X-ray Ptychography with a Laboratory Source
Darren J. Batey, Frederic Van Assche, Sander Vanheule, Matthieu N. Boone, Andrew J. Parnell, Oleksandr O. Mykhaylyk, Christoph Rau, Silvia Cipiccia
XX-ray Ptychography with a Laboratory Source
Darren J. Batey, Frederic Van Assche, Sander Vanheule, Matthieu N. Boone, Andrew J. Parnell, Oleksandr O. Mykhaylyk, Christoph Rau, and Silvia Cipiccia
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Diamond Light Source, Harwell Science andInnovation Campus, Fermi Avenue, Didcot, UK UGCT-RP, Department of Physics and Astronomy, Ghent University, Belgium Soft Matter Analytical Laboratory, Department of Chemistry,University of Sheffield, Sheffield, UK Department of Physics and Astronomy,University of Sheffield, Sheffield, UK Department of Medical Physics and Biomedical Engineering,University College London, London, UK (Dated: February 12, 2021) a r X i v : . [ phy s i c s . a pp - ph ] F e b bstract X-ray ptychography has revolutionised nanoscale phase contrast imaging at large-scale syn-chrotron sources in recent years. We present here the first successful demonstration of the techniquein a small-scale laboratory setting. An experiment was conducted with a liquid metal-jet X-raysource and a single photon-counting detector with a high spectral resolution. The experiment useda spot size of 5 µ m to produce a ptychographic phase image of a Siemens star test pattern witha sub-micron spatial resolution. The result and methodology presented show how high-resolutionphase contrast imaging can now be performed at small-scale laboratory sources worldwide. INTRODUCTION
Ptychography is a coherent scanning-diffraction imaging technique that produces quan-titative images at resolutions beyond the imaging performance of conventional, lens-based,microscopy systems [1]. Ptychography is now routinely applied at X-ray synchrotron sourcesacross the world, obtaining highly sensitive, quantitative, images at the highest spatial reso-lutions, down to tens of nanometres [2–7]. Until now, the high level of coherence required forX-ray ptychography has limited the application of the technique to high brilliance sourcessuch as synchrotron and, more recently, FEL facilities [8]. It was recently postulated thatthe new generation of X-ray laboratory sources may have sufficient brilliance to conducta ptychographic experiment, given the correct experimental setup [9]. We present herea demonstration of such an experiment and the first proof of concept for far field X-rayptychography performed using an X-ray laboratory source.A ptychography scan consists of recording 2D intensity patterns downstream from a sam-ple that is irradiated by a localised spot of coherent radiation. The 4D ptychographic datasetis 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 refractiveindex of the object at wavelength limited resolutions across an extended field of view [10–14].The success of the inversion step in extracting the phase relies strongly on the stability ofthe instrumentation and coherent properties of the beam. The coherence manifests itselfin interference fringes that hold the relative phase information. The coherent fraction ofa 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 well2onfined the source of radiation is laterally in space. The latter is determined by the sourcebandwidth - how well confined the source of radiation is in wavelength, or longitudinallyin 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 brillianceof third generation light sources is of the order of 10 photons s − mm − mrad − × photons s − mm − mrad − EXPERIMENT AND RESULTSExperimental configuration
The experiment was designed and conducted to explore the possibility of ptychographicimaging in a laboratory setting. The data were collected at the University of SheffieldSoft 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 Uni-versity [18, 19]. The X-ray source is an Excillum liquid gallium metal jet (LMJ), which has abrilliance of approximately of 5 × photons s − mm − mrad − IG. 1. Experimental configuration. Ptychography setup (not to scale) showing the experimentallayout as implemented at SMALL, Sheffield, UK. 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 energyresolution. Increasing the bandwidth of the data analysed from 200 eV to 1 keV increasesthe contribution of the Bremsstrahlung background. The theoretical resolution achievablefor 200 eV and 1 keV bandwidths are 100 nm and 540 nm respectively [23]. Conversely, thereconstructions of the experimental data showed a decrease in resolution for the narrowerbandwidth (1200 nm for 200 eV and 930 nm for 1 keV), suggesting that the experiment isphoton limited. The best reconstruction, Figure 2(b), was obtained with 1 keV bandwidth.Both reconstructions included the correction for the source position and direction. Thesecorrections were essential to compensate for long-term instabilities of the source during theacquisition (see method for details). Figure 2(a) confirms a beam profile of 5 µ m in extent.A line profile across the reconstructed phase image of the object shows that the spokes arewell resolved (Figure 2(c)). The half-bit resolution of the image is 930 nm (Figure 2(d)), afactor of more than 5 beyond the spot size at the sample.4 IG. 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) Lineplot from the dashed black line in (b). The raw data is represented by the solid black line and the10 pixel moving average is represented by the solid red line. d) Fourier ring correlation of the twosplit exposure reconstructions showing 1.08 µ m − spatial frequency (corresponding to 930 nm). Discussion and summary
Performing lab-based X-ray ptychography has required advances in lab-sources [20] anddetector technologies [19]. The high brilliance of the LMJ has provided the coherent fluxrequired for the ptychography technique. The hyperspectral detector has been required tocharacterise spectrally the source and assess the temporal coherence.Our analysis of the results suggests that the experiment was limited by the photon statis-tics and point-to-point stability of the source. The effect of the latter was mitigated via thereconstruction algorithm that modelled the source shift and direction. The use of differentor additional optical components for focussing the X-ray beam to the sample could help tobetter harness the coherent flux, increasing the photon statistics and reducing the sensitivityto long term source instabilities.We have demonstrated that it is possible to perform X-ray ptychography with a LMJsource and have shown how to perform ptychography in a laboratory setting, releasing tothe laboratory environment a technique otherwise confined to synchrotron facilities. Theexperimental breakthrough achieved with a LMJ is a first step toward expanding X-rayptychography to other bright compact light sources: from inverse Compton scattering [24],5o laser-plasma based [25] and compact storage rings [26].
METHODSExperimental configuration
X-ray source
The X-ray beam is generated using a JXS-D2-001 liquid metal-jet labo-ratory source modified to a higher power performance (Excillum AB, Kista, Sweden) withGallium as anode material. The focal spot size of the source can be varied within a relativelywide range between 5 µ m and more than 50 µ m, by tuning the projection of the electronbeam 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 µ m. A three-dimensional single reflectionmulti-layered ellipsoidal mirror (FOX3D 11-600 Ga, Xenocs, Grenoble, France) is used tofocus the X-ray beam. The centre of the mirror is located 11 cm downstream of the X-raysource, coinciding with the first mirror focus. The resulting beam is slightly converging, withthe second mirror focus located approximately 5.2 m downstream of the mirror. Due to thechromatic behaviour of the mirror reflectivity, the mirror also acts as a spectral band-passfilter, enhancing the relative intensity of the 9.25 keV K-alpha emission line of Gallium bydrastically reducing the Bremsstrahlung continuum spectrum. Scanning system
The portable ptycho-scope end-station developed at the I13-1 branch-line of the Diamond Light Source was used for positioning the sample and the pinhole (Fig-ure 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 controlledwith a python data collection software connected to an MCS control box over an RS232protocol. The software scans the position point-by-point, triggers the detector through aUSB-BNC connection and uses the detector ready status for synchronising the motion withthe detector readout and beam status.The instrument was set up with a 5 µ m diameter, 50 µ m thick, tungsten pinholeplaced 4 m from the source. During the experiment, a flux through the pinhole of ∼ × photons s − was measured. The sample was placed 1 cm downstream of thepinhole and scanned in the plane perpendicular to the optical axis of the beam on a squaregrid of 20 ×
20 steps with step size of 1 µ m, following a snake-like trajectory.6 -ray detector The pnCCD based Color X-ray Camera (SLcam) [27] was used to mea-sure the diffraction patterns. The detector has a physical pixel pitch of 48 µ m, and anactive area of 264 ×
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 readoutas well as raw data processing. The energy resolution of the SLcam is approximately 144 eVFWHM 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 pipeswere placed between the sample and the detector as well as between the mirror and thepinhole to reduce the air absorption and scattering. The detector exposure at each pointwas 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 nitridemembrane with an outer spoke separation of 4 µ m and an inner spoke separation of 50 nm.An area of 400 µ m was scanned during the experiment. Data processing
Detector frame processing
The SLcam captures raw frames containing only a few photonevents per frame. The raw frames are subsequently pre-processed into diffractograms for theptychography reconstruction, using a cluster-finding algorithm and subsequent rebinning ofthe 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 responseand sub-pixel accuracy can be achieved [30]. Using SpeXiDAQ [28], the raw frames are storedand afterward processed and split by time or energy into different datasets. The time-basedsplitting was used for assessing the spatial resolution (see post-processing section below),the energy-based splitting for investigating the spectral properties. The spectrum has beengenerated by integrating the photon counts in each of the 5 eV energy bin datasets. Thespectrum recorded is shown in Figure 3: the escape peak of the K-alpha line in the Siliconbulk and the double and triple photon pile-up of the K-alpha are visible, beside the main GaK-alpha and K-beta peaks. The source spectrum has been retrieved by adding the counts ofthe escape peak, those of the double pile-up ( ×
2) and of the triple pile-up ( ×
3) to the K-alphapeak. The energy bandwidth was investigated and matched to the resolution achievable fromthe experimental conditions (flux and geometry). The data shown in Figure 2 was produced7
IG. 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 shownin red. using a single output bin ranging from 8 .
75 keV to 9 .
75 keV.
Image reconstruction
The image reconstruction process takes a model of the experiment, including knowledgeof the illumination conditions and scanning coordinates along with the recorded intensitymeasurements, 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 anda defocus of 10 mm. The convergence angle is calculated from the beam on the detector,and the defocus was chosen to produce a 5 µ m spot creating a balance between the truefocal distance of the mirror and the beam width imposed by the pinhole. The scanning8oordinates 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 sourceinstability, experimental errors and signal degradation due to noise and decoherence. Thebeam intensity was monitored during the acquisition by integrating the flux received onthe detector. The intensity variations, shown in Figure 4(a), are a manifestation of thesource instabilities. The source appears to fluctuate across the first 100 positions, with asignificant sudden drop in intensity at position 131 of the scan. Scan positions 131 and132 were removed from the data prior to the reconstruction (see Figure 4). The sourcefluctuations translate into point-to-point instabilities at the sample plane and correspond toeither a translation, a tilt, or a combination of the two in the beam profile. PtyREX employsa scan correction built on the annealing method of Maiden et al. [31], but is extended toalso 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).The impact of the source properties, detector readout, and beam-sample positions onthe reconstruction quality, was investigated. In order to understand the effects of eachelement and to extract the maximum image quality, a multidimensional parameter sweepwas performed on the HPC cluster of Diamond Light Source. The parameters includedwere the number of source states [32, 33], number of scan correction trials [31], detectorthreshold levels, and the bandwidth of the diffraction data. Each parameter permutationwas executed on the split and complete exposure data, allowing for a quantitative comparisonof 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. Thecorrelation 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 alternatelyassigning a camera time-frame series to the odd or even dataset. Since the frame intervalis very short (2.5 ms) compared to the expected timescale of source fluctuations, thesehalf datasets can be considered to be statistically independent measurements of the samesource-object-camera system, including its fluctuations. The obtained FRC curve is shown inFigure 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 µ m − , corresponding to a resolution of9 IG. 4. Source and illumination stability. a) Fluctuation of total intensity measured by integratingthe 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 ofthe arrow represents the re-calculated position, the direction of the arrow represents the directionof 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 twopoints removed during the reconstruction are marked as black dots both in (a) and (b).
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
O.O.M thanks EPSRC for the capital equipment grant (EP/M028437/1) to purchase thelaboratory-based Xenocs Xeuss 2.0/Excillum SAXS beamline used for the data collection.The Research Foundation - Flanders (FWO) is acknowledged for the financial support tothis work (Grant number G0A0417N).The authors acknowledge Dr. Christian David for the design and production of theSiemens star test pattern. 10
ONTRIBUTION
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