Tunable coherent soft X-rays

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 6, NOVEMBER/DECEMBER 2004 1405

Tunable Coherent Soft X-RaysKristine M. Rosfjord, Yanwei Liu, and David T. Attwood

Abstract—A new, tunable, spatially and spectrally coherent softX-ray undulator branchline at the Advanced Light Source (ALS)is under operation. Using the third harmonic from an 8-cm periodundulator, this branch delivers coherent soft X-rays with photonenergies ranging from 200 to 1000 eV. Here, the beamline layoutand characterization are presented. The characterization includesmeasurements of available coherent photon flux as well as a seriesof double-pinhole experiments to measure spatial coherence in thefocal plane.

Index Terms—Coherence, harmonic, soft X-rays, undulator.

I. INTRODUCTION

THE AVAILABILITY of high-power spectrally and spa-tially coherent soft X-rays would facilitate a wide variety

of experiments as this energy region contains several impor-tant K and L absorption edges. Specifically, there are the carbonand oxygen K edges that are critical for biological imaging inthe water window and the L edges of magnetic materials iron,nickel, and cobalt for which imaging and scattering studies canbe performed.

Generation of coherent radiation at soft X-ray wavelengthsis even more challenging than that at EUV wavelengths due tothe tighter phase-space (shorter wavelength) constraints. In re-cent years, there has been significant progress in the develop-ment of compact EUV sources, particularly plasma-based lasers[1]–[3], and high-order harmonic generation of intense fem-tosecond lasers [4], [5]. They are now capable of producingcoherent radiation at EUV wavelengths with photon flux levelssufficient for practical experiments. However, when scaling toshorter wavelengths, both sources face unfavorable demands onexcitation schemes. Photon energies of several hundred elec-tronvolts have not yet been reached with useful flux levels usingthese sources.

Electron beam driven sources, undulators in particular,readily generate very useful power levels at these short wave-lengths but require extensive spatial filtering to achieve thedesired degrees of spatial coherence. Extending available spa-tial coherence to soft X-ray wavelengths is the focus of this

Manuscript received June 30, 2004; revised September 20, 2004. This workwas supported in part by the Department of Energy, Office of Basic EnergySciences, and by the National Science Foundation, EUV Engineering ResearchCenter.

K. M. Rosfjord was with the University of California, Berkeley, and theCenter for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley,CA 94720 USA. She is now with the Massachusetts Institute of TechnologyLincoln Laboratory, Lexington, MA 02420 USA (e-mail: [email protected]).

Y. Liu is with the Center for X-Ray Optics, Lawrence Berkeley National Lab-oratory, Berkeley, CA 94720 USA (e-mail: [email protected]).

D. T. Attwood is with the Department of Electrical Engineering and ComputerSciences, University of California, Berkeley, and the Center for X-Ray Optics,Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/JSTQE.2004.838036

paper. Free-electron lasers (FELs), essentially long undula-tors exhibiting self-amplification of the spontaneous emission(SASE), offer a future possibility of achieving spatial coherenceat high peak power in femtosecond duration pulses. To date,FELs have achieved wavelengths as short as 95 nm (13 eV) [6]with efforts underway worldwide to extend these capabilities tothe soft X-ray and X-ray wavelengths [7].

Undulators at synchrotron radiation facilities provide tunablecoherent radiation at short wavelengths [8], [9]. The spectralcoverage (tuning range) of an undulator is determined by theundulator period, the electron energy, and the strength of mag-netic field, expressed in the undulator equation as [10]

(1)

where is the on-axis wavelength of undulator radiation,the undulator magnetic structure period, and

(2)

the relativistic factor. The deflection parameter is defined as

cm (3)

Equation (1) implies a cutoff in the short wavelength endfor a particular undulator. For example, the advanced lightsource (ALS), optimized for generation of extreme ultravi-olet/soft X-ray (EUV/SXR) radiations, has a storage ring with

GeV. At beamline 12.0, an 8-cm period undulator(U8) is used. This gives a cutoff wavelength of 2.89 nm orphoton energy of 427 eV.

From (1), scaling to shorter wavelengths with undulators canbe done in a rather straightforward manner using shorter undu-lator periods (e.g., 5-cm U5 available at ALS) and/or higher en-ergy (6–8 GeV) electron beams, available at other facilities. Onthe other hand, undulator harmonics provide an alternative wayto reach shorter wavelengths, thus giving an additional advan-tage of covering both longer and shorter wavelengths using oneundulator structure. Here, we present a new coherent soft X-raybranchline (beamline 12.0.2) at the ALS which can deliver co-herent soft X-rays from 200 eV to 1 keV by utilizing the thirdharmonic from the 8-cm period undulator.

II. UNDULATOR RADIATION HARMONICS

The key feature of undulator radiation is its very high spectralbrightness. This is realized by limiting the amplitude of the elec-tron’s modulation in the magnetic structure so that the radiationfrom individual periods largely overlaps. The small amplitude“undulating” of electrons generally requires small K values. Atthe limiting case of , the motion of the electrons can

1077-260X/04$20.00 © 2004 IEEE

1406 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 6, NOVEMBER/DECEMBER 2004

be well approximated to a sinusoidal oscillation following theperiodic magnetic field. Such N-cycle oscillation produces pro-nounced interference effects, enhancing the radiation both spec-trally, to a resonant wavelength as expressed in (1), and spatially,to a forward cone with an extending angle much smaller (a factorof ) than the characteristic synchrotron radiation angle of

.With increasing K values, the oscillation of electrons, al-

though still periodic following the magnetic field, begins todeviate from a sinusoidal function [10]. As a result, in thefrequency domain, harmonics of the fundamental frequencywill emerge and grow with increasing K values. The theoret-ical characterizations of undulator harmonics can be carriedout using relativistic electrodynamics and have been pre-sented in literature [11], [12]. Here, we rewrite the results informs resembling those of the fundamental harmonic as in[10]. At the forward direction (on-axis), only odd harmonics

will appear, with corresponding wavelengthsas

(4)

For most cases, the useful portion of undulator radiation is con-tained in the central radiation cone, defined as

(5)

The definition of the central radiation cone angle corresponds toa relative bandwidth of caused by an angular-dependentDoppler shift [10], which is also the natural (minimal) bandwidthassociated with the finite number of oscillations the electronundergoes in the undulator. The power in the central radiationcone is

(6)

Factor has the form of [12]

(7)where denotes the Bessel function of the first kind. Exceptfor is generally a monotonic increasing func-tion of (for moderate values), showing the energy transferfrom the fundamental to higher harmonics as value increases.For small , . For , important in thispaper, for smalland for very small . For very small

, this gives a third harmonic central radiation cone power of

(8)

which we note has a factor. The analytic expression of (8)is quite useful in that, for low , it explicitly exhibits the de-pendencies of harmonic power on the major parameters, such

Fig. 1. Central radiation cone power for fundamental and third harmonic ofU8 undulator at the ALS.

as . For higher , the full (7) is required. These equa-tions are somewhat idealistic in that they assume a monoener-getic electron beam but are rather accurate for the parametersconsidered here. Finite electron beam energy spread, typicallyof order 10 for a modern storage ring, broadens the spectralbandwidth associated with the central radiation cone but to anegligible degree for the undulator lengths and harmonic num-bers considered here. Finite electron beam size and divergencedo not affect these results but have a strong affect on the degreeof spatial coherence and, thus, coherent power and are consid-ered further in Section IV.

Using the previous formulas, the central radiation conepowers for the fundamental and third harmonic are calculated.The results are shown in Fig. 1.

III. BEAMLINE LAYOUT

The layout of this new coherent soft X-ray beamline isshown in Fig. 2. The branchline consists of four mirrors and amonochromator. The coatings on each mirror are chosen as atradeoff between reflectivity, ease of deposition, and materialcost. First is a 2 horizontally deflecting planar mirror coatedin gold which deflects the beam into beamline 12.0.2. The nextis a spherical vertically deflecting mirror coated in iridium thatfocuses the source onto the exit slit. Next along the beam pathis the monochromator composed of a varied line-space gratingand an exit slit, enabling a bandwidth of as low as 0.1%. Lastlyare two pairs of tungsten coated mirrors comprising the Kirk-patrick–Baez (K–B) [13] focus system for the two subbranches,one at 14 demagnification and the other 8 demagnification.The former is optimized for use at 500 eV and the latter at800 eV. In each subbranch demagnification is equivalent in thehorizontal and vertical directions. The horizontally deflectingK–B mirror images the source onto the pinhole plane, whereasthe vertically deflecting K–B mirror images the exit slit ofthe monochromator onto the pinhole place. With the previousoptical components the beamline has an efficiency of 0.57% at500 eV. This efficiency value will degrade, somewhat, in timedue to contamination of the beamline optics thereby decreasingthe flux delivered to the focal plane. This will not effect theresultant wavefront properties.

ROSFJORD et al.: TUNABLE COHERENT SOFT X-RAYS 1407

Fig. 2. Beamline layout of the new coherent soft X-ray beamline at the ALS.

TABLE IBEAMLINE SUMMARY GIVING SPATIALLY COHERENT FLUX DELIVERED TO THE FOCAL PLANE OF THE BEAMLINE

Using the theoretical reflectivity of one gold, one iridium,and two tungsten mirrors [14], along with the experimentallydetermined grating reflectivity,1 the efficiency of the beamlineand the flux delivered to the experimental endstations can bedetermined. This is summarized in Table I. This table liststhe beamline efficiency, the spatially coherent flux [10] in thecentral radiation cone, and the part of this spatially coherentflux delivered to the beamline focal plane for the energy regionof 500–800 eV.

IV. BEAMLINE CHARACTERIZATION

The new beamline was characterized with regards to spatialcoherence and flux. The flux in the central radiation cone andthe flux through a spatially filtering pinhole were measured andcompared with the theoretical values found above. Airy patternswere also recorded from pinhole diffraction. A double-pinholecharacterization was performed to determine the complex co-herence factor with regard to transverse distance in both the ver-tical and horizontal directions.

A. Flux in Central Radiation Cone

The flux in the central radiation cone was measured by de-tecting the current on a photodiode placed directly behind thefocal plane of the 14 branchline. The flux was then calculatedwith the knowledge of the photodiode’s responsivity for a spe-cific wavelength [16]. The photodiode used was a GaAsP–AuSchottky photodiode from Hamamatsu, product number G2119.At 500 eV, this diode has a responsivity of 1 W/0.164 A.

1In a joint effort between Lawrence Berkeley Laboratory and Hitachi, anew grating process has been developed to increase diffraction efficiencya factor of 8 in the soft X-ray region [15].

The upstream beam defining apertures (shown in Fig. 2) areset to correspond to a collection angle of 33.6 rad in both hor-izontal and vertical directions, matching the central radiationcone angle at 500 eV as calculated in Table I. The monochro-mator exit slit width is set to 31 m, corresponding to a relativebandwidth of 0.61% (1/165).

A current of 0.225 mA was measured on the diode placed di-rectly behind the focal plane of the 14 branchline when theALS current was equal to 353 mA. This diode current corre-sponds to a flux in the central radiation cone of

mA mW

photons/s. (9)

The theoretical value expected for the flux in the central radi-ation cone arriving at the focal plane on beamline 12.0.2 can bedetermined using (6) and Table I. Inserting the undulator param-eters and the experimental ALS current into (6) yields a flux of6.08 10 photons/s in the central radiation cone coming out ofthe U8 undulator. Multiplying this number by the beamline ef-ficiency of 0.00567 stated in Table I for 500 eV yields a photonflux of 3.45 10 photons/s in the central radiation cone at thefocal plane of the beamline.

The flux measured is a factor of 2.02 smaller than that pre-dicted. Several factors can contribute to this difference. Thespectrum in the central radiation cone can be broadened by boththe limited number of undulator periods and the fact that theelectron beam has nonnegligible divergence angles [10]. For ourexperiment, the electron beam has a divergence angle of 23 radin horizontal direction, which is comparable to the central ra-diation cone (33.6 rad). With the monochromator still set to


an ideal bandwidth of 1/165, which assumes zero divergence,a broader bandwidth in the central radiation cone will result inlower photon flux passing through the monochromator. Otherpossible reasons include incorrect alignment of all optical ele-ments in the beamline and performance degradation of the op-tics due to less than ideal coatings and carbon contaminationthat is known to accumulate over time.

B. Spatially Coherent Flux

The spatially coherent flux of the 14 branchline of beam-line 12.0.2 was experimentally determined by detecting the fluxafter an appropriately sized pinhole. The pinhole diameter waschosen to create a resultant angle twice that of the incomingangle to create a clearly defined airy pattern.

To determine the incoming angle of the radiation to the pin-hole, the beamline was viewed as one large optic demagnifyingthe radiation spot either 14 or 8 depending on the subbranchused, as shown in Fig. 3. The half-angle of the radiation fromthe undulator can be defined as [10]

(10)

where is the root mean square (rms) angular divergence ofthe beam in the storage ring. For the ALS, rad and

rad, and thus rad and radat 500 eV. The larger of these values is chosen so that a greaterfiltering is required. The 14 demagnification of the coherentoptics branchline results in an incident angle 14 greater thanthat shown previously or rad at 500 eV. Theangle to be created from the filtering pinhole is chosen to betwice the incident angle or mrad at 500 eV.

The diameter of the spatially filtering pinhole is then chosenbased on according to the equation for diffraction through apinhole [17]

(11)

This corresponds to a pinhole with a diameter of 2.65 m.This pinhole was fabricated by the Center for X-Ray Optics’nanofabrication team. Scanning electron microscopy (SEM)measurements of completed pinholes measured a 2.5- mdiameter.

To measure the spatially coherent flux at 500 eV, the 2.5- mpinhole was placed at the focal plane of the 14 subbranch.A current of 0.232 A was detected on the photodiode placedbehind the pinhole with an ALS current of 268.7 mA. This diodecurrent corresponds to a spatially coherent flux of

A W

photons/s. (12)

This measurement has the central radiation cone bandwidth of0.61%.

Assuming Gaussian distributions of the electron beam’stransverse spatial and angular distributions, in both the vertical

Fig. 3. View of beamline used to determine single pinhole size for spatialfiltering. Beamline is represented in the diagram by one large optic thatdemagnifies the radiation by a factor of M (8 or 14 depending on thesubbranch).

Fig. 4. Spatially coherent power [10] in the central radiation cone powerfor fundamental and third harmonic of U8 undulator at the ALS. Beamlineefficiency of 0.00567 was used in the generation of these curves.

and horizontal directions the spatially coherent power can bewritten as [10]

(13)

where and are the elliptical beam diameters in the elec-tron storage ring (520 and 32 m, respectively), andare as given in and below (10), and is the beamline efficiency.This formulation, as embodied in (13) and (10), is somewhatidealistic in that Gaussian distributions are assumed, which isnot strictly true for . One could improve this by using a moredetailed computational model, assuming that the beam distri-butions are well known; however, the degree to which a com-parison with the experiment would be improved is small whenbeamline uncertainties, such as alignment, aberrations, and con-tamination, are considered. As a result, we leave that for futurecomparisons. Based on the use of (13), Fig. 4 gives the spatiallycoherent power delivered to the focal plane of the beamline forthe first and third harmonics of the U8 undulator of beamline12.0.2. A beamline efficiency of 0.00567 was used for thesecurves based on the use of one gold, one iridium, and two tung-sten mirrors [15] and a varied line-space grating.

As for central radiation cone flux, (6) and Table I are usedto determine a theoretical flux of 2.63 10 photons/s in thecentral radiation at the focal plane of the beamline for an ALScurrent of 268.7 mA.

The amount of this central radiation cone flux focused into the2.5- m pinhole is determined by examining the focused spotof the beamline. A picture of the focal spot of the beamlineis shown in Fig. 5. Examining this image using Matlab, it wasdetermined that the intensity ratio of a 2.5- m diameter circle


Fig. 5. Image of the focal spot of the 14� branchline on the YAG phosphor.Focal spot is 60 � 9:4 �m FWHM.

in the highest intensity part of this focused beam to the focusedbeam itself is 0.61%. Assuming the pinhole had been positionedin the beam path to optimize the flux through it, this ratio rep-resents the part of the central radiation cone that passes throughthe pinhole.

The pinholes used are not empty, but rather have 0.1- mSi N , 12-nm gold, and 6-nm chrome in the hole left from thecreation of the pinhole. These materials have a transmission of45.9% at 500 eV. Taking into consideration this transmission,the theoretically determined coherent flux can be expressed as

photons/s. (14)

This is a factor of 4.16 greater than the experimental valuefound. A factor of 2.02 of this error can be attributed to theflux found in the central radiation cone as was found previously.The additional factor of two is nominally identified with theintensity ratio process used to determine the theoretical valueof spatially coherent flux.

C. Airy Patterns

A wave normally incident on a circular aperture will producean airy intensity distribution in the far field if it has a sufficientlevel of spatial coherence [17]. As a first-order measurementof the spatial coherence of the beamline, we will look at thefar-field patterns generated by the 2.5- m diameter pinhole. Thefar-field patterns are recorded on a , 1024 1024 pixel(24.8 m/pixel) charge-coupled device (CCD) camera.

Placing the 2.5- m diameter pinhole at the focal plane of the14 branch, airy patterns were generated at 500 eV (200-msexposure time) and 600 eV (1-s exposure time) as shown inFigs. 6 and 7. These images were recorded with the CCD cameraplaced 1.44 m downstream from the pinhole plane.

These are the first high-quality airy patterns seen at this shortof a wavelength.

The flux measured through a pinhole is not the spatially co-herent flux that will be available for future experiments. In thesemeasurements, the photodiode was placed immediately after thepinhole. This caused the diode to record all of the radiationthrough the pinhole, including the flux diffracted into the airyrings. Only that flux in the central lobe of the airy pattern willbe used in future experiments.

The power in the central lobe is 84% [18] of the power ofthe entire airy pattern. Therefore, of the 1.44 W (1.77 10

Fig. 6. Airy pattern and its cross section recorded using a 2.5-�m diameterpinhole at the focal plane of beamline 12.0.2 at the ALS. This picture is recordedat a wavelength of 2.48 nm (500 eV) with an exposure time of 200 msec.

Fig. 7. Airy pattern and its cross-section recorded using a 2.5 �m diameterpinhole at the focal plane of beamline 12.0.2 at the ALS. Picture was recordedat a wavelength of 2.07 nm (600 eV) with an exposure time of 1 s.

photons/s) found through the 2.5- m diameter pinhole, 1.18 W(1.48 10 protons/s) is in the experimentally useful centrallobe within the central radiation cone bandwidth of 0.61%.

D. Double-Pinhole Characterization

The magnitude of the complex coherence factor of the softX-ray branchline was measured using the classical Thompsonand Wolf experiment [19] using the Young’s double-slit setup[20] as has been discussed at short wavelengths by [21]–[25]. Inthis experiment, the Young’s slits are replaced by pinhole pairsplaced at the focal plane of the beamline to better characterizethe two-point spatial coherence. The soft X-rays pass throughthe pinholes and then propagate 1.44 m to the far-field regionwhere they are detected on the CCD camera.

The visibility can be described as the sharpness of the fringesor [26]

Visibility (15)

for the quasi-monochromatic case of undulator radiation passedthrough a monochromator where and are the max-imum and minimum intensity of the fringe pattern, respectively,and and are the intensities on each of the pinholes.If the double pinholes are centered about the incident radiationsuch that , then the visibility is simply equal to themagnitude of the complex coherence factor.


Fig. 8. Measured two-pinhole interference patterns at a photon energy of 500 eV (2.48 nm) and their respective lineouts for vertical pinhole separations of (a) 2�m, (b) 6 �m, and (c) 8 �m. Each individual pinhole of the two-pinhole pairs has a diameter of 450 nm to ensure a spatially coherent wavefront over the individualpinhole. (d) Measured magnitude of the complex coherence function versus the pinhole separation. Least square error Gaussian curve is fitted to these data points.All data was taken on beamline 12.0.2 of the ALS.

Fig. 9. Measured two-pinhole interference patterns at 500 eV ( ), 600 eV (?), 700 eV ( ), and 800 eV ( ) and their respective lineouts for a 5-�m verticalpinhole separation at a photon energy of (a) 600 eV (2.07 nm), (b) 700 eV (1.77 nm), and (c) 800 eV (1.56 nm). Note that airy envelope decreases for increasingenergy. (d) Measured magnitude of the complex coherence function versus the pinhole separation. Least square error Gaussian curve is fitted to each energy’s setof data points. All data was taken on beamline 12.0.2 of the ALS. Coherence length as calculated by (17) and (18) are 5.4 �m (500 eV), 4.9 �m (600 eV), 4.2 �m(700 eV), and 3.6 �m (800 eV).

In order to use the simple model of (15), the wavefront overeach individual pinhole must be spatially coherent .To determine the diameter of the individual pinhole where this

full spatial coherence is achieved, the beamline is once againmodeled as a single optic imaging an incoherent source as seenin Fig. 3.


Fig. 10. Measured two-pinhole interference patterns at a photon energy of 500 eV (2.48 nm) and their respective lineouts for horizontal pinhole separations of(a) 1 �m, (b) 4 �m, and (c) 8 �m. (d) Measured magnitude of the complex coherence function versus the pinhole separation. Least square error Gaussian curve isfitted to these data points. All data was taken on beamline 12.0.2 of the ALS.

Following Born and Wolf’s calculation [18] for the degree ofcoherence in the image of an incoherent light source, the com-plex coherence factor between two points in the image planecan be expressed as

(16)

Solving (16) for a wavelength of nm (500 eV), wefind that for nm, . Thus, a pinholediameter of 450 nm for each individual pinhole was used for ahigh spatial coherence wavefront from each pinhole. In practice,the spatial coherence achieved from the 450 nm will be greaterthan that anticipated by (16). Equation (16) uses the assump-tion that the source is completely incoherent; whereas, the un-dulator has a low level of spatial coherence. Also, (16) assumesan aberration-free imaging system. The existence of aberrationsin beamline 12.0.2 will cause the coherence length to increaseproportionally with the expanded focal spot size.

The results of the double-pinhole characterization are shownin Figs. 8–10. These figures display the results of pinholes sep-arated be varying distances in the vertical direction at 500 eV,pinholes separated by 5 m in the vertical direction at varyingenergies, and separated at varying distances in the horizontal di-rection at 500 eV, respectively. The images obtained on the CCD

camera are displayed as well as cross-sectional lineouts of theimages. A graph of complex coherence factor versus pinholeseparation is also shown with a least square error fit Gaussiancurve to the experimental data points.

The value of the magnitude of the complex coherence factoris determined from each interferogram in the Fourier domain asin [21] and [22].

The least squares error fitted Gaussian curves are used to de-termine the transverse coherence length of the beam with re-gards to direction and energy. Following Goodman [26] andMandel [27], who defined a lateral coherence length determinedas

(17)

where the integration variable is the distance between thetwo pinholes and the complex coherence variable is defined as

for

for (18)

where is the mean and is the standard deviation of the fittedGaussian.


TABLE IITABULATED VALUES OF THE EXPERIMENTALLY DETERMINED AND PREDICTED COMPLEX COHERENCE LENGTH (L ) VERSUS ENERGY FOR BEAMLINE 12.0.2.

PREDICTED VALUES WERE CALCULATED USING (16) AND (17). DIFFERENCE IN EXPERIMENTAL AND PREDICTED VALUES CAN BE ATTRIBUTED

TO COMPLICATIONS OF BEAMLINE OPTICS

The coherence lengths determined from the curves givenin Figs. 8–10 are summarized in Table II. These values aregreater than what is predicted based on the simple model of(16). This model assumes a perfect single optic and neglectsthe aberrations present in the beamline. Coming out of theundulator, the beam has dimensions of 260 16 m rms [10].With 14 demagnification, this would correspond with a beamat the focal plane of 44 2.7 m (FWHM). As shown in Fig. 5,the FWHM of the experimental focal spot is 60 9.4 m. Thissuggests the presence of modest aberrations in the beamlineK–B optics, more so in the vertical direction. As such, as thefocal spot size increases due to aberrations, the coherencelength also increases [28]. The model of (16) also assumesincoherent illumination of the focusing mirror. However, thesmall vertical size and divergence of the electron beam emittedfrom the undulator actually result in partially coherent illumi-nation of the optics, especially in this vertical direction. Thispartial coherence will result in an increased spatial coherence[28]. Lastly, the beamline monochromator affects the expectedspatial coherence. By using the monochromator to limit thebandwidth of the radiation, the upstream angular aperture isunderfilled, effectively reducing in (16). The exit slits alsoact as an additional vertical spatial filter which induces greaterspatial coherence.

V. CONCLUSION

This paper reported the successful use of pinhole spatial fil-tering techniques on third harmonic undulator radiation to getbroadly tunable coherent radiation in the soft X-ray region. Aspatially coherent power of 1.41 W was measured at an elec-tron energy of 500 eV. Spatial coherence at 500, 600, 700, and800 eV was experimentally determined with a transverse coher-ence length in the image plane of several microns, as expected.

ACKNOWLEDGMENT

The authors would like to thank E. Gullikson for the designand alignment of beamline 12.0.2. They would also like to thankB. Harteneck, A. Liddle, and E. Anderson for the fabrication ofhigh-quality pinholes. Lastly, the authors would like to thankP. Denham, D. Kemp, S. Rekawa, and the entire CXRO engi-neering team for all of their help at beamline 12.0.2.

REFERENCES

[1] H. Daido, “Review of soft X-ray laser researches and developments,”Rep. Progress Phys., vol. 65, no. 10, pp. 1513–1576, Oct. 2002.

[2] G. J. Tallents, “Experiments and simulations of short pulse laser pumpedextreme ultraviolet lasers,” IEEE J. Select. Topics Quantum Electron.,vol. 10, Nov. 2004.

[3] J. J. Rocca, “Table-top soft X-ray lasers,” Rev. Scientific Instrum., vol.70, no. 10, pp. 3799–3827, Oct. 1999.

[4] E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I.P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane,and H. C. Kapteyn, “Coherent soft X-ray generation in the water windowwith quasiphase matching,” Science, vol. 302, no. 5642, pp. 95–98, Oct.2003.

[5] E. Seres, J. Seres, F. Krausz, and C. Spielmann, “Generation of coherentsoft-X-ray radiation extending far beyond the titanium L edge,” Phys.Rev. Lett., vol. 92, no. 16, pp. 163 002/1–163 002/3, Apr. 2004.

[6] V. Ayvazyan et al., “Generation of GW radiation pulses from a VUVfree-electron laser operating in the femtosecond regime,” Phys. Rev.Lett., vol. 88, no. 10, pp. 104 802/1–104 802/4, Mar. 2002.

[7] C. Pellegrini and S. Reiche, “The development of X-ray free-electronlasers,” IEEE J. Select. Topics Quantum Electron., vol. 10, Nov. 2004.

[8] D. Attwood, K. Halbach, and K.-J. Kim, “Tunable coherent X-rays,”Science, vol. 228, no. 4705, pp. 1265–1272, June 1985.

[9] D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Be-guiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki,and J. H. Underwood, “Tunable coherent radiation in the soft X-ray andextreme ultraviolet spectral regions,” IEEE J. Quantum Electron., vol.35, pp. 709–720, May 1999.

[10] D. T. Attwood, Soft X-rays and Extreme Ultraviolet Radiation. Cam-bridge, U.K.: Cambridge Univ. Press, 1999, ch. 5.

[11] A. Hofmann, The Physics of Synchrotron Radiation. Cambridge, U.K.:Cambridge Univ. Press, 2004.

[12] K.-J. Kim, “Characteristics of synchrotron radiation,” in Physics Parti-cale Accelerators, AIP Conf. Proc. 184 (Amer. Inst. Physics, New York,1989), M. Month and M. Dienes, Eds., pp. 565–632.

[13] P. Kirkpatrick and A. V. Baez, “Formation of optical images by X-rays,”J. Opt. Soc. Amer., vol. 38, no. 9, pp. 766–774, Sept. 1948.

[14] http://www.cxro.lbl.gov/optical_constants/asf.html [Online][15] E. Gullikson, private communication.[16] F. Scholze, H. Henneken, P. Kuschnerus, H. Rabus, M. Richter, and

G. Ulm, “Determination of the electron-hole pair creation energy forsemiconductors from the spectral responsivity of photodiodes,” NuclearInstrum. Methods Phys. Res. Section A—Accelerators SpectrometersDetectors Associated Equipment, vol. 439, no. 2–3, pp. 208–215,Jan. 2000.

[17] J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1996, pp. 77–78.

[18] M. Born and E. Wolf, Principles of Optics. Cambridge, U.K.: Cam-bridge Univ. Press, 2002, pp. 439–443.

[19] B. J. Thompson and E. Wolf, “Two-beam interference with partiallycoherent light,” J. Opt. Soc. Amer., vol. 47, no. 10, pp. 895–902,Oct. 1957.

[20] T. Young, Course of Lectures Natural Philosophy Mechanical Arts I.[21] C. Chang, P. Naulleau, E. Anderson, and D. Attwood, “Spatial coherence

characterization of undulator radiation,” Opt. Commun., vol. 182, no.1–3, pp. 25–34, Aug. 2000.

[22] R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y.Liu, and D. T. Attwood, “Absolute determination of the wavelength andspectrum of an extreme-ultraviolet beam by a Young’s double-slit mea-surement,” Opt. Lett., vol. 27, no. 9, pp. 707–709, May 2002.

[23] T. Ditmire, J. Tisch, E. T. Gumbrell, R. A. Smith, D. D. Meyerhofer, andM. H. R. Hutchinson, “Spatial coherence of short wavelength high-orderharmonics,” Appl. Phys. B—Lasers Opt., vol. B65, no. 3, pp. 313–328,Sept. 1997.


[24] Y. Takayama, T. Hatano, T. Miyahara, and W. Okamoto, “Relationshipbetween spatial coherence of synchrotron radiation and emittance,” J.Synchrotron Radiation, pt. 4, vol. 5, pp. 1187–1194, July 1998.

[25] R. Coisson, “Spatial coherence of synchrotron radiation,” Appl. Optics,vol. 34, no. 5, pp. 904–908, Feb. 1995.

[26] J. W. Goodman, Statistical Optics. New York: Wiley, 2000, pp.163–176.

[27] L. Mandel, “Fluctuations of photon beam: The distribution of the photo-electrons,” in Proc. Physical Soc. London, vol. 74, 1959, pp. 233–243.

[28] C. Chang, P. Naulleau, and D. Attwood, “Analysis of illumination co-herence properties in small-source systems such as synchrotrons,” Appl.Opt., vol. 42, no. 14, pp. 2506–2512, May 2003.

Kristine M. Rosfjord received the B.E. degree inelectrical engineering from the Georgia Institute ofTechnology, Atlanta, in 1999, and the M.S. and Ph.D.degrees in electrical engineering and computer sci-ence from the University of California, Berkeley, in2001 and 2004, respectively.

Yanwei Liu received the B.S. degree in physics fromWuhan University, Hubei, China, in 1993, the M.S.degree in optics from the Institute of Physics, ChineseAcademy of Sciences, Beijing, China, in 1996, andthe Ph.D. degree in applied science and technologyfrom the University of California, Berkeley, in 2003.His Ph.D. research concentrated on coherence prop-erties of extreme ultraviolet (EUV) and soft X-raysources.

He now works at the Center for X-Ray Optics atLawrence Berkeley National Laboratory, Berkeley,

CA, developing novel mask inspection and imaging tools for use in EUVlithography.

David T. Attwood received the B.S. degree in engi-neering science from Hofstra University, Hempstead,NY, in 1963, the M.S. degree from Northwestern Uni-versity, Evanston, IL, in 1965, and the Ph.D. degree inapplied physics at New York University, New York,in 1972.

He worked in the Laser Fusion Program atLawrence Livermore Laboratory from 1972 to 1983.He founded the Center for X-Ray Optics at LawrenceBerkeley National Laboratory in 1983, was a Sci-entific Director of the Advanced Light Source from

1985 to 1988, was Co-director of the EUV Virtual National Laboratory from1997 to the present time. He joined the faculty of the University of California,Berkeley, in 1986 where he Co-founded the Applied Science and TechnologyPh.D. program, and he joined the Electrical Engineering and Computer ScienceDepartment in 1993.

Documents

Tunable coherent soft X-rays