Development of microperiodic mirrors for hard x-ray phase-contrast imaging

Development of microperiodic mirrorsfor hard x-ray phase-contrast imaging

Dan Stutman,1,* Michael Finkenthal,1 and Nicolae Moldovan2

1Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21030, USA2Advanced Diamond Technologies, Incorporated, Romeoville, Illinois 60446, USA

*Corresponding author: [email protected]

Received 27 May 2010; revised 21 July 2010; accepted 28 July 2010;posted 28 July 2010 (Doc. ID 129097); published 24 August 2010

Differential phase-contrast imaging with hard x rays can have important applications in medicine,material sciences, and energy research. Phase-contrast methods based on microperiodic optics, suchas shearing interferometry, are particularly attractive because they allow the use of conventionalx-ray tubes. To enable shearing interferometry with x rays up to 100keV, we propose using grazing-incidence microperiodic mirrors. In addition, a simple lithographic method is proposed for the productionof themicroperiodic x-raymirrors, based on the difference in grazing-incidence reflectivity between a low-Z substrate and a high-Z film. Using this method, we produced prototype mirrors with 5–100 μm periodsand 90mm active length. Experimental tests with x rays up to 60keV indicate good microperiodic mirrorreflectivity and high-contrast fringe patterns, encouraging further development of the proposed imagingconcept. © 2010 Optical Society of AmericaOCIS codes: 340.0340, 340.7440.

1. Introduction

X-ray differential phase-contrast (DPC) imagingrelies on the refraction of x rays passing through anobject. Because for hard x rays the refraction anglesare in the microradian range, the basic techniqueused for DPC imaging is to angularly filter, withmicroradian resolution, the transmitted x-ray beam,thus converting the angular beam deviations fromrefraction into intensity changes on a conventionaldetector. The angular filtering is done using x-ray op-tics such as crystals or gratings (see [1] for a recentreview).

The fundamental advantage ofDPC imaging is thatit is sensitive to density gradients in themeasured ob-ject rather than to its bulk x-ray absorption. In med-ical imaging, for instance, refraction has a contrastenhancing effect at tissue boundaries, which enablesthe detection of soft tissues that are otherwise invisi-ble in conventional x-ray imaging. The ultrasmall

angle scattering occurring inmicrostructured soft tis-sue, such as cartilage, tendon, ligament, or muscle,has also a volume contrast enhancing effect [1–5]. An-other benefit of DPC formedical imaging is that it canimprove contrast and resolution at a similar or lowerdose than in conventional x-ray imaging. This is pos-sible because DPC uses x rays that are not absorbedby the body andbecause the soft tissue refraction coef-ficients decrease with x-ray energy much slower thanthe absorption ones. In particular, by using for DPCa spectrum with mean energy in the 50–80keVrange, approximately, the soft tissue dose is mini-mized while refraction strongly dominates overabsorption [1,6].

X-ray phase contrast is also of interest for imagingand nondestructive characterization in materialsciences, in particular as concerns low-Z materials.The structure and defects of materials ranging frompolymers, to fiber composites, to wood, and to engi-neered biomaterials can be probed on themicrometerscale using x-ray phase contrast [7–9]. Some of thetechniques used for x-ray phase contrast can alsobe applied with neutrons [10]. Recently, x-ray phase

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contrast has gained attention in fusion energy re-search, where the capability of refraction-based ima-ging to measure the density gradients in an objectcan be used for the diagnosis of high-density plasmasin inertial confinement fusion and other high-energy-density physics experiments [11].

Until recently, research on x-ray DPC imaging hasbeen done mostly at synchrotrons, using crystal op-tics; the high intensity of the synchrotron compen-sates for the low efficiency (less than a hundredthof a percent) of the crystal optics [1,12]. Althoughthere are efforts to develop tabletop synchrotrons[13], or to use narrow Kα lines from conventionaltubes [14], the crystal method has not yet enteredthe domain of practical applications. It is thus ofinterest to develop more efficient DPC methodsand optics that can work with conventional medicalor industrial x-ray tubes.

A DPC method that can work with conventional x-ray sources is Talbot–Lau shearing interferometry,in which microperiodic optics, such as gratings, areused to angularly filter the refracted x rays withmicroradian resolution [15–17]. The Talbot interfero-meter includes first a “beam splitter” (typically a π-shift phase grating), which divides (or “shears”), withthe Talbot effect, the incoming beam into a fewmicroradian wide beamlets. The Talbot effect con-sists of a “replication” of the grating pattern by thewave intensity, at periodic distances along the beam,called Talbot distances, dT ¼ k=η2 · g2=ð2λÞ, with λbeing the x-ray wavelength, g the grating period, k ¼1; 2;… the order of the pattern, η ¼ 1 for a π=2 phase-shifting grating or for an absorption grating, and η ¼2 for a π phase grating [18]. The beam splitter thuscreates at the “Talbot distance” a microperiodicfringe pattern, which changes shape (shifts) with re-spect to the unperturbed pattern when a refractiveobject is introduced in the beam. The DPC imagingconsists thus in measuring the changes in the fringepattern induced by the object, with respect to thepattern without the object. To achieve microradianangular sensitivity at hard x-ray wavelengths, theperiod g must be in the micrometer range, resultingin a Talbot distance of a few tens of a centimeter.

The fringe pattern can, in principle, be directlymeasured using a microscopic pixel detector [17].This is, however, quite inefficient. For most practicalapplications, the fringe pattern changes are con-verted into intensity changes on a macroscopic pixeldetector, by introducing an “analyzer” absorptiongrating placed behind the beam splitter and havingthe period of the Talbot pattern. Finally, for such aninterferometer to function with an extended spot x-ray tube, a “source” absorption grating is placed infront of the source, thus dividing it into an arrayof quasi-coherent line sources [16–18].

The gratings are made by microlithography in thinSi wafers or photoresist [19,20]. The absorption grat-ings are difficult to fabricate; they are typically madeby filling with gold the gaps in regular transmissiongratings. The “grating shearing method” described

above has demonstrated performance similar to thecrystal method at energies below a few tens of kilo-electron volts [21].

This method is, however, less useful at energiesabove a few tens of kiloelectron volts. The reasonis that it is difficult to fabricate micrometer-periodabsorption gratings with the thickness required toblock higher energy x rays. This is illustrated inFig. 1 with a plot of the Au thickness needed for95% absorption, as a function of the photon energy.As seen, several hundred micrometer depth gratingswould be needed in the range of interest for clinicalDPC imaging. Depending on the grating period, thepresent technological limit is, however, around50–100 μm [19,20,22]. This limits the contrast ofthe grating shearing method for high-energy x rays,as illustrated in Fig. 1 by the fringe contrast com-puted for an interferometer having 30 μm thick,4 μm period Au analyzer grating (throughout the pa-per we used for x-ray phase-contrast and optics cal-culations the XWFP wave propagation code [23] andthe XOP optics package [24]).

A new type of optics is therefore needed to enableefficient DPC imaging at x-ray energies above a fewtens of kiloelectron volts. The method proposed inthis paper is to replace the absorption gratings inthe shearing interferometry setup with grazing-incidencemicroperiodicmirrors. Efficient interferom-eters could be built for energies up to nearly 100keVby usingmirror optics. In addition, we propose a litho-graphic method for the fabrication of the microperio-dic mirrors that is simpler, less costly, and moreflexible than that of the above-mentioned absorptiongratings.

The structure of the paper is as follows. In Section 2we describe the proposed concept of mirror-basedshearing interferometry and how it could be appliedfor DPC imaging. In Section 3 we describe the

Fig. 1. Gold thickness needed for 95% absorption as a function ofx-ray energy. Also shown is the fringe contrast for a grating inter-ferometer having a 30 μm thick, 4 μm period Au analyzer. At ener-gies of clinical interest, the analyzer becomes transparent tox rays, drastically reducing the interferometer contrast.

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lithographicmethodandmirror fabricationdetails. InSection 4 we present results obtained by testing pro-totype microperiodic mirrors with x rays having en-ergy up to 60keV. In Section 5 we briefly discussthe challenges in the proposed concept, as well asother possibilities of using this type of optics.

2. Phase-Contrast Imaging with Microperiodic Mirrors

The newly proposed method for microperiodic-mirror-based DPC imaging is sketched in Fig. 2. Themirrors consist simply of alternating reflective andnonreflective strips. Incidence angles below the criti-cal angle for total reflection are used to achieve largereflectivity for hard x rays.

When illuminated by a point source, the “beamsplitter” mirror produces on the detector, throughthe Talbot effect, a fringe pattern of periodg1 ∼ few μm. When a refractive object is inserted inthe beam path, the pattern shifts by a small amount(a fraction of g1). An “analyzer” mirror of period g2 ∼g1 converts this fringe shift into an intensity changeon the detector, as sketched in Fig. 2b). In order tomake the setup work with an x-ray tube having anextended focal spot, the source is divided into an ar-ray of quasi-coherent line sources using a third,“source,” mirror of period g0 ¼ g2 · L=dT [Fig. 2c)], si-milar to the previously described grating method.This choice of period ensures that the fringe patternsfrom each of themicrosources overlap at the analyzer[15–18].

The characteristic dimensions of the proposed in-strument are also shown in Fig. 2. To obtain goodfringe contrast, the x rays incident on the beam split-ter should be quasi-coherent, with a minimum trans-verse coherence length of the order of its period,similar to the grating method [18]. This imposes aminimal distance L between the source and the beamsplitter of the order of the meter. A practical value forthe mirror length is M ≈ 10–15 cm, although x-raymirrors nearly 1m long can be manufactured nowa-days. For operation at x-ray energies above a few tens

of kiloelectron volts, the incidence angle θ must bearound 1mrad.

“Hybrid” interferometers combining a phase-grating beam-splitter at normal incidence with agrazing-incidence analyzer mirror (and a source mir-ror, if needed) would also be possible, because forhard x-ray energies, the contrast or visibility of theTalbot pattern created by the grating beam splitterwill vary little along the analyzer length. For in-stance, XWFP calculations for a π-shift phase gratingilluminated by an extended source show that, at thefirst Talbot distance, the longitudinal extent of theregion of good fringe visibility is about 1=3 of this dis-tance [18]. For a 10 μm period, a π phase grating at50keV, this would translate into an ∼15 cm long re-gion of high fringe contrast, comparable to the ana-lyzer mirror length.

The grazing-incidence operation limits the field ofview height in Fig. 2 toM · sinðθÞ, which for the abovevalues would be of the order of 100–200 μm. The fieldof view width is limited only by the practical mirrorwidth of 10 cm or more. The mirror interferometerconcept is thus well suited for line scan imaging inwhich the detector is a linear array and the interfe-rometer or the object is spatially scanned to obtainthe image of an area of interest [Fig. 2c)]. For lowerenergy applications, the incidence angle could never-theless be increased to enable 2D phase-contrastimaging with a field of view having a height of about1mm.

Two basic configurations are possible for the mi-croperiodic mirror optics [Fig. 3a)]. In the first one,the reflective strips are perpendicular to the incom-ing rays, similar to the layout in Fig. 2. This effectiveperiod setup can produce very small period patternsfrom patterns having a large period at normal inci-dence; for instance, a 1mm period pattern at normalincidence would appear as a 1 μm effective periodpattern at 1mrad incidence angle. This capabilitycan be used to achieve high angular resolving powerat short Talbot distances. In this configuration, thefringes would be parallel to the detector in the linescan imaging system [Fig. 3a)].

In the second configuration [Fig. 3b)], the reflectivestrips are parallel to the incoming rays and the mir-ror has a physical period of a few μm. In this setup,the fringes will be perpendicular to the axis of a

Fig. 2. (Color online) Layout of microperiodic-mirror-based DPCimaging concept: a), b) with point source, and c) with extended spotsource. The addition of a “source mirror” enables the interferom-eter to work with a high-power, extended spot x-ray tube.

Fig. 3. Layout of “effective period” and of “physical period” mir-rors. For simplicity, only the beam-splitter mirror and its fringepattern are shown.


linear detector [Fig. 3b)]. While more difficult to pro-duce, this physical period configuration has the ad-vantage of reduced sensitivity to possible objectmovement. This is illustrated in Fig. 4, which showsthe XWFP computed fringe pattern for a small plas-tic sphere in front of a 6 μm period beam splitter,together with the pixels of a linear array detector.As can be seen, while in the effective period setup,a small object displacement perpendicular to thebeam-splitter lines will produce a large variationin the intensity profile recorded by the detector, inthe physical period setup, the intensity profile is “car-ried” with the object along the detector, makingphase-contrast imaging no more sensitive to move-ment than conventional x-ray imaging. The physicalperiod configuration is thus best suited for clinicalapplications. In addition, in this setup, the unifor-mity of the fringe pattern is less likely to be affectedby mirror surface waviness, similar to viewing alongstraight railroad tracks laid over a hilly terrain.

To avoid the strong parallax possible at grazingincidence when using the fan-shaped beam from anx-ray tube, in both configurations, the reflective pat-terns can be shaped to match the divergence of thebeam. This also allows achieving an arbitrarily widefieldofviewin thephase-contrastmeasurementdirec-tion, thus enabling line scan imaging of extended ob-jects such as, for instance, a large body joint [Fig. 2c)].

The Talbot effect has been studied mainly withgratings at normal incidence [16–18]. The few mea-surements at oblique incidence indicate that, at graz-ing angles, the intensity distribution within a Talbotfringe will become asymmetric, but the periodicityand contrast of the overall pattern should not be af-fected [25]. This assumption is supported by x-raydiffraction experiments using Young slits producedby grazing-incidence reflection on micrometer-sizedmirrors. While the far-field interference patternwas asymmetric, the fringes were still periodic andclearly defined [26].

An additional effect possible with grazing-incidence mirrors is distortion of the fringe patterndue to wavefront propagation along the length of theperiodic mirror. To evaluate the magnitude of this

effect, we used XWFP calculations. Because theXWFP code does not treat reflective optics, we mod-eled the microperiodic mirrors as alternating opaquebars and transparent gaps, periodically staggered atthe grazing angle along the mirror length. The com-puted fringe pattern at the first Talbot distance be-hind such a grazing-incidence structure, having a4 μm effective period and 10 cm length, and illumi-nated by a 50keV point source at 1:2mrad incidenceangle, is shown in Fig. 5. As is seen, the propagationeffects are negligible in a first approximation, withthe grazing-incidence fringe contrast comparable tothat achievable at normal incidence.

The microperiodic mirror optics could thus allowDPC imaging with good contrast and optical through-put over abroad energy range, extending, inprinciple,from a few kiloelectron volts to nearly 100keV. In par-ticular, themethod should be useful for the 50–80keVrange, optimal for soft tissue DPC imaging at a lowdose. This possibility is illustrated inFig. 6with a plotof the computed spectral dependence of the fringecontrast for a “mirrors-only” (mirror beam splitterþmirror analyzer) and for a hybrid “grating mirror”(phase grating beam splitter þmirror analyzer)system, having each 4 μm period and optimized for50keV central energy. The contrast was computedassuming the above “opaque bar” mirror model, to-gether with plane wave illumination. Also shown inFig. 6 is the maximal transmission of a mirror basedinterferometer, considering Ta mirrors with 5Å sur-face roughness (seeSection3)and including thereflec-tion on a third “source”mirror and the absorption of a50 μm thickW filter. The spectrum of aWanode x-raytube operated at 100kV and filtered with 50 μm W isalso shown for comparison. As seen, a “grating-mirror” device has over 50% contrast between about

Fig. 4. Illustration of the different sensitivity to object movementof the effective and physical period configurations. While in theeffective period setup, an object movement perpendicular to thegrating lines can induce a large change in the measured intensityprofile; in the physical period setup, the intensity profile is “car-ried” with the object along the detector.

Fig. 5. XWFP computed fringe pattern at the first Talbot distancefor simulated grazing-incidence structure of 4 μm effective periodat 50keV, showing that at high x-ray energy, the effects of thewave propagation along the mirror length are small.


40–70keV, while the maximal contrast of the “mir-rors-only” interferometer is lower but decreases lessrapidly at higher energies. The contrast curve in bothconfigurationsmatcheswell the broad interferometertransmission curve. Finally, the overall response ofthe instrument matches well the spectrum of the100kV tungsten tube. Inaddition, themultiplemirrorreflections together with the W filter effectivelysuppress the radiation outside ∼30–75keV, whichis useful in medical applications.

3. Lithographic Method and Microperiodic MirrorFabrication

To achieve high reflectivity for hard x rays, the mi-croperiodic mirrors must work at incidence anglesbelow the critical angle for total reflection, θc ≈1:6 × 10−3λpρ, where λ is the wavelength in nmand ρ is the density of the medium in g=cm3 [26,27].A simple and flexible lithographic method of micro-periodic mirror fabrication is thus possible based onthe difference in critical angle between a high-Zmetal film (e.g., Ta, Au, Pt) and a low-Z substrate(e.g., Si or glass). The principle of this method is illu-strated in Fig. 7, which plots the reflectivity of a600Å thick Au film and that of a Si substrate, atan incidence angle of 1:15mrad. The radiation below∼20keV is suppressed by a 50 μm thick Wabsorptionfilter. A mirror surface roughness of 5Å, typical ofultrapolished optical substrates, was assumed. Asseen, the reflectivity of the Au film exceeds by a large

factor that of the Si substrate over the ∼40–70keVinterval. In addition, the mirror spectral range canbe simply changed by varying the incidence angle(see also Section 4). High-Z coatings on glass werealso used in the above-quoted experiments to makeYoung slits for 8keV synchrotron x rays [26].

The benefits of this method of mirror fabricationare simplicity, low cost, and flexibility. The reflectivestrips can be patterned using microlithographic tech-niques to any desired shape; for instance, they can bemade divergent to match the fan-shaped beam of anx-ray tube, or “checkerboard”-shaped for simulta-neous DPC imaging in two orthogonal directions.

The critical component in this fabrication methodis the low-Z substrate, which must have a large area(≥10 cm × 10 cm), together with ≤5–10Å roughness toavoid degradation of the grazing-incidence reflectiv-ity and with submicrometer flatness to avoid distor-tion of the fringe patterns. While very expensive inthe past, such large area ultrapolished optical sub-strates have become cost effective in recent years.

For the first experimental tests of the proposed op-tics, we produced prototype microperiodic mirrors bylithographic patterning of thin Ta films on glass sub-strates. The substrates were optical flats manufac-tured by Custom Scientific Solutions, Inc. [28],having 100mm diameter, 5mm thickness, ≤5Å nom-inal roughness, and flatness ≤λ=10ðλ∼ 6300ÅÞ. Toallow for an easy lift-off process, negative photoresistdesigned for negative slope sidewalls (typema-N1405from Microchem Co.) was used to make the litho-graphic patterns. The exposure and developmentwere optimized for dimension control to �0:1 μm.Electron-beam evaporation of Ta rather than Auwas preferred, to avoid “spitting” and deposition oflarge particles, deleterious to roughness and reflectiv-ity. A Ta film of 600Å nominal thickness was evapo-rated at normal incidence and with no motion of thesubstrates. The lift-off process was executed at roomtemperature and without sonication, to prevent exfo-liating the Ta strips from the substrates.

Using the above technique, we produced two mir-rors having a 90mm active length and a set of fourpatterns each, as shown in Fig. 8a). Two of the pat-terns were of the effective period type, having normalincidence periods of 14 and 0:7mm, respectively. Theother two were of the physical period type, with per-iods of 100 and 5 μm, respectively. A visible light in-terferogram of one of the mirrors placed on areference optical flat is shown in Fig. 8b), confirmingthat the lithographic processing did not degrade thehigh degree of flatness of the mirror. A microscopeimage of the 5 μm physical pattern is also shownin Fig. 8b), indicating that good quality reflective mi-crostrips can be produced by this method overlarge areas.

4. Tests of Microperiodic Mirrors with Hard X Rays

The basic setup used for the mirror tests is shown inFig. 9. The x-ray source was a 60kV, 1mA Apogeetube, manufactured by Oxford Instruments, Inc.,

Fig. 6. (Color online) Fringe contrast for “mirrors-only” and for“grating-mirror” interferometer of 4 μm period and 50keV meanenergy. Also shown are the overall interferometer transmissionfor a three-mirror system and the spectrum of a W tube at100kV filtered with a 50 μm W absorber.

Fig. 7. (Color online) Grazing-incidence reflectivity plots describ-ing the principle of lithographic mirror fabrication: a) reflectivityof Au and Si at 1:15mrad and transmission of a 50 μmW filter andb) mirror reflectivity after filtering out the low-energy photons.


and having aWanode with an∼60 μmdiameter spot.The low-energy radiation was cut off using a 0:3mmthick Si filter having ∼8keV cutoff energy or a 65 μmthick Cu filter having ∼16keV cutoff energy. Thebeam incident on the mirrors was precollimated toan ∼2mm × 50mm cross section by slits, not shownin Fig. 9, and a knife-edge absorber was used to blockthe nonreflected or direct light falling on the detector.A thin strip of direct light was nevertheless includedin some measurements to obtain a direct measure ofthe intensity and position of the incident beam. Re-motely controlled micropositioning stages were usedto align the mirrors under x-ray illumination.

The detector used for imaging tests was a high-resolution and high-sensitivity model XR-4S x-raycamera, recently developed byDALSA, Inc., for mam-mography and other high-resolution applications

[29]. The camera has a 25 μm pixel, 16 bit, 5 cm ×5 cm active area, cooled CCD, coupled to a high effi-ciency and resolution scintillator. Theworking energyrange is 10–100keV approximately, and the nominalresolving power is ∼10 line pairs=mm (∼50 μm). Ourtests show that the camera is sufficiently sensitiveand low-noise to allow high-resolution imaging atx-ray fluxes as low as ∼105 photons=cm2 s. This cap-ability allowed performing measurements at largedistances from the x-ray tube (up to∼3m), thusmini-mizing the pattern broadening effects due to the finitesource size.

A. Measurements of Mirror Reflectivity

The first tests consisted in measuring the x-ray spec-tra reflected by the Ta mirror at grazing incidenceand comparing them with theoretical predictions.For spectral measurements we used a 0:5mm thick,6mm diameter Amptek Si detector [30], collimatedwith a 0:5mm diameter tungsten pinhole and posi-tioned at a few meters from the x-ray mirror. Thereflected spectra were measured using the non-patterned portion of the Ta coating [Fig. 8a)] and cor-rected for the energy dependence of the response ofthe Si detector. The 0:3mm Si filter was used to cutoff the radiation below 8keV. The incident spectrumwas obtained by placing the detector in the directlight. The incidence angle was determined from thedistance between the direct light and the reflectedlight images obtained with the DALSA camera.

The results in Fig. 10a) show that, at an incidenceangle of 1mrad, the Ta film reflects nearly 80% of theincident light, up to 60keV, the highest energy avail-able fromthe tube.As the incidenceangle is increased,the higher energy photons are progressively cut off,due to the increase in critical angle. The experimentalresults agree quite well with the predictions of theXOPcode for thespectraofa60keVWanode, reflectedfrom a Tamirror [Fig. 10b)]. Tomatch the experimen-tal spectra, we nevertheless had to assume a Ta filmroughness of about twice thenominal roughness of theglass substrate. This likely indicates that the filmdepositionprocess amplified the roughness of the sub-strate. The high energy cutoff caused by the incidence

Fig. 8. (Color online) a) Layout of Ta patterns in the prototypemicroperiodic mirrors. b) Visible light interferogram of one ofthe mirrors placed on an optical flat; the inset also shows a micro-scope image of the 5 μm physical pattern.

Fig. 9. (Color online) Optical setup for microperiodic mirror tests.The low-energy radiation is cut off by a Si or Cu filter spectrum,and the direct light is suppressed by a knife-edge absorber. A high-sensitivity and high-resolution x-ray CCD camera enables workingat source detector distances up to ∼3m.

Fig. 10. (Color online) a) Measured spectra of incident (direct)and reflected light at 60kV source voltage and varying mirrorangle. b) Spectra predicted with the XOP code, assuming a 10Åmirror roughness.


angle increase also occurs at several kiloelectron voltslower energy values than predicted.

The overall conclusion is, nevertheless, that thelithographic method of mirror fabrication enables ob-taining large reflectivity at high x-ray energies, closeto theoretical calculations. Similar conclusions wereobtained in synchrotron experiments using high-Zcoated mirrors [27].

B. Measurements of Mirror Contrast

Another parameter critical for the proposed opticsconcept is the contrast between the high-Z film andthe low-Z substrate. This parameter was evaluatedby simple imaging experiments, in which the inten-sity reflected by the nonpatterned Ta layer wascompared to that reflected by the uncoated glasssubstrate. DALSA camera images obtained for inci-dence angles of 1.5 and 2mrad are presented inFig. 11. The plots on the right show also the verticalintensity profile through a region including the directand the reflected light image (dotted line in Fig. 11).The source was operated at 60kV, 1mA and the inci-dent spectrum filtered with 0:3mm Si, as above. Thedata indicate good contrast between the reflective andnonreflective regions for angles as low as 1:5mrad. Asexpected, the contrast increases as the incidence an-gle increases. The fraction of light reflected by the Tafilm is in rough agreement with the spectrally re-solved reflectivity that can be derived from Fig. 10:up to ∼75% of the direct intensity is reflected at1:5mrad incidence, 45% at 2mrad, and 30% at2:5mrad. The fraction of light reflected by the glasssubstrate is ∼13%, 3.5%, and 0.5%, respectively.

At incidence angles below 1:5mrad, however, theSi filter transmits too many low-energy photons toallow good contrast between the Ta film and the glasssubstrate. To increase the energy range of the mir-rors, we thus changed from Si to the Cu filter. Theresults confirm that by cutting off the radiation be-low ∼16keV, good contrast can be achieved also at

1mrad incidence angle, and implicitly at high x-ray energies, consistent with the XOP calculationsin Fig. 7.

C. Imaging Tests with Single Mirror

To evaluate the contrast and quality of the microper-iodic patterns, we also performed imaging experi-ments using a single mirror and the DALSA x-raycamera in a magnifying geometry (source-to-detectordistance ∼1:8m, magnification m∼ 3). The spatialresolution of this imaging system, Δr∼ p=mþsð1–1=mÞ, with p being the detector resolving powerand s the source extent, is limited, primarily by thesource size, toΔr∼ 55 μmat themirror location. Thisin turn limited our testing capability to larger period(≥50 μm) patterns only. For such large periods, thediffraction effects can be expected to be small inthe geometry of our experiments; for instance, thefirst Talbot distance for a 100 μm pattern at 20keVenergy and at m ¼ 2 magnification would be around16m.

An image of the 100 μm physical period pattern at2:5mrad incidence angle is shown in Fig. 12a). Thedata were obtained using the Apogee tube at60kV, 1mA and camera integration times of severalseconds. The spectrum was shaped with the Si filter.As illustrated in Fig. 12, with proper filtering, goodcontrast microperiodic patterns can be obtained atany angle. The height of the images at the detectoris consistent with the full length of the pattern con-tributing to the image. The quality of the pattern inthe central region is quite remarkable, keeping inmind the grazing-incidence angle and the 90mmlength of the reflecting strips. The peripheral imageof the pattern, on the other hand, is distorted andblurred by the strong parallax arising from the diver-gent x-ray beam. This clearly shows that in a prac-tical phase-contrast system, the mirror patternsmust match the divergence of the beam.

Fig. 11. (Color online) Images of the nonpatterned region of amirror (inset), showing the contrast between the glass substrateand the Ta film at varying incidence angles and with an Si filter;the right panels show the intensity profiles in the vertical direction(along the dotted-line box).

Fig. 12. (Color online) a) Image of the 100 μmphysical period pat-tern at 2:5mrad incidence angle. b) Horizontal intensity profile inthe image (along the dotted-line box); also shown is the computedprofile for a 100 μm period grid of 100% contrast, viewed with adetector having a Gaussian point spread function of 55 μmFWHM.The comparable intensity modulation indicates a high intrinsiccontrast for the mirror-produced pattern.


The intensity modulation along the dotted regionin the 2:5mrad image is shown in Fig. 12b). For com-parison, we also show the limit that can be expectedfor the modulation, obtained by computing withXWFP the intensity profile of a 100 μm period pat-tern, having 100% contrast, and imaged with a55 μm FWHM Gaussian point spread function. Ascan be seen, the experimental modulation is not farfrom the computed limit, suggesting that the truecontrast of the 100 μm fringe pattern must be inthe 70%–80% range.

Images obtained from the effective period patternhaving a 14mmnormal incidence period, at incidenceangles of 6, 3.5, and 2:8mrad (effective periods of 85,50, and 40 μm, respectively) are shown in Fig. 13a).The intensity profile along the vertical box in the2:8mrad image is also shown in Fig. 13b). As is ex-pected, the modulation of the effective period patterndecreases rapidly with decreasing angle, as the effec-tive period decreases below the resolving power of ourimaging system. The comparison of the experimentalintensity modulation with the computed limit indi-cates again quite good micropattern contrast. Theeffective period pattern exhibits, nevertheless, signif-icant reflectivity variation along the mirror length,with the front side reflecting more than the rear side.A likely explanation is nonuniformity in the Ta de-position.

D. Imaging Tests with Two Mirrors

Finally, we have tested the patterns obtained fromcombining two grazing-incidence microperiodic mir-rors. While the periods accessible with our presentsetup are too large for phase-contrast imaging(≤10 μm would be necessary), these experiments de-monstrated that the reflective micropatterns can be

accurately aligned under x-ray illumination and atgrazing-incidence angles. In addition, using the sec-ond mirror as an “analyzer” of the pattern producedby the first, we could confirm in a direct experimentalway the high contrast of themicropatterns. To reduceto the minimum possible (a few micrometers) thegeometric broadening due to our finite source size,the experiments were done using a large source-to-mirror distance of 3m and low magnification ofm ¼ 1:05. The distance between the mirror centerswas ∼10 cm.

Results obtained with the 100 μm physical periodpatterns are shown in Fig. 14. To minimize the ef-fects of the strong parallax, the mirrors were usedin an “antiparallel” configuration, as sketched inFig. 14a). The individual light patterns reflectedby each mirror at an incidence angle of ∼1:7mrad,obtained right before placing the second mirror inthe path of the light reflected by the first, are shownin Fig. 14b); a band of direct light is also visible at thetop of the image. As seen, the two images are slightlymisaligned, due to the difference in magnificationand parallax for the two mirrors. After illuminatingthe second mirror with light reflected from the first,the two slightly misaligned aligned patterns produceas expected moiré patterns. That these are indeedmoiré patterns arising from successive reflectionson the mirrors was also verified by laterally shifting

Fig. 13. (Color online) a) Images of the 14mm normal periodpattern at decreasing incidence angle/effective period. b) Verticalintensity profile in the 6mrad image, along the dotted-line box;also shown is the intensity profile computed as in Fig. 12, butfor an 85 μm period grid.

Fig. 14. (Color online) a) “Antiparallel” setup used for two-mirrorimaging in the physical period configuration. b) Images of indivi-dual 100 μm physical patterns from the two mirrors at 1:7mradincidence, before placing the second mirror in the path of the raysreflected by the first. c) Moiré patterns obtained by double reflec-tion from the patterns at different “phase” differences between thetwo patterns. d) Horizontal intensity profile of the upper moirépattern.


one of the mirrors by a few tens of micrometers; thishad the expected effect of shifting the moiré patternby a fraction of its period [Fig. 14c)]. The maximalintensity modulation of the moiré pattern is ∼80%,indicating again good intrinsic contrast of thephysical patterns.

The fringe contrast of a two-mirror system wasalso evaluated in the effective period configuration.The mirrors were placed in a parallel geometry witha few tens of micrometers effective period and one ofthe mirrors then translated along its length, to varythe overlap or “phasing” between the two reflectivepatterns [Fig. 15a)]. The experiments were doneagain at a large source distance and low magnifica-tion, to avoid geometric broadening. The images ofthe doubly reflected pattern for ϕ ¼ 0 phasing (reflec-tive strips from the first mirror overlapping withreflective strips of the second one) and for ϕ ¼ πphasing (reflective strips overlapping with nonre-flecting strips) are shown in Fig. 15b). A strongextinction of the reflected intensity (factor of ≥4decrease) is observed for ϕ ¼ π phasing, indicatingthat quite good pattern contrast is also obtained inthe effective period configuration.

5. Conclusions

Although our experiments do not yet demonstratephase-contrast imaging or Talbot pattern formation,the results obtained with the prototype mirrors sug-gest that the proposed concept has good potential forphase-contrast imaging with hard x rays:

– The lithographic method of mirror fabricationenables achieving large reflectivity and good contrastbetween the reflective and the nonreflective mirrorstrips, up to the highest x-ray energies available;the method also enables producing precise patternshaving small physical period, over large areas and atmodest cost.

– In both physical and effective period configura-tions, the fringe quality and contrast appear good, atleast for the periods accessible in our experiments;the quality of the physical period fringe patterns isparticularly encouraging for clinical applications.

– Using x-ray illumination, it is possible to pre-cisely align the microperiodic patterns at grazingincidence; moreover, the alignment appears to beslightly sensitive to vibrations and drifts.

Further experiments using a microfocus x-ray tubeor synchrotron light are necessary to study Talbotpattern formation with the microperiodic mirrors.We note, nevertheless, that in “mirrors-only” interfe-rometers, even in the absence of a properly definedTalbot pattern, local interference patterns wouldform, and from the comparison of the light patternsobtained in the absence of the refracting object andthose obtained after its introduction in the x-raypath, one could unfold the structure of the object.Furthermore, in the case of “mirror-grating” hybridinterferometers, the formation of the Talbot patternwill be assured by the phase grating. Phase gratingsfor hard x-ray energies can be much more easilyproduced than absorption gratings, because the grat-ing thickness needed for the π phase shift is of theorder of tens of micrometers. For instance, a 75 μmSi grating was demonstrated for π phase shift at60keV [22].

The experiments also revealed some challenges inthe mirror fabrication. For instance, while the x-rayimages of the physical period patterns from the twomirrors look similar [Fig. 14b)], the images of the ef-fective period patterns show significant differences,with one of the mirrors producing a narrower andmore blurry pattern than the other. Surface charac-terization with atomic force microscopy is needed toelucidate the cause for this effect.

The total reflection mirrors limit the field of viewheight of a hard x-ray DPC system to around 100 μm.At lower x-ray energies, one could, however, considerusingmicroperiodically patternedmultilayermirrorsto increase the field of view to the centimeter range.For instance, W=B4C multilayers have been fabri-cated that efficiently reflect E ≤ 5keV x rays atangles ≥15mrad [31]. Micropatterned, broadbandcrystalline reflectors, such as highly oriented pyroly-tic graphite [32], might also offer a way to increasethe field of view height of phase-contrast systemsat high energies.

Finally, it might be possible to apply the micropat-terned mirror concept for DPC imaging with neu-trons. Efficient neutron mirrors can be made usingmultilayer technology [33] or through total reflectionat grazing-incidence angles [34]. As for x rays, the ad-vantage of mirror optics for neutron DPC imagingwould be the broad spectral range and high contrastand throughput.

We kindly thank the DALSA Corporation for pro-viding the high-resolution x-ray camera used in ourexperiments. We also thank T. Weitkamp from the

Fig. 15. (Color online) a) “Parallel” setup used for the effectiveperiod two-mirror experiments. b) Double-reflection images ofthe effective period patterns from the two mirrors at ∼2mrad,at “phasing” of 0 and π. The double reflection from the nonpat-terned region is also shown, indicating that without patternsthe intensity does not change significantly.


European Synchrotron Radiation Facility (ESRF) forsharing the XWFP code.

References1. S.-A. Zhou and A. Brahme, “Development of phase-contrast X-

ray imaging techniques and potential medical applications,”Phys. Medica 24, 129–148 (2008).

2. C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N.Wernick, “Multiple-image radiography for human soft tissue,”J. Anat. 208, 115–124 (2006).

3. T. Yuasa, E. Hashimoto, A. Maksimenko, H. Sugiyama, Y.Arai, D. Shimao, S. Ichihara, and M. Ando, “Highly sensitivedetection of the soft tissues based on refraction contrast byin-plane diffraction-enhanced imaging CT,” Nucl. Instrum.Methods Phys. Res. A 591, 546–557 (2008).

4. J. Li, Z. Zhong, D. Connor, J. Mollenhauer, and C. Muehleman,“Phase-sensitive x-ray imaging of synovial joints,” Osteoar-thritis Cartilage 17, 1193–1196 (2009).

5. P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A.Bravin, “Analyzer-based imaging technique in tomographyof cartilage and metal implants: a study at the ESRF,” Eur.J. Radiol. 68, S41–S48 (2008).

6. R. A. Lewis, “Medical phase contrast x-ray imaging: currentstatus and future prospects,” Phys. Med. Biol. 49, 3573 (2004).

7. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C.Bronnimann, C. Grunzweig, and C. David, “Hard-x-raydark-field imaging using a grating interferometer,” Nat. Ma-ter. 7, 134–137 (2008).

8. Yogesh S. Kashyap, P. S. Yadav, Tushar Roy, P. S. Sarkar, M.Shukla, and A. Sinha, “Laboratory-based x-ray phase-contrastimaging technique for material and medical science applica-tions,” Appl. Radiat. Isot. 66, 1083–1090 (2008).

9. S. Mayo, R. Evans, F. Chen, and R. Lagerstrom, “X-rayphase-contrast micro-tomography and image analysis of woodmicrostructure,” J. Phys. Conf. Ser. 186, 012105 (2009).

10. M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C.David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys.Rev. Lett. 101, 123902 (2008).

11. J. A. Koch, O. L. Landen, B. J. Kozioziemski, N. Izumi, E. L.Dewald, J. D. Salmonson, and B. A. Hammel, “Refraction-enhanced x-ray radiography for inertial confinement fusionand laser-produced plasma applications,” J. Appl. Phys.105, 113112 (2009).

12. H. Suhonen, M. Fernandez, A. Bravin, J. Keyrilainen, and P.Suorttia, “Refraction and scattering of x-rays in analyzerbased imaging,” J. Synchrotron Radiat. 14, 512–521 (2007).

13. M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R.Feidenhans, and F. Pfeiffer, “Hard x-ray phase-contrast imag-ing with the compact light source based on inverse Comptonx-rays,” J. Synchrotron Radiat. 16, 43–47 (2008).

14. C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, andZ. Zhong, “Diffraction-enhanced imaging of musculoskeletaltissues using a conventional x-ray tube,” Acad. Radiol. 16,918–923 (2009).

15. J. F. Clauser, “Ultrahigh resolution interferometric x-rayimaging,” U.S. patent 5,812,629 (22 September 1998).

16. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrie-val and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).

17. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori,“Phase tomography by x-ray Talbot interferometry for biologi-cal imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).

18. T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer,“Tomography with grating interferometers at low-brilliancesources,” Proc. SPIE 6318, 63180S (2006).

19. C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A.Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction grat-ings for hard x-ray phase contrast imaging,” Microelectron.Eng. 84, 1172–1177 (2007).

20. E. Reznikova, J.Mohr,M.Boerner, V.Nazmov, andP.-J. Jakobs,“Soft x-ray lithography of high aspect ratio SU8 submicronstructures,” Microsyst. Technol. 14, 1683–1688 (2008).

21. M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, andF. Pfeiffer, “Soft-tissue phase-contrast tomography with anx-ray tube source,” Phys. Med. Biol. 54, 2747–2754 (2009).

22. T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C.Grünzweig, E. Hempe, S. Popescu, M. Hoheisel, and C. David,“Phase-contrast imaging and tomography at 60keV using aconventional x-ray tube source,” Rev. Sci. Instrum. 80,053701 (2009).

23. T. Weitkamp, “XWFP: an x-ray wavefront propagation soft-ware package for the IDL computer language,” Proc. SPIE5536, 181–189 (2004).

24. M. Sanchez del Rio and R. J. Dejus, “XOP: recent develop-ments,” Proc. SPIE 3448, 340–345 (1998).

25. M. Testorf, J. Jahn, N. A. Khilo, and A. M. Goncharenko,“Talbot effect for oblique angle of light propagation,” Opt.Commun. 129, 167–172 (1996).

26. S. Aoki, N. Watanabe, T. Ohigashi, H. Yokosuka, Y. Suzuki, A.Takeuchi, and H. Takano, “Production of reflection pointsources for hard x-ray Gabor holography,” Jpn. J. Appl. Phys.44, 417–421 (2005).

27. Y. Suzuki, A. Takeuchi, and Y. Terada, “High-energy x-ray mi-crobeamwith total-reflection mirror optics,” Rev. Sci. Instrum.78, 053713 (2007).

28. http://www.customscientific.com/.29. http://www.dalsa.com/public/ls/datasheets/xr4s_datasheet_

101708.pdf.30. http://www.amptek.com/.31. K. Ichiyanagi, K. Ichiyanagi, T. Sato, S. Nozawa, K. H. Kim, J.

H. Lee, J. Choi, A. Tomita, H. Ichikawa, S. Adachi, H. Ihee,and S. Koshihara, “100ps time-resolved solution scatteringutilizing a wide-bandwidth x-ray beam from multilayeroptics,” J. Synchrotron Radiat. 16, 391–394 (2009).

32. G. Jost, S. Golfiera, R. Lawaczecka, H.-J. Weinmanna, M.Gerlachb, L. Cibikb, M. Krumreyb, D. Fratzscherc, J. Rabec,V. Arkadievc, M. Haschkec, N. Langhoffc, R. Wedelld, L.Luedemanne, P. Wuste, and H. Pietscha, “Imaging-therapycomputed tomography with quasi-monochromatic x-rays,”Eur. J. Radiol. 68S, S63–S68 (2008).

33. M. Schneider, J. Stahn, and P. Boni, “Focusing of cold neu-trons: performance of a laterally graded and parabolicallybent multilayer,” Nucl. Instrum. Methods Phys. Res. A 610,530–533 (2009).

34. M. V. Gubarev, B. D. Ramsey, D. E. Engelhaupt, J. M. Burgess,and D. F. R. Mildner, “An evaluation of grazing-incidenceoptics for neutron imaging,” Nucl. Instrum. Methods Phys.Res. B 265, 626–630 (2007).


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Development of microperiodic mirrors for hard x-ray phase-contrast imaging