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Normal incidence spectrometers for the extreme ultraviolet using blazed multilayer coated diffraction gratings
Optics Communications 92 ( 1992) 177-182 North-Holland
OPTICS COMMUNICATIONS
Normal incidence spectrometers for the extreme ultraviolet using blazed multilayer coated diffraction gratings A. R i d g e l e y RutherfordAppleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, UK
Received 30 March 1992
By coating EUV reflecting multilayers onto diffraction gratings a normal incidence spectrometer can be built for use in the traditional grazing incidence region (2-30 nm). The design of blazed multilayer gratings instruments is discussed with reference to analogous soft X-ray crystal instruments. The Johanne crystal spectrometer configuration is a particularly appropriate design concept for such an instrument. High spectral resolution is achievable because the grating operates in a high order (5-10) with the multilayer coating acting as an order sorter. Wavelength tunability can be achieved by interchangable gratings or with mechanical linkages.
1. Introduction The region 2-30 n m has traditionally been one o f the most difficult spectral regions in which to work. Below 2 nm X-ray diffracting crystals can be used effectively and above 30 n m normal incidence optics can be used. In the past the intermediate 2 - 3 0 nm region has been covered using grazing incidence optics. The use o f grazing incidence optics has several disadvantages, the two most significant being small F-number and astigmatism. The development of multilayer coatings having high normal incidence reflectivity in this region (henceforth called the extreme ultraviolet or E U V ) has enabled the advance o f normal incidence techniques into this region. One o f the latest technologies to have been developed is the successful coating o f blazed diffraction gratings to function at normal incidence in this region. The earliest successful coating o f a multilayer onto a grating was by Keski-Kuha [ 1 ] onto a sinusoidal grating. Barbee [2 ] was the first to report multilayer coating of lamellar gratings. Coatings onto blazed gratings have been reported by Jark [3], Rife et al. [4], and Keski-Kuha et al. [5]. The latter multilayer grating coated by GSFC was recently flown on a SERTS rocket experiment [ 6 ]. Rife [ 7 ] has discussed the use o f multilayer coated gratings in some depth in the context o f traditional gratElsevier Science Publishers B.V.
ing mounts. Barbee [ 2 ] has discussed the use of multilayer gratings in more general terms. He showed that the multilayer grating can be scanned over a wide wavelength range away from absorption edges, and discussed the use o f a double multilayer spectrometer analogous to a double crystal spectrometer. Experiments with multilayer coatings have not yet exploited the full potential o f this new technology, and have concentrated on enhancing the reflectivity o f gratings used in traditional fashion, rather than regarding the multilayers as pseudo-crystals. This author believes that multilayer coated gratings should be regarded as pseudo-crystals with enhanced resolution rather than gratings with enhanced reflectivity. This view leads one to look to crystal spectrometer designs rather than grating spectrometer designs, and the Johanne curved crystal geometry in particular.
2. Basic theory of the multilayer grating The basic principle o f using a multilayer coated grating is shown in fig. I. The multilayer coating behaves as a Bragg reflector, so that for rays impinging on a grating facet at grazing angle 0, only wavelengths satisfying the Bragg condition will be reflected at an angle 0 + A0 on the other side o f the nor177
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index correction factor, as has been pointed out by Barbee [2 ]. The reciprocal dispersion of the grating is given by differentiating eq. (5), A0 n A2 - 2dg sin y cos 0"
Fig. 1. Basicprinciple of the multilayerblazed grating. mal, where A0 is the rocking curve width of the multilayer. The Bragg condition for a multilayer is given (for negligible x) by 2=2din sin( 1 - $ x / s i n 2 0 )
,
( 1)
where 2 is the first order wavelength, dm is the multilayer spacing, and ~ is the mean refractive index decrement of the multilayer coating. The rays must simultaneously satisfy the grating equation: nX=dg (sin a - s i n f l ) ,
(2)
where dg is the grating spacing, n is the diffraction order for the grating, ot and fl are the angles of incidence and diffraction, respectively. If 7 is the blaze angle the angles are related in an optimised design according to the equations: ot-fl=2),, O=rc/2-a-
(3) (4)
~, .
Substituting for ot and fl in eq. (2) from eqs. (3) and (4) we obtain n2 = 2dg sin y sin 0.
(5)
Dividing eq. (5) by eq. ( 1 ): dg s i n T / ( 1 n~m
~ )
(6)
This means that if a multilayer grating is wavelength scanned by changing theta, the grating order will remain constant, apart from the effect of the refractive 178
(7)
For even the most finely ruled gratings d 8 is of order 1 gm whereas dm will be comparable to the wavelength being analysed (10 nm). Therefore even for small values of y (about 3 degrees), n will be quite large (5-10). This can be used to advantage as the limited pass band of the multilayer enables it to be used as an order sorter. If 10th order is selected for example 9th and 1 lth orders will be excluded if2/A2 for the multilayer coating exceeds 10. This is possible in principle as multilayer mirrors having resolving powers greater than 50 are now commonly available. The use of a high order means that the grating has a high theoretical resolving power. For instance a 1200 line/mm grating 25 m m wide used in 10th order will in theory have a resolving power of 300000. More realistically perhaps the high dispersion of the high order can be used to achieve a more modest resolving power, but good by EUV standards, in a compact instrument. A 1200 line/mm grating with radius 400 m m will give a reciprocal dispersion of about 0.2 n m / m m in 10th order. This is a resolution of 0.005 nm using a 25 gm slit, which is quite respectable for the EUV. Higher radius gratings will of course give correspondingly higher resolution. Equation (6) shows that the order number does in fact have some dependence on wavelength due to the wavelength dependence of the refractive index term. At any particular wavelength, eqs. (2) and (5) can be satisfied simultaneously by choosing the value of dm which satisfies eq. (2). At other wavelengths however there will be some mismatch between the 0 value which satisfies eq. (2) and the one which satisfies eq. (5). This is quantified in table 1 which is based on some measurements by Urch and Martin [ 8 ] of refractive index decrement values of an Ovionyx multilayer mirror. The optimum dm values to match a 600 l i n e / m m grating blazed at 3.4 degrees and used in 10th order have been listed. An average dm value ( = 10.72 nm) has been taken (excluding the 2.355 nm wavelength
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Table 1 Wavelength (grating) (nm)
~-a
Optimum d~ (nm)
Wavelength (multilayer) (nm)
Order fraction
2.355 3.157 4.479 6.788 7.222 7.68 7.97 8.175 9.359 9.815 10.33 10.43 11.61
1.8 exp-3 2.3 3.0 5.1 8.6 9.7 11 13 19 21 22 21 30
11.32 10.86 10.50 10.33 10.57 10.56 10.60 10.70 10.80 10.80 10.79 10.69 10.89
2.220 3.102 4.552 7.011 7.290 7.760 8.023 8.152 9.246 9.697 10.215 10.410 11.395
-0.63 -0.19 +0.15 +0.30 + 0.08 +0.09 +0.06 -0.03 -0.13 -0.13 -0.12 -0.02 -0.22
point) and the central wavelength reflected by the multilayer with this spacing for the theta values derived from eq. (5) have been listed. Finally the deviation of this wavelength from the initial wavelength has been listed as a fraction of the wavelength spacing between adjacent orders. If this fraction is around 0.5 or greater there will be considerable risk of orders being mixed. In fact it is seen that, with the exception of the 2.355 nm point, the order fraction is small enough not to be a problem. This means that wavelength scanning over a wide range is a feasible proposition.
respect with reference to X-ray fluorescence spectroscopy. Using a plane multilayer grating the resolving power can be increased over that of the plane multilayer mirror providing the grating has a fine enough ruling spacing and is used in a high enough order. Putting in typical values for commercial gratings and mechanical collimators in eq. (7), it is seen that a resolving power of around 600 can be obtained at 10 nm using a 1200 line/mm grating with blaze angle 6.8 degrees and used in 10th order with a slit collimator of 1 mrad resolution.
3. The multilayer grating applied to a Bragg spectrometer
4. The plane multilayer grating in a divergent beam
In a conventional Bragg spectrometer a mechanically collimated beam of X-rays is incident on a plane crystal. Only the narrow range of wavelengths which satisfy the Bragg criterion at this angle are diffracted by the crystal. Wavelength scan is achieved by rotating the crystal and detector together, such that the detector always intercepts the reflected beam. Plane multilayer mirrors can be, and are, used to extend the range of Bragg spectrometers into the EUV where there is a lack of suitable crystals. The disadvantage of multilayer mirrors is the wavelength resolution of 100 or less limits the science that can be achieved. Luck and Urch [ 9 ] have discussed the use of multilayer mirrors and large 2d crystals in this
When an X-ray source is small enough to approximate to a point source, as in laser-produced plasmas for example, the arrangement shown in fig. 2 is useful. An X-ray spectrum is obtained by virtue of the fact that rays from the source hit the crystal at different theta values along the crystal. Because there is no focussing in this spectrometer the source to detector distance is usually kept as small as possible. A multilayer mirror could be used in place of a crystal for EUV applications of this spectrometer but would have the disadvantage of having the low spectral resolution of the multilayer coating. By using a multilayer grating instead of a mirror the resolution can be improved as the angular spread of a wavelength resolution element will be defined by the grat179
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5. The use of the Johanne configuration for the multilayer grating
"POINT SOURCE"
Fig. 2. Schematic of plane "mini" spectrometer.
ing spacing rather than the multilayer coating resolution. The resolving power can be defined by the number of rulings illuminated by a wavelength resolution element, and will be given by the equation
R=nw/dg where w is the width of grating illuminated by one wavelength resolution element. The resolving power can also be defined as 2/A2, where A2 is obtained by differentiating eq. (5) and substituting for A0 from the equation A0= (w sin 0 ) / u, where u is the distance of the "point" source from the grating. This gives the following expression for the resolving power
R=u/(wcos O). These two methods of calculating the resolving power must yield the same result, which will happen for w given by
w=x/ud,/(u cos 0 ) . As an example, putting in values of u = 5 0 ram, dg=833 nm, n = 10, 0=45, a theoretical resolving power of around 900 is obtained for a nominal grating width of around 75 ~tm.
In order to achieve high spectral resolution it is generally necessary in the soft X-ray region to employ focussing crystal spectrometers. The Johanne crystal spectrometer can be regarded as the standard configuration in this respect. In the Johanne crystal geometry a crystal is bent to a cylindrical shape. It then follows that a source placed on a Rowland circle which includes the crystal will, to good approximation, be imaged monochromatically (within the spectral resolution of the crystal) at a point on the Rowland circle symmetrically on the other side of the crystal normal. It also follows that if an extended source is placed outside the Rowland circle a detector placed around the Rowland circle will record a spectrum with resolving power determined by the crystal rocking curve. This principle has been used in the recording of Tokamak X-ray spectra [ 10 ]. The same principle applies to a multilayer mirror coating on a concave surface. In this case however the spectral resolving power is much less than a crystal, due to the much smaller number of layers involved. An EUV multilayer will have a resolving power of about 50 in contrast to a crystal resolving power of 1000 or more. By coating the multilayer onto a diffraction grating it will have a resolving power pertaining to the grating, as described in section 2, provided there is a narrow entrance slit on the Rowland circle. If a blazed diffraction grating is used the blaze normal not the grating normal is appropriate for locating the diffracted beam, as shown in fig. 3. With the entrance slit at a given point P on the Rowland circle a narrow range of spectrum is obtained, centred on P'. To change wavelength it is necessary to move P and P' symmetrically about the blaze normal, it is seen from eqs. (2) and (3) that this maintains the blaze condition and the order number (if the effect of the refractive index term is ignored).
6. Means of achieving wavelength tunability The principle disadvantage of the Johanne config-
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mal incidence Johanne instrument would have the advantage of being more compact because of using a higher order. This author has outlined such an arrangement [ 12 ].
6.2. Changing wavelength range using mechanical linkages
GRATING Fig. 3. Schematic of blazed mu]tilayer grating used in "Johanne" configuration.
uration for a grating spectrometer is that both the entrance slit and detector have to be moved relative to the grating in order to change the wavelength range. This disadvantage is somewhat mitigated by the fact that the low spectral resolution of the multilayer gives some free spectral range even for a fixed optical arrangement. For example at 10 nm say there is about 1 nm of working spectrum range in 10th order and about 2 nm in 5th order. To make a more generally useful instrument however a means of changing the wavelength outside such a restricted range is needed.
Although the relative motion required to change wavelength range is a symmetrical movement of the entrance slit and detector about the blaze normal, the grating remaining stationary, there is no need for this to be the case in absolute motion. It is possible to have the entrance slit or detector stationary and move the other two elements. It will be most generally useful to have a stationary entrance slit (with stationary source) and to move the grating and detector. This is achievable by use of a suitable mechanical linkage, one possible arrangement is shown in fig. 4. A circular rail is built to the exact Rowland circle dimensions and is rotatable about one point on its circumference. The fixed entrance slit is mounted at this point. The grating and detector are constrained to move around the Rowland circle by means of springs pressing them against this rail. The grating is also constrained to move along a straight rail R1 connecting it to the entrance slit. Likewise the detector is constrained to move along a second straight
6.1. Changing wavelength range by means of interchangable gratings One way of extending the range of the instrument is to have a selection of gratings, each optimised for a different order. Thus it would be possible to cover the range 10-20 nm using six gratings having d spacings appropriate to orders 5 to 10 inclusive. This method has the advantage that both the source and detector can remain fixed, and would be appropriate in applications where both the source and detector are unwieldy. Time resolved measurements of laser produced plasmas with high spectral resolution would be an example. Such measurements can be made with the very ingenious high resolution fiat field spectrometer invented by Hettrick et al. [ 11 ], but a nor-
RAIL R2
DETECTOR
SLIT
RAIL R3
GRATING Fig. 4. A mechanical linkage to effect wavelength changes.
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rail R2 connecting the detector a n d the entrance slit. Rail R2 is constrained to m o v e along a t h i r d straight rail R3 which connects R2 to the grating along the blaze normal. R2 a n d R3 are inclined at an angle 9 0 - 7 to each other. A change in wavelength range is accomplished by rotating the R o w l a n d circle rail. The mechanical linkages and physical constraints placed on the optical c o m p o n e n t s will then ensure the Johanne focussing conditions are m a i n t a i n e d within engineering tolerances.
7. Summary The basic theory o f how a multilayer coated grating will work has been presented, a n d some spect r o m e t e r configurations have been considered a n d c o m p a r e d with analogous crystal arrangements. A multi-layer spectrometer would have the advantage o f bringing the region 2 - 3 0 n m within the range o f n o r m a l incidence spectrometers with the corresponding advantages o f reduced astigmatism a n d greater aperture. Also, because the multilayer grating
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is used in a fairly high order, c o m p a c t instruments having high spectral resolution can, in principle, be made. M e t h o d s o f changing wavelength range have been discussed.
References [ 1] R.A.M. Keski-Kuha, Appl. Optics 23 (1984) 3534. [ 2 ] T.W. Barbee Jr., Rev. Sci. Instrum. 60 (1989) 1588. [3] W. Jark, Optics Comm. 65 (1986) 201. [4] J.C. Rife, T.W. Barbee Jr., W.R. Hunter and R.G. Cruddace, Appl. Optics 28 (1989) 2984. [ 5 ] R.A.M. Keski-Kuha, R.J. Thomas, J.S. Gum, C.E. Condor, Appl. Optics 29 (1990) 4529. [6] R.J. Thomas, R.A.M. Keski-Kuha, W.M. Neupert, C.E. Condor and J.S. Gum, Appl. Optics 30 ( 1991 ) 2245. [7] J.C. Rife, NRL Memorandum, Report 6278 (1988). [8] D.S. Urch and E. Martin, Central Laser Facility Annual Report RAL-91-025 ( 1991 ) p. 68. [ 9 ] S. Luck and D.S. Urch, Physica Scripta 41 (1990) 749. [ 10] J. Dunn, R. Barnsley, K.D. Evans and N.J. Peacock, Proc. IAU Colloq. no. 102 on UV and X-ray spectroscopy of astrophysical and laboratory plasmas, J. Phys. (Paris) C1 (1988) 88. [ 11 ] M.C. Hettrick, J.H. Underwood, P.J. Batson and M.J. Echart, Appl. Optics 27 (1988) 200. [ 12 ] A. Ridgeley, Central Laser FacilityAnnual Report RAL-90026 (1990) p. 70.
OPTICS COMMUNICATIONS
Normal incidence spectrometers for the extreme ultraviolet using blazed multilayer coated diffraction gratings A. R i d g e l e y RutherfordAppleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, UK
Received 30 March 1992
By coating EUV reflecting multilayers onto diffraction gratings a normal incidence spectrometer can be built for use in the traditional grazing incidence region (2-30 nm). The design of blazed multilayer gratings instruments is discussed with reference to analogous soft X-ray crystal instruments. The Johanne crystal spectrometer configuration is a particularly appropriate design concept for such an instrument. High spectral resolution is achievable because the grating operates in a high order (5-10) with the multilayer coating acting as an order sorter. Wavelength tunability can be achieved by interchangable gratings or with mechanical linkages.
1. Introduction The region 2-30 n m has traditionally been one o f the most difficult spectral regions in which to work. Below 2 nm X-ray diffracting crystals can be used effectively and above 30 n m normal incidence optics can be used. In the past the intermediate 2 - 3 0 nm region has been covered using grazing incidence optics. The use o f grazing incidence optics has several disadvantages, the two most significant being small F-number and astigmatism. The development of multilayer coatings having high normal incidence reflectivity in this region (henceforth called the extreme ultraviolet or E U V ) has enabled the advance o f normal incidence techniques into this region. One o f the latest technologies to have been developed is the successful coating o f blazed diffraction gratings to function at normal incidence in this region. The earliest successful coating o f a multilayer onto a grating was by Keski-Kuha [ 1 ] onto a sinusoidal grating. Barbee [2 ] was the first to report multilayer coating of lamellar gratings. Coatings onto blazed gratings have been reported by Jark [3], Rife et al. [4], and Keski-Kuha et al. [5]. The latter multilayer grating coated by GSFC was recently flown on a SERTS rocket experiment [ 6 ]. Rife [ 7 ] has discussed the use o f multilayer coated gratings in some depth in the context o f traditional gratElsevier Science Publishers B.V.
ing mounts. Barbee [ 2 ] has discussed the use of multilayer gratings in more general terms. He showed that the multilayer grating can be scanned over a wide wavelength range away from absorption edges, and discussed the use o f a double multilayer spectrometer analogous to a double crystal spectrometer. Experiments with multilayer coatings have not yet exploited the full potential o f this new technology, and have concentrated on enhancing the reflectivity o f gratings used in traditional fashion, rather than regarding the multilayers as pseudo-crystals. This author believes that multilayer coated gratings should be regarded as pseudo-crystals with enhanced resolution rather than gratings with enhanced reflectivity. This view leads one to look to crystal spectrometer designs rather than grating spectrometer designs, and the Johanne curved crystal geometry in particular.
2. Basic theory of the multilayer grating The basic principle o f using a multilayer coated grating is shown in fig. I. The multilayer coating behaves as a Bragg reflector, so that for rays impinging on a grating facet at grazing angle 0, only wavelengths satisfying the Bragg condition will be reflected at an angle 0 + A0 on the other side o f the nor177
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index correction factor, as has been pointed out by Barbee [2 ]. The reciprocal dispersion of the grating is given by differentiating eq. (5), A0 n A2 - 2dg sin y cos 0"
Fig. 1. Basicprinciple of the multilayerblazed grating. mal, where A0 is the rocking curve width of the multilayer. The Bragg condition for a multilayer is given (for negligible x) by 2=2din sin( 1 - $ x / s i n 2 0 )
,
( 1)
where 2 is the first order wavelength, dm is the multilayer spacing, and ~ is the mean refractive index decrement of the multilayer coating. The rays must simultaneously satisfy the grating equation: nX=dg (sin a - s i n f l ) ,
(2)
where dg is the grating spacing, n is the diffraction order for the grating, ot and fl are the angles of incidence and diffraction, respectively. If 7 is the blaze angle the angles are related in an optimised design according to the equations: ot-fl=2),, O=rc/2-a-
(3) (4)
~, .
Substituting for ot and fl in eq. (2) from eqs. (3) and (4) we obtain n2 = 2dg sin y sin 0.
(5)
Dividing eq. (5) by eq. ( 1 ): dg s i n T / ( 1 n~m
~ )
(6)
This means that if a multilayer grating is wavelength scanned by changing theta, the grating order will remain constant, apart from the effect of the refractive 178
(7)
For even the most finely ruled gratings d 8 is of order 1 gm whereas dm will be comparable to the wavelength being analysed (10 nm). Therefore even for small values of y (about 3 degrees), n will be quite large (5-10). This can be used to advantage as the limited pass band of the multilayer enables it to be used as an order sorter. If 10th order is selected for example 9th and 1 lth orders will be excluded if2/A2 for the multilayer coating exceeds 10. This is possible in principle as multilayer mirrors having resolving powers greater than 50 are now commonly available. The use of a high order means that the grating has a high theoretical resolving power. For instance a 1200 line/mm grating 25 m m wide used in 10th order will in theory have a resolving power of 300000. More realistically perhaps the high dispersion of the high order can be used to achieve a more modest resolving power, but good by EUV standards, in a compact instrument. A 1200 line/mm grating with radius 400 m m will give a reciprocal dispersion of about 0.2 n m / m m in 10th order. This is a resolution of 0.005 nm using a 25 gm slit, which is quite respectable for the EUV. Higher radius gratings will of course give correspondingly higher resolution. Equation (6) shows that the order number does in fact have some dependence on wavelength due to the wavelength dependence of the refractive index term. At any particular wavelength, eqs. (2) and (5) can be satisfied simultaneously by choosing the value of dm which satisfies eq. (2). At other wavelengths however there will be some mismatch between the 0 value which satisfies eq. (2) and the one which satisfies eq. (5). This is quantified in table 1 which is based on some measurements by Urch and Martin [ 8 ] of refractive index decrement values of an Ovionyx multilayer mirror. The optimum dm values to match a 600 l i n e / m m grating blazed at 3.4 degrees and used in 10th order have been listed. An average dm value ( = 10.72 nm) has been taken (excluding the 2.355 nm wavelength
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Table 1 Wavelength (grating) (nm)
~-a
Optimum d~ (nm)
Wavelength (multilayer) (nm)
Order fraction
2.355 3.157 4.479 6.788 7.222 7.68 7.97 8.175 9.359 9.815 10.33 10.43 11.61
1.8 exp-3 2.3 3.0 5.1 8.6 9.7 11 13 19 21 22 21 30
11.32 10.86 10.50 10.33 10.57 10.56 10.60 10.70 10.80 10.80 10.79 10.69 10.89
2.220 3.102 4.552 7.011 7.290 7.760 8.023 8.152 9.246 9.697 10.215 10.410 11.395
-0.63 -0.19 +0.15 +0.30 + 0.08 +0.09 +0.06 -0.03 -0.13 -0.13 -0.12 -0.02 -0.22
point) and the central wavelength reflected by the multilayer with this spacing for the theta values derived from eq. (5) have been listed. Finally the deviation of this wavelength from the initial wavelength has been listed as a fraction of the wavelength spacing between adjacent orders. If this fraction is around 0.5 or greater there will be considerable risk of orders being mixed. In fact it is seen that, with the exception of the 2.355 nm point, the order fraction is small enough not to be a problem. This means that wavelength scanning over a wide range is a feasible proposition.
respect with reference to X-ray fluorescence spectroscopy. Using a plane multilayer grating the resolving power can be increased over that of the plane multilayer mirror providing the grating has a fine enough ruling spacing and is used in a high enough order. Putting in typical values for commercial gratings and mechanical collimators in eq. (7), it is seen that a resolving power of around 600 can be obtained at 10 nm using a 1200 line/mm grating with blaze angle 6.8 degrees and used in 10th order with a slit collimator of 1 mrad resolution.
3. The multilayer grating applied to a Bragg spectrometer
4. The plane multilayer grating in a divergent beam
In a conventional Bragg spectrometer a mechanically collimated beam of X-rays is incident on a plane crystal. Only the narrow range of wavelengths which satisfy the Bragg criterion at this angle are diffracted by the crystal. Wavelength scan is achieved by rotating the crystal and detector together, such that the detector always intercepts the reflected beam. Plane multilayer mirrors can be, and are, used to extend the range of Bragg spectrometers into the EUV where there is a lack of suitable crystals. The disadvantage of multilayer mirrors is the wavelength resolution of 100 or less limits the science that can be achieved. Luck and Urch [ 9 ] have discussed the use of multilayer mirrors and large 2d crystals in this
When an X-ray source is small enough to approximate to a point source, as in laser-produced plasmas for example, the arrangement shown in fig. 2 is useful. An X-ray spectrum is obtained by virtue of the fact that rays from the source hit the crystal at different theta values along the crystal. Because there is no focussing in this spectrometer the source to detector distance is usually kept as small as possible. A multilayer mirror could be used in place of a crystal for EUV applications of this spectrometer but would have the disadvantage of having the low spectral resolution of the multilayer coating. By using a multilayer grating instead of a mirror the resolution can be improved as the angular spread of a wavelength resolution element will be defined by the grat179
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5. The use of the Johanne configuration for the multilayer grating
"POINT SOURCE"
Fig. 2. Schematic of plane "mini" spectrometer.
ing spacing rather than the multilayer coating resolution. The resolving power can be defined by the number of rulings illuminated by a wavelength resolution element, and will be given by the equation
R=nw/dg where w is the width of grating illuminated by one wavelength resolution element. The resolving power can also be defined as 2/A2, where A2 is obtained by differentiating eq. (5) and substituting for A0 from the equation A0= (w sin 0 ) / u, where u is the distance of the "point" source from the grating. This gives the following expression for the resolving power
R=u/(wcos O). These two methods of calculating the resolving power must yield the same result, which will happen for w given by
w=x/ud,/(u cos 0 ) . As an example, putting in values of u = 5 0 ram, dg=833 nm, n = 10, 0=45, a theoretical resolving power of around 900 is obtained for a nominal grating width of around 75 ~tm.
In order to achieve high spectral resolution it is generally necessary in the soft X-ray region to employ focussing crystal spectrometers. The Johanne crystal spectrometer can be regarded as the standard configuration in this respect. In the Johanne crystal geometry a crystal is bent to a cylindrical shape. It then follows that a source placed on a Rowland circle which includes the crystal will, to good approximation, be imaged monochromatically (within the spectral resolution of the crystal) at a point on the Rowland circle symmetrically on the other side of the crystal normal. It also follows that if an extended source is placed outside the Rowland circle a detector placed around the Rowland circle will record a spectrum with resolving power determined by the crystal rocking curve. This principle has been used in the recording of Tokamak X-ray spectra [ 10 ]. The same principle applies to a multilayer mirror coating on a concave surface. In this case however the spectral resolving power is much less than a crystal, due to the much smaller number of layers involved. An EUV multilayer will have a resolving power of about 50 in contrast to a crystal resolving power of 1000 or more. By coating the multilayer onto a diffraction grating it will have a resolving power pertaining to the grating, as described in section 2, provided there is a narrow entrance slit on the Rowland circle. If a blazed diffraction grating is used the blaze normal not the grating normal is appropriate for locating the diffracted beam, as shown in fig. 3. With the entrance slit at a given point P on the Rowland circle a narrow range of spectrum is obtained, centred on P'. To change wavelength it is necessary to move P and P' symmetrically about the blaze normal, it is seen from eqs. (2) and (3) that this maintains the blaze condition and the order number (if the effect of the refractive index term is ignored).
6. Means of achieving wavelength tunability The principle disadvantage of the Johanne config-
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mal incidence Johanne instrument would have the advantage of being more compact because of using a higher order. This author has outlined such an arrangement [ 12 ].
6.2. Changing wavelength range using mechanical linkages
GRATING Fig. 3. Schematic of blazed mu]tilayer grating used in "Johanne" configuration.
uration for a grating spectrometer is that both the entrance slit and detector have to be moved relative to the grating in order to change the wavelength range. This disadvantage is somewhat mitigated by the fact that the low spectral resolution of the multilayer gives some free spectral range even for a fixed optical arrangement. For example at 10 nm say there is about 1 nm of working spectrum range in 10th order and about 2 nm in 5th order. To make a more generally useful instrument however a means of changing the wavelength outside such a restricted range is needed.
Although the relative motion required to change wavelength range is a symmetrical movement of the entrance slit and detector about the blaze normal, the grating remaining stationary, there is no need for this to be the case in absolute motion. It is possible to have the entrance slit or detector stationary and move the other two elements. It will be most generally useful to have a stationary entrance slit (with stationary source) and to move the grating and detector. This is achievable by use of a suitable mechanical linkage, one possible arrangement is shown in fig. 4. A circular rail is built to the exact Rowland circle dimensions and is rotatable about one point on its circumference. The fixed entrance slit is mounted at this point. The grating and detector are constrained to move around the Rowland circle by means of springs pressing them against this rail. The grating is also constrained to move along a straight rail R1 connecting it to the entrance slit. Likewise the detector is constrained to move along a second straight
6.1. Changing wavelength range by means of interchangable gratings One way of extending the range of the instrument is to have a selection of gratings, each optimised for a different order. Thus it would be possible to cover the range 10-20 nm using six gratings having d spacings appropriate to orders 5 to 10 inclusive. This method has the advantage that both the source and detector can remain fixed, and would be appropriate in applications where both the source and detector are unwieldy. Time resolved measurements of laser produced plasmas with high spectral resolution would be an example. Such measurements can be made with the very ingenious high resolution fiat field spectrometer invented by Hettrick et al. [ 11 ], but a nor-
RAIL R2
DETECTOR
SLIT
RAIL R3
GRATING Fig. 4. A mechanical linkage to effect wavelength changes.
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rail R2 connecting the detector a n d the entrance slit. Rail R2 is constrained to m o v e along a t h i r d straight rail R3 which connects R2 to the grating along the blaze normal. R2 a n d R3 are inclined at an angle 9 0 - 7 to each other. A change in wavelength range is accomplished by rotating the R o w l a n d circle rail. The mechanical linkages and physical constraints placed on the optical c o m p o n e n t s will then ensure the Johanne focussing conditions are m a i n t a i n e d within engineering tolerances.
7. Summary The basic theory o f how a multilayer coated grating will work has been presented, a n d some spect r o m e t e r configurations have been considered a n d c o m p a r e d with analogous crystal arrangements. A multi-layer spectrometer would have the advantage o f bringing the region 2 - 3 0 n m within the range o f n o r m a l incidence spectrometers with the corresponding advantages o f reduced astigmatism a n d greater aperture. Also, because the multilayer grating
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is used in a fairly high order, c o m p a c t instruments having high spectral resolution can, in principle, be made. M e t h o d s o f changing wavelength range have been discussed.
References [ 1] R.A.M. Keski-Kuha, Appl. Optics 23 (1984) 3534. [ 2 ] T.W. Barbee Jr., Rev. Sci. Instrum. 60 (1989) 1588. [3] W. Jark, Optics Comm. 65 (1986) 201. [4] J.C. Rife, T.W. Barbee Jr., W.R. Hunter and R.G. Cruddace, Appl. Optics 28 (1989) 2984. [ 5 ] R.A.M. Keski-Kuha, R.J. Thomas, J.S. Gum, C.E. Condor, Appl. Optics 29 (1990) 4529. [6] R.J. Thomas, R.A.M. Keski-Kuha, W.M. Neupert, C.E. Condor and J.S. Gum, Appl. Optics 30 ( 1991 ) 2245. [7] J.C. Rife, NRL Memorandum, Report 6278 (1988). [8] D.S. Urch and E. Martin, Central Laser Facility Annual Report RAL-91-025 ( 1991 ) p. 68. [ 9 ] S. Luck and D.S. Urch, Physica Scripta 41 (1990) 749. [ 10] J. Dunn, R. Barnsley, K.D. Evans and N.J. Peacock, Proc. IAU Colloq. no. 102 on UV and X-ray spectroscopy of astrophysical and laboratory plasmas, J. Phys. (Paris) C1 (1988) 88. [ 11 ] M.C. Hettrick, J.H. Underwood, P.J. Batson and M.J. Echart, Appl. Optics 27 (1988) 200. [ 12 ] A. Ridgeley, Central Laser FacilityAnnual Report RAL-90026 (1990) p. 70.