ultrafast soft x-ray scattering and reference-enhanced

Journal of Electron Spectroscopy and Related Phenomena 166–167 (2008) 65–73

Contents lists available at ScienceDirect

Journal of Electron Spectroscopy andRelated Phenomena

journa l homepage: www.e lsev ier .com/ locate /e lspec

Ultrafast soft X-ray scattering and reference-enhanced diffractive imaging ofweakly scattering nanoparticles

Sébastien Bouteta,c,∗, Michael J. Boganb,1, Anton Bartyb, Matthias Frankb, W. Henry Bennerb,Stefano Marchesinib,d, M. Marvin Seibert c, Janos Hajdua,c, Henry N. Chapmanb,2

a Linac Coherent Light Source, Stanford Linear Accelerator Center, 2575 Sand Hill Road, Menlo Park, CA 94025, USAb Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USAc Laboratory of Molecular Biophysics, Institute of Cell and Molecular Biology, Uppsala University, Husargatan 3, Box 596, S-75124 Uppsala, Swedend Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

a r t i c l e i n f o

Article history:Available online 10 July 2008

Keywords:Soft-X-ray free-electron-laserSpherical nanoparticlesX-ray diffractive imaging

a b s t r a c t

We report the first successful reconstruction of the real space image from coherent X-ray diffractionpatterns of membrane-supported nanoparticles using single ultrafast pulses. The particles consisted of145-nm spherical polystyrene spheres that were size-selected by differential mobility analysis. We inves-tigated the dependence of signal intensity on the number of spherical nanoparticles irradiated by singleultrafast pulses at the FLASH FEL facility. We demonstrate detection of as few as two 145-nm diameterparticles irradiated by a single 32 nm fs-long FLASH pulse focused to 2.4 J cm−2. In this case the noisein the diffraction pattern, due to photon-counting statistics and scattering from the supporting siliconnitride membrane, was the largest contributor to the recorded intensity. We were able to reconstructhigh-resolution images of the nanoparticles using a strong scattering reference object to aid the phaseretrieval of the coherent diffraction pattern. This method of reference-enhanced diffractive imaging mayallow the imaging of weakly scattering objects at FLASH and other future X-ray FEL sources.

Published by Elsevier B.V.

1. Introduction

The FLASH (Free-electron-LASer in Hamburg) soft-X-ray free-electron-laser (FEL) [1,2] located on the Deutsches Elektronen-Synchrotron (DESY) site in Hamburg, Germany, has recently beenused to image nanostructured nonperiodic objects by reconstruct-ing images from coherent diffraction patterns using phase retrievalalgorithms [3]. Single-shot diffraction experiments on nanofabri-cated samples and nanoparticles have been performed with 32and 13.5 nm photons, and FLASH is currently lasing at 7 nm. Thetechnique of flash diffractive imaging, in which an intense X-raypulse which destroys the sample is used to image the sample beforethe onset of radiation damage, was demonstrated successfully at aresolution limited only by the wavelength of the X-rays and thedetector geometry [3,4]. The sub-nm wavelength photon pulses

∗ Corresponding author at: Linac Coherent Light Source, Stanford Linear Acceler-ator Center, 2575 Sand Hill Road, Menlo Park, CA 94025, USA. Tel.: +1 650 926 8676;fax: +1 650 926 3615.

E-mail address: [email protected] (S. Boutet).1 Current address: PULSE, Stanford Linear Accelerator Center, 2575 Sand Hill Road,

Menlo Park, CA 94025, USA.2 Current address: Centre for Free-Electron Laser Science, Universität Hamburg

and DESY, Notkestraße 85, 22607 Hamburg, Germany.

from future hard-X-ray free-electron-lasers are anticipated toeventually facilitate near-atomic resolution imaging of nanometer-to-micrometer-sized objects without the need for crystallization[5–7].

Since radiation damage during the exposure limits the resolu-tion of the data obtained, pulses shorter than the manifestationof damage in the sample are required to reduce the effect. Toinvestigate the practical limitations of single pulse X-ray diffrac-tive imaging, spherical nanoparticles are being used as a standardtest sample due to favorable experimental characteristics, such assize-uniformity, and the ease of signal and damage modeling. A con-tinuum model for the imaging experiments performed at FLASH[8] and femtosecond time-resolved measurements of nanoscaledynamics [9] show that irradiated spherical nanoparticles main-tain their integrity for structures at least larger than 3 Å duringthe 25 fs pulses. Although data was collected with many hundredsof nanoparticles irradiated per pulse, these results give credenceto the concept of flash imaging individual nanometer and sub-nanometer-sized objects such as single nanoparticles, molecules,or larger clusters of molecules.

Here we investigate the dependence of signal intensity on thenumber of spherical nanoparticles irradiated by single focusedfemtosecond X-ray pulses. Samples were mounted on supportingsilicon nitride membranes that contributed a relatively large degree

0368-2048/$ – see front matter. Published by Elsevier B.V.doi:10.1016/j.elspec.2008.06.004

http://www.sciencedirect.com/science/journal/03682048

http://www.elsevier.com/locate/elspec

mailto:[email protected]

66 S. Boutet et al. / Journal of Electron Spectroscopy and Related Phenomena 166–167 (2008) 65–73

of background scattering to the measurements yet we demonstratedetection of as few as two 145 nm diameter particles irradiated by asingle 32 nm fs-long FLASH pulse, focused to 1014 W cm−2. We alsoshow that a strong scattering reference object can be used to aidreconstruction of individual supported nanoparticles irradiated bya single 13.5 nm FLASH pulse. These results are important for futurework focused on injected and supported nanoparticles at FLASHand other future X-ray FEL sources.

2. Experimental

Experiments were performed at FLASH during two separateruns. During the first run, the FEL produced a laser beam with awavelength of 32 nm while the wavelength was 13.5 nm for thesecond run. The nanoparticles were held on 20 ± 5 nm thick Si3N4membranes. The free-standing membranes were supported on sil-icon wafers (20 mm × 25 mm), with a total of 282 square openings(referred to as windows) of four different widths (200, 100, 50and 20 !m). The transmission of the beam through the supportingmembrane was 44% and 84% at 32 and 13.5 nm respectively. Despitethe relatively high absorption of these membranes, especially atlonger wavelengths, these membranes have many advantageouscharacteristics which made them ideal for these experiments. Theyare very sturdy which made the sample handling straightforwardwith minimal loss of the membranes despite their very thin struc-ture. They can be fabricated in a large quantity, allowing manysamples to be mounted on the same large wafer, which reduces theneed to often vent the sample chamber. Nanoparticles depositedas described below adhere to the membranes very well allow-ing essentially loss-less sample transport and transfer to vacuum.The supporting Si wafer effectively acts as an aperture locatedat the interaction plane, which is ideal for diffractive imagingmeasurements. And finally, nanofabricated objects can be accu-rately machined on these Si3N4 membranes without disturbing thenanoparticles using a focused ion beam (FIB), for example. Thesefabricated patterns can be designed to act as reference scatterers,as described below.

The spherical nanoparticles used in this work were polystyrenespheres (PostNova, Germany) with a reported diameter of 140 nmand a coefficient of variance of 6.2%. They were provided in asurfactant-free solution at a concentration of 1.5 × 1014 particles/ml(p/ml). To characterize the sphere size distribution and to reducetheir size-polydispersity we used scanning mobility particlespectrometry [10]. The method and apparatus for positioning size-selected spheres onto Si3N4 foils has been described in detail [11].An electrospray aerosol generator (TSI model 3480) was used toaerosolize solutions of 1.5 × 1012 to 1.5 × 1013 p/ml prepared in25 mM ammonium acetate in water. The electrospray dropletswere introduced into a flow of 1.5 lpm air and 0.1 lpm CO2 tominimize corona discharge. The droplets were immediately charge-reduced by exposure to ionized air created by a 210Po "-source andallowed to evaporate to dryness, resulting in an aerosol of discreteaerosolized spheres with a known charge distribution [12]. A bipo-lar equilibrium charge distribution was achieved via the presenceof positively charged ions and free electrons in the ionized carriergas of the aerosol. As a result the charge carried by the sphereswas predominantly zero, while a small fraction was singly charged(positively or negatively), and an even smaller fraction was doublycharged. The size-polydisperse spheres passed into a differentialmobility analyzer (DMA) (TSI, model 3081) via a conductive siliconetube and were size-classified based on their electrical mobility. Aportion of the size-selected aerosol was sampled into a conden-sation particle counter (CPC) (TSI, model 3786) to monitor thegas phase particle concentration (number/cm3) and the remain-

ing aerosol was delivered to a nanometer aerosol sampler (NAS)(TSI, model 3089) for electrostatic capture onto a substrate. The Siwafers supporting the Si3N4 foils were positioned with electricallyconductive tape onto a 5 cm diameter electrode (−10 kV) in the NAS.

At FLASH, the sample wafer was placed at the focal plane ofan ellipsoidal mirror with a 2 m focal length which focused theFLASH beam to a 17 !m FWHM Gaussian spot. A sample windowwas centered on the focused beam using beam-based alignmentwith the attenuated beam in the case of the 32 nm run and opticallywith the aid of a long-range microscope (Infinity, model K2) for the13.5 nm run. The attenuation necessary to ensure the sample wouldnot get damaged by the X-ray beam was achieved with a differen-tially pumped gas attenuator provided by the FLASH facility. Twoorders of magnitude attenuation was necessary to prevent dam-age of the sample during alignment since the focused FLASH laserbeam at full power is capable of vaporizing all material. The aver-age pulse energy delivered was 4 and 20 !J for the 32 and 13.5 nmruns respectively. This corresponds to 6.5 × 1011 and 1.4 × 1012 pho-tons per pulse respectively. The pulses were 25 ± 5 fs long in bothcases. The pulse duration was deduced from the energy spectrummeasured over many shots as described in Ref. [2].

The experimental geometry is represented schematically inFig. 1. The Si3N4 membrane, with a certain number of nanopar-ticles is supported by the Si wafer. The technique of diffractiveimaging aims to measure the appropriately sampled diffractionpattern from the illuminated object and it is therefore very simplein concept. No imaging optic is required. Only a two-dimensionaldetector is needed a certain distance downstream of the sample(54 mm in these experiments). However, with ∼1012 photons per25 fs long pulse delivered by FLASH and focused to such a smallarea, the power density is on the order of 1013 W cm−1, whichis more than sufficient to cause all material within the Rayleighvolume to turn into a plasma. Using the known absorption crosssection of the material at the wavelength used [23] and assumingthis cross-section is constant during the pulse, we can calculate thatthe sample was heated to up to 60,000 K if we assume all the energydeposited by the photons becomes thermal energy. On average,each atom in the sample received a deposited dose of roughly 5 eV.A hole in the detector is required to let the direct beam pass without

Fig. 1. Schematic representation of the experimental geometry. The FEL beam (i) isincoming from the left and passes through a Si3N4 window (ii) that is supported bya Si wafer (iii). Nanoparticles are randomly distributed on the Si3N4 window andin a separate case a nanostructured pattern was milled into the Si3N4. A gradedmultilayer mirror (iv) with a central hole (v) is used to spatially separate the directbeam from the diffracted beam (vi). An upward facing CCD camera (vii) records thediffraction pattern.

S. Boutet et al. / Journal of Electron Spectroscopy and Related Phenomena 166–167 (2008) 65–73 67

damaging the detector. A simple beamstop in front of the detectorwould be ablated by the beam and create undesired backgroundon the detector. Since no detector with a central hole was available,a 45◦ graded multilayer mirror with a central hole was developedand used to separate the direct beam from the diffracted X-rays.An upward facing CCD camera with 20 !m pixel pitch from RoperScientific (model PI-MTE) was used to measure the diffraction pat-terns. This novel mirror-detection system has been described indetail [13]. The entire beamline, sample chamber and detector sys-tem was held under high vacuum due to the strong absorption ofVUV photons in air at the wavelength used in these experiments.

3. Results

3.1. 32-nm results

A sample wafer was prepared by depositing size-selected 145-nm diameter polystyrene spheres on different areas of the waferfor different periods of time. The sample wafer contained a regu-lar array of Si3N4, windows and the masking of certain areas duringparticle deposition allowed the preparation of columns of windowswith different particle densities. The particle density was measuredfor two entire rows of windows after the FLASH measurement bycounting the number of spheres visible on an electron micrograph

over a certain area. The two rows characterized were those immedi-ately above and below the row that was probed and destroyed withthe FLASH beam. These electron micrographs are shown in Fig. 2.An average particle density was measured for four columns of win-dows and values of 0.66, 0.24, 0.049 and 0.0089 particles/!m2 wereobtained. Some other windows were left intentionally blank, withno particles on other parts of the wafer for calibration purposes.

Diffraction patterns from a window belonging to each of thesefour columns in addition to a blank window were measuredusing the 32 nm FEL radiation from FLASH. These windows were100 !m × 100 !m. The images collected by the CCD for the blankwindow as well as the two lowest particle densities are shown inFig. 3. The strong horizontal and vertical streaks come from scatter-ing off the edges of the windows. These streaks were present eventhough the main Gaussian focal spot was 17 !m FWHM [2,9] dueto the presence of a weak broad halo surrounding the main beam.

The size of the focal spot has been accurately characterized asa Gaussian with a FWHM of 17 !m in both directions. When theSi3N4 membrane is irradiated by this spot, a hole is created wherethe intensity is above the damage threshold of Si3N4. An exampleelectron micrograph is shown in Fig. 4. The FEL beam is seen to havevaporized the supporting membrane in an approximately ellipticalregion. Such images allow us to estimate the number of particleshit by the beam at an intensity at least as large as the Si3N4 damage

Fig. 2. Electron micrographs of Si3N4 windows with varying density of 145 nm polystyrene spheres. The particle density for each sample is (a) 0.66, (b) 0.24, (c) 0.049 and(d) 0.0089 particles/!m2. The scale bar corresponds to 10 !m.


Fig. 3. Single-shot diffraction patterns from Si3N4 windows with varying density of 145 nm polystyrene spheres. (a) Blank window. (b) Window with 2 particles hit by thebeam. (c) Window with 22 ± 5 particles hit by the beam.

threshold intensity. We calculate an effective number of spheresilluminated by the beam. The five sample windows studied corre-spond to 300 ± 17, 108 ± 10, 22 ± 5, 4 ± 2 and 0 particles hit by theGaussian beam.

The measured diffraction intensities were averaged over circlesof constant scattering angle ! to give the radial average intensityas a function of momentum transfer q = 2/" sin(!/2), where " is thewavelength. The radially averaged intensity was calculated for allfour particle densities as well as the blank window and they areshown in Fig. 5a. The integrated intensity with the intensity fromthe blank window subtracted is also shown for each particle den-sity in Fig. 5b. Each of these curves was normalized to the sameincident intensity. The energy of the pulses delivered by FLASH fol-lows a Gamma distribution and strong fluctuations, up to 100% fromshot to shot are observed. A gas ionization detector upstream ofthe focusing mirror is used to measure the incident pulse energy

Fig. 4. Electron micrograph of a typical Si3N4 window after the single FLASH pulse.A hole is left where the power density of the beam was above the damage thresholdof Si3N4. The weak halo of the FEL beam was sufficiently intense to remove thepolystyrene spheres without damaging the Si3N4 membrane over some area of thesample. The scale bar corresponds to 10 !m.

for every shot. The accuracy of the gas ionization detector isroughly 10% introducing a relatively large error in the normalizedintensity.

The total integrated diffracted intensity scales with the indepen-dently measured particle densities to within the statistical erroron the number of particles hit by the beam and the statisticalerror due to the normalization of every shot. The signal is veryweak for the lowest density but a few particles on a windowcan still be differentiated from a blank sample. Close inspectionof the diffraction pattern of Fig. 3b reveals the presence of peri-odic oscillations in a direction roughly 15◦ from the vertical. Theseoscillations suggest the presence of only two scattering centersand the period of the oscillation suggests the two particles areroughly 4 ± 1 !m apart. The low signal level makes it difficult tofit the diffraction pattern and the spacing between the two scat-tering centers was only estimated from the average spacing of thefringes in the diffraction pattern. Verification that 2 latex sphereswere indeed the scattering sources is not possible due to the lowsignal level of the data. However, characterization of the samplewith a scanning electron microscope before the measurement atFLASH showed very low level of impurities on the sample and wetherefore can confidently identify the two scattering centers as two145 nm latex spheres. Despite the presence of a large supportingmembrane generating a background signal more than 10 timeslarger than the two particles, the data shows that it is still pos-sible to observe the presence of as few as two 145 nm polystyrenespheres with a single 25 fs FEL pulse containing ∼6.5 × 1011 photonsfocused to a peak intensity of 2.4 J cm−2. The signal is however tooweak to allow an image to be reconstructed using phase retrievalalgorithms.

3.2. 13.5-nm results

A second sample was prepared by depositing a very smallamount of the same 145 nm polystyrene nanospheres onto a dif-ferent wafer. The deposition time was such that only between 1and 3 particles were present on every 20 !m square Si3N4 windowon the wafer. The sample was then taken to a FIB instrument andnanostructured patterns were milled through the 20 nm thick Si3N4membranes, away from the nanoparticles. An electron micrographof such a sample is shown in Fig. 6e. The letter F and a representationof a flash of light were milled all the way through the membrane.The width if the lines of the milled structure were between 150and 200 nm. Two 145 nm polystyrene spheres are present, one tothe right of the flash (particle 1) and the second roughly 7 !m above


Fig. 5. Integrated intensity as a function of momentum transfer (q = 2/" sin(!/2) where ! is half of the scattering angle) for varying density of 145 nm polystyrene spheres.The number of spheres hit with the peak intensity of the pulse is indicated for each curve. (a) Raw intensity. (b) Intensity after subtraction of the intensity from the blankwindow.

the letter F. The entire 20 !m wide window can be seen with thegray area representing the Si3N4 and the Si wafer support showingup white. A zoomed-in view of the electron micrograph is seen inFig. 6d where the polystyrene spheres are visible as small whitedots.

This sample was placed in the focused beam of FLASH which waslasing at 13.5 nm. The diffraction pattern was measured using thesame camera system as for the 32 nm measurements except thata different graded multilayer mirror capable of reflecting 13.5 nmX-rays was used [13].

Fig. 6. Diffractive imaging of two 145 nm polystyrene spheres with a reference object. (a) Diffraction pattern collected from a single FEL pulse of 1012 photons. The datahas the dark noise subtracted, was corrected for the Ewald curvature and for the misalignment and warping of the 45◦ detector mirror. (b) Reconstructed exit wave of theentire Si3N4 window. The edges of the window are visible in the reconstruction. The complex-valued exit wave is represented with the color saturation proportional to theamplitude of the wave and the hue proportional to the phase, with a white background to make the window frame visible. (c) Zoomed in view of the reconstructed exit waverepresented as in (b) but on a dark background instead to highlight the presence of the 2 nanoparticles. (d) Electron micrograph of the FIBed pattern and the 2 nanoparticlesbefore the FLASH beam destroyed the sample. (e) Electron micrograph of the entire Si3N4 window before the FLASH measurement.


The diffracted intensity measured is shown in Fig. 6a. The datashown had a dark image subtracted, was corrected for the curvatureof the Ewald sphere and also corrected for the reflectivity gradi-ent and the non-flatness of the 45◦ mirror. The mirror correctionswere calculated using regular arrays of holes in Si3N4 membranesto generate arrays of Bragg peaks on the CCD. A correction mapwas calculated that would make these patterns centrosymmetricand this same map was applied to the data shown here.

A faint cross is present in the center of the diffraction patternand this is due to the presence of the 20 !m frame of the Si3N4window. The cross is weaker than for the 32 nm data because thepenetration length of 13.5 nm X-rays in Si is 4.8 times larger than at32 nm. The transmission through the wedged edge of the anisotrop-ically etched Si frames has an exponential profile with a 1/e width of0.47 !m. This soft edge scatters less than the sharper 0.21 !m widetransmission edge at 32 nm wavelength. The center of the diffrac-tion pattern was misaligned with the hole in the mirror and someof the missing data was later filled in using centrosymmetric equiv-alent data. This reduced the number of missing data points near theorigin. This data is very important since the low angle diffractioncorresponds to the overall shape of the object. Good knowledge ofthe low angle data puts strong constraints on the possible low fre-quency modes in the image and therefore puts a strong constrainton the shape of the object which favors convergence to a singlesolution [14].

The phases of the diffracted wave are lost in the measurementsince only the intensity or the square of the wave is measured.Knowledge of the phase for each pixel in the data would provide acomplete complex wave exiting the sample. A simple Fourier trans-form of the complex diffraction pattern yields the exit wave sincethe measurement was performed in the far-field. Phases can beretrieved if the diffraction pattern is sampled more finely than theNyquist frequency of the band-limited diffraction intensity pattern[15]. The Fourier transform of the diffraction intensities gives theautocorrelation function of the object, and the diffraction band limitis set by the finite extent of this function. That is, the autocorrela-tion function of the scattering object should fit within the field ofview of the detector (although this is not a strict requirement [16]).Equivalently, the scattering object should be smaller than the fieldof view of the detector by typically at least a factor of two. This istypically achieved with an isolated object although it is also possi-ble to isolate a small part of a large object by limiting the illuminatedarea.

With a properly sampled diffraction pattern, the phases can beretrieved iteratively using Gerchberg–Saxton iterative transformalgorithms as has been demonstrated multiple times for varioustypes of samples [3,4,15,17,18]. These algorithms consist of per-forming successive projections of the current iterate on the set ofsolutions satisfying the modulus constraint and the set of solutionssatisfying the support constraint [19]. The modulus constraint issimply that the diffracted amplitudes of the solution match themeasured diffracted amplitudes. The support constraint is appliedat the image plane and corresponds at the very least to the factthat the object is isolated and therefore an area of zero densityis known to exist around the object. By successively imposing themodulus constraint at the diffraction plane and the support con-straint at the image plane, a fixed point where a solution satisfiesboth constraints can in principle be reached. A better knowledge ofthe overall shape of the object and therefore a tighter support leadsto more rapid and more reproducible convergence of the algorithmto a solution.

The shrinkwrap algorithm [20] was used to reconstruct the com-plex wave exiting the sample. This algorithm used a periodicallyupdated support constraint which is based on the latest iterate.It requires no prior knowledge of the sample other than that it is

isolated. A large support is used at the beginning and after every70 iterations the current iterate is used to calculate a tighter sup-port by thresholding the current solution image. This works well forhigh contrast compact objects and tends to fail more often with dis-continuous objects since a detached part of the support can shrinkaway completely.

Multiple reconstructions were performed starting with randomphases and using a support consisting only of the thresholdedautocorrelation obtained by Fourier transforming the measuredintensity. The solution that was deemed best was chosen as thatwith the smallest value of #2 = ˙Am

2 − Ar2, where Am is the mea-

sured diffracted amplitude and Ar is the reconstructed amplitude.This solution was used to set a tight support around the entireobject consisting of the FIB pattern, the two nanoparticles, as wellas the frame of the Si3N4 window. Then 50 reconstructions startingwith random phases and using this fixed support were performed.Each of these reconstructions converged rapidly, within a hundrediterations or less. The rapid convergence was due to the very tightsupport and the lack of fine structure within the object. All 50reconstructed images were properly aligned and averaged togetherand the resulting image is shown in Fig. 6b for the whole win-dow. The frame of the window can be seen although it is very faintcompared to the object itself due to the softness of the edge. Theimage is shown to represent the complex exit wave, with ampli-tude mapped onto the color saturation and the phase representedby the hue on a white background, which makes the frame visible.Fig. 6c shows a zoomed in view of the reconstructed complex wave-field but this time on a dark background to emphasize the presenceof the polystyrene spheres. Comparison of the reconstructed imageand the electron micrograph shows excellent agreement. The phaseadvance of the wave passing through the FIB cutout is constant forthe whole pattern. A different phase advance is obtained for the twopolystyrene spheres, which are 180 ± 20◦ out-of-phase with the FIBpattern. The resolution of the reconstruction was estimated by cal-culating the phase retrieval transfer function (PRTF) [21] which is ameasure of the reproducibility of the phases retrieved as a functionof the resolution shell. A value of 1 corresponds to 100% agreementof the retrieved phases between all images. The PRTF is shown inFig. 7 and was calculated using the 50 reconstructions used to pro-

Fig. 7. Phase retrieval transfer function (PRTF) of the reconstructed image. Thereproducibility of the retrieved phases for 50 different reconstructions is plottedas a function of the momentum transfer or the resolution shell. The PRTF falls below1/e at a lower resolution than the diffraction limit of 28 nm at the edge of the CCD.


duce the image of Fig. 6b–c. Using the point where the PRTF dropsbelow 1/e as the resolution measure, we determine that the imagewas accurately recovered to a resolution of 40 nm. This is not quitediffraction limited since the edge of the CCD corresponds to a 28 nmresolution. This is not surprising looking at the diffraction pattern.While there is signal all the way out to the edge of the detectoralong some directions, a large part of the high angle data is mostlynoise and reliable phases cannot be expected to be retrieved fromthis noise.

4. Discussion

To a first approximation when absorption is negligible the exitwave can be interpreted as being proportional to the electron den-sity of the sample. The density profile of each of the nanoparticlesobtained from the reconstruction is shown in Fig. 8a. The densitycurve of particle 1 was offset for clarity. The expected result for a145 nm polystyrene sphere was calculated using the TEMPEST pro-gram [22] which solves Maxwell’s equations numerically for a givengeometry. Using the known index of refraction of polystyrene at13.5 nm [23], the amplitude of the exit wave was calculated, con-volved with a 40 nm Gaussian corresponding to the resolution ofthe image and is shown in Fig. 8a. While the fit is excellent for par-ticle 2, some unexpected shoulder appears on the edges of particle1. Furthermore, particle 1 has roughly twice the electron densityof particle 2. The possibility that this was due to the presence ofa dimer aligned with the FEL beam was investigated. At 13.5 nm,refraction and absorption are significant and a focusing of the beamby the first sphere leads to a non-uniformly illuminated secondsphere which could generate the shoulder observed. Simulationsusing TEMPEST did reveal a slight narrowing of the central peak ofthe exit wave along with the presence of shoulders but the agree-ment with the data was no better than the single sphere. Based onthis and the lack of other evidence from the electron micrograph,we cannot unequivocally conclude whether particle 1 is a dimer. Itseems unlikely to have been the case due to the low concentrationof dimers in the solution. However, such dimers aligned perpendic-ular to the membrane where observed on other samples preparedunder similar conditions. A likely explanation may simply be thatthe beam was twice as intense on particle 1 as it was on particle

2, the one farther away from the FIB structure. The reconstructedexit wave can only be proportional to the electron density if theillumination is uniform over the entire object. For non-uniform illu-mination, the reconstruction is proportional to the electron densitymultiplied by the illumination function. Since the FWHM of thebeam was 17 !m and the two particles were 7 !m apart, it is likelythat the illumination was weaker on the second particle, leadingto the factor of two difference in reconstructed density. There isno way to know for sure if the illumination is the cause due to theabsence of a shot-to-shot beam profile diagnostic. We thereforecannot conclusively determine the cause for the density differenceobserved between the two particles.

Although a quantitative interpretation of the density of eachnanoparticle is difficult, it is quite interesting to compare the 32 and13.5 nm results. In the first case, 2 polystyrene spheres on a Si3N4provided barely enough signal to even conclusively determine thepresence of the 2 particles. However, in the second case, the addi-tion of a strongly scattering reference object, even if this object is apriori unknown, not only made obvious the presence of 2 particlesbut it also allowed a real space image of the nanoparticles to beretrieved. This real space image could also have been recovered, toa lower resolution using 32 nm light. Although the reference objectwas not technically unknown in this case, the image was retrievedwithout using any knowledge of it. This idea of using a complicatedreference in holography is not new [24,25], and in fact diffractiveimaging is itself an extension of this idea where the interferencebetween every small part of the object and the rest of it is used toretrieve the phases.

In the future, clever engineering may allow small unknownbiomolecules to be attached to larger well-known particles andthis would greatly boost the diffraction signal. This could allowimaging of very small proteins that scatter too weakly to be imagedalone using hard X-ray FEL sources such as the Linac Coherent LightSource (LCLS), the European X-ray free electron laser (XFEL) and theSpring-8 Compact SASE Source (SCSS), which will come online inthe coming years. The future single molecule imaging experimentsplanned for these facilities [5,6,26] are not expected to provide suf-ficient signal for particles on the order of a few tens of nanometersor less [25] and including a large known reference could extend theapplicability of the technique to smaller objects.

Fig. 8. (a) Density profile of the 2 nanoparticles reconstructed shown in Fig. 6. Particle 1, which is closer to the FIB pattern, has roughly twice the density of particle 2. Theexpected profile from a 145 nm polystyrene sphere is also shown, properly scaled for each particle. (b) Integrated intensity versus momentum transfer for each component ofthe reconstructed image. The FIB pattern makes up most of the measured intensity. The diffracted intensity from the nanoparticles is 2 orders of magnitudes or more belowthe intensity of the FIB reference object. Also shown are the expected curves from a single 145 nm polystyrene sphere as well as a dimer made of 2 spheres aligned with theFEL beam.


It is possible to extract extremely weak signal that is buried inthe noise of the large object as was the case with the data presentedhere. The radially integrated intensity from each part of the samplewas extracted using the reconstructed image. The diffracted inten-sity of the FIB structure alone was calculated by setting the densityoutside the FIB object to zero and performing a Fourier transform.The obtained pattern was then radially integrated. This curve isplotted in Fig. 8b along with the integrated intensity from eachparticle individually, the window frame along with the noise andthe entire field of view of the image. These curves display real pho-ton counts per resolution shell. One can see that the FIB structureor reference object makes up most of the scattered intensity andover a large range of angles it is indistinguishable from the inten-sity from the entire field of view. The intensity from the particlesis more than two orders of magnitudes smaller than that of the FIBstructure, and over most of the scattering range it is one order ofmagnitude or more below the intensity of the window frame andthe noise. Even so, an accurate reconstruction of the particles toa resolution close to 40 nm was achieved. However, these recon-structions are not perfect as can be seen from a comparison withthe expected integrated intensity curve from a 145 nm polystyrenesphere also shown in Fig. 8b. The expected curve for a dimer alignedwith the FEL beam is also shown for comparison. These were calcu-lated using the exit wave calculated with TEMPEST. The position ofthe minima in the intensity from the nanospheres does not matchwhat is expected from the particle size.

5. Conclusions

The discrepancy between the theory and the data highlightsthe need to properly design the reference object. The total signallevel at high angles determines the resolution of the entire objectand therefore a strong signal from the reference (the FIB struc-ture) allows in theory to image the unknown part of the object (thespheres) with the same resolution. However, just any random refer-ence such as the one used here is likely to have deep minima in thediffracted intensity leading to high noise for some Fourier compo-nents. An object with no zeros in the diffracted intensity and witha flat noise spectrum over all Fourier components can be shownto be an ideal holographic reference object [27] and such an objectwould be an ideally suited reference to enhance the diffraction sig-nal. However, it should be pointed out that in these zeroes of thereference-structure transform the diffraction intensity is equal tothe intensity in the case of having no reference structure at all. Phaseretrieval is still robust in this case because we are phasing the entirepattern as a whole and are not relying on a particular knowledge ofthe reference structure to obtain the object structure.

We also note that adding a large reference signal to a small objectsignal will actually increase the noise in the measurement of theobject signal, in the case of photon-counting statistics. However, itappears that adding the reference signal is advantageous: when thesignal from the object is weaker than one photon per pixel, or moregenerally when the signal is less than the threshold required forreliable phase retrieval [28]. As we have seen in this study, addingthe reference structure is also advantageous when there is a back-ground noise source such as the scattering from the supportingmembrane.

The diffracted signal from the small object is obviously notincreased by the addition of the reference. The interferencebetween the two objects is the key factor allowing imaging of thesmall object. If one were to subtract the reference signal from thetotal signal, then the larger the reference is, the more noise from itwould contribute to the signal of interest. The signal-to-noise ratiowould then be, after subtraction of the noisy reference, O2/R, where

O is the diffracted amplitude of the object and R is the diffractedamplitude of the reference. However, this is not what is done here.We do not separate the signal from each part of the image. Weuse the entire signal, equal to R2 + O2 + 2RO to retrieve the phases.The noise of this diffraction pattern is (R2 + O2 + 2RO)1/2 and growswith the strength of the reference signal, which would seem toindicate a larger reference contributes more noise and is there-fore not preferable. However, the signal-to-noise ratio also growswith the strength of the reference signal by the same factor. There-fore, since a higher signal-to-noise ratio allows more reliable phasesto be retrieved, a clear image can be reconstructed. If we assumethe signal O to be small compared to the reference R, then R itselfdetermines the resolution of the image one can obtain for the com-bination of the reference and the object. The resolution will belimited to the scattering angle at which R is on the order of 1 andthe signal is of the same order as the noise. The signal from theobject only represents a small fractional change to the total signalbut as far as the phase retrieval algorithm is concerned, it repre-sents a small part of the image in the same way as any other part ofthe image. Therefore, the small object can be reconstructed to thesame resolution as the large reference and the more signal from thereference, the better the resolution will be since the signal-to-noiseratio of the entire pattern grows as R.

Our results clearly show that a large reference object allowsimaging of single nanoparticles on a membrane which could notbe imaged without the presence of the reference. Clever use inthe future of known references with a proper scattering strengthas well as the development of artificially made biostructures withideal holographic reference properties [29] could prove invaluablein pushing the limits of diffractive imaging to small particles. Theresolution achievable on a small particle would only be limited bythe resolution achievable on the large reference by itself. Therefore,if a reference object can be imaged with atomic resolution, thenanother particle next to it of any size smaller than the referenceobject can be imaged with atomic resolution as well.

The results presented here clearly demonstrate the feasibility ofimaging single 145 nm particles with a single FEL shot and representa key step toward imaging of biomolecules using hard X-ray FEL inthe coming years. With a sample delivery system which removesthe need for a supporting membrane, the signal-to-noise ratio canbe sufficiently high to allow a single free-standing nanoparticle tobe imaged in a single shot [4]. The method of enhanced-referencediffraction may also be beneficial to molecular imaging, for exampleby attaching the unknown molecule of interest to a much larger(known or unknown) reference molecule.

Acknowledgments

Special thanks are due to the scientific and technical staff ofthe FLASH at DESY, Hamburg, in particular to R. Treusch, J. Schnei-der, S. Dusterer, T. Tschentscher, J. Feldhaus, R.L. Johnson, U. Hahn,T. Nunez, K. Tiedtke, S. Toleikis, E.L. Saldin, E.A. Schneidmiller, andM.V. Yurkov. We are grateful to our collaborators in T. Möller’s groupat Technische Universitat Berlin for accomodating our experimentin their vacuum chamber. We also thank T. McCarville, F. Weber,and M. Haro for technical help with these experiments. This workwas supported by the following agencies: The U.S. Department ofEnergy by Lawrence Livermore National Laboratory in part underContract W-7405-Eng-48 and in part under Contract DE-AC52-07NA27344, Lawrence Livermore National Laboratory (the project05-SI-003 from the Laboratory Directed Research and DevelopmentProgram of LLNL); The National Center for Electron Microscopy;and the Natural Sciences and Engineering Research Council ofCanada (NSERC Postdoctoral Fellowship to M.J.B.); The Stanford Lin-


ear Accelerator Center under DOE contract DE-AC02-76- SF00515;the European Union (TUIXS); The Swedish Research Councils; theDFG-Cluster of Excellence through the Munich-Centre for AdvancedPhotonics.

References

[1] V. Ayvazyan, et al., Eur. J. Phys. D 37 (2006) 297–303.[2] W. Ackermann, et al., Nat. Photon. 1 (2007) 336–342.[3] H.N. Chapman, et al., Nat. Phys. 2 (2006) 839–843.[4] M.J. Bogan, W.H. Benner, S. Boutet, U. Rohner, M. Frank, A. Barty, M.M. Seibert,

F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S.P. Hau-Riege, M. Svenda, E.Marklund, E. Spiller, J. Hajdu, H.N. Chapman, Nano Lett. 8 (2008) 310–316.

[5] R. Neutze, et al., Nature 406 (2000) 752–757.[6] G. Huldt, A. Szoke, J. Hajdu, J. Struct. Biol. 144 (2003) 219–227.[7] J.C.H. Spence, B. Doak, Phys. Rev. Lett. 92 (2004) 198102.[8] S.P. Hau-Riege, R.A. London, M. Bergh, H.N. Chapman, Phys. Rev. E 76 (2007)

046403.[9] H.N. Chapman, et al., Nature 448 (2007) 676–679.

[10] I.W. Lenggoro, B. Xia, K. Okuyama, J. Fernandez de la Mora, Langmuir 18 (2002)4584–4591.

[11] M.J. Bogan, et al., J. Aerosol Sci. 38 (2007) 1119–1128.[12] A. Wiedensohler, H.J. Pissan, J. Aerosol Sci. 19 (1988) 867–870.[13] S. Bajt, et al., Appl. Opt. 47 (2008) 1673–1683.[14] P. Thibault, et al., Acta Cryst. A 62 (2006) 248–261.[15] D. Sayre, Acta Cryst. 5 (1952) 60–65.[16] J. Miao, et al., J. Opt. Soc. Am. A 15 (1998) 1662–1669.[17] J. Miao, P. Charalambous, J. Kirz, D. Sayre, Nature 400 (1999) 342–344.[18] M.A. Pfeifer, G.J. Williams, I.A. Vartaniants, R. Harder, I.K. Robinson, Nature 442

(63–66) (2006) 342–344.[19] S. Marchesini, Rev. Sci. Instr. 78 (2007) 011301.[20] S. Marchesini, et al., Phys. Rev. B 68 (2003) 140101.[21] D. Shapiro, et al., Proc. Natl. Acad. Sci. USA 102 (2005) 15343–15346, 140101.[22] R. Guerrieri, K.H. Tadros, J. Gamelin, A.R. Neureuther, IEEE Trans. CAD 10 (9)

(1991) 1091–1100.[23] B.L. Henke, E.M. Gullikson, J.C. Davis, Atomic Data Nucl. Data Tables 54 (2 (July))

(1993) 181–342.[24] A. Szöke, J. Imag. Sci. Technol. 41 (1997) 332–341.[25] H. He, et al., Appl. Phys. Lett. 85 (2004) 2454–2456.[26] G.K. Shenoy, J. Stöhr (Eds.) LCLS the First Experiments, SLAC (2000) [available

online at <http://www.slac.stanford.edu/pubs/slacreports/slac-r-611.html>].[27] E.E. Fenimore, T.M. Cannon, Appl. Opt. 17 (1978) 337–347.[28] Starodub, et al., J. Synchrotron Radiat. 15 (2008) 62–73.[29] S. Marchesini, et al. Nat. Photon. (2008), in press.

http://www.slac.stanford.edu/pubs/slacreports/slac-r-611.html

ultrafast soft x-ray scattering and reference-enhanced

Documents