Efﬁciency of a grazing-incidence off-plane grating in the

Efficiency of a grazing-incidence off-plane gratingin the soft-x-ray region

J. F. Seely, L. I. Goray, Benjawan Kjornrattanawanich, J. M. Laming, G. E. Holland,K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen

Efficiency measurements of a grazing-incidence diffraction grating in the off-plane mount were performedusing polarized synchrotron radiation. The grating had 5000 grooves�mm, an effective blaze angle of 14°,and was gold coated. The efficiencies in the two polarization orientations (TM and TE) were measured inthe 1.5–5.0 nm wavelength range and were compared with the efficiencies calculated using thePCGrate-SX code. The TM and TE efficiencies differ, offering the possibility of performing unique sciencestudies of astrophysical, solar, and laboratory sources by exploiting the polarization sensitivity of theoff-plane grating. © 2006 Optical Society of America

OCIS codes: 050.1950, 050.1960, 300.6560.

1. Introduction

To achieve the science objectives for planned astro-physical and other missions, high spectral resolutionand instrument sensitivity are required in the soft-x-ray wavelength range (1–20 nm). This can beachieved only by grazing-incidence diffraction grat-ings. Although the in-plane (classical) grating mounthas traditionally been considered for future missions,with the grating grooves perpendicular to the inci-dent beam, it has been suggested that the off-plane(conical) grating mount can provide superior perfor-mance. The choice of grating mount (in-plane oroff-plane) depends on the ability to reliably design,produce, and replicate optimized gratings with high

diffraction efficiencies. The accurate experimentalmeasurement of the efficiencies of test gratings andthe validation of efficiency simulation codes are es-sential to this process.

Compared with gratings in the classical in-planemount, gratings in the off-plane mount have thepotential for superior resolution and efficiency.1–5

Grazing-incidence off-plane gratings have been sug-gested for the Constellation-X mission.6

The absolute efficiencies in higher orders in graz-ing off-plane diffraction geometries may reach veryhigh values comparable to those obtained in the firstorder, which permits use of the high orders in theshortest-wavelength part of the operating range tothe maximum extent possible.7 In addition, efficiencycalculations indicate that off-plane gratings, whenproperly oriented, can provide polarization sensitivi-ty.7 The polarization measurements can provideunique information about astrophysical sources notpossible with existing instruments such as the XMM-Newton Reflection Grating Spectrometer and Chan-dra.

Off-plane grating efficiencies were first measuredby Werner8 using an electron-bombarded anode atfour discrete wavelengths in the 0.83–4.45 nm range.At the U.S. Naval Research Laboratory (NRL), Nevi-ere et al. measured off-plane and in-plane efficienciesin the 20–110 nm wavelength range.9

Off-plane grating measurements using an electron-bombarded x-ray source were carried out in associa-tion with a rocket spectrometer mission by Cash andco-workers5,10,11 More recently, measurements of testgratings were performed by McEntaffer et al.12,13

J. F. Seely ([email protected]) and J. M. Laming arewith the Space Science Division, U.S. Naval Research Laboratory,Washington, D.C. 20375. L. I. Goray is with the InternationalIntellectual Group, Incorporated, P.O. Box 335, Penfield, NewYork 14526. B. Kjornrattanawanich is with the Universities SpaceResearch Association, National Synchrotron Light Source, Beam-line X24C, Brookhaven National Laboratory, Upton, New York11973. G. E. Holland is with SFA Incorporated, 2200 DefenseHighway, Suite 405, Crofton, Maryland 21114. K. A. Flanagan,R. K. Heilmann, C.-H. Chang, and M. L. Schattenburg are with theKavli Institute for Astrophysics and Space Research, Massachu-setts Institute of Technology, Cambridge, Massachusetts 02139.A. P. Rasmussen is with the Columbia Astrophysical Laboratory,550 West 120th Street, New York, New York 10027.

Received 2 August 2005; revised 3 October 2005; accepted 6October 2005; posted 6 October 2005 (Doc. ID 63842).

0003-6935/06/081680-08$15.00/0© 2006 Optical Society of America

1680 APPLIED OPTICS � Vol. 45, No. 8 � 10 March 2006

in association with plans for the Constellation-Xmission.

Measurements of a test grating, fabricated on asilicon wafer at the MIT Space Nanotechnology Lab-oratory, were performed at four discrete wavelengthsin the 0.99–4.48 nm range.14 Measurements of sev-eral MIT test gratings were performed in off-planeand in-plane mounts using the Advanced LightSource synchrotron, in one polarization orientation,by Rasmussen et al.15

We report here the first detailed calibration of anoff-plane grating using polarized synchrotron radi-ation in the two polarization orientations (TM andTE). The measured efficiencies are compared withthe efficiencies calculated by the PCGrate-SX codein the two polarizations and using realistic grooveprofiles derived from atomic force microscope (AFM)measurements of the grating.

2. Conical Diffraction Pattern

The 5000 groove�mm master grating was fabricatedat the MIT Space Nanotechnology Laboratory. Thegrating pattern was recorded holographically in re-sist on a bias-cut silicon wafer, and the wafer wasanisotropically etched.14 Replica gratings were pro-duced by nanoimprint lithography and were coatedwith 5 nm of titanium and 20 nm of gold.16 Scanningelectron microscope images of the groove facets indi-cated a blazed groove profile and low microroughness.The design blaze angle was 7.5°, but as discussedbelow the efficiency measurements and the PCGrate-SX code calculations, using the groove profile derivedfrom AFM, indicate that the effective blaze angleafter coating was approximately 13°–15°.

The efficiency calibrations were performed at theNRL beamline X24C at the National SynchrotronLight Source. The beamline’s monochromator provideddispersed radiation to a large calibration chamber thatis a distance of 15 m from the monochromator and30 m from the synchrotron. The synchrotron radia-tion from the bending magnet is polarized with theelectric vector in the plane of the storage ring. TheX24C beamline optics, operating at grazing angles inthe x-ray and extreme-ultraviolet wavelength re-gions, preserve the polarization. Thus the beam de-livered to the calibration chamber has the electricvector primarily in the horizontal direction. Thebeam polarization measured in the 10–30 nm rangeis 80%–90%, and the polarization is expected to bethe same at shorter wavelengths.

The grating was mounted in the off-plane orienta-tion as shown schematically in Fig. 1. The gratingwafer was mounted by a three-point support on agoniometer platform with the grooves parallel to theincident radiation. The goniometer platform could berotated by computer control about two orthogonalaxes in the horizontal plane to precisely adjust theincidence angle (�), with respect to the normal to thegrating surface, and the azimuthal angle (�) aboutthe incident radiation beam. The goniometer wasmounted on a support plate with x and y motions toaccurately position the grating in the radiation beam.

The support plate could also be rotated in a yaw angleabout an axis perpendicular to the goniometer baseand at the center of the grating, thereby varying thealignment of the grooves with the incident radiationbeam. Finally, the support plate (and goniometer)could be rotated by 90° about the incident radiationbeam to the TE �� 0°� or TM �� 90°� polarizationorientations. Thus the grating had four rotationaland two translational degrees of freedom.

The conical diffraction pattern was recorded by aphosphor- �Gd2O2S:Eu-�coatedcomplementarymetal-oxide semiconductor (CMOS) imager with 50.8 mmsquare active area and 48 �m pixels. The CMOS im-ager was mounted on a support fixture with fourcomputer-controlled motions: x, y, rotation about thevertical axis, and pitch about the horizontal axis. Thelarge area of the CMOS imager provided the ability tocapture the entire conical diffraction pattern asshown in Fig. 2. The CMOS imager is controlled by aUSB interface to a notebook computer, and the expo-sure and image download times are typically 10 s.Thus one can quickly recognize the diffraction fea-tures and move to the desired grating angles andincident wavelengths in practically real time.

The imager is composed of two 50.8 mm �25.4 mm CMOS chips in close proximity. The fainthorizontal artifact at the center of the image in Fig. 2is the small gap between the two chips. The other twohorizontal artifacts are two rows of insensitive pixelsused for reading out the chips. These artifacts caneasily be removed in software (not done in Fig. 2) andin practice do not significantly obscure the diffractionfeatures. In addition, the artifacts are greatly re-duced, and the signal-to-noise ratio is increased,when the CMOS imager is cooled with liquid nitrogenvia a copper strap (the CMOS imager was not cooledfor this grating calibration).

While the grating motions are accurately cali-brated, we performed metrology on the conical dif-fraction pattern to confirm the expected changeswhen the grating is moved or the incident wavelengthis altered. This is illustrated by the small subimages

Fig. 1. Schematic of the off-plane grating and the conical diffrac-tion pattern.

10 March 2006 � Vol. 45, No. 8 � APPLIED OPTICS 1681

at the bottom of Fig. 2. From left to right, the foursubimages are of the visible light beam from themonochromator (the zero diffraction order of themonochromator gratings attenuated by a sapphirewindow) when the test grating was withdrawn fromthe beam, the 1.6 nm wavelength beam when thegrating was withdrawn and the 1.6 nm beam whenthe grating had been moved into the beam at twopositions separated by 211 �m in the direction per-pendicular to the beam. In practice, the visible lightbeam travels the same path as the dispersed beamand can be used to visually set up the grating andimager geometry before the calibration vacuumchamber is pumped. The shadow of the grating’s sil-icon wafer substrate is seen in the last two subimages�1.6 nm beam�, and the grating’s roll angle about thebeam is also apparent in the shadow.

In most cases, the grating angles were selected tocorrespond to an off-plane configuration proposedfor the Constellation-X mission. The grating waspositioned at a grazing angle of 1.73° (� � 88.27°) or2.00° (� � 88.00°) and the grating was yawed by anangle of 1.0°, so the blazed groove facets slightlyfaced the incident beam. Referring to the gratingequation for conical diffraction, sin � � sin �� m��d sin ,1,8,17,18 for a 1.73° grazing angle the

diffraction cone angle is � 2.0° and the incidenceangle with respect to the grating normal is �� 30.0°. The �1 order was closest to being on blazeand appeared near the top �� 0� of the diffractioncone as illustrated in Fig. 2. The on-blaze condition isthat the angles of incidence and diffraction from thegrating facets are equal (specular reflection), andthen � � � � 2 where ε is the blaze angle.

A 0.5 mm aperture defined the size and position ofthe beam that was incident on the grating. The ap-erture ensured that the beam illuminated a fixedarea on the grating. The 0.5 mm beam underfilled the5 cm grating grooved area at a typical grazing angleof 1.73°.

When measuring grating performance at a smallgrazing angle, the grating position and angular ori-entation, and the incident radiation beam positionand divergence, must be precisely controlled andmust be stable. In particular, when the radiationbeam is scanned in wavelength, the movement of thebeam on the grating and the detector must be smallrelative to the grating and the detector size. In ourcase, the size of the dispersed beam on the CMOSimager, positioned 80 cm from the grating and120 cm from the 0.5 mm aperture, was typically2 mm (42 pixels). Thus the dispersed beam’s half-angle divergence from the 0.5 mm aperture was0.036°. The beam movement in the CMOS imageswhen the incident wavelength was scanned by themonochromator was measured to be up to four pixels,corresponding to a 0.009° angular shift from the0.5 mm aperture. The pixel shift is small compared tothe pixel separation between the orders (160 pixels ata 1.6 nm wavelength and greater at longer wave-lengths). The pixel shift is predictable and could beremoved from the data. In any case, the stability ofthe beam, which is critically important for the cali-bration of grazing-incidence optics, was well withinthe beam divergence and was typically �3% of thediffraction spot separation. This permitted precisionmetrology of the conical diffraction pattern in theCMOS images.

By illuminating the test grating with the zeroorder of the monochromator gratings and insertingthin metal filters in the beam, it was possible toilluminate the test grating with broadband radia-tion. Figure 3 shows portions of CMOS images forthe case of two broad bands of radiation, providedby the monochromator’s filtered zero order, andthree discrete wavelengths (2.1, 3.0, and 5.0 nm)dispersed by the monochromator’s first order. Thelower wavelength limit of the two bandpasses�2 nm� was established by the selected monochroma-tor grazing angle (5.4°). The upper wavelength limitswere determined by the beam filtration. Numerousthin metal filters are mounted on two translationvacuum feedthroughs at the X24C beamline, and oneor two selected filters can be easily moved into thebeam. The 2–7 nm bandpass was established by a158 nm thick aluminum filter (the wavelengthstransmitted by the filter longer than the aluminum Ledge at 17 nm were dispersed beyond the field of view

Fig. 2. CMOS image of the conical diffraction pattern for a wave-length of 1.6 nm. Shown below the CMOS image are subimages ofthe visible light beam and the 1.6 nm beam. The two subimages ofthe shadow of the grating in the 1.6 nm beam, shown at the lowerright, illustrate how rapid feedback from the CMOS images can beused to establish grating alignment under x-ray illumination.


of the CMOS imager). The 2–4 nm bandpass wasestablished by a 200 nm thick nickel filter in combi-nation with the aluminum filter.

Figure 3 illustrates the ability to easily illuminatethe test grating with selected monochromatic radia-tion or bright broadband radiation. This simulatesthe two extreme cases when a spectrometer contain-ing the off-plane grating is illuminated by a radiationsource with primarily spectral line emission or con-tinuum emission. In addition, when illuminated bymonochromatic radiation at the X24C beamline, theabsence of continuum dispersed between the orderspermits the study of monochromatic radiation scat-tered from the grating facets. These are criticallyimportant measurements for the test gratings thatcan determine the ability to carry out the scienceobjectives of an astrophysical or solar mission.

3. Efficiency Measurements

Although the CMOS images provided snapshots ofthe entire conical diffraction pattern and could beused to derive the efficiencies, a more accurate tech-nique is to use absolutely calibrated silicon photo-diodes with a known linear response over manydecades and low noise. The photodiodes were of twotypes, AXUV-100 with a 10 mm � 10 mm active areaand AXUV-96 with a 6 mm � 16 mm area, both fromInternational Radiation Detectors Inc. Three photo-

diodes were mounted on the same support fixture asthe CMOS imager and could be moved into the radi-ation beam under computer control. The three pho-todiodes had the following apertures: 6.4 mm round(photodiode type AXUV-100), 9.6 mm round (AXUV-100), and 3 mm � 16 mm rectangular (AXUV-96). Onthe basis of the positions of the dispersed orders inthe CMOS image, a selected photodiode could be ac-curately moved to the dispersed orders for the mea-surement of the absolute intensity. An additionalphotodiode was mounted between the grating and the0.5 mm aperture for the purpose of measuring thedirect beam without having to move the grating fromthe beam. The beam underfilled all the photodiodeapertures, and the photodiodes were cross calibrated.

Since the zero-order beam diffracted from the testgrating does not move in angle when the incidentwavelength is scanned, it was possible to position aphotodiode in the zero order and scan the wavelengthin small steps �0.01 nm� while recording the photo-diode current at each step. Small wavelength stepsare necessary to observe polarization anomalies thatwere predicted (by PCGrate-SX calculations7) to oc-cur primarily in the TM orientation. The absolutezero-order efficiency was derived by dividing by thedirect beam current. The resulting zero-order effi-ciency is shown in Fig. 4, and no efficiency jumpsresulting from TM polarization anomalies were ob-served.

The 3 mm � 16 mm aperture was sufficiently tallto intercept a number of diffracted orders near the topof the diffraction cone when scanned horizontallyacross the diffraction pattern under computer con-trol. The efficiencies in the dispersed orders werenormalized by the zero-order absolute efficiency mea-sured by the silicon photodiode (Fig. 4). Shown inFig. 5 are the 0- and �1-order TM efficiencies whenthe wavelength was stepped from 3.0 to 5.1 nm in0.1 nm increments. The change in the horizontal po-

Fig. 3. CMOS images of the conical diffraction pattern for illu-mination by monochromatic radiation with wavelengths of 2.1, 3.0,and 5.0 nm and by broadband radiation of 2–4 and 2–7 nm.

Fig. 4. The measured zero-order TM efficiency for � � 88.00°.


sition of the �1 order is consistent with the gratingequation that predicts a horizontal change by m��d.1

Shown in Fig. 6 are the TM efficiencies of the0, �1, and �2 orders measured by positioning the6.4 mm apertured photodiode in the orders. Smallfeatures appear near the K edges of O �2.28 nm� andN �3.10 nm� resulting from slightly different thinfilms on the surfaces of the two photodiodes used forthe measurements (the SiO2 photodiode surfaces arenitrided for radiation hardness).

The efficiencies measured in the TE grating orien-tation, recorded prior to the TM measurements, arenot as complete as the TM data because prominentpolarization anomalies were not predicted to occur inthe TE orientation. In addition, the CMOS imager andthe photodiode detectors were positioned closer to thegrating during the TE measurements, and this af-

fected the quality of the short-wavelength ��3 nm�data where the diffracted orders were not well sepa-rated. However, the diffracted orders were well sep-arated at the longer wavelengths ��3 nm�, and themeasured TE efficiencies in the 0 and �1 orders areshown in Fig. 7 along with the TM efficiencies forcomparison. The efficiencies measured in the TE andTM orientation significantly differ, and this indicatesthat the grating has polarization sensitivity when inthe off-plane mount.

4. Efficiency Calculations

The measured TM and TE efficiencies were comparedwith the efficiencies calculated by the PCGrate-SXcode developed by Goray.7 For the case of normal-incidence gratings with opaque coatings (e.g., gold oraluminum) and multilayer interference coatings, thiscode has been validated by detailed comparisons withefficiencies measured using synchrotron radiation(Refs. 19 and 20 and references therein). PCGrate-SXwas recently used to design and fabricate the

Fig. 5. Detector scans through the 0 and �1 orders for 3.0–5.1 nmincident wavelengths and � � 88.00°.

Fig. 6. Measured TM efficiencies in the 0, 1, and 2 orders and for� � 88.00°.

Fig. 7. Measured zero- and first-order efficiencies in the (a) TEorientation with � � 88.00° and (b) TM orientation with � �88.27°.


multilayer-coated grating for the Extreme Ultravio-let Imaging Spectrometer for the Solar-B mission.20

Initial comparisons indicated that the efficienciescalculated assuming a 7.5° blaze angle, the valueexpected from the grating fabrication process, were infundamental disagreement with the measured effi-ciencies. This can be seen by calculating the on-blazewavelength: � � 2d sin sin , where the assumedblaze angle is � 7.5° and the grazing angle on thegrating facets is � 1.75° (differing slightly from thegrazing angle of 1.73° with respect to the gratingsurface). The calculated on-blaze wavelength is� � 1.6 nm, while the observed TM �1-order effi-ciency peaks at 3.3 nm (Fig. 6) implying a 15° blazeangle.

An AFM study of the grooved area confirmed thelarger than expected blaze angle. The AFM scansacross the grooves near the center of the grating areshown in Fig. 8(a), where each scan is displaced ver-tically by 1 nm for ease of viewing. The standard

deviation of the data points from the average scancurve is 0.89 nm and is a measure of the microrough-ness of the groove profile. The histogram of the anglesbetween each pair of scan points is shown in Fig. 8(b),where a Gaussian curve is fitted to the angle distri-bution. The top corners of the groove profiles arerounded, and this results in a rather broad distribu-tion of angles with a centroid value of 13°. The aver-age values of the blaze angles measured at sevenpoints distributed on the grooved area ranged from8.9° to 15°, and the microroughness values rangedfrom 0.66 to 0.92 nm. Thus there was considerablevariation of the grooves over the 5 cm patterned area.AFM data that were taken before the titanium andgold coating of the imprinted grating showed micro-roughness of approximately 0.2 nm (Ref. 16) andblaze angles of around 8°, which indicate that depo-sition of the metal films onto the polymer-based im-print resist led to the observed changes in grooveprofile.

PCGrate-SX calculations were initially performedusing a representative groove profile from the AFMimage shown in Fig. 8 and with 1.0 nm microrough-ness. The incident beam was assumed to be 80%polarized. The efficiencies calculated for the gratingin the TE and TM orientations are shown by the solidcurves in Fig. 9. A sharp spike (or jump) in efficiencyoccurs when the diffraction angle of an order, mea-sured from the grating normal, exceeds 90°. Thus, asthe wavelength increases, efficiency jumps in thelower orders occur when higher orders are diffracted

Fig. 8. (a) AFM scans across the grooves near the center of thegrating. (b) Histogram of the angles of pairs of points on the AFMscans giving a measure of the average blaze angle.

Fig. 9. Calculated (solid curves) and measured (dashed curves)efficiencies in the (a) TE and (b) TM grating orientations.


into the grating surface and become evanescent. Theefficiency jumps are deeper in the TM orientationwhere the electric vector of the diffracted wave isapproximately parallel to the surface of the grating(see Fig. 1 for � � 90°).

Shown by the dashed curves in Fig. 9 are the mea-sured efficiencies from Fig. 7. As seen in Fig. 9(a), thecalculated and measured TE efficiencies are in goodoverall agreement, except that the small anomalousjumps in efficiency were not observed. Large differ-ences between the calculated and measured TM effi-ciencies occur in Fig. 9(b), including the absence ofthe predicted large anomalous jumps in efficiency.The measurement of the TM zero-order efficiencywith small wavelength steps �0.01 nm� shown inFig. 4 conclusively indicates that efficiency jumps arenot observed. Other comparisons indicated that themeasured TM second order, and the measured ratioof the two-to-one orders, significantly disagree withthe calculations.

There are several possible explanations for the dis-agreements between the calculated and measured ef-ficiencies. First, the AFM images indicate that thegroove profile varies over the grooved area, and thecalculated efficiencies differ significantly when differ-ent groove profiles are assumed. Second, the incidentbeam is not purely �100%� polarized, and this some-what reduces the ability to observe strong polariza-tion effects in the TM orientation. Finally, themicroroughness along the grooves was not measuredby AFM scans along the grooves, and incorrect as-sumed microroughness may affect the calculated ef-ficiencies.

To illustrate the sensitivity of the calculated effi-ciencies to small changes in the assumed groove pro-file, Fig. 10 shows the TM efficiencies calculatedassuming a 36.2 nm groove depth (rather than the24.8 nm depth for the calculations shown in Fig. 9)and 0.5 nm microroughness. Efficiency jumps are ab-

sent, and the calculated efficiencies shown in Fig. 10are in qualitative agreement with the measured TMefficiencies shown in Fig. 6, although the absolutevalues of the calculated and measured efficienciesdiffer.

5. Discussion

The absolute efficiency of a 5000 groove�mm gratingin the off-plane mount was measured in the TM andTE orientations using polarized synchrotron radia-tion. The measured efficiencies were compared withthe efficiencies calculated using the PCGrate-SXcode. The efficiency jumps predicted by code calcula-tions were not observed, presumably because of thevariation of the groove profile over the area illumi-nated by the grazing-incidence radiation beam. Thecalculated and measured TE absolute efficiency val-ues were in good agreement, while significantdifferences occurred for the TM values. Further ex-perimental and computational studies are necessaryto identify the cause of the TM differences, includingmore detailed AFM characterizations of the shapeand microroughness of the groove profile across thegrating area. Also, the calculation model should beimproved to more accurately predict TM efficiencieswith anomalies.

For a given wavelength, the measured first-orderTE and TM efficiencies differ, and the off-plane grat-ing therefore has polarization sensitivity. This can beexploited to measure the polarization of radiationfrom astrophysical, solar, and laboratory sources inthe soft-x-ray region.

This work was supported by the U.S. Office ofNaval Research and by the National Aeronautics andSpace Administration. The National SynchrotronLight Source is operated by the U.S. Department ofEnergy.

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Fig. 10. Calculated TM efficiencies for an assumed groove profilewith a 36.2 nm depth and 0.5 nm microroughness.


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Efﬁciency of a grazing-incidence off-plane grating in the