Nave et al. Vol. 14, No. 5 /May 1997/J. Opt. Soc. Am. B 1035

Precision vacuum-ultraviolet wavelengths of Fe IImeasured by

Fourier-transform and grating spectrometry

Gillian Nave

National Institute of Standards and Technology, Gaithersburg, Maryland 20899

Sveneric Johansson

Department of Physics, University of Lund, Solvegatan 14, S-223 62 Lund, Sweden;Lund Observatory, University of Lund, Sweden

Anne P. Thorne

Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2BZ, UK

Received April 4, 1996; revised manuscript received November 6, 1996

We have measured the wavelengths of 236 Fe II lines between 150 and 200 nm, using Fourier-transform spec-trometry. These measurements have been combined with those of 237 lines from 92.7 to 150 nm in high-resolution grating spectra. Ritz wavelengths for all 473 lines have been determined from energy-level valuesderived from ultraviolet, visible, and infrared Fourier-transform spectrometry and are recommended as wave-length standards with an uncertainty ranging from 0.009 to 0.07 pm (0.005–0.02 cm21). Recent developmentsin calibrating the spectra from Ar II line standards are discussed. © 1997 Optical Society of America[S0740-3224(97)01905-X]

1. INTRODUCTIONHigh-resolution vacuum-ultraviolet (VUV) grating spec-trographs can now determine wavelengths with a preci-sion of better than 0.1 pm. However, accurate wave-length standards over the whole spectral region ofinterest are required if the wavelengths are to be put onan absolute scale. Although wavelength standards of therequired accuracy are available,1,2 their spectral coverageis relatively limited. One example of problems caused bythe inadequacy of current VUV wavelength standards isgiven by the Goddard High-Resolution Spectrograph onthe Hubble Space Telescope, which is calibrated with anon-board platinum lamp for which Ritz wavelengths weredetermined to ;0.05 pm at the National Institute ofStandards and Technology (NIST), Gaithersburg,Maryland.3 Although the accuracy of this wavelengthcalibration is sufficient for most purposes, it was foundthat, to utilize the full accuracy of the Goddard High-Resolution Spectrograph and to measure, for example,isotopic abundances of heavy elements, the calibrationshould be based on standard lines in the actual spectrumunder study.4 These standards can be generated by labo-ratory Fourier-transform (FT) spectrometry of astrophysi-cally abundant species like Fe II.Until recently, a short-wavelength limit of approxi-

mately 178 nm for FT spectrometry (FTS) was deter-mined by the quartz beam splitter of the FT spectrometer.The use of a MgF2 beam splitter in recent research at Im-perial College, London, has extended the wavelength cov-erage down to approximately 140 nm.5 The accuracy ob-

0740-3224/97/0501035-08$10.00 ©

tainable is ;0.005 cm21 (0.01 pm at 150 nm), which ismore than an order of magnitude better than is possiblewith a high-resolution grating spectrograph.In the wavelength region below 150 nm it is still neces-

sary to use grating spectra. However, the accuracy of thelines in both FT and grating spectra can be improved byreplacement of the measured wavelengths with Ritzwavelengths determined from energy levels measured inUV, visible, and IR FT spectra. With complex spectralike Fe II it is particularly important to use the highest-resolution spectra available to identify the lines. Thisminimizes the possibility of misidentifying a line or offailing to detect weaker, blended lines that may distortthe line profile and shift the wavelength away from theRitz wavelength.In this paper we present wavelengths of ;500 lines of

Fe II from 90 to 200 nm that have been observed in FTand grating spectra. The study is an extension of previ-ous papers in which Fe I and Fe II wavelengths in the vis-ible, UV, and IR regions were reported.6–8 Ritz wave-lengths for the observed lines have been determined fromenergy levels based on the same FT spectra used in theseprevious papers and from new FT spectra measured inthe VUV. All the measurements are now on the samerelative wave-number scale, and recent developments incalibrating this scale with Ar II lines are discussed.

2. SPECTRAThe spectra used in all the investigations were the sameas those used in our previous studies of the Fe I

1997 Optical Society of America

1036 J. Opt. Soc. Am. B/Vol. 14, No. 5 /May 1997 Nave et al.

spectrum.6–9 Three different spectrometers wereused: the f/60 IR–visible–UV FT spectrometer at theNational Solar Observatory, Tucson, Arizona, for the re-gion 2000–35 000 cm21 (5 mm–285 nm); the f/25 VUV FTspectrometer at Imperial College, for the region33 000–67 000 cm21 (300–150 nm); and the 10.7-mnormal-incidence grating spectrograph at NIST, for theregion 50 000–110 000 cm21 (200–90 nm). A MgF2 beamsplitter was used in the Imperial College spectrometer forthe region 55 000–67 000 cm21 (180–150 nm).5

The light source used for the FT spectra was a high-current hollow cathode of pure iron run in 100–500 Pa(0.8–4 Torr) of neon or argon with dc currents of 0.32–1 A.Neon generally gave the better signal-to-noise ratio forFe II. A similar source was used for recording the grat-ing spectra, with a pressure of approximately 130 Pa (1Torr) of neon or 30–40 Pa (0.2–0.3 Torr) of argon. How-ever, not all Fe II energy levels are excited by a continu-ous hollow-cathode discharge, and for this reason gratingspectra were also measured with a pulsed hollow-cathodedischarge. The peak currents used were 100 A, with apulse width of 70 ms, a frequency of 100 Hz, and a gaspressure of 30–40 Pa (0.2–0.3 Torr) argon or 130 Pa (1Torr) neon.The total number of FT spectra was 28, covering the

range 150 nm to 5 mm. The resolution of each spectrumwas chosen to provide roughly 3–4 points in each Dopplerwidth and ranged from 0.08 cm21 in the VUV, where thefull width at half-maximum is approximately 0.3 cm21, to0.01 cm21 in the IR, where the Doppler width is approxi-mately 0.03 cm21. Between 15 and 20 scans were coaddedfor each spectrum in the visible and the IR regions, with5–10 scans being coadded in the UV and the VUV re-gions.The wave number, intensity, and width for all the lines

in both FT and grating spectra were obtained withBrault’s DECOMP and GREMLIN programs.10 In the FTspectra a Voigt profile was fitted to the lines. In the grat-ing spectra many lines appeared slightly asymmetric orsaturated, and it was found that we obtained better wave-lengths of these lines by taking the peak of the line pro-file.The wave-number scale obtained from a FT spectrom-

eter is strictly linear and is set by the helium–neon sam-pling laser. Since the sampling laser beam does not fol-low exactly the same path in the interferometer as thesource beam, further calibration is necessary to obtain anabsolute wave-number scale. In principle, only one ref-erence line is required, but in practice several are neededfor reliable calibration. All the FT spectra used herewere calibrated from 26 Ar II lines in the visible,11 and thecalibration was extended to the VUV and the IR withbroadband overlapping spectra.6–8

The transfer of the calibration from the Ar II referencelines to the longest IR wavelengths near 5 mm and theshortest VUV wavelengths near 150 nm required five cali-bration steps in each case, with each step being measuredin at least two spectra. Further confirmation of the cali-bration was obtained by comparison of measured wave-lengths of strong lines in the VUV with Ritz wavelengthsdetermined from visible and IR spectra. Small discrep-ancies of the order of 0.002 cm21 were found between dif-

ferent calibration methods, particularly in extending thecalibration to the VUV region. These have been takeninto account in estimating the uncertainty of the calibra-tion.The wave-number accuracy for any line in the FT spec-

tra is determined by the uncertainty in the calibration, bythe statistical uncertainty of the measurement of the po-sition of the line, and by possible pressure and illumina-tion shifts. The statistical uncertainty for a fully re-solved, symmetric line can be shown to be given by thehalf-width at half-maximum divided by the signal-to-noise ratio.12 The uncertainty Ds in the wave-number(s) calibration includes a contribution of 0.0003 cm21

from the Ar II calibration lines and is further discussed inSection 5. The uncertainty in the calibration rangesfrom Ds 5 3 3 1028s in the visible spectra to approxi-mately Ds 5 1 3 1027s in the VUV spectra. Illumina-tion shifts may affect the wave numbers of our visible andIR spectra (s , 35 000 cm21), in which the hollow cath-ode was focused on the entrance aperture. They are es-timated to be less than 2 3 1028s (0.001 cm21 at35 000 cm21).6 The spectra at shorter wavelengths wereall taken without such focusing and should be immunefrom illumination shifts. The final uncertainty of astrong line (signal-to-noise ratio of .100) in any FT spec-trum ranges from 0.0005 cm21 in the IR to 0.005 cm21 inthe VUV.We have estimated the maximum likely pressure shifts

by comparing wave numbers of the same lines in twospectra taken with gas pressures of 50 Pa (0.4 Torr) and500 Pa (4 Torr) of neon. The spectra were calibratedwith low-excitation Fe I lines. The difference in wavenumbers between the high-pressure spectrum and thelow-pressure spectrum was approximately 20.001 cm21

for 3d64s–4p lines with an upper-level excitation energyof 60 000 cm21. For 3d64p–4d lines with an upper-levelexcitation energy of 110 000 cm21, the difference is ap-proximately 20.003 cm21. Since there are lines from lev-els of higher excitation that we could not compare, andsince we are unable to estimate possible pressure shifts inthe spectrum taken at lower pressure, we have assumed acontribution from pressure shifts to the uncertainty of0.005 cm21 at 100 000 cm21, or 5 3 1028s. We have notattempted to correct the wave numbers for a possiblepressure shift.The grating spectra were calibrated with Ritz wave-

lengths determined from the FT spectra, with particularcare being taken to avoid lines that were either saturatedon the photographic plate or significantly asymmetric.The uncertainty of an unblended, unsaturated line is 0.16pm; for saturated lines this rises to 0.5 pm. Near60 000 cm21, the crossover region with FTS, these uncer-tainties amount to 0.06 and 0.2 cm21, respectively.

3. ANALYSISAn initial identification of lines in the FT spectra wasmade with the energy levels reported by Johansson,13

which were obtained from grating spectra and interfero-metric measurements, and with roughly 400 new energylevels determined from the grating and the FT spectraused in the present study. Improved values for the older

Nave et al. Vol. 14, No. 5 /May 1997/J. Opt. Soc. Am. B 1037

levels were obtained from the FT spectra by means of theELCALC program.14 Each line was assigned a weight in-versely proportional to the square of the uncertainty, witha minimum uncertainty of 0.003 cm21 to allow for errorsin the calibration and for undetected blends. Lines thatwere doubly identified or for which the identification wassuspect were assigned a low weight. From theseweighted lines the ELCALC program uses an iterativemethod to calculate improved level values and to estimatethe uncertainty of each level.15 These improved levelvalues will be reported at a later date.Lines in the UV grating spectra were then identified

from the revised energy levels. VUV lines in both the FTand the grating spectra were selected as recommendedstandards. The lines chosen were all unblended lineswith reliable identifications—any line with more than oneidentification or with an identification that was suspectwas rejected. The benefits of high-resolution spectra areparticularly important in this step, as a small discrimina-tor can be used to reduce chance coincidences in matchingpredicted and experimental lines.Many of the odd-parity levels belonging to highly ex-

cited subconfigurations of 3d54s4p are not well popu-lated in the continuous hollow-cathode discharge. Withthe exception of a few levels that mix with the3d6(5D)5p subconfiguration, the only decay channels arein the VUV and do not appear in our FT spectra. Conse-quently, accurate Ritz wavelengths could not be derivedfor many lines between 101 and 109 nm, where the spec-trum is dominated by lines from these levels.

4. Fe II WAVELENGTHSThe recommended Fe II wavelengths are presented inTables 1 and 2 below. Classifications for many of thelines were reported by Johansson,13 and the remainderwill be reported at a later date. Above 150 nm good FTmeasurements were recorded, and Table 1 presents linesmeasured in these FT spectra. The observed signal-to-noise ratio is given in column 1 and is a rough indicationof the intensity of the line emitted from a continuousiron–neon hollow-cathode run in 300 Pa (4 Torr) neon at acurrent of 500 mA. The values have not been correctedfor the spectrometer response and are given solely to aidin identification. The second column gives the Ritz wavenumber calculated from the energy levels, with the corre-sponding Ritz wavelength in column 3. The fourth col-umn gives the fractional part of the experimentally ob-served wavelength. The experimental wavelengths havea much larger uncertainty than the Ritz wavelengths,and use of the latter is recommended in all cases.The uncertainty in the Ritz wavelength is given in col-

umn 5. It has been calculated from the root sum ofsquares of the uncertainties in the energy-level values (asderived from the ELCALC program) and of systematic ef-fects resulting from pressure and illumination shifts. Webelieve that the value of ds 5 1 3 1027s taken for theseshifts is a conservative upper limit.An illustration of the precision of the FT wavelengths is

given in Fig. 1, in which the difference between the ob-served and the Ritz wavelengths for all lines in Table 1 isplotted as a function of wavelength. The open circles

represent a subset of lines with a signal-to-noise ratio ofbetter than 100, and the two dotted lines mark the stan-dard deviation, dl 5 65 3 1028l, of the subset of linesused to calibrate the spectra. The standard deviation ofthe 19 lines with a signal-to-noise ratio of .100 is 0.017pm (0.006 cm21 at 60 000 cm21), similar to the uncertain-ties in the Ritz wavelengths in Table 1. The remainderof the lines are of lower signal-to-noise ratio, with morethan half of the lines having a signal-to-noise ratio of,20. These have a larger uncertainty, and the standarddeviation is 0.04 pm (0.014 cm21 at 60 000 cm21).Below 150 nm only grating measurements were avail-

able, and these are presented in Table 2. The intensitiesin column 1 are measurements of the photographic-plateblackening caused by a pulsed neon hollow cathode. Al-most all lines with an intensity value of .1200 are satu-rated on the photographic plate, and the correspondingmeasured wavelengths are consequently less accuratethan for unsaturated lines. The remaining columns inTable 2 are the same as corresponding columns inTable 1.The precision of the grating measurements is shown in

Fig. 2. Here the open circles represent the sharpest grat-ing lines, in which the intensity is between 200 and 1200(so the line is neither saturated nor too weak), and thewidth is less than 4 pm. The two dotted lines mark thestandard deviation of the sharpest grating lines of 0.16pm—a factor of 4 greater than the FT measurements.

5. DISCUSSIONThe uncertainties in the Ritz wavelengths presented inTables 1 and 2 range from 0.009 to 0.07 pm, correspond-ing to an uncertainty in wave number of0.005–0.02 cm21. However, all the wavelengths in thetable, and in the previous three papers on precision wave-lengths in the iron–neon hollow cathode,6–8 are depen-dent on the calibration of the FT data.This calibration ultimately depends on 26 Ar II lines in

the visible that were measured by Norlen11 with Fabry–Perot interferometry and a hollow-cathode lamp bymeans of krypton line standards; his uncertainty wasclaimed to be 0.0003 cm21. Recently, Whaling et al.16 re-measured these 26 Ar II lines by FTS, using hollow-cathode lamps similar to ours and molecular CO lines aswavelength standards. They concluded that Norlen’swave numbers were systematically lower than theirs by7 3 1028s, corresponding to 0.0014 cm21 at20 000 cm21, and that the difference could not be attrib-uted to the difference in pressure between the two dis-charges.The new Ar II measurements of Whaling et al.16 remain

to be confirmed, and in the interests of consistency wehave put our new measurements on the same absolutescale as the three previous papers on iron wavelengths,based on Norlen’s measurements. However, a shift of 73 1028s is of the same order as our estimated uncertain-ties and would result in an increase in our wave numbersof 0.007 cm21 at 100 000 cm21 (20.007 pm at 100 nm)and 0.0035 cm21 at 50 000 cm21 (20.014 pm at 200 nm).Experiments in different laboratories are currently underway to verify the new Ar II measurements.

1038 J. Opt. Soc. Am. B/Vol. 14, No. 5 /May 1997 Nave et al.

Table 1. Fe II Wavelengths Measuredin FT Spectra

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

42 50 128.7155 199.486460 .48643 0.03616 50 248.4403 199.011152 .01113 0.02614 50 333.6068 198.674417 .67438 0.02213 50 341.8696 198.641808 .64179 0.02872 50 368.7547 198.535780 .53579 0.02666 50 453.9212 198.200650 .20065 0.02277 50 593.3373 197.654484 .65452 0.02283 50 698.5591 197.244264 .24429 0.02268 50 710.8687 197.196385 .19638 0.02329 50 719.4497 197.163022 .16296 0.02211 50 752.8487 197.033275 .03327 0.05515 50 780.8013 196.924817 .92485 0.022105 50 961.1489 196.227915 .22791 0.02251 51 314.1945 194.877852 .87780 0.02214 51 324.6056 194.838321 .83838 0.03183 51 396.4367 194.566017 .56602 0.02119 51 437.1904 194.411863 .41191 0.02431 51 671.6740 193.529631 .52963 0.02228 51 746.9200 193.248217 .24823 0.031119 51 915.0167 192.622494 .62248 0.02258 51 921.4916 192.598473 .59848 0.02416 52 156.1312 191.732013 .73203 0.02310 52 337.5596 191.067373 .06733 0.033110 52 476.8035 190.560387 .56041 0.02036 52 499.2185 190.479026 .47902 0.02617 52 672.1483 189.853657 .85374 0.02882 52 742.2755 189.601224 .60124 0.02180 52 808.4547 189.363617 .36361 0.02231 52 876.2600 189.120789 .12080 0.0229 52 888.2149 189.078040 .07797 0.02126 52 931.0362 188.925075 .92511 0.02276 52 945.5068 188.873440 .87346 0.02429 52 960.8190 188.818832 .81881 0.02219 52 966.1693 188.799759 .79973 0.02376 52 985.6483 188.730351 .73032 0.0206 52 998.8415 188.683370 .68340 0.02287 53 015.0232 188.625778 .62579 0.02070 53 058.0089 188.472960 .47293 0.02118 53 072.9525 188.419892 .41990 0.02123 53 075.2236 188.411830 .41182 0.02214 53 152.4721 188.138004 .13798 0.02121 53 157.4658 188.120330 .12030 0.02129 53 163.9854 188.097260 .09726 0.025100 53 176.5380 188.052859 .05286 0.02013 53 195.6157 187.985417 .98540 0.03060 53 263.2857 187.746585 .74659 0.02548 53 281.0682 187.683925 .68391 0.02263 53 289.0362 187.655862 .65590 0.020267 53 400.4778 187.264242 .26423 0.023537 53 488.6746 186.955464 .95546 0.021237 53 534.8525 189.794201 .79419 0.023184 53 554.4386 186.725886 .72589 0.0236 53 733.6455 186.103137 .10329 0.02062 53 761.9103 186.005295 .00529 0.02117 53 770.7471 185.974727 .97474 0.020112 53 822.4646 185.796025 .79601 0.027363 53 870.0104 185.632041 .63203 0.023136 53 918.1796 185.466202 .46620 0.02437 53 956.1325 185.335745 .33573 0.020115 54 072.0803 184.938326 .93828 0.028

(Table continued)

Table 1. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

49 54 105.5014 184.824089 .82406 0.02516 54 154.2861 184.657591 .65761 0.023188 54 163.3144 184.626811 .62680 0.0238 54 210.2169 184.467072 .46709 0.020

129 54 220.8025 184.431059 .43106 0.02299 54 235.4026 184.381410 .38140 0.02012 54 242.9884 184.355624 .35559 0.02152 54 244.9841 184.348842 .34885 0.02072 54 263.8179 184.284858 .28484 0.021104 54 347.8091 184.000058 .00007 0.02033 54 358.2687 183.964652 .96465 0.02847 54 360.7924 183.956112 .95610 0.02336 54 363.7184 183.946211 .94617 0.02714 54 469.9659 183.587411 .58740 0.020189 54 496.9573 183.496483 .49647 0.02013 54 577.6083 183.225325 .22536 0.02196 54 585.7161 183.198110 .19810 0.02014 54 595.2976 183.165958 .16595 0.0209 54 623.3931 183.071747 .07183 0.02071 54 630.9789 183.046326 .04632 0.021274 54 636.9235 183.026411 .02640 0.0244 54 828.4636 182.387018 .38711 0.0268 54 989.7227 181.852163 .85203 0.0194 55 083.9388 181.541121 .54117 0.0236 55 269.4341 180.931833 .93169 0.02613 55 387.4998 180.546153 .54618 0.0195 55 427.2854 180.416557 .41659 0.01912 55 520.7500 180.112841 .11286 0.0208 55 530.0350 180.082725 .08271 0.0199 55 562.2062 179.978454 .97848 0.0205 55 566.7477 179.963745 .96372 0.01912 55 576.3292 179.932719 .93270 0.0195 55 612.5017 179.815683 .81566 0.02321 55 706.9755 179.510733 .51072 0.0197 55 748.4317 179.377243 .37725 0.0198 55 760.9642 179.336928 .33692 0.02724 55 934.3313 178.781077 .78108 0.01949 55 967.2869 178.675804 .67580 0.02512 56 007.4971 178.547525 .54759 0.02149 56 116.1957 178.201674 .20168 0.02214 56 131.2244 178.153962 .15399 0.0229 56 195.4402 177.950381 .95033 0.0199 56 285.3156 177.666233 .66631 0.0204 56 354.9810 177.446604 .44657 0.02012 56 417.0877 177.251262 .25124 0.02121 56 520.3709 176.927360 .92736 0.03055 57 322.2096 174.452452 .45245 0.01967 57 418.8505 174.158833 .15882 0.0197 57 563.3973 173.721505 .72148 0.02121 57 613.1530 173.571476 .57148 0.01919 57 654.6092 173.446670 .44667 0.0196 57 774.2858 173.087384 .08738 0.0709 57 789.6165 173.041467 .04147 0.0199 57 872.5113 172.793607 .79360 0.01823 57 892.7068 172.733330 .73333 0.0249 57 905.7490 172.694425 .69437 0.01929 57 924.2460 172.639278 .63927 0.01922 57 947.8528 172.568948 .56895 0.01827 57 957.7778 172.539396 .53940 0.019

(Table continued)

Nave et al. Vol. 14, No. 5 /May 1997/J. Opt. Soc. Am. B 1039

Table 1. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

6 58 017.5645 172.361596 .36167 0.01823 58 038.5133 172.299382 .29936 0.01819 58 048.5349 172.269636 .26963 0.0188 58 074.2251 172.193430 .19347 0.01812 58 111.8996 172.081795 .08180 0.01916 58 138.1880 172.003985 .00395 0.03132 58 162.2207 171.932912 .93290 0.0184 58 203.7520 171.810230 .81029 0.01913 58 291.5461 171.551463 .55152 0.02772 58 377.1012 171.300044 .30004 0.01917 58 526.6390 170.862366 .86237 0.0195 58 713.1535 170.319586 .31965 0.01810 58 792.3591 170.090130 .09021 0.0196 58 851.3480 169.919642 .91962 0.0208 58 922.7033 169.713870 .71383 0.01819 58 934.6408 169.679493 .67952 0.0194 58 946.2890 169.645964 .64586 0.0206 59 034.0658 169.393720 .39373 0.01920 59 040.2691 169.375922 .37591 0.0187 59 045.7527 169.360192 .36014 0.0183 59 050.1053 169.347708 .34778 0.0208 59 095.5335 169.217526 .21752 0.01914 59 127.0268 169.127395 .12738 0.01912 59 145.0463 169.075867 .07584 0.01911 59 177.4659 168.983241 .98319 0.0196 59 236.1672 168.815784 .81586 0.01814 59 295.9273 168.645647 .64566 0.01811 59 406.8658 168.330712 .33078 0.01816 59 439.8395 168.237332 .23732 0.0225 59 583.6788 167.831195 .83132 0.01728 59 756.2426 167.346533 .34652 0.0209 59 793.9052 167.241125 .24109 0.01811 59 829.1998 167.142466 .14250 0.0185 59 844.7229 167.099111 .09908 0.01833 59 916.1255 166.899978 .89999 0.01730 60 124.2289 166.322299 .32231 0.01812 60 142.3641 166.272147 .27210 0.0198 60 226.8874 166.038798 .03889 0.01844 60 259.7328 165.948296 .94829 0.01823 60 285.5219 165.877307 .87728 0.0198 60 426.3164 165.490809 .49080 0.01819 60 442.0049 165.447854 .44785 0.0185 60 550.8564 165.150430 .15036 0.01718 60 580.2181 165.070386 .07035 0.02635 60 638.6687 164.911272 .91129 0.0186 60 695.7359 164.756220 .75621 0.01816 60 710.4650 164.716248 .71626 0.01916 60 746.5300 164.618456 .61849 0.02636 60 842.8397 164.357878 .35788 0.01938 60 910.1273 164.176311 .17630 0.01940 61 072.4425 163.739972 .73998 0.018116 61 112.3128 163.633146 .63313 0.01967 61 147.1023 163.540047 .54003 0.01850 61 186.4238 163.434948 .43493 0.02026 61 202.9065 163.390933 .39093 0.0186 61 242.0930 163.286385 .28646 0.0178 61 249.4263 163.266835 .26692 0.01867 61 307.2429 163.112864 .11286 0.017

(Table continued)

Table 1. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

7 61 342.5596 163.018956 .01898 0.017143 61 381.3539 162.915924 .91592 0.0189 61 461.9925 162.702177 .70223 0.0178 61 466.8028 162.689444 .68937 0.01819 61 503.9354 162.591222 .59120 0.01833 61 518.6601 162.552305 .55230 0.017193 61 664.2501 162.168517 .16851 0.0185 61 722.6918 162.014969 .01500 0.0178 61 753.4219 161.934346 .93436 0.0176 61 835.7607 161.718719 .71871 0.01720 61 968.5269 161.372240 .37226 0.01844 62 003.7245 161.280634 .28063 0.01914 62 076.1997 161.092336 .09229 0.01739 62 478.4524 160.055181 .05518 0.0176 62 489.6442 160.026515 .02655 0.01729 62 631.4621 159.664163 .66416 0.01724 62 804.4808 159.224308 .22429 0.01811 62 848.7069 159.112263 .11222 0.0177 62 870.9613 159.055942 .05590 0.01816 62 960.7879 158.829016 .82905 0.0186 63 033.9425 158.644686 .64480 0.0208 63 038.4603 158.633316 .63338 0.01628 63 093.3723 158.495253 .49524 0.0179 63 171.9919 158.298000 .29796 0.01625 63 239.5207 158.128966 .12897 0.0178 63 320.9170 157.925698 .92572 0.01713 63 355.0492 157.840616 .84064 0.0189 63 370.9070 157.801118 .80109 0.0162 63 530.9593 157.403573 .40359 0.0196 63 539.3282 157.382841 .38280 0.01733 63 684.3274 157.024505 .02448 0.01814 63 707.4575 156.967495 .96753 0.01811 63 774.6770 156.802049 .80196 0.01830 63 823.4508 156.682221 .68222 0.0176 63 935.4059 156.407860 .40791 0.01751 63 947.1710 156.379084 .37906 0.0176 64 092.1702 156.025299 .02531 0.01754 64 140.1709 155.908534 .90852 0.01711 64 156.3433 155.869233 .86926 0.01810 64 162.5484 155.854159 .85417 0.01810 64 197.0865 155.770309 .77031 0.01917 64 297.6413 155.526700 .52670 0.01812 64 320.0838 155.472434 .47246 0.0214 64 356.5953 155.384230 .38425 0.01711 64 386.1882 155.312813 .31277 0.01715 64 405.7743 155.265582 .26557 0.01717 64 417.8686 155.236431 .23643 0.02046 64 532.9565 154.959583 .95957 0.0189 64 721.3461 154.508529 .50861 0.0176 65 251.7004 153.252711 .25271 0.0185 65 460.1837 152.764619 .76462 0.01614 65 491.6026 152.691331 .69127 0.0175 65 521.9679 152.620569 .62051 0.0164 65 617.2059 152.399052 .39912 0.0172 65 647.8222 152.327978 .32793 0.0163 65 720.8830 152.158637 .15858 0.0165 65 846.4356 151.868509 .86854 0.0165 67 623.7153 147.877116 .87721 0.0186 68 042.0301 146.967984 .96797 0.017

aRitz wave number calculated from the energy levels.bRitz wavelength calculated from the energy levels.cFractional part of experimental wavelength.dEstimated uncertainty of Ritz wavelength (1 pm 5 10 mÅ).

1040 J. Opt. Soc. Am. B/Vol. 14, No. 5 /May 1997 Nave et al.

Table 2. Fe II Wavelengths Measuredin Grating Spectra

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

1191 65 720.8830 152.158637 .15871 0.0161256 65 751.6131 152.087523 .08671 0.0161285 66 099.1046 151.287980 .28793 0.0191217 66 160.9679 151.146519 .14651 0.019892 66 308.3103 150.810659 .81058 0.0171400 66 361.3605 150.690099 .69023 0.018154 66 713.7464 149.894145 .89450 0.0231390 66 935.8088 149.396865 .39646 0.0181332 66 951.0405 149.362877 .36306 0.0191157 67 324.5515 148.534224 .53411 0.0191243 67 339.9890 148.500173 .49993 0.0191369 67 413.7535 148.337683 .33734 0.0211408 67 425.7377 148.311318 .31103 0.0241304 67 506.0134 148.134951 .13465 0.0201367 67 523.1664 148.097320 .09717 0.0161092 67 574.8792 147.983986 .98464 0.0161187 67 623.7153 147.877116 .87703 0.0181022 67 661.6407 147.794229 .79419 0.0161163 67 679.2726 147.755725 .75551 0.0191112 67 682.3366 147.749036 .74884 0.019174 67 731.2277 147.642385 .64250 0.0241230 67 773.5128 147.550268 .55023 0.0161290 67 850.2963 147.383292 .38250 0.0161118 67 860.5558 147.361009 .36088 0.0161053 67 946.4718 147.174676 .17523 0.0171192 68 055.8111 146.938224 .93800 0.0181070 68 061.6162 146.925691 .92565 0.0161228 68 091.3246 146.861587 .86081 0.015536 68 183.2747 146.663534 .66339 0.022973 68 186.7936 146.655965 .65590 0.0181252 68 257.5085 146.504029 .50336 0.0161172 68 406.9773 146.183919 .18382 0.019654 68 482.4750 146.022760 .02284 0.0151254 68 525.8454 145.930341 .93023 0.016379 68 643.5715 145.680066 .68018 0.015803 68 925.5624 145.084054 .08406 0.023250 69 051.5173 144.819410 .81951 0.0191213 69 095.4930 144.727240 .72718 0.017104 69 126.7691 144.661759 .66182 0.0211125 69 185.0998 144.539793 .53977 0.0181171 69 205.0684 144.498087 .49814 0.0231144 69 277.0323 144.347985 .34746 0.0181275 69 312.1862 144.274774 .27447 0.0221218 69 407.0650 144.077552 .07743 0.0161254 69 534.6119 143.813271 .81315 0.0201276 69 686.5710 143.499671 .49927 0.016975 69 738.9351 143.391923 .39196 0.0151198 69 921.8979 143.016713 .01641 0.017559 69 925.1694 143.010022 .01027 0.016273 70 160.1245 142.531104 .53121 0.0151205 70 319.5331 142.207998 .20870 0.0191123 70 364.1209 142.117884 .11777 0.0181074 70 429.1131 141.986738 .98676 0.0161242 70 479.4375 141.885355 .88517 0.0171106 70 548.3133 141.746833 .74670 0.0181214 70 585.8178 141.671519 .67208 0.016672 70 624.7800 141.593361 .59328 0.0181074 70 674.2542 141.494242 .49407 0.018

(Table continued)

Table 2. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

1181 71 677.3182 141.488108 .48797 0.0181261 70 736.3314 141.370068 .36936 0.017155 70 750.0831 141.342590 .34264 0.015639 70 908.3838 141.027047 .02702 0.019382 71 219.0210 140.411927 .41183 0.016744 71 426.9003 140.003275 .00312 0.0151292 71 553.0729 139.756402 .75658 0.0161137 71 560.0198 139.742834 .74233 0.015817 71 741.4750 139.389384 .38925 0.015728 71 752.3982 139.368164 .36795 0.015164 71 771.2578 139.331542 .33150 0.015362 71 841.6915 139.194941 .19498 0.014580 72 042.8728 138.806236 .80621 0.015966 72 178.4406 138.545526 .54542 0.0191008 72 484.1175 137.961258 .96084 0.015918 72 550.7888 137.834477 .83437 0.0321024 72 639.0534 137.666992 .66636 0.0201062 73 008.8755 136.969648 .96993 0.0141037 73 069.4681 136.856067 .85680 0.019924 73 072.9870 136.849476 .84963 0.016118 73 233.1458 136.550190 .55020 0.0171087 73 293.1707 136.438360 .43771 0.017775 73 392.4144 136.253863 .25368 0.017383 73 492.5514 136.068211 .06828 0.017866 73 676.6914 135.728136 .72811 0.015319 73 684.0213 135.714634 .71460 0.016328 73 737.1263 135.616893 .61683 0.0151033 73 938.1867 135.248110 .24876 0.015407 74 007.4259 135.121576 .12168 0.016298 74 315.6262 134.561202 .56113 0.016703 74 366.8694 134.468481 .46843 0.015876 75 069.0934 133.210614 .21086 0.0141237 75 928.5566 131.702754 .70284 0.029640 75 996.6413 131.584763 .58490 0.014956 76 387.8282 13.910909 .91109 0.014129 76 403.6641 130.883775 .88416 0.0141126 76 521.0833 130.682938 .68300 0.0141102 76 526.3304 130.673978 .67406 0.0291183 76 724.9523 130.335695 .33560 0.015196 76 923.4185 129.999423 .99953 0.0131139 77 034.8076 129.811449 .81146 0.0141168 77 143.3557 129.628792 .62879 0.0141285 77 155.3670 129.608612 .60799 0.014431 77 375.0131 129.240689 .24056 0.014922 77 573.7704 128.909552 .90953 0.0131199 78 179.9547 127.910026 .90974 0.0141201 78 291.6856 127.727484 .72754 0.014594 78 333.0222 127.660082 .66026 0.0151071 78 409.8951 127.534924 .53481 0.0141169 78 641.5525 127.159239 .15924 0.0131165 78 663.6591 127.123504 .12338 0.018232 78 676.7349 127.102377 .10223 0.019801 78 742.7285 126.995853 .99609 0.019996 78 751.0961 126.982360 .98234 0.0131026 78 780.1340 126.935555 .93558 0.0361305 78 946.5553 126.667971 .66750 0.0181215 79 011.3715 126.564060 .56407 0.020578 79 046.8474 126.507259 .50742 0.025761 79 132.3870 126.370509 .37064 0.024

(Table continued)

Nave et al. Vol. 14, No. 5 /May 1997/J. Opt. Soc. Am. B 1041

Table 2. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

431 79 173.1432 126.305457 .30575 0.019476 79 387.9100 125.963765 .96365 0.020986 79 834.0101 125.259898 .25989 0.014937 80 073.8050 124.884786 .88458 0.014214 81 503.9498 122.693440 .69349 0.014751 81 908.6643 122.087206 .08722 0.0131129 82 112.0318 121.784832 .78481 0.0131063 82 148.8840 121.730199 .73042 0.0141150 82 362.1026 121.415065 .41504 0.013856 82 367.7461 121.406746 .40683 0.013858 82 412.2595 121.341170 .34121 0.0131180 82 442.5468 121.296592 .29615 0.012750 82 537.8476 121.156540 .15661 0.0131162 82 557.8166 121.127234 .12717 0.014212 82 589.4009 121.080912 .08112 0.014215 82 593.8710 121.074359 .07451 0.013746 82 649.3936 120.993023 .99305 0.014937 82 683.4970 120.943119 .94304 0.012626 82 765.7241 120.822963 .82306 0.0131296 82 788.7980 120.789288 .78887 0.0131067 83 386.3424 119.923715 .92315 0.0181300 83 407.5431 119.893233 .89243 0.025764 83 426.4278 119.866094 .86599 0.016939 83 507.3579 119.749927 .74986 0.022826 83 565.1130 119.667163 .66714 0.018935 83 929.6364 119.147424 .14725 0.0141056 83 971.3602 119.088222 .08829 0.012726 84 117.2955 118.881616 .88166 0.014127 84 238.9373 118.709950 .70988 0.0131167 84 316.1544 118.601234 .60148 0.0131285 84 401.1686 118.481772 .48214 0.012841 84 528.5547 118.303218 .30328 0.0121038 84 609.9634 118.189390 .18937 0.015701 84 892.6434 117.795837 .79580 0.012888 84 918.5831 117.759855 .75982 0.013728 85 036.9326 117.595963 .59580 0.013879 85 191.1839 117.383038 .38269 0.0121201 85 602.1688 116.819470 .82010 0.012346 85 948.2262 116.349114 .34916 0.0121112 86 207.8124 115.998768 .99866 0.012862 86 243.7749 115.950398 .95014 0.0131210 86 318.4877 115.850037 .84973 0.012518 86 469.2861 115.648000 .64784 0.0121194 86 560.1869 115.526553 .52627 0.0121183 86 905.7589 115.067173 .06775 0.012533 86 966.8409 114.986355 .98636 0.0121174 87 140.6950 114.756946 .75656 0.0121217 87 232.2846 114.636457 .63613 0.012876 87 287.3352 114.564157 .56409 0.012530 87 356.1829 114.473866 .47393 0.013691 87 361.3312 114.467120 .46731 0.0121005 87 379.4492 114.443386 .44335 0.0121229 87 408.8126 114.404940 .40460 0.012750 87 529.7431 114.246879 .24640 0.012108 87 629.2000 114.117212 .11703 0.012111 87 637.2120 114.106779 .10673 0.012372 87 870.4818 113.803860 .80376 0.012277 87 930.7301 113.725884 .72587 0.012286 87 967.7270 113.678054 .67811 0.012957 88.082.2826 113.530210 53032 0.012

(Table continued)

Table 2. Continued

IsRitz

a

(cm21)lRitz

b

(nm)lexp

c

(nm)dld

(pm)

1235 88 229.7255 113.340486 .33999 0.012406 88 451.7603 113.055975 .05597 0.012534 88 513.9273 112.976571 .97655 0.0121225 88 581.8330 112.889965 .88980 0.012888 88 640.4188 112.815351 .81533 0.0121262 88 648.8911 112.804570 .80412 0.0121189 88 663.5088 112.785972 .78589 0.0121061 88 719.5015 112.714790 .71480 0.0171130 88 723.3906 112.709849 .70989 0.0121262 88 734.6565 112.695540 .69524 0.0111253 88 763.3280 112.659138 .65888 0.0121266 88 776.7631 112.642088 .64167 0.0121274 88 853.5283 112.544771 .54422 0.012793 88 908.0175 112.475796 .47584 0.012686 89 249.6078 112.045310 .04535 0.012218 89 335.8510 111.937144 .93701 0.028313 89 442.0772 111.804201 .80426 0.012383 89 682.5627 111.504396 .50436 0.0111269 89 924.1441 111.204839 .20461 0.012310 89 964.1798 111.155351 .15532 0.012726 90 023.9515 111.081549 .08152 0.0111094 90 165.5067 110.907157 .90718 0.012836 90 237.1548 110.819097 .81916 0.0121017 90 373.2059 110.652266 .65226 0.012639 90 468.7906 110.535356 .53488 0.061806 90 712.5262 110.238359 .23835 0.0121227 90 783.1403 110.152612 .15260 0.0111225 90 866.4262 110.051649 .05171 0.0111264 90 907.4563 110.001978 .00171 0.0111257 90 980.8631 109.913224 .91324 0.0121115 91 175.7932 109.678234 .67828 0.0111281 91 190.3525 109.660723 .66033 0.011649 91 257.2793 109.580300 .58047 0.013741 93 797.1181 106.613084 .61368 0.011622 94 175.1980 106.185070 .18556 0.0111095 98 753.6815 101.262048 .26196 0.010610 98 908.2953 101.103754 .10388 0.010464 99 208.5448 100.797769 .79790 0.010328 100 262.2675 99.738419 .73844 0.010313 100 452.2786 99.549758 .54974 0.010173 100 457.0246 99.545055 .54505 0.010874 100 547.7936 99.455191 .45519 0.010656 101 009.8182 99.000277 .00036 0.0101203 101 020.8204 98.989495 .98940 0.010484 101 547.6008 98.475985 .47598 0.010588 105 729.6727 94.580828 .58085 0.010217 106 361.2321 94.019219 .01934 0.0101101 106 892.7095 93.551750 .55171 0.0101190 107 267.9198 93.224517 .22446 0.010258 107 395.1821 93.114047 .11423 0.0101169 107 462.8499 93.055414 .05542 0.0091191 107 502.0737 93.021461 .02143 0.009720 107 509.6190 93.014933 .01519 0.0101202 107 524.2015 93.002318 .00234 0.0091179 107 571.6829 92.961268 .96125 0.009863 107 581.8480 92.952484 .95232 0.010632 107 704.5491 92.846589 .84691 0.0091216 107 745.7461 92.811089 .81103 0.0091255 107 854.5791 92.717436 .71718 0.009542 107 886.8624 92.689692 .68980 0.010

aRitz wave number calculated from the energy levels.bRitz wavelength calculated from the energy levels.cFractional part of experimental wavelength.dEstimated uncertainty of Ritz wavelength in

picometers (1 pm 5 10 mÅ).

1042 J. Opt. Soc. Am. B/Vol. 14, No. 5 /May 1997 Nave et al.

ACKNOWLEDGMENTSS. Johansson thanks V. Kaufman for help with the VUVgrating registrations and the NIST Atomic Spectroscopygroup for their hospitality during his visits. He also ac-knowledges financial support from the Swedish NaturalScience Research Council. A. P. Thorne acknowledges fi-nancial support from the Paul Instrument Fund of the

Fig. 1. Differences in picometers (1 pm 5 0.01 Å) betweenwavelengths directly measured by FTS and wavelengths derivedfrom the FTS energy levels. The open circles represent lineswith a signal-to-noise ratio of .100. The dotted lines mark thestandard deviation, Dl 5 5 3 1028l, of the subset of lines usedto calibrate the spectrum.

Fig. 2. Differences in picometers (1 pm 5 0.01 Å) betweenwavelengths directly measured by grating spectroscopy andwavelengths derived from the FTS energy levels. The opencircles represent lines that are unblended and are neither weaknor saturated on the photographic plate. The dotted lines markthe standard deviation of these lines of 0.16 pm.

Royal Society for the development of the VUV interferom-eter. We are grateful to one of the referees, W. Whaling,for helpful discussions on the calculation of Ritz wave-lengths and energy levels.

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