High-resolution soft-X-ray monochromators of new design

213

Nuclear Instruments and Methods m Physics Research A291 (1990) 213-218 North-Holland

HIGH-RESOLUTION SOFT-X-RAY MONOCHROMATORS OF NEW DESIGN G. BONFANTE, G. NALETTO and G . TONDELLO Department of Electronics and Informatics, University of Padova, Padova, Italy

We have applied the principle of sagittal focusing to obtain high-resolution soft-X-ray monochromators for application to undulators, as planned for the new generation of synchrotron radiation facilities. Grazing incidence optical configurations (like Czerny-Turner and those utilizing a grating with variable line spacing) are particularly attractive . These configurations have the advantage of using fixed entrance and exit slits. We have analyzed such configurations using sagittal focusing and have shown that the resolution obtainable is comparable with that of a spherical grating monochromator of similar size (which, by contrast, needs moving entrance and exit slits) .

1. Introduction In recent years it has become apparent that the limit in resolution for soft-X-ray monochromators dedicated to synchrotron radiation (SR) is due more to slope errors in the optical figuring of the components than to the cleverness of the design [1]. As a consequence, attention must be paid to the monochromator design's sensitivity to slope errors . In this respect it is known that, at present, plane or spherical surfaces can be fabricated with better surface figuring than aspherical ones, with limits as low as 0.2-0 .3 and 1 arc sec (rms) respectively . In addition, the slope errors are rather randomly distributed, so the total effect increases as C, n being the number of optical elements in the monochromator. For these reasons, the best performing instrument is one that places only one spherical optical element, namely the grating, between the entrance and exit slits. This is the case with the spherical grating monochromator (SGM), based on the Rowland mounting with an external condensing element, as suggested by Rense and Violett [2]. However, with the SGM, when the grating ritates to tune the wavelength, so does the Rowland circle . The expected high resolution may be achieved only if a translation of the entrance and exit slits is coupled to this rotation . This gives rise to refocusing problems in the pre-condensing and post-focusing systems because of the slits' movement . The requirement for simplicity in the scanning mechanism and the need for fixed slits are quite important in light of both mechanical reliability and experimental convenience . Hence some other configurations satisfying the latter requirement have been proposed, but they nonetheless fail to achieve the ultimate limit resolution obtainable with the SGM (i .e . a limit set by slope errors).

The variable line spacing monochromator (VLSM) proposed by Hettrick and Underwood [31, employs a focusing mirror together with a plane grating between the slits. The main aberrations are corrected by varying the grooves' spacing throughout the length of the grating; good resolution is possible . However, due to the presence of two surfaces inside the monochromator, the overall effect of the slope errors is larger than in the SGM. Even worse in this respect is the case of the CzernyTurner monochromator (CTM) [4], where a plane grating is illuminated with parallel light using one collimating mirror and one refocusing mirror . Here we have a total of three reflections . In the present work we have developed some optical schemes based on the CTM and VLSM configurations that circumvent the effect of slope errors on the collimating and/or focusing mirrors. Thus it is possible to achieve the same resolution as with the SGM, but with the great advantage of fixed entrance and exit slits. 2. Sagittal focusing in grazing incidence Regarding the effect of the slope error imperfections, sagittal focusing is far superior to the more commonly used tangential focusing . Consider for example fig. 1 which shows the difference between tangential and sagittal collimating of a point source (by means of a cylindrical mirror, for example) . An actual slope imperfection may be thought of as a local slight rotation of the ideal surface. It can be shown that, while a tangential slope error 4 produces a tangential deviation of the reflected ray equal to 24, a sagittal slope error deflects sagittally lust by 2 cos y S~5, where y is the incidence angle measured with respect to

0168-9002/90/$03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)

ll(b). MONOCHROMATORS

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G Bonfante et al. / High-resolution soft-X-ray nionochromators 'I'0 I'

\ II'1Y

siDl ; \II ;N'

Fig. 1 . Collimating a point source by means of a cylindrical mirror, either tangentially (a) or sagittally (b).

Fig. 3 Optical scheme of a SF-VLSM. Mo is an ellipsoidal mirror collimating the SR source on entrance slit S, of the monochromator. M, is an ellipsoidal mirror working m sagittal focusing and G is a plane grating with variable line spacing.

the normal . If it is reasonable to expect that there are no largely selective directions in the figuring-accuracy distribution of the optical sufaces, then it is possible to decrease the effect of the slope errors in the grazing incidence reflections by a substantial factor (= 20 for a 3 ° grazing angle) in the sagittal direction with respect to the tangential direction. Therefore, if we consider a monochromator in which the collimating and/or focusing mirrors work in the sagittal direction, their contribution to the total slope-errors effect in the sagittal direction is practically negligible at small grazing angles . This is the way the optical layout of the ordinary CTM has been changed to a new one called the sagittally focusing Czerny-Turner monochromator (SFCTM) . Similarly the VLSM optical layout can be changed to a new one called the sagittally focusing variable line spacing monochromator (SF-VLSM). Normally, both the CTM and the VLSM, like all the other existing grazing-incidence monochromators, work with a global equatorial-dispersion plane (which, in the case of SR, usually turns out to be the vertical plane) . The focusing of the mirrors in the dispersion direction is performed tangentially . In our approach though, the equatorial-dispersion plane of the grating coincides with the sagittal planes of the mirrors (instead of the equatorial ones); thus the dispersive focusing is accom-

plished sagittaly and the slope-errors effect in the dispersive direction is greatly reduced. A possible optical layout of a SF-CTM is shown in fig. 2. A plane grating is positioned in a crossed way between two sagittally collimating and focusing mirrors. Wavelength scanning is accomplished by rotating the grating; the entrance and exit slits remain fixed. Similarly, fig. 3 shows the scheme of a SF-VLSM; there is only one focusing mirror before the grating that works to convergent light. Of course, proper correction of the residual aberrations must be realized in both schemes with a judicious choice of optics, as is usual in these kind of mountings; some examples will be treated here. The advantage of these mountings lays in the fact that practically the only resolution-limiting element, as far as the slope errors are concerned, is the (plane) grating. As in the case of the SGM, this holds true even if the mirrors used inside the monochromator are aspheric. Since the mirror surfaces are vertical, their size is determined by the horizontal divergence of the SR, which usually is larger than the vertical divergence . This fact is of little concern for use with undulators, where the divergence in both directions is very limited . One possible additional concern could be the reflection efficiency of the monochromator with regard to the

TOP VIEW

T

SIDE VIEW Fig. 2. Optical scheme of a SF-CTM . MQ is an ellipsoidal rrurror collimating the SR source on entrance slit S, of the monochromator. M, and M Z are paraboloidal mirrors working m sagittal focusing and G is a plane grating.

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G. Bonfante et al. / High-resolution soft-X-ray monochroniators

polarization of the beam . In effect, we have one p-type and one s-type reflection in the SF-VLSM (two of the former in the SF-CTM) . This does not produce any problem at the photon energies typical of soft X-rays, i.e., between 200 and 1000 eV [5]. For softer radiation, however, the difference between the two reflection coefficients must be taken into account properly . 3. The proposed monochromators We have analyzed various possible optical schemes for high-resolution monochromators on an undulator bean-dine of the storage ring Elettra under development at the Sincrotrone Trieste. The spectral output of such an insertion device is planned to lie in the 100-1000 eV photon energy range, but we have mainly restncted ourselves to the 280-1000 eV region ; this region spans the electron core levels of such important elements as C (284 eV), N (400 eV), and O (532 eV). Moreover, this region can be fully covered by a single grating with a groove spacing of 1100 1/mm, at a constant 174 ° deviation between the incidence and diffraction directions. In the schemes of figs . 2 and 3 it is preferable to work with the outside spectrum of the grating for two main reasons. One is that, with the inside spectrum, the illuminated area on the grating could easily turn out to be prohibitively large. The other involves reflectivity and order sorting considerations ; in fact, with the outside spectrum, the incidence angle a on the grating decreases while the wavelength increases. Note, however, that when working in grazing incidence with the outside spectrum, blazed gratings are not recommended; laminar gratings with symmetric grooves shapes are better . For this reason, some cases using the inside spectrum have also been studied. For the optical study, we approximated the undula-

for as a source with an energy-dependent Gaussian profile both in size and in divergence. This is a rather simplified assumption consistent with the planned use of a pinhole in front of the undulator. The actual expected vertical and horizontal sizes of the source at 600 eV photon energy are a, = 70 lrm rms and ah = 220 [Lm rms, the corresponding angular divergences are a, = 26 brad rms and ai, = 36 [rad rms. Using a highly demagnifying ( :25) pre-collimating ellipsoidal mirror, a focus of _ 8 lrm extension and ~ 2 mrad divergence (3a criterion) in the vertical direction is obtained . In this way, a horizontal entrance slit with 10 wm minimum width can be used . In order to minimize the effect of its surface slope errors, as well as the thermally induced slope deviations due to the large power density originating with the insertion device, dispersive focusing is accomplished sagittally by the mirror . The behaviors of the various configurations have been evaluated with a ray-tracing code developed especially for grazing-incidence optics . The surface slope errors have been simulated by a randomly oriented Gaussian angular perturbation (with standard deviation ,r) of the normal to the surface in the point of impact of each incoming ray. The resolution criterion employed is the one suited for a monochromator : the bandpass is defined as the full width at half maximum (FWHM) of the exit beam spectral composition, as long as the exit slit is wide enough to pass a given fraction of the monochromator wavelength focal distribution intensity (87% in our calculations) . Finally, all the cases investigated use optical elements working with a 3° grazing angle. 3.1 . The SF-CTM

The simplest configuration of a SF-CTM from an aberration point of view uses two off-axis paraboloids as collimating and focusing mirrors . This case is ideally

Table 1 Parameters of the SF-CTM . Component

Demagnifying mirror (demagnification = 25)

Shape

ellipsoidal

Collimating mirror

paraboloidal

Grating

plane

Refocusing mirror

paraboloidal

Orientation

horizontal equatorial plane

Dimensions [mm21 90X 4

horizontal equatorial plane

500 X 20

vertical equatorial plane

250 x 30

equatorial plane inclined by 6° over horizontal plane

500 X 10

Distances

source-rrurror : 20 m nurror-entrance slit : 800 mm

entrance slit-mirror: 4700 mm (outside spectrum) 1900 mm (inside spectrum) nurror-grating . 300 mm

grating-nurror : 300 mm mirror-exit slit . 1900 mm (outside spectrum) 4700 mm (inside spectrum) H(b) . MONOCHROMATORS

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G Bonfante et al. / High-resolution soft-X-ray monochromators 0 0 M

0 0 N

E N N in O

n in ro ro o

400 .

600 .

800 .

;

1000 .1200 .

400 .

600 .

800 .

1000 .1200 .

Photon energy (eV) Photon energy (eV) Fig. 4. The spot size containing 87% of the flux obtained by ray tracing for the various configurations considered (left : spectral dimension; right . spatial dimension) . Curve a: SF-CTM, outside spectrum ; curve b : SF-CTM, inside spectrum ; curve c: SF-VLSM, outside spectrum ; curve d: SF-VLSM, inside spectrum .

free from any aberrations, and the only factors limiting the resolution are the slope errors and the geometric diffraction equivalent of the source size . So, to optimize the resolution, it is convenient to operate asymmetrically, with an entrance arm larger than the exist arm (distances S j M 1 and M2S2 respectively in fig. 2) . The parameters of the analyzed configuration are reported in table 1 . We have considered slope errors of T = 1 f.rad on the plane grating, 5 Brad on the paraboloidal mirrors and 10 t,rad on the external focusing ellipsoidal mirror (the value for the latter is greater in order to include some thermally induced deformations). Fig. 4 (curve a) shows the spot size of the image containing 87% of the flux, in the range of 280-1000 eV, for this case . Correspondingly, fig. 5 (curve a) shows the expected resolution . Note that, as predicted, the effect on the resolution of the slope errors of the mirrors is very limited. An additional characteristic of this type of mounting is that we can trade the entrance and exit directions and use the inside order of the grating. In this case, the size of the grating is still acceptable due to the shortness of the entrance arm (distance S 2 M 2 in fig. 2), except near the horizon wavelength where some loss of flux can be experienced . In the analyzed case, i.e . with S 2 M 2 = 1900 mm and a grating length of 250 mm, this loss varies between = 5% at 400 eV and = 50% at 280 eV . Fig. 4 (curve b) shows the spot size (87%) of the image on the exit slit in this case . Comparing the two cases of outside and inside spectra, one can see that the spectral size of the image changes with energy much less

in the inside spectrum than in the outside spectrum, where, particularly at lower energies, it becomes very large. This means that with the inside spectrum the exist slit can stay nearly constant in width while scanning . However, the spatial size of the image is larger ( x 3)

3 tw

w a w c O

0 LO m

400 . 600 . 800 . 1000 . 1200 . Photon energy (eV)

Fig. 5. The spectral resolution predicted for the various monochromators considered. Curve a: SF-CTM, outside spectrum ; curve b: SF-CTM, inside spectrum ; curve c: SF-VLSM, out side spectrum ; curve d: SF-VLSM, inside spectrum ; curve e: SGM, inside spectrum .

G. Bonfante et al / High-resolution soft-X-ray monochromators

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Table 2 Parameters of SF-VLSM. Component

Shape

Orientation

Dimensions [mmz ]

Distances

Collimating mirror

ellipsoidal

horizontal equatorial plane

430 X 18

entrance slit-mirror 4000 mm (outside spectrum) 1200 mm (inside spectrum) mirror-grating : 300 mm

VLS grating

plane

vertical equatorial plane

250 X 20

Demagnifying mirror (demagnification = 25)

ellipsoidal

horizontal equatorial plane

using the inside spectrum due to the magnification . In fig. 5 (curve b) the resulting resolution is shown : it is somewhat greater at the low energies, This basic configuration of the SF-CTM can have some variants . One has been already described [61 and uses cylindrical mirrors instead of paraboloidal ones . In this case, the focusing in the spatial direction is made by a cylindrical grating. The resolution obtainable is somewhat smaller because of the greater slope errors on a cylindrical grating rather than on a plane one; also, not working the grating with (totally) parallel light, there is the need of positioning it in the middle and consequently only a symmetric configuration is possible. 3.2 . The SF-VLSM

The VLSM configuration, as devised by Hettrick and Underwood [31, makes use of a grating in convergent light. The grating is plane, with parallel lines and variable line spacing: the variation of the spacing satisfies the local grating equation for a particular wavelength A o. Rotating the grating causes' a very slight degradation of the ideal performances because some residual aberrations varying roughly with the aperture are present. For the small apertures considered here, the aberrations are very little - smaller than the ones produced by the slope errors (except near the low energy limit: in fact, here the diffraction angle ß tends to approach 90' for the case of the outside spectrum, and the optical aberrations are dominant). So, with a VLSM applied to SR, very good values of resolution can be obtained, provided of course that the grating has excellent tolerances . As for the CTM, sagrttal focusing can benefit the VLSM performance making it comparable to that of the SGM, while still keeping fixed entrance and exit beams. Fig. 3 shows the scheme of a SF-VLSM that has the same pre-condensing system as the SF-CTM and uses an ellipsoidal mirror as the focusing element inside the monochromator. It is convenient to keep the focusing

90X 4

source-mirror 20 m mirror-entrance slit : 800 mm

grating-exit slit : 3700 mm (outside spectrum) 6500 mm (inside spectrum)

mirror and the grating close together in order to have the best coupling between the demagnification of the mirror and the dispersion of the grating. These two optical elements can in principle be positioned anywhere between the entrance and exit slits. In the best configuration, the entrance arm should be larger than the exit one (S,M, and GSZ respectively to fig. 3), as for the SF-CTM . Unfortunately, in this position the optics are very large and the residual aberrations of the grating become too great near the horizon wavelength . So, we have compromised by putting the ellipsoidal mirror at the middle position . The parameters of the configuration are reported in table 2. The groove spacing is optimized for 400 eV ; in fact, it appears convenient to optimize it at a point near the low-energy limit to reduce the aberrations in the more-critical region . Here again we have assumed slope errors with r = 1 grad on the plane grating, 5 brad on the ellipsoidal mirror and 10 wrad on the precondensing one. Fig. 4 (curve c) shows the image spot size (87%). Even with the SF-VLSM it is possible to use the inside spectrum, by adopting a small value for the entrance arm and by tolerating a loss of flux at the extreme low energies . With S,G = 1200 mm and a grating length of 250 mm, the loss vanes between = 5% at 330 eV and = 30°ío at 280 eV . The situation is very similar to that of the SF-CTM . For the blurs and the resolution we obtain curves d of figs . 4 and 5 respectively ; here again the spatial blurs are greater in the inside spectrum case . 4. Conclusions In fig. 5, curve e shows the resolution expected from a SGM of comparable characteristics (i .e., groove frequency 1100 1/mm, total included angle 174') and comparable total size (R = 75 m, corresponding to a length of = 8 m), when the entrance and exit slits are always kept on the Rowland circle. In this case the 11(b). MONOCHROMATORS

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G Bonfante et al. / High-resolution soft-X-ray monochromators

inside spectrum is used and the value of the standard deviation surface-slope errors on the grating is assumed to be T = 1 p rad, as in the cases previously considered . Moreover, a pre-condensing system with two cylindrical mirrors has been adopted in order to collimate the SR radiation and also compensate for the astigmatism of the spherical grating. The fact that curve e is comparable with curves a-d, shows that the SF-CTM and the SF-VLSM achieve the same resolution as the SGM. Note also that, because slope errors are the main resolution limiting factors, there is no great advantage in increasing the size of the monochromator above a given point. In conclusion, it has been proved that the sagittal focusing is very beneficial for the spectral resolution . When applied to schemes as the CTM and the VLSM,

sagittal focusing can lead to configurations for SR monochromators that allow spectral resolution as high as that of the SGM, but with fixed entrance and exit slits.

References [1] G.P. Williams, Nucl . Instr. and Meth . A246 (1986) 294. [2] W.A . Rense and T. Violett, J . Opt . Soc . Am 49 (1959) 139. [3] M.C . Hettnck and J.H . Underwood, AIP Conf. Proc 147 (1986) 237. [4] M.R . Howells, Nucl . Instr. and Meth . 177 (1980) 127. [5] B.L. Henke, P. Lee, T.J . Tanaka, R.L Shimabukuro and B K. Fulikawa, Atom . Data Nucl . Data Tables 27 (1982) 1 . [6] G. Bonfante and G Tondello, submitted to Appl . Opt. (1989) .