3194 OPTICS LETTERS / Vol. 31, No. 21 / November 1, 2006

Crystal optics as guard apertures for coherentx-ray diffraction imaging

Xianghui Xiao, Martin D. de Jonge, Yuncheng Zhong, Yong S. Chu, and Qun ShenAdvanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439

Received June 27, 2006; revised August 27, 2006; accepted August 30, 2006;posted August 31, 2006 (Doc. ID 72386); published October 11, 2006

A crucial issue in coherent x-ray diffraction imaging experiments is how to increase the signal-to-noise ratiowhen measuring relatively weak diffraction intensities from a nonperiodic object. A novel crystal guard ap-erture is described that makes use of a pair of multiple-bounce crystal optics to eliminate unwanted para-sitic scattering background. This background is often produced by upstream optical elements such as acoherent-beam defining aperture. Recent experimental observation and theoretical analysis confirm the ef-fectiveness of the crystal guard aperture method with coherence-preserved wave propagation through thecrystal guard aperture and dramatically reduced scattering background in coherent x-ray diffractionimages. © 2006 Optical Society of America

OCIS codes: 340.7440, 340.7460, 340.6720, 180.7460, 050.1940, 030.6140.

X-ray coherent diffraction imaging (CDI) is a recentlydeveloped microscopic technique.1 Compared withother microscopic techniques, it can image nonperi-odic materials without lens optics2 and has the poten-tial to reach nanometer spatial resolutions. Coherentdiffraction imaging is done in two steps, first by re-cording a diffraction pattern from the nonperiodicspecimen, using a coherent incident x-ray beam, andsecond by retrieving the specimen’s density functionfrom the diffraction pattern with an iterative phasingmethod.3 Applications of x-ray CDI range from struc-ture determinations of nanoparticles4,5 to reconstruc-tions of x-ray optical wavefields6 and to high-resolution imaging of intact biological cells and otherspecimens.7,8

One of the main difficulties for achieving high spa-tial resolution using CDI is the ability to accuratelymeasure weak diffraction intensities from a nonperi-odic sample with high signal-to-noise ratios. Simula-tion results9 suggest that the signal-to-noise rationeeds to be at least 5 to reconstruct the original ob-ject by iterative phase-retrieval methods. Since afully coherent x-ray beam is usually generated at ex-isting synchrotron sources by selecting a coherentportion of an undulator x-ray beam by using a coher-ence beam-defining aperture (CBDA), reduction ofthe unwanted parasitic scattering from the CBDA iskey to achieving high signal-to-noise ratios in coher-ent diffraction images. To date, most x-ray diffractiveimag-ing experiments have been done with soft x-rays,1,4,6,8

where a guard aperture (GA) is employed to removeparasitic and high-order scattering from the up-stream CBDA. However, the usual guard edge or pin-hole GAs have two failure modes: insufficient inser-tion leading to transmission of CBDA scatter oroverinsertion resulting in the production of furtherscattering. Since the GA may itself produce scatter-ing, sometimes additional GAs are employed, whichin turn need to be positioned very carefully to mini-mize overall secondary scattering. This situation be-comes worse for hard x-rays, since diffracted signals

are further concentrated around the forward direc-

0146-9592/06/213194-3/$15.00 ©

tion, and specular reflections may arise from thethicker CBDA edges that are needed at higher ener-gies.

In this Letter, we describe a novel crystal guard ap-erture (CGA) that can essentially remove parasitichigh orders and specular scattering from the up-stream CBDA. The CGA is based on the fact thatx-ray diffraction from a perfect crystal such as siliconcan be used as an angular filter because x-ray reflec-tivity is extremely high only in a very narrow intrin-sic angular width and decreases rapidly outside thisnarrow angular region. Although crystals are used insmall-angle scattering experiments based on theoriginal work of Bonse and Hart,10 to our knowledge,the work presented here represents the first timethat crystal optics are employed to define a fully co-herent x-ray beam in CDI experiments.

Our CDI experiment was performed using 8.1 keVx-rays at station 32-ID-B of the Advanced PhotonSource at Argonne National Laboratory. The experi-mental setup is schematically shown in Fig. 1(a). A10 �m pinhole was used as the CBDA, and an open-faced z-shaped channel-cut11 silicon (111) perfectcrystal was employed as the CGA, which was locatedabout 77 cm from the CBDA pinhole. We used a 5 �melectrodeposited lead microparticle12 as our testspecimen, located 17 cm downstream from thechannel-cut crystal. The coherent diffraction patternfrom the specimen was collected by using a lens-coupled Roper ChemiPro charge-coupled device(CCD) area detector positioned 35 cm from the speci-men. The CCD has 2048�2048 pixels, and the physi-cal pixel size is 13 �m; with a 10� lens the effectivepixel size was 1.3 �m. Polished CdW crystal was usedas scintillator. We have adopted this setup to satisfythe oversampling requirement1,2 in the holographicregime, where a wavefront phase curvature can beused in the phase-retrieval process.13,14

To be useful in CDI experiments the crystal opticneeds to preserve the wavefronts of the incident co-herent x-ray beam. In particular, the phase curvatureinduced by the crystal must be quite simple and pre-

dictable. Otherwise, it may be difficult to distinguish

2006 Optical Society of America

November 1, 2006 / Vol. 31, No. 21 / OPTICS LETTERS 3195

between the incident illumination curvature and thephase structure of the sample. In the case of an inci-dent plane wave, it is well known that the diffractedwave is also planar with a phase shift that dependson the angular deviation from the Bragg angle. Whena coherent beam-defining aperture of a few microme-ters in size is used, the wave after the aperture is nota planar wave. To evaluate the effect of crystal dif-fraction on this curved wave, a dynamic crystal dif-fraction theory15 that can be applied to curved wave-fields was used to calculate the diffracted wavefieldfrom the crystals. The diffraction wave from a 10 �mpinhole was assumed to be the incident wave of thecrystals, and double-bounce diffraction was calcu-lated. The results of our calculation after propagatingthe crystal-diffraction wave to the sample plane andto the detector plane are shown in Figs. 1(b) and 1(c),respectively. By choosing the incident angle, we madethe central peak of the pinhole diffraction the one be-ing diffracted, and most of the high-order peaks wereblocked.

As we expect, the phase curvature of the crystal-diffracted wave shown in Fig. 1(b) and 1(c) is very

Fig. 1. (Color online) Crystal guard edge aperture. (a)Sketch of the experimental setup. The amplitudes andphases of pinhole diffraction wave EO and crystal diffrac-tion wave EH are given in (b) at the sample position and (c)at the CCD position.

similar to that of the incident wave. The phase of a

crystal-diffraction wave changes by � relative to theincident wave almost linearly as a function of thespatial coordinate across the crystal diffraction peakregion. The phase shift makes the principal directionof the diffraction wave deflected by a tiny angle��1 �rad�, which would cause the whole diffractionpattern from the specimen to shift by only a smalldistance in the detector plane. Therefore the phasecurvature after the CGA is essentially the same asthat of the incident beam.

We started our experiment using the conventionalCDI setup with a 10 �m pinhole as CBDA and a25 �m pinhole as a guard aperture (PGA) to evaluatethe background in the pinhole guarding arrange-ments. Figure 2(a) shows a typical Airy diffractionpattern from the 10 �m CBDA alone. Stray scatter-ing from the pinhole edge is clearly visible in thehigh-scattering-angle region. Figure 2(b) shows atypical coherent diffraction pattern from the 5 �mlead microparticle with the CBDA-PGA setup. It isseen that the stray scattering has intensity compa-rable with the sample signal in the high-angle region.Although white-field correction, i.e., subtraction ofthe pattern without the specimen in the beam, mayhelp to alleviate the stray-scattering problem, it isdifficult to remove the stray scattering completelywhen it is strong.

We then proceeded to insert the channel-cut Sicrystal optic into the setup, replace the PGA, tune tothe vertically diffracting (111) reflection, and repeatthe same measurements without and with thesample. Figure 2(c) shows the remnant of the Airydiffraction pattern from the CBDA after the crystal.

Fig. 2. Experimental results. Diffraction patterns areshown for a (a) 10 �m pinhole, (b) lead microparticle withCBDA-PGA setup, (c) 10 �m pinhole with CGA, and (d)lead microparticle with the CBDA-CGA setup. The displaypalettes of (a) and (c), (b) and (d) are set the same. The scat-ter on the right side in (c) was blocked by the beam stop.

The intensities are shown on a logarithmic scale.

3196 OPTICS LETTERS / Vol. 31, No. 21 / November 1, 2006

Compared with Fig. 2(a) the scatter in the vertical di-rection has been almost entirely eliminated by thecrystal. In the horizontal direction the diffraction andscattering pass through the crystal. This could be re-moved by an additional horizontal-diffracting crystalor a PGA. Figure 2(d) shows the diffraction pattern ofthe lead microparticle sample that was used in Fig.2(b). A 25 �m pinhole was used after the CBDA butbefore the crystal. The stray-scattering intensities inthe radial seen in Fig. 2(b) have been entirely re-moved in Fig. 2(d).

Due to the existence of noise and stray scatteringin the raw images, it is hard to evaluate the identitybetween Fig. 2(b) and 2(d) directly. One rough mea-surement of the identity between 2(b) and 2(d) is tocalculate the cross correlation between them. Be-cause the stray scattering in Fig. 2(b) is strong in theright-side region but weak in the left side, we usedonly the left half of those two images in the cross-correlation calculation, which gives a result of 0.99.This suggests that the two diffraction patterns ob-tained using the two different setups are almost iden-tical. A more reliable evaluation of the quality ofthese images is to compare their reconstructions.This work is ongoing, and we hope to present resultsin a future paper.

It is known that Bragg diffraction from a crystalexhibits a diffuse-scattering streak along a directionperpendicular to the crystal surface, which is termeda crystal truncation rod. The intensity of the trunca-tion rod in a single bounce diffraction decays as ��−2,where �� is the angular deviation from the exactBragg peak. This effect can be seen upon close inspec-tion of Fig. 2(c) and 2(d), as the weak backgroundstreaks in the vertical direction. Because we useddouble-bounce Bragg diffraction from a channel-cutcrystal in our experiment, the truncation rod inten-sity is proportional to ��−4, which is comparable withthe coherent scattered intensity from a nonperiodicsample in the small-angle regime. This problem canbe easily solved by employing more than two reflec-tions until the truncation rod intensity is reduced toa negligible level.10

In conclusion, we have shown that crystal opticscan be used to remove unwanted scattering in coher-ent diffraction imaging experiments, overcoming thelimitations of the traditional guarding scheme, whichhas so far presented a major problem for the applica-tion of CDI in the hard x-ray regime. Our calculationdemonstrates that the phase curvature of a diffractedcoherent wave from a crystal is almost identical tothat of the incident coherent wave in the diffraction

peak region. Our measurements demonstrate thatthe crystal guard aperture can indeed both preservethe incident-beam coherence and greatly reduce thestray-scattering background in coherent hard x-raydiffraction imaging experiments. This new methodmay also play an important role in the future devel-opments of other coherent scattering studies such asproposed movable-aperture lensless transmissionmicroscopy.16 We hope that the more effective crystalaperture will also generate interest in the rapidlyevolving research area of coherent diffraction opticsusing coherent hard x-rays.

We are grateful to Hanfei Yan (Advanced PhotonSource) for fruitful discussions on crystal diffractiontheory. The use of the Advanced Photon Source issupported by the U.S. Department of Energy, Officeof Science, Office of Basic Energy Sciences, undercontract W-31-109-ENG-38. X. Xiao’s e-mail addressis xhxiao@aps.anl.gov.References

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