
successive iterations, i.e., Om+1(r, Rj) and Om(r, Rj), and modifying the current position to
γδ=+
RR
,
(8)
j
mod
jj
where the unitless magnication parameter
γγγ(, )
xy
is a function of the iteration number as suggested in the
original work53. The lateral shift δj is usually of the sub–0.01 pixel order and was calculated with the
cross-correlation technique53,55. Due to the invariance of the Fourier-transform to the object’s lateral transla-
tion36,56, we observed that the translation correction should be always applied (e.g., some tens of iterations) to
rene the object and probe functions.
Results and Discussion
In this study, the sample was raster-scanned with step-sizes (Δx, Δy) of a few hundreds of nm, i.e., less than wp/4
to ensure a sucient (>70%) overlap between the adjacent areas. A random oset of about 15% of the step-sizes
was added to each position to avoid the periodic artefacts (known as the raster grid pathology)37. At each scan
position, the diraction pattern was accumulated three times with 2 s exposure time and an 1 MHz readout speed.
Each diraction pattern was rotated with an angle −θ to suit the sample’s coordinates, resulting in a resized image
(~1448 × 1448 pixels) with the strongest scattering signals along the x-axis. To improve the signal-to-noise ratio
and reduce the computing time, we numerically integrated the diraction intensity by binning 2 × 2 pixels into 1
pixel and cropped each diraction pattern to N × N pixels (with N = 600). All diraction patterns were then rem-
apped onto the Ewald sphere for curvature correction57,58, following by a 2D Gaussian smoothing kernel with a
standard deviation of 5. A representative diraction pattern of the sample is shown in Fig.2b, with the maximum
spatial frequency kmax ≈ 16 μm−1. A high dynamic range close to six orders of magnitude was obtained, which is
crucial to achieve high-resolution imaging with the ePIE algorithm. e linear oversampling ratio is related to the
probe’s diameter as
λΘ=Θ =≈.zpw/(2)76
xy p
0
, which is entirely satised the oversampling requirement. Note
Figure 4. Phase retrieval transfer function (PRTF) computed from ve hundred independent ePIE
reconstructions. e resolution cuto of the ePIE, determined by the spatial frequency at which the PRTF
reaches a value of 1/e, is greater than the experimental cuto kmax ≈ 16 μm−1.
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that the eective probe’s beam might be slightly larger than the used FWHM diameter wp, yielding a possible
smaller oversampling ratio. In principle, the smallest resolvable period on an object, i.e., the half-pitch distance
resolution, is given according to the Rayleigh criterion as,
λΔ= =.rzpN/(2)31 7
0
nm.
In the following, we rst explore in details the performance of the modied ePIE framework with a small data
set of 169 DPs, probing an area of about 5 × 5 μm of the object. e spatial resolution of reconstruction can be
drawn from multiple independent ePIE reconstructions. Second, we present a full eld of view of the sample with
a data set of 900 DPs, which covers the whole Si3N4 window.
e rst ptychographical scan includes 13 × 13 positions with the step-sizes Δx = Δy = 300 nm. e ePIE
started with a probe guess of unity and a random object guess. e ePIE performed 500 iterations with probe
updates aer 120 iterations and translation renement aer 250 iterations. e ePIE code was written in Matlab
(R2016a) and ran on a Tesla K40 GPU accelerator. Figure3 (top) shows the normalised error as a function of
the number of iteration, monitoring the progress of image reconstruction. Snap-shots of the on-the-y recon-
structed object are also depicted to illustrate the improvement (Fig.3a–c) when dierent numerical techniques
were applied. Essentially, by applying probe update or translation correction, the error metric quickly drops by
Figure 5. Amplitude and phase of the object (a,b) and probe (c,d), respectively, obtained aer a thousand ePIE
iterations from a collection of 900 far-eld diraction patterns of the sample. (c) An intensity line prole (blue-
lled) is extracted along the green line in (a) compared to its corresponding part of the SEM image (yellow-
lled) shown in Fig.2a. Note the dierent imaging methods between the ePIE image (transmission) and the
SEM (reection).
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about an order of magnitude within a few tens of iterations. It then reduces exponentially slow with iteration,
representing the characteristics of the well-known ER algorithm built within the ePIE. e nal reconstructed
amplitude and phase of the object and probe are shown in Fig.3d–g. e retrieved lines are quite homogenous
in the phase’s picture, while their amplitudes are signicantly modulated (~40%) from line to line along the
x-axis. is eect has been also observed in many other independent reconstructions. We strongly believe that the
cross-talk between the object and the probe mainly accounts for the eect. We have performed additional ePIE
reconstructions applying the modulus enforced probe approach47 and observed much less modulation. However,
the corresponding normalised errors are about an order of magnitude higher. e far-eld probe’s modulus was
measured by moving the sample out of the 30 nm beam.
e spatial resolution can be directly determined if a well-characterised knife-edge sample is available. In CDI,
a phase retrieval transfer function (PRTF) has been oen used as a powerful mean to gauge the spatial resolution
of reconstruction and is given as14,16,59,60
=
|〈 〉|FT f
I
k
rR
k
PRTF ()
{(,)}
() ,
(9)
j
2
j
where
〈〉frR(, )
j
is the mean ESW at a xed position Rj, calculated from several independent reconstructions. e
resolution cuto of the ePIE reconstruction can be dened as the spatial frequency at which the PRTF reaches a
value of 1/e ≈ 0.37. We note, however, that the PRTF might strongly depend on the applied numerical meth-
ods14,16. Further, care must be taken into account to remove the outliers (failed solutions) before computing the
PRTF61.
Figure4 shows the PRTF obtained from five hundred independent reconstructions with the same set-
ting parameters. Here, the resolution cuto exceeds the experimental cuto kmax, which corresponds to the
diraction-limited resolution of 31.7 nm. e resolution of our setup is currently limited by the highest scattering
angle recorded with the CCD camera. In addition to using a larger CCD’s sensor, dierent modications might
be applied to increase the dynamic range of the measured DPs, which is directly related to the highest scatter-
ing angle. First, a mechanical beamstop is used to block the brightest undiracted light, allowing to measure
the high-angle diracted signals with longer exposure time. However, the use of a beamstop oen complicates
the experimental design and is very time-consuming. Second approach is to stitch dierent diraction patterns
recorded for various exposure durations, while removing the oversaturated signal44. Care must be considered in
reading the sensor output, because artefacts (e.g., saturation trail) might occur for oversaturated CCD sensors.
For a full-field scan, we consider a ptychographical data set of 30 × 30 positions with the step-sizes
Δx = Δy = 400 nm raster-scanning over the whole window (~15 × 15 μm). e ePIE reconstruction performed
one thousand iterations with a random object estimate, following with probe updates after 120 iterations,
and translation correction aer 300 iterations. Figure5 shows the reconstructed amplitude and phase of the
object5(a,b) and the probe5(c,d), respectively. A comparison between the ePIE and SEM image is given in
Fig.5e, showing excellent agreement between the two approaches. Note that the ePIE image is obtained in a
transmission conguration while the SEM image is obtained in a reection mode. Compared to the SEM image,
the ePIE object shows blurred edges, indicating possible sample’s defects from the e-beam lithography’s prepa-
ration. We observe slightly modulated transmission (~15% in average) of the object (5a) along the y-axis with a
mean period of about 310 nm, which is probably due to the nearly periodic features of the sample leading to the
strong cross-talking between object and probe. In a recent report47, this artefact is greatly reduced when the MEP
method was applied.
roughout this work we use for each position a loose support calculated from the inverse FT of the exper-
imental diraction pattern6. We however strongly believe that the visual quality of the object and the progress
of image reconstruction might be greatly improved with a dynamic support scheme (e.g., shrink-wrap54). e
acquisition time of the nine hundred diraction patterns was about two and half hours. Consequently, we limited
ourselves to the thermal dri and mechanical vibrations present in the laboratory. Future developed photon-rich
ux EUV sources with high repetition rates (≥100 kHz)62 might help to reduce exposure time and enhance the
quality of the experimental data.
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Acknowledgements
N.X.T. acknowledges the Dalton Nuclear Institute and an endowment from BNFL for nancial support. We thank
the Photon Science Institute for providing us with the ultrafast laser facility.
Author Contributions
N.X.T. designed, built and optimised the EUV beamline for ptychography. S.M.L. designed and fabricated the
sample, and X.L.Z. characterised the sample. N.X.T., R.S. and V.C. conducted the experiments. N.X.T. analysed
the experimental data and prepared the manuscript. M.A.D. and F.L. planed and initiated the project. All authors
contributed to the manuscript.
Additional Information
Competing Interests: e authors declare no competing interests.
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