WO2010086324A1

WO2010086324A1 - Spectrograph with an elliptical mirror

Info

Publication number: WO2010086324A1
Application number: PCT/EP2010/050919
Authority: WO
Inventors: Gheorghe Sorin Chiuzbaian; Coryn Frank Hague
Original assignee: Universite Pierre Et Marie Curie (Paris 6); Centre National De La Recherche Scientifique
Priority date: 2009-01-27
Filing date: 2010-01-27
Publication date: 2010-08-05
Also published as: FR2941528A1

Abstract

The invention relates to a spectrograph comprising a means (3) for focussing radiation emitted by a sample illuminated by a source of radiation, and a means (4) for diffracting the focussed radiation, in which, according to the invention, the diffraction means includes a flat diffraction network with a variable pitch, and the focussing means includes an elliptical mirror, the sample being placed in one of the focal points (F1) of an ellipsoid surface defining the elliptical mirror.

Description

Elliptical mirror spectrograph

The invention relates to a spectrograph working in the field of X-rays (that is to say for radiation whose energy E is substantially between a few electron volts and 1200 electron volts, which corresponds to at wavelengths λ between approximately 1 and 250 nanometers).

For the following we give the following definitions. The resolution of a spectrograph is the elementary quantity of energy ΔE or wavelength Δλ that the spectrograph is able to discriminate.

The resolving power PR of such a spectrograph is the ratio λ / Δλ or E / ΔE (it is recalled that the energy E and the wavelength λ of a radiation are linked by the relation E.λ = 1239, 8 for E expressed in electron volts and λ in nanometers).

The angular dispersion of a network is the quantity dβ / dλ where β is the diffraction angle. The reciprocal angular dispersion is the quantity dλ / dβ. The efficiency of a mirror is the ratio between the number of photons reflected by the mirror and the number of photons intercepted by the mirror, and the efficiency of a network is the number of photons diffracted by the grating, for one order given diffraction, and the number of photons intercepted by the network.

Finally, the angular acceptance of the spectrograph corresponds to the solid angle of the cone formed by the photons coming from a point source. The actual acceptance takes into account the reflectivity of the mirror. BACKGROUND OF THE INVENTION

The development of such spectrographs has accelerated over the last twenty years with the increasing availability of synchrotron sources, allowing samples to be analyzed by quasi-elastic and inelastic scattering of photons from such a source. In this respect, the use of diffraction gratings has been known since at least the nineteenth century, and in particular, spherical diffraction gratings operating according to the Rowland geometry. The radiation source and the detector are precisely positioned on a circle whose diameter is equal to the radius of the spherical diffraction grating. The latter has uniformly spaced lines and plays both the role of diffuser and the role of focus. However, this configuration implies that the detector is placed tangentially to the Rowland circle, so that it receives the rays in grazing incidence. Modern CCD sensors have their effectiveness drop when they work in this way.

To overcome the Rowland geometry, it has been proposed to replace the uniformly spaced lines of the spherical diffraction grating by lines engraved in a variable pitch. Thus, a rectified focal curve can be obtained. In addition, the variation of the pitch of the lines makes it possible to at least partially compensate for the optical aberrations. A number of instruments based on this scheme are in operation or are about to enter service. However, the main disadvantage of this type of instrument lies in the poor correction of high order optical aberrations for large spherical diffraction gratings. Only short portions of the diffraction grating can be used to achieve a high resolution, which limits the angular acceptance of the instrument. In addition, the corrections made by the variation of the pitch are valid over a rather limited range of energy.

It is also known from the document "A high efficiency ultrahigh vacuum compatible flat field spectrometer for extreme ultraviolet wavelengths "from REVIEW OF SCIENTIFIC INSTRUMENT Vol. 76, July 20, 2005 to separate the focusing and dispersion functions by providing a spherical focusing mirror and a spherical diffraction grating distinct from the focusing mirror.

It is also known from US 4,776,696 to separate the focus and dispersion functions by providing spherical focusing mirrors and a diffraction grating distinct from the focusing mirrors.

In these two documents, the diffraction grating comprises lines extending in a variable pitch, which makes it possible to compensate for the variation of angle of incidence of the rays striking the grating, and also to compensate for the optical aberrations generated by the grating. mirror.

However, such spectrographs have certain limitations. Indeed, an increase in angular acceptance implies the use of large optics. But the aberrations generated by a large spherical mirror can not be fully corrected, so that when the size of the mirror increases, these aberrations lead in practice to a lower resolution. Moreover, optimization of the spherical mirror torque / variable pitch diffraction grating can only be carried out for a determined radiation energy.

It is also known from the document "Instrumentation for analysis and utilization of extreme-ultraviolet and soft x-ray high-order harmonies" issued from REVIEW OF SCIENTIFIC INSTRUMENTS Vol.75, No. ll, October 29, 2004 to separate the functions of focusing and dispersing by providing a toroidal focusing mirror and a diffraction plane plane with dashes extending in a variable pitch, distinct from the focusing mirror. Again, a Optimization toroidal mirror torque / diffraction grating variable pitch can be conducted for a specific radiation energy. Thus only short portions of the diffraction grating can be used to achieve a high resolution, which limits the angular acceptance of the instrument.

In the cousin field of monochromators, it is known from US 4,553,253 to use a plane diffraction grating to diffuse radiation and then to focus by means of an elliptical mirror. An upstream plane mirror reflects the radiation source back to the plane diffraction grating so that the diffracted rays appear to come from one of the ellipsoid surface foci defining the elliptical mirror. This focuses the radiation to the other focus of the ellipsoid surface. The peculiarity of such monochromators is to treat the radiation coming from a very distant source and therefore an almost parallel beam. In addition, a narrow slot selects the desired wavelength radiation. In the example illustrated in this document, the diffraction grating is a constant pitch network at 1200 lines per millimeter.

OBJECT OF THE INVENTION The object of the invention is to propose a spectrograph allowing both a high resolution and a large angular acceptance to treat a strongly divergent source.

BRIEF DESCRIPTION OF THE INVENTION In order to achieve this goal, a spectrograph is proposed comprising means for focusing a secondary radiation emitted by a sample illuminated by an X-UV radiation source, followed by diffraction means. focused radiation, in which, according to the invention, the diffraction means comprise a plane-to-dash diffraction grating and the focusing means comprise an elliptical mirror having a reflective surface extending along an ellipsoidal surface, the sample being placed at one of the ellipsoid surface foci.

Thus, the sample forms a source of secondary radiation whose photons are reflected by the elliptical mirror towards the plane diffraction grating which returns the diffracted photons to a focal point which turns out to be an image of the second focus of the ellipsoid surface, which thus constitutes a virtual image of the source. The variation of the pitch of the lines of the diffraction grating may be chosen to compensate for the angle of incidence variation of the convergent beam of photons reflected by the elliptical mirror and approaching the diffraction grating.

Unlike the spectrograph of the prior art with a spherical mirror and a variable pitch diffraction grating, the inventors have realized that in the spectrograph of the invention, the optimal arrangement of the lines of the diffraction grating with variable pitch, that which minimizes High order optical aberrations, is substantially independent of the energy of the incident radiation, so that a same diffraction grating can cover a broad spectrum of radiation energy.

In addition, the placement of the sample at the first focus of the ellipse provides a virtual image at the second focus that is near perfect. Thus, it is possible to use long elliptical mirrors and diffraction gratings of suitable length, whose entire length can be exploited, which allows a significant increase in the opening of the instrument.

Preferably, the rays diffracted by the diffraction grating are received by a detector placed downstream of the diffraction grating. According to one particular aspect of the invention, the range of energy that it is desired to detect by means of the detector is selected by rotating the diffraction grating around an axis parallel to the lines of the latter, which has the effect of effect of modifying the angle of incidence of the rays reaching the diffraction grating. This selection is then made constant deflection angle.

It is also possible to select a different deflection angle by moving the detector, so that it is possible to select a new angle of incidence and diffraction angle pair.

The change of deflection angle leads to a change in the focal length (i.e., the distance at which the diffracted rays are focused). The detector will then be advantageously moved in conjunction with the rotation of the diffraction grating so that the plane of the detector coincides with the focal plane in which the image is formed. In all rigor the detector must then be oriented a few degrees to fit the focal plane, but in general, the depth of field of the focusing is sufficient to allow the perpendicularity of the plane of the detector with respect to the focal axis, given its small size.

The inventors have furthermore noted that the optimum arrangement of the lines of the diffraction grating with variable pitch, that which minimizes the high order optical aberrations for a given incidence, remains valid for a wide range of angles of incidence.

Thus, the same diffraction grating makes it possible to cover both a wide range of energy and a wide range of deflection angles, or, which amounts to the same, a wide range of diffraction angles. BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood in the light of the description which follows and the figures of the appended drawings, among which: FIG. 1 is a schematic diagram of the spectrograph according to the invention, the angles and the pitch of the lines on the network; diffraction has been exaggerated for the sake of clarity;

FIG. 2 is a schematic diagram of the spectrograph of FIG. 1, showing the diffraction grating in a distinct angular position corresponding to a different deflection angle;

FIG. 3 is a graph illustrating the acceptance of the elliptical mirror used as a function of the energy of the incident radiation;

FIG. 4 is a graph illustrating the absolute efficiency of the variable pitch diffraction grating as a function of the energy of the incident radiation;

FIG. 5 is a graph showing the width at half height of the Gaussian adjusted at best to the image as a function of the energy of the incident radiation;

FIG. 6 is a graph showing, as a function of the dispersion in the focal plane, on the one hand the intensity of the image in the form of a curve, and on the other hand the intensity per pixel in the form of crenels, for different radiation energies.

FIGS. 7a, 7b, 7c, 7d are graphs illustrating, as a function of the dispersion in the plane of the detector, the intensity of the image for different radiation energies, on the one hand for the elliptical mirror spectrograph according to the invention as illustrated in Figure 1 and on the other hand for spherical mirror or toroidal spectrographs of the prior art, all things being equal. DETAILED DESCRIPTION OF THE PRINCIPLE OF THE INVENTION With reference to FIG. 1, the spectrograph of the invention is associated with a radiation beam of the X-UV 1 domain, suitable for examining the electronic structure of complex materials. This X-UV beam is generally provided by a synchrotron and is processed by a monochromator to provide an intense beam of photons with a predetermined energy.

The X-UV beam thus calibrated illuminates a sample 2. The atoms of the sample thus illuminated undergo electron-photon interactions giving rise to the emission of photons of various wavelengths, that is identical to that of the incident radiation (collisions elastic), or different (inelastic collisions). Sample 2 thus forms the source of a secondary X-ray, whose photons are scattered in all directions. It is then a question of recovering as much as possible.

For this purpose, a collecting mirror 3 is used, which has a reflection surface extending along an ellipsoidal surface. We shall speak here of elliptical mirror 3. It should be noted that the sample 2 is placed precisely at one of the foci Fl of the ellipsoid surface. The photons coming from the sample and reflecting on the elliptical mirror are focused, according to a well-known geometric property, towards the second focus F2 of the elliptical surface. The second focus F2 is the place of an almost perfect image of the source, whatever the wavelength of the radiation used. The path of the rays focused by the elliptical mirror 3 is cut by a diffraction plane grating with variable pitch 4, arranged across the beam converging to the second focus F2 as illustrated. The rays are thus diffracted by the diffraction grating 4 to a focal point F 'which is an image of the focus F2, so that the latter acts as a virtual source.

As can be seen here, the photons which approach the diffraction grating 4 at one of its edges do not have the same incidence as the photons which approach the diffraction grating at the other of its edges. Thus, as illustrated, the angle α is smaller than the angle LL2. It is therefore appropriate to choose the pitch of the lines of the diffraction grating 4 so as to compensate for this difference in angle of incidence, and the possible optical aberrations induced by the elliptical mirror 3.

A detector 5, in this case a CCD sensor, is arranged so that its plane coincides with the focal plane P of formation of the image. According to a particular aspect of the invention, the plane diffraction grating 4 is rotatably mounted, here around a median axis Z (seen in end in FIG. 2). The rotation of the grating makes it possible to vary the angle of incidence of the beam reflected by the elliptical mirror 3 and which approaches the diffraction grating 4, and thus also the diffraction angle β of the diffracted radii by the grating. As seen in Figure 2, the diffraction grating was rotated by an angle ψ and the detector moved so that the deflection angle is increased. The increase or decrease of the deflection angle makes it possible to vary the spectral range of the radiation received by the detector 5 since it causes the change of the diffraction angle β. This is a zoom effect particularly interesting and very simple to implement. Of course, the rotation of the diffraction grating 3 causes a displacement of the focal point F ', as illustrated in FIG. 2. It is therefore expedient to move the detector

5 in conjunction with the rotation of the diffraction grating 3 so that the detector is in the mean focal axis, and that his plane coincides with the plane P 'of formation of the image at the new focal point F ".

It is possible to determine a relation between the angle ψ of rotation of the diffraction grating 4 and the position of the focal point F, as well as between this same angle ψ and the direction of the mean focal axis A. It is therefore possible to determine, for each angular position of the diffraction grating, the optimal position of the detector 5. Thus it is very simple to automatically link the rotation of the diffraction grating 4 with the displacement in the space of the detector 5. For this purpose , the detector 5 is preferably mounted on a moving element provided with various degrees of freedom whose displacements are slaved to the rotation of the diffraction grating 4.

Remarkably, it is thus possible to cover with the same diffraction grating radiation from 180 to 1500 electron volts, with a deviation angle variation of about 11 degrees (it is recalled that the deflection angle is equal to to the 180 ° complement of the sum of the moduli of the angle of incidence α and the diffraction angle β or, which amounts to the same, to 180 - (α - β), since β is conventionally counted negatively) . In another embodiment, the inventors have succeeded in covering the energy range of 50 to 1500 electron volts with only two different diffraction gratings while ensuring a very high resolution. DETAILED DESCRIPTION OF AN EXEMPLARY EMBODIMENT

The following description relates to a spectrograph produced by the inventors at the Laboratory of Physical Chemistry-Matter and Radiation of the University Pierre and Marie Curie / PARIS VI. An X-ray beam from a synchrotron radiation line is focused at a point on a sample, which forms a secondary radiation source having a Gaussian intensity distribution with a standard deviation of substantially σ = 1.1 micrometers , and emitting in all directions.

The elliptical mirror is cut along an ellipsoid surface having a half-major axis of 1550 millimeters and a half-minor axis of 61.38 millimeters. The elliptical mirror is about 900 millimeters away from the secondary source, which is placed at one of the Fl foci of the ellipsoid surface. The elliptical mirror has a length of 250 millimeters and is placed relative to the secondary source so that incident radiation from the secondary source and reaching the center of the mirror makes an angle Φ = 87.5 ° with respect to the normal of the mirror. mirror in the center.

The variable pitch diffraction grating which intercepts the rays reflected by the elliptical mirror is placed at substantially 200 millimeters thereof. Only radiation diffracted in external order (negative order) is taken into consideration. The focal plane in which the image of the secondary source is focused is located substantially 2000 millimeters away from the diffraction grating. The angle of incidence α on the grating is smaller than the modulus of the diffraction angle β (the angles are measured with respect to the normal and by convention β takes negative values), so that to intercept all the radiation reflected by the elliptical mirror, the length of the network required is only 120 millimeters. Thus, for a moderate network length, the radiation intercepted by a mirror is collected more than twice its length. In return, the diffracted angle remains within a range limited since θ <| β | <90 ° (where 2Θ is the 180 ° complement of the deflection angle or, which amounts to the same, 2Θ = α - β and for the zero order α = | β | = θ).

We recall the formula of networks: N.λ = d. (sinα + sinβ) where λ is the diffracted wavelength (in nanometers), N is the diffraction order (here N = -1) and d is the pitch between the lines at the center of the variable-pitch diffraction grating ( here 1/1800 millimeters or 556 nanometers). The range of energy covered by the diffraction grating is extended by making θ variable, by rotating the variable-pitch diffraction grating as explained above. As indicated, this extension of energy range is achieved without loss of resolution thanks to the use according to the invention of an elliptical mirror coupled to the diffraction grating with variable pitch, which proves impossible with a spherical mirror or toroidal.

The inventors have determined the variation of the pitch of the lines of the diffraction grating by determining the parameters of a fourth degree polynomial which defines the optimum variation of the pitch of the lines for an average wavelength corresponding to an energy of 700 electron volts. , and a value of 2Θ average of 174 degrees. The diffraction grating used has a line density of 1800 lines per millimeter at its center.

For the distribution of the lines of the network thus determined, the inventors have found that the same reciprocal angular dispersion can be maintained for an energy range of 280 electron volts.

(4.4 nanometers) to 950 electron volts (13 nanometers) without affecting the quality of the focus, provided of course to move the detector to account for the variation of the angle 2Θ and that of the distance Focal. In practice, the detector is mounted on a table that can move 400 millimeters Y and 300 millimeters X, which covers a variation of 2Θ ranging from 176 ° to 165 ° (a variation of the deflection angle from 4 ° to 15 °).

It is also shown that the reciprocal angular dispersion dλ / dβ is proportional to cosβ for a given value of θ. The maximum reciprocal angular dispersion is therefore obtained for cosβ tending towards zero, or for β tending towards 90 degrees. In practice one chooses β <I 89, 3 I degrees to avoid a too important contribution of diffuse diffusion of the network itself.

As has been explained, the possibility of varying θ and β by pivoting the diffraction grating without affecting the quality of the focusing makes it possible to study a spectral range, wide or narrow, according to the choice of β. This is a zoom effect. Alternatively it is possible to choose the angle of incidence and the diffraction angle to satisfy the blaze condition over the entire energy range covered by the diffraction grating, for maximum efficiency. 1 / EFFICIENCY

It is obvious that the amount of radiation intercepted by the spectrograph depends on the effective length of the elliptical mirror and the width of the detector located here substantially 3.1 m from the source. The actual acceptance must be corrected for the reflectivity of the mirror. This depends on the angle of incidence of the radiation, its wavelength and the nature of the coating. Figure 3 shows the effective acceptance of the elliptical mirror used in this embodiment.

To know the efficiency of the instrument as a whole, the absolute efficiency of the network should also be taken into account. Figure 4 presents the efficiency calculated (using the NEPHIERE calculation code put online by the Canadian Light Source) of a variable-pitch diffraction grating of 1800 lines / millimeter in various configurations made possible by the invention. The network is considered blazed under a blaze angle Θ _B = -1.5 °. The condition of blaze is respected if: α - Θ _B = I β I + Θ _B For a very high resolving power PR (PR> 10 ⁴ ) obtained for β = -89,3 °, the efficiency of the network falls towards the low energy but the recovery with a second network for low energy is possible. Better efficiency is obtained over a large energy range by varying β so that 8000>PR> 5000. The best efficiency is obtained by giving priority to blaze conditions. 2 / RESOLUTION

The resolving power depends on the size of the source, the quality of the optics and the resolution of the detector. The resolving power of an optical system is often defined according to the Rayleigh criterion: two spectral lines separated by Δλ will be resolved if

Δλ = 2,643.σ _image . (dλ / dβ) where σ _image is the standard deviation of the Gaussian form adjusted best to the image. At order -1 the resolving power is equal to:

PR = λ / Δλ = E / ΔE = - (12398 / E / d.cosβ). (r / 2, 643.σ _image ) where r is the distance between the center of the network and the detector. Figure 5 shows the width at half height of the Gaussian form allowed to obtain a PR = 10 ⁴ with r = 2000 millimeters (it should be noted that the width at half height is equal to 2.35 σ _image ).

Finally, Figure 6 presents simulations (performed using SHADOW which is a code of X-ray X-ray Domain Optics Simulation Distributed by the Center for Nanotechnology, University of Wisconsin) integrating source size and slope and roughness error values for the optics specified for the spectrograph. These simulations confirm that a resolving power of 10 ⁴ is reached at high energies, and largely exceeded by the Rayleigh criterion for the lowest energies. At the two extremes illustrated in the figure, the half-height width of the Gaussian adjusted to one of the peaks forming the image is 80 μm (for 280 eV) and 34 μm (for 930 eV).

Finally, while a resolving power of at least 10 ⁴ can be obtained with the mentioned variable pitch diffraction grating having a pitch of 1800 lines per millimeter in the center, the resolution will depend on the performance of the detector used. In FIG. 6, the slots forming rectangles represent a pixel width of 13 μm. It will be advantageous to use known methods to reduce the effective size of the pixels if necessary. This is done either geometrically by a slight rotation of the detector or electronically by measuring the charge induced on neighboring pixels.

By way of illustration, simulations were carried out (using SHADOW) to compare, as a function of the position on the detector, the intensity of the radiation reaching the detector, for a spectrograph according to the invention and for spectrographs of the prior art toroidal or spherical mirror, all things being equal. FIGS. 7a and 7b each illustrate a simulation performed for a radiation energy belonging to the radiation energy range in which the arrangement of the lines of the diffraction grating with variable pitch is optimal, while FIGS. 7c and 7d each illustrate a simulation performed for radiation energy outside this range. In light of these four figures, it appeared that the coupling of an elliptical mirror to a variable pitch plane diffraction grating makes it possible to obtain a very high image intensity, compared to couplings with a spherical mirror or toroidal, and this even outside the range of radiation energy where the arrangement of the diffraction grating lines is variable pitch is optimal. The selection according to the invention of an elliptical mirror thus makes it possible to increase the performance of the spectrograph very clearly.

The invention is not limited to what has just been described, but on the contrary covers any variant within the scope defined by the claims.

Claims

Spectrograph comprising means for focusing (3) a secondary radiation emitted by a sample illuminated by an X-ray source, and diffraction means (4) for focusing radiation, characterized in that the diffraction means comprise a planar diffraction grating extending in a variable pitch, and the focusing means comprises an elliptical mirror having a reflective surface extending along an ellipsoidal surface, the sample being placed at one of the foci (F1) of the ellipsoid surface.

2. Spectrograph according to claim 1, wherein the diffraction grating is pivotally mounted about an axis (Z) parallel to its lines.

3. Spectrograph according to claim 2, comprising a detector (5) of the diffracted radiation, the detector being associated with means of its displacement slaved to a rotation of the diffraction grating so as to make a detecting plane of the detector coincide with a formation plane. (P) an image of the sample after diffraction by the diffraction grating.

4. A method of using a spectrograph according to claim 3, wherein it causes a pivoting of the diffraction grating to select a specific spectral range of the secondary radiation to be analyzed.