I I,

Measurement of the efficiency of gold transmission gratings in the 100 to 5000 eVphoton energy range.

L. E. Ruggles+, M. E. Cuneo, J. L. Porter, D. F. Wenger, and W. W. SimpsonSandia National Laboratories*, Albuquerque, NM 87185-1673

Three x-ray spectrometers, each with a transmission grating dispersion element, areroutinely used at the Z soft x-ray facility to measure the spectrum and temporal history ofthe absolute soft x-ray power emitted from z-pinch and hohlraum radiation sources, Ourgoal is to make these measurements within an accuracy of Al O%. We periodically “wcharacterize the efficiency of the gratings used in the spectrometers by using an electron- Q3m

QC3impact soft x-ray source, a monochromator, grazing-incidence mirrors, thin filters, and an ~x-ray CCD detector. We measure the transmission efficiency of the gratings at many am

c?~~photon energies for several grating orders. For each grating, we calculate efficiency as a=+s~function of photon energy using published optical constants of gold and multiple-slit _ ~

Fraunhofer diffraction theory and fit the calculation to the measurements using the ephysical parameters of the grating as variables. This article describes the measurementapparatus and calibration techniques, dkcusses the grating efficiency calculation andfitting procedure, and presents recent results.

I*Sandia is a multi-program laboratory operated by Sandia Corporation, a LockheedMartin Company, for the U. S. Department of Energy under Contract No. DE-AC04-94AL85000.~leruggl@sandia.gov

I. Introduction.

The absolute intensity and temporal history of x-ray emission from z-pinches andhohlraum wall surfaces is of great importance for many experiments on the Z, and thisimportance has lead to the design, construction, calibration, and routine use of threetransmission grating spectrometers (TGS) at this facility. Each of these instruments usesa gold transmission grating to disperse the x-ray spectrum onto an array of sixteensubnariosecond-response silicon photodiodes and onto a gated microchannel-plate-intensified x-ray detector. Our goal is to measure the absolute soft x-ray power with thetransmission grating spectrometers to within an accuracy of HO%.

The measurement of soft x-ray power with a transmission grating spectrometerrequires at Ieast a knowledge of-the source size, the transmission grating efficiency, andthe silicon photodiode sensitivity. Assuming that these three elements are the majorsources of and contribute equally to the total uncertain of the the power measurement,each element must be contribute an uncertainty of less than &6%. In pursuit of this ratherambitious goal, we have developed the capability of measuring the efficiency of thetransmission gratings used in these instruments. The high level of accuracy desired hasyet to be realized and will take some effort to achieve.

DISCLAIMER

This report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.

DISCLAIMER

Portions of this document may be illegiblein electronic image products. Images areproduced from the bestdocument.

available original

The development of this capability is also motivated by a need for rapidaccomplishment of the transmission grating calibrations. Experiments using the TGSS onthe Z are frequent, and the periods of time for which the gratings are available are shortand infrequent, so we deveIoped the capability to perform the testing here at Sandia sothat it could be done quickly. The possibility of damage to the gratings in the Zenvironment is also a concern, and frequent checks of the gratings are needed to assurecorrect x-ray power and energy measurements.

II. Apparatus and Measurement Techdques.

The x-ray source used for these measurements is a multiple-anode Mansonsource, available from Austin Instrumentss. One of six anodes can be selected withoutbreaking open the vacuum system, and the source produces reasonable flux (-1010photons/sec-sr) for most of the common& and La sources between 100 eV and 6000 eV.The source size is -100 p.min diameter for an -100 pa electron beam at 5000 eV to 8000eV. The source flux from a clean metal anode is very stable for long periods if thevacuum is good,( 10-7Torr) and the electron beam current is low (-100 pa). Thebremsstralung spectrum produced by the electron beam has an endpoint at the anode biasvoltage and is a source of spectral contamination. We approach the problem ofproducing a monochromatic source from this spectrum containing bright emission linesand a bremsstrahlung continuum with three different methods that depend upon thephoton energy desired for calibration.

The majority of the calibration points (500 eV to 1750 eV) are obtained with aHettrick Scientific SNR monochromator7. With the -100 pm diameter x-ray sourcepositioned at the entrance slit location, an 8-meter radius spherical grating is rotatedabout its surface normal to vary the grating’s apparent groove density and to select thephoton energy of interest. Abeam of photons exits the instrument through a 100 ~ slit.The transmission grating is placed 134 mm beyond the exit slit with its’ dispersionperpendicular to the SNR dispersion, and an x-ray detector (described later) is placed 205mm beyond the transmission grating to record the x-ray spectrum. A 1 pm thickberyllium filter is placed at the SNR monochromator exit slit to block any visible lightthat may be present. The sources used with this instrument are listed in Table 1, and arecorded spectrum from a Cu La source is shown in Figure 1.

VLa 511.3eV Co La 776.2 eV Ge La 1188.0 eVCr L. 572.8 eV Ni La 851.5 eV Mg & 1253.6 eVMn La 637.4 eV Cu La 929.7 eV Al Km 1486.5 eVFe La 705.0 eV ZnLa 1011,7 eV Si & 1939.7 eV

Table 1. emission lines for SNR calibration method

A combination of grazing incidence mirrors and thin filters is used for the photonenergy range between 100 eV and 300 eV. The mirror trap7 consists of a set of fourmirrors with the first mirror 150 mm from the Manson source anode. The mirrors in each

mirror trap are mounted at the same angle of grazing incidence so that the beam entersand exits the trap on the same axis. The transmission grating is placed 486.9 mm fromthe source anode with its dispersion perpendicular to the mirror reflection plane, andthex-ray detector is placed 142.9 mm beyond the transmission grating. The sources, filters,and mirror sets used are listed in table 2, and the calculated throughput of each filter-@or combination is shown in Figure 2. This method is used for sources with singlebright emission lines in the high-throughput energy band of the mirror trap and thin filter.The carbon & and oxygen& emission lines are usually present regardless of anodematerial and must be blocked by the filter or absorbed by the mirrors.

emission line mirror set m.Be& 108.5 eV Rh at 10° lpm BeB & 183.3 eV Rh at 4° lpm B + 1 pm parylene-N + O.:C & 277 eV Rh at 4“ 1 pm parylene-N + 0.1 prn Al

Table 2. emission lines for mirrors and filter calibration method

pmAl

Thick filters are used for photon energies from 2200 eV to 5500 eV. The filtermaterial, filter thickness and anode voltage are chosen to produce a narrow energybandpass at the emission line. The filters are 135 mm from the source, the transmissiongrating is 239.2 mm from the source, and the x-ray detector is 825.6 mm beyond thetransmission grating. The sources we have developed for calibration by this method arelisted in Table 3, and the transmission of the filters is shown in figures 3a and 3b.

emission line ~ anode biasNbLa 2164eV 7.5 pm Zr 5000 vMo La 2292 eV 9pm Nb 5000 vV K. 4949 eV 51 pmTi 7000 vCr ~ 5410 eV 43pmv 7000 v

Table 3. emission lines for thick filter calibration method

The x-ray detector used for these measurements is a back-illuminated, back-thinned CCD purchased from Roper Scientific ‘. The chip is a SITE 1024x 1024 pixel-25 nun square device, cooled to 40”C. The detector has a sensitivity of -.025 counts pereV over the photon energy range of interest, has a thermal noise of.4 count per pixel persecond, a read noise of -145 counts, and saturates at 216counts/pixel. Thesecharacteristics allow long integration times for small signals. The detector has a fewblemishes (areas of below average sensitivity) that appear at the lower photon energies,bit the data reduction techniques described later minimize their effect.

The bremsstrahlung produced by the electron impact source is a source of spectralcontamination that must be reduced or eliminated for all three calibration methods. Forthe SNR monochromator, bremsstrahlung at the first monochromator grating order isn’t aproblem. The second and higher monochromator grating orders are not diffracted atphoton energies near the upper end of the monochromators energy range because of a

decrease in reflectivity of the gold grating at higher photon energies (incident grazingangle = 2.80). At photon energies approaching the lower end of the monochromatorsenergy range the source can be operated at a lowered anode voltage to reduce thebremsstralung endpoint to a lower photon energy, eliminating most of the second andthird order contamination. The reduced anode voltage is accompanied by a decrease insource flux. This source flux reduction, combined with a decreased monochromator fiistorder efilciency at lower energies, limits the practical range of the SNR calibrationmethod to photon energies above 500 eV (V L~. Determination of the usefulness of themonochromators output beam is made by examining the spectrum dispersed by thetransmission grating for the presence of higher monochromator orders. A spectrum froma vanadium anode with an unacceptable amount of higher order contamination is shownin figure 4.

The low energy calibrations performed with the mirror-filter combination arefreed from bremsstrahlung by a thin filter and the sharp mirror cutoff just above theemission lines of interest. A careful choice of mirror angle, mirror coating, and filtermaterial can produce a nmow energy bandpass at the emission line and effectively ~remove most of the bremsstralung. The photon energy bandpass of this system is wideenough to pass some bremsstrahlung, however, resulting in an increase in the photonenergy uncertainty. A recorded spectrum from a boron anode is shown in Figure 5.

The high energy calibrations with thick filters are done with the bremsstralungendpoint at a photon energy below the high energy transmission window of the filter.The response of the filters used for the high photon energy calibrations is shown inFigure 6.

The method used for calibration is one of comparison. The CCD is exposed to thex-ray source to determine the input flux (beam) and then the transmission grating isinserted and the CCD is exposed to the dispersed spectrum. A region of the dispersedspectrum image on the CCD is chosen that includes the spectrum and the image isintegrated perpendicular to the dispersion into a one-dimensional array ofcounts/pixel/second vs. pixel. The same region of the beam image is also integratedperpendicular to the dispersion into a one-dimensional array of counts/pixel/second vs.pixel. Since the source is monoenergetic, the absolute CCD sensitivity is not important,but the relative sensitivity distribution across the CCD must be known within the errorrequired of the calibration. We have flat fielded this detector at low (108 ev) and high(1486 eV) photon energies and found the statistical uncertainty in sensitivity to be lessthan &15%. Our technique of integrating a fifty-to-two-hundred-pixel-wide spectruminto a one pixel wide array reduces this uncertainty to ~5Yo. Randomly noisy pixels atthe wrong location can cause much larger errors and must be recognized and discarded.

A point~source projection technique is used to determine the flux incident uponthe transmission grating slit. The measured flux at the CCD is projected from the CCD tothe grating location toward a point at the source location by dividing the transmissiongrating slit width (60 to 100 pm) by the projected width of a CCD pixel (24 pm). Theprojected slit width is usually a few pixels. The beam array is integrated in the dispersiondirection in the zero order region of the dispersed spectrum image (the zero order line isusually 10 to 20 pixels wide) to obtain the counts/second incident upon the transmissiongrating slit. The transmission grating slit is assumed to be its’ nominal width and thatassumption is also used in the TGS data unfoldlO.

“

The dispersed spectrum array is integrated over the full width of each spectral lineto obtain the counts/second for each order. The efficiency is then obtained by simplydividing the count rate for each order by the beam count rate incident upon the slit.

This data reduction technique is valid if the source is small and distant, and thereare no scattering elements in the ,projection. However, scattering elements are present inthe SNR grating and the mirrors used for two of the above calibration arrangements, andthese elements produce a large uncertainty in the determination of the source flux in thereflection plane. The scattering elements produce diffuse secondary sources in thereflection plane that are very difficult to define. The scatter perpendicular to thereflection plane is small, and measurements of the transmission of a slit placed at thetransmission grating location and situated both perpendicular and parallel to the reflectionplane showed large uncertainties (&109io)in measured transmission of the slit whenparallel and small uncertainties (*1 %) when perpendicular. The scattering problem isdependent upon photon energy and surface figure, and difficult to quantify, so we situatethe transmission grating with its’ slit perpendicular to the SNR monochromatordispersion and the mirror reflection plane.

III, Efficiency Calculation and Fitting Procedure.

The conversion efficiency of a transmission grating bounded by an infinitely long slit hasbeen summarized by Eidmann et al.] using results from Schnopper et al? and theFraunhofer diffraction theory presented by Born and Wol~. Using Eidmann’s results, thegrating efficiency for the zero* and m* orders of diffraction is written as:

(m )~ _ sin(mn(a/d)) 2(1+ c; – 2C*C2),m— m#O,

~o=(:Y+(%Yc’+2:(1-3clc*$‘=0>

(1)

(2)

with the abbreviations c1= exp( - 2nnz~L) and C2= COS(27C(n, - l)z~l.). The grating barthickness is represented as Zo,and n = n, + ;nz is the complex refraction index of thegrating material in the soft x-ray region. The ratio of the gap between grating bars to thebar period is (a/d).The complex refraction index can be represented in terms of the complex atomicscattering factors4 f = fl + if2 by:

n2=(#)(&)f,,

(3)

(4)

where r. is the classical electron radius, p is the density of the grating material, and AWis the weight per atom of the grating material (atomic weight/N~. The complex atorriic

scattering factors f] and f2are available for the elements via the Lawrence BerkeleyLaboratory’s Center for X-ray Optics web site5. The fine structure present near edges inthe scattering factors carI be ignored for this application.

The efficiency of a transmission grating can be accurately calculated using theprevious relations by assuming the grating bars have a perfectly rectangular cross sectionand are regularly spaced, the source and detector ‘&eat an appropriate distance from thegrating, and the grating material is pure. These conditions are generally met except forthe grating bar profile and spacing, and the deviations from an ideal grating becomeevident when a grating is characterized. Irregular bar spacing manifests itself as scatteredenergy between the diffraction orders, asymmetric bar cross sections cause positive vs.negative order asymmetries, and the effects of nonrectangular bar cross sections areevident in the photon energy regions where the bars are partially transmissive. Eidmann,et al}, discuss these deviations from an ideal profile and use numerical methods toapproximate (&30Yo)their effects on grating efficiency.We have chosen to instead dismiss deviant gratings from use in the spectrometers if wecannot accurately calculate the first few orders (excluding the O*order) with the highaccuracy required to do a good unfold of the spectrometer datal”. Gratings with largeperturbations can be identified by optical microscope and SEM and are set aside.Gratings with less obvious problems’such as good periodicity but irregular bar profilescan be identified with a preliminary characterization at a few photon energies and anexamination of the dispersion, resolution, scatter between diffraction orders, and positiveVS.negative order symmetry.

Transmission gratings may be constructed on a thin continuous membrane, on asupporting mesh, or bothG,and the grating efficiency calculation must include thecharacteristics of these structures. We have included mass absorption coeftlcients forboth a mesh of variable open-area and thickness and a membrane of variable thickness inour fitting routine.A selected grating is calibrated by measuring as many orders as practical (usually zerothrough seven) at the photon energies available. The measured efficiencies are comparedto the calculated efficiencies for a nominal grating geometry and the differencesminimized by varying the grating parameters ~, (a/d), and the open area of the supportstructure. The fit is performed by an iterative examination of plots comparing measuredand calculated values and adjustment of the parameters effecting the regions of poor fit.The parameter (a/d) is varied to adjust high order ratios and magnitudes, the parameter Z.adjusts the shape of the efficiency curves in the region of bar transmission, The open arearatio affects the overall efficiency in all orders, and the thickness of the grid andmembrane affect the efficiency in the regions near edges and at high photon energies.

IV. Results.

One TGS is used primarily for measuring the z-pinch power and spectrum, andhas a higher photon energy range (250 eV to 2250 eV). This spectrometer has a gratingof the type manufactured by the Submicron Structures Laboratory at MIT and availablefrom X-OPT, Inc.11 The nominal grating characteristics area 200 nm period, 100 nmgap, and 400 nm thick gold structure mounted on a polyimide fii. A 63.5pm x 10 mmslit is mounted -250 ~ above the grating surface. The gratings FS 194 (Figure 7) and

FS268 (Figure 8) for this instrument have been calibrated for a number of photonenergies and the measurements and fitted response agree over most of the energy range.The fitted response of FS 194 is presently used for data unfolds of this spectrometer, andthe results are in good agreement with measurements of z-pinch power and energymeasured by other diagnostics lO.

The other two TGSS are generally used to measure hohlraum wall emission at 80to 150 eV, and the photon energy range for these spectrometers (100 eV to 900 eV) islower than the z-pinch TGS. The gratings used are manufactured by Heidenhain12, andhave a 500 nm period, 250 nm gap, and are 200 nm thick, free standing structures. Thegratings are mounted on a 70 pm x 2.5 mm slit. The gratings HD1 and HD4 used inthese instruments have also been calibrated at a number of photon energies, and themeasurements and fitted first order response is shown in Figure 9 (HD4) and Figure 10(HDl). The HD1 grating was also characterized at the NSLS U3C bearnline at13rookhaven National Laboratory, and the calibrations obtained there are included forcomparison without explanation.

The uncertainties in these calibrations appear to include the followingcontributions, which can be added in quadrature to estimate the probable error bars (seeFigs. 7 through 10). Most of the following numbers are estimates.

distance measurements and point source projection technique *5 yospectral contamination effects (lst order only) *5%CCD sensitivity, linearity, and counting statistics &loqo

grating uniformity along slit *5yofit of calculated efficiency to measured efficiency *5%beam and line integration technique, scattering, background subtraction *5%

total estimated uncertainty *15 %

The window of missing calibration sources between 277 eV and 511 eV is<omeconcern for the calibration of the gratings with a polyimide membrane, because thegrating efficiency in this spectral region depends greatly upon this membrane. Ourfuture work will include”efforts to include this energy range in our calibration capability.

References.

‘K. Eidmann, et al., Journal of X-Ray Science and Technology 2,259-273 (1990).‘H. W. Schnopper, et al., Applied Optics 16, 1088 (1977).3M. Born and E. Wolf, Principles of Optics, 6th cd., p. 401, Pergamon, New York, 1989.4B. Henke, et al., Atomic Data and Nuclear Data Tables 27, No. 1, p. 8 (1982).5CXR0 website, www.cxro-lbl.gov.‘M. L. Schattenburg, E. H. Anderson, and H. I. Smith, Ninth International Conference onVacuum Ultraviolet Radiation (VUV9) Proceedings, Univerity of Hawaii (1989).7Hettrick Scientific, Kensington, CA8Austin Instruments, www.austinst.com.‘Roper Scientific, Tucson AZ., www.roperscientific.com.%f. E. Cuneo, Wire Array Z-Pinch Source Power and Spectrum Characterization with a

Transmission Grating Spectrometer, these proceedings.llX-OPT, Inc., Gainesville, FL12Heidenhtin Gmbh, Traunreut, Deutschland

Figure captions.

Fig. 1. X-ray calibration spectrum using the SNR (Cu La to A8*order) measured withtransmission grating FS 194. Note the small Z“dand 3rdorder SNR peaks between the ls’and Otiorder transmission grating peaks.

Fig. 2. Mirror and filter throughput plot for the three low energy emission lines. (a) Be

& @) BKa(c)c Ku.

Fig. 3a. Thick filter transmission for zr (a) and Nb (b) filters. The bremsstrahlungendpoint should be below 3000 eV and 3500 eV for the Nb La and Mo La sources,respectively.

Fig. 3b. Thick falter transmission for Ti (a) and V (b) filters. The bremsstrahlungendpoint should be below 6500 eV and 7200 eV for the V Ka and Cr & sources,respectively.

Fig. 4. A contaminated SNR spectrum (V L~ with unacceptably large 2“dand 3d ordersfrom the SNR present.

Fig. 5. An x-ray calibration spectrum using the mirror trap and filters for B & There isno bremsstrahlung, C IQ, or O & between 1stand Ohorders with the anode bias at 8000volts.

Fig. 6. FS 194 ls’order efficiency vs. photon energy. This grating is presently in use onthe Z.

Fig. 7. FS268 ls’order efficiency vs. photon energy.

Fig. 8. HD4 ls’order efficiency vs. photon energy.

Fig. 9. HDl ls’order efficiency vs. photon energy. The squares are measurements fromNSLS and the circles are present results.

Tables.

Table 1. emission lines for SNR calibration method.Table 2. emission lines for mirrors and falter calibration method.Table 3. emission lines for thick filter calibration method.

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