Multilayer based soft-x-ray polarimeter at MAX IV Laboratory

REVIEW OF SCIENTIFIC INSTRUMENTS 87, 025102 (2016)
Multilayer based soft-x-ray polarimeter at MAX IV Laboratory
Walan Grizolli, Joakim Laksman, Franz Hennies, Brian Norsk Jensen,
Ralf Nyholm, and Rami Sankaria)
MAX IV Laboratory, P.O. Box 118, SE-22100 Lund, Sweden
(Received 12 September 2015; accepted 18 January 2016; published online 4 February 2016)
A high precision five rotation-axes polarimeter using transmission multilayers as polarizers and
reflection multilayers as analyzers has been designed and manufactured. To cover the extreme
ultraviolet regime, Mo/Si, Cr/C, Sc/Cr, and W/B4C multilayers for transmission and reflection have
also been designed and produced. The polarimeter mechanics is supported on a hexapod to simplify
the alignment relative to photon beam. The instrument is designed so that it can be easily transferred
between different beamlines. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4941066]
I. INTRODUCTION
The impact of circularly polarized synchrotron radia-
tion has increased rapidly since the introduction of ellipti-
cally polarizing undulators (EPUs) two decades ago.1,2
The
tunability of the photon energy combined with full control
of the polarization is of importance for a large variety of
experiments at synchrotron radiation facilities. In gas phase
studies, it has allowed to observe photo-electron circular
dichroism3–5
and is vital to understand the dynamics of
inner-valence and core-excited molecules.6–8
For metals and
crystals, it can be used to probe properties such as magnetic
circular dichroism9,10
as well as electronic and magnetic
structures with applications in magneto-optical memories.11,12
In life science, it provides information regarding the chirality
of biological compounds.13–15
To better understand these
processes, information about the polarization is crucial since
the magnitude of observed effects depends on the degree of
polarization.
An EPU produces practically, completely, and circularly
polarized light when the first harmonic of the undulator
radiation is used. The first harmonic, however, covers only
limited photon energies and higher harmonics must be used
to extend the energy range; the drawback is a reduction in
the degree of circular polarization. The degree of circular
polarization of the undulator radiation can be estimated by
simulations, but interaction with beamline optics changes
the polarization and, unless measured, the polarization state
is rarely known precisely. In addition, modern EPUs can
be tuned to produce certain states of elliptical light that
will be circular at the experiment end station, compensating
beamlines effects. This is crucial for maximizing the degree
of circular polarization but requires information about the
polarization at each setting. At present, MAX IV Laboratory
has three beamlines based on EPUs (beamlines I101116
and
SPECIES17
at the MAX II ring, and I318
at MAX III ring)
spanning a photon energy range of 5–1200 eV. The importance
of the polarization studies increases even further when the
MAX IV Laboratory will be completed since virtually all
the vacuum ultraviolet (VUV) and soft-X-ray beamlines will
a)Electronic mail: rami.sankari@maxlab.lu.se
be based on EPUs. To analyze the polarization at these
beamlines, two polarimeters were designed and built for MAX
IV Laboratory: a compact VUV polarimeter19
and a high
accuracy, multilayer based soft-X-ray polarimeter which is
described in more detail in this paper.
It is worth noticing that although indicative measurements
about linear or circular polarization can be made with simpler
instruments,20
reference samples,21
or simple spectroscopic
instruments,22
polarimeters are still the main instruments when
complete information about the polarization is needed: with
these devices, it is possible to disentangle between polarized
(linearly or circularly) and unpolarized light; this is not
possible with simple instruments. There are several examples
of both reflection23–25
and multilayer26,27
based polarimeters
but as shown by Veyrinas and co-workers,28
spectroscopic
instrumentation can also be used for complete polarization
analysis. In addition, recent development in non-resonant
multilayers, see, e.g., Refs. 27 and 29, allows to cover the high
energy side of the soft-X-ray region with a self-calibrating
method, widening the operation range of the polarimeters.
II. MECHANICAL DESIGN
The polarimeter is based on rotating both the transmission
and reflection multilayers around the photon beam, and
therefore, it must be placed so that the axis coincides with
the photon beam. The stand and the vacuum chamber, as
well as the polarimeter itself, are manufactured by Toyama
Co. Ltd., Japan. Earlier, high accuracy devices at BESSY26
and Diamond27
have shown the importance of decoupling the
actual instrument from the vacuum. Here, this was realized by
using a Kuban hexapod support provided by Symetrie, France,
which also allows for high accuracy, automatized alignment of
the polarimeter itself. This makes it possible to place the polar-
imeter accurately and with high reproducibility: deviations are
below 1 µm in all translations and 1 µrad in rotations.
A. Stand and chamber
The design of the instrument is such that both the hexapod
and the support for the vacuum vessel sit on the same bottom
plate (see Fig. 1). Three MAX IV Laboratory standard legs
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19:48:38

025102-2 Grizolli et al. Rev. Sci. Instrum. 87, 025102 (2016)
FIG. 1. Left: The support for the vacuum chamber and the hexapod system supporting the mounting plate where the polarimeter mechanics is attached. Right:
Polarimeter mechanics showing all the motorized motions and their assignment. Please see text for details.
for height adjustment are placed between the bottom plate and
a base plate and are located under the support points of the
hexapod. These legs take the weight of the whole setup and
transfer the support points down to the floor via the base plate,
which is used as support point for all the translations and height
adjustment. Four adjustable legs at the corners of the bottom
plate are used only to prevent the bending vibrations of this
plate—they are not meant to take load but only add stiffness to
the setup. The mounting plate for the polarimeter is supported
by two sturdy support columns mounted on the top plate of
the hexapod. The vacuum chamber is in turn connected to that
via low-coupling edge-welded bellows.
B. Polarimeter
For reliable measurements, and to ease the data analysis
and operation, the two independent rotation axes for the
polarizer (acting as a phase shifter) and analyzer must
coincide, and stay stable. Earlier, similar set-ups rely on back-
to-back mounted rotation stages which are known to produce
gravitational sag, specifically in the usually heavier analyzer
side (see, e.g., discussion in Ref. 27). For this instrument,
a different approach was proposed by the manufacturer:
increased accuracy in manufacturing and assembling allows
for an instrument which is supported not only at the middle
but also at both ends. The same principle, relying on high
accuracy manufacturing, has been found very effective in the
whole MAX IV Laboratory design and was applied to this
instrument too. The azimuthal rotation stages for the polarizer
and analyzer stages (α and β) are identical except that the
latter has an additional stage for housing the independently
controlled 2θ detector arm. For aligning the instrument relative
to the photon beam, we chose a similar pinhole system as
described by Nahon:24
one set of pinholes allows light to pass
whereas the other set has a large area photodiode behind it.
The horizontal alignment of these pinhole units relative to the
optical axis of the polarimeter is manual only. It has been
set and locked by the manufacturer when the instrument was
characterized in atmosphere. Vertical movement is motorized
and equipped with an absolute encoder for placing the desired
pinhole on the pre-defined optical axis of the instrument. The
ranges and accuracy of movements together with concentricity
and parallelism (or perpendicularity) of all the axis pairs
are presented in Table I. These values are obtained by a
combination of autocollimator, laser tracker, and linear height
gauge measurements provided by the manufacturer.
The polarimeter was purchased with a set of multilayers
optimized for ca. 100 eV, 300 eV, 400 eV, and 500 eV
photon energies, and a broad band multilayer working in
the c.a. 600-1200 eV photon energy range. The polarizers
are completely free standing multilayers. The characteristics
of these multilayers, fabricated by magnetron sputtering, are
presented in Table II. All the multilayers are manufactured
by NTT Advanced Technology Corp., Japan. They were also
tested before delivery with a laboratory based X-ray source
(Cu Kα). The multilayers can be exchanged in-vacuum during
the operation: a movable sample exchange unit can house five
polarizers and five analyzers. Two wobble sticks mounted on
the vacuum chamber are used for transferring the multilayers
from the exchange unit to the rotation stages.
C. Stability and alignment
Stability is one of the main aims of the MAX IV Labo-
ratory, and the polarimeter was one of the first instruments
where stability was a crucial design parameter. Well defined,
large contact area support points are needed and the base plate
has three 5 mm high protrusions towards the floor for that.
A thin layer of viscoelastic material (Terostat®) is placed
between the protrusions and the floor to take out the effects of
local roughness of the floor and thus spread the load evenly.
This support is transferred to the base plate of the hexapod,
19:48:38

TABLE I. Ranges and accuracy of movement together with concentricity and parallelism of all the axis pairs.
Optical axis Angular range (deg) Resolution (deg)
Polarizer rotation, α −5 to 365 0.0063
Analyser rotation, β −5 to 365 0.0063
Incidence angle, polarizer, θP −5 to 185 0.0008
Incidence angle, analyzer, θA −5 to 95 0.0008
Detector angle, 2θA −5 to 185 0.0125
Axis pair alignment Angular (deg) Lateral (µm)
α, β 0.007 5 ∥ 7.6
α,θP 0.001 6 ⊥ 33
β,θA 0.000 95 ⊥ 48
β,2θA 0.004 4 ⊥ 43
θ,2θA 0.008 4 ⊥ 5
Multilayer polarizer, θP 0.000 6 ∥ 0.2
Multilayer analyzer, θA 0.000 4 ∥ 4.1
holding the polarimeter itself, via the three height adjustment
legs and the hexapod as described in Section II A. It is worth
mentioning that the height adjustment legs are right below
the laser tracker nests and leveling is facilitated by a very
direct response to the adjustment. The instrument, in general,
adheres to the design principles for all MAX IV Laboratory
components and instruments: the floor is brought as close to
the photon beam as possible by strong links which have a large
contact area. Stability of the polarimeter itself was tested with
a vibrometer (Polytec OFV-534 Compact Sensor Head with
OFV-500 Control Unit). The results show that the instrument
picks up some noise from the floor with an eigenfrequency of
ca. 13 Hz but the amplitude remains low, ca. 100 nm, which
is perfectly acceptable for an end-station-type of instrument.
The measurements also show that there is a coupling between
the vacuum vessel and the polarimeter but it is very weak.
Seeing some coupling is not surprising as the vacuum vessel
and its stand are necessarily connected via the bottom plate
and the bellows by design, but the weakness of this coupling
serves as proof of successful design principles for this movable
TABLE II. Characteristics of the multilayers. Period length d is given in
nanometers, N presents the number of layer pairs, and Γ gives the ratio of
layer thickness of the first element to the period length d. Roughness of
the interfaces and surfaces, ρ is a root means square (rms) value; the actual
measurements ranged between 3 and 4 Å.
Analysers d (nm) N Γ ρ (Å)
Mo/Si 9.40 100 0.33 <4
Cr/C 3.09 280 0.33 <4
Sc/Cr 2.615 400 0.50 <4
W/B4C 1.715 350 0.24 <4
Polarisersa
Mo/Si 9.40 100 0.33 <4
Cr/C 3.145 280 0.33 <4
Sc/Cr 2.56 400 0.50 <4
W/B4C 1.718 350 0.24 <4
aThese polarizers have window size of 6 mm×6 mm. Si frames are designed to have up
to 8 mm×8 mm window area and to accept a 2 mm beam down to 21◦ grazing incidence
angle without cutting the transmitted beam.
instrument. One should note also that the hexapod with its
active compensation of positioning is not a stiff link in the
classical sense. Nevertheless, it is clear that the instrument
is capable of keeping its position and direction easily within
1 µm and 1 µrad, respectively.
For preliminary alignment of the instrument at a beamline,
the top plate of the hexapod is equipped with four laser tracker
target nests.30
A 3D model of the beamline and the polarimeter
was used in a software package (Spatial Analyzer, by New
River Kinematics) to conduct the fiducialization and the
alignment. The nests were fiducialized in-air to the optical axis
of the polarimeter, using a coordinate measuring arm (Romer
Absolute Arm, model 7525). A laser tracker (Leica AT 401)
was used for the alignment to the beamline. The alignment
procedure was tested at the SPECIES beamline of the MAX
II ring. Once the laser tracker was referenced to the beamline
coordinate system, the alignment of the polarimeter took only
about 30 min, which is important, since the polarimeter will
often have to be moved between beamlines. The precision of
the preliminary alignment of the polarimeter to the beamline
is expected to be better than 100 µm.
For final alignment, a set of pinholes at the front and
back of the instrument are used: Upstream signal from the
photodiode behind the largest front pinhole (Ø2 mm) is
maximized by translating the polarimeter along horizontal and
vertical axis by using the hexapod. The accuracy of the front
alignment can be increased by repeating the procedure until the
smallest pinhole is in use (Ø50 µm). The power of the hexapod
based system is evident when aligning the downstream end of
the instrument: the front pinhole location can be set as a center
of rotation for the hexapod, and the optimal place for the back
of the instrument is found by scanning two hexapod rotations,
one along the horizontal direction and one along the vertical
direction. Again, the alignment begins with the largest pinhole
and final adjustment is done with one of the smallest pinholes
downstream of the polarimeter. The design goal was that this
procedure alone is enough to place the polarimeter mechanics
inside the vacuum vessel but, in principle, the method based
on polarizer and analyzer supports, as described in Ref. 27, is
possible.
19:48:38

D. Control of the instrument
In terms of hardware, the motions are realized by eight
Phytron stepper motors (type: VSS32.200, VSS42.200, and
VSS52.200). All the axes are equipped with the Renishaw
Resolute absolute encoders. The motors and the encoders are
controlled by an IcePAP31
unit. In the commissioning phase, a
temporary control and data acquisition program that integrates
the IcePAP driver, the hexapod, and photodiode readouts in the
same graphical user interface was written in MATLAB.32
The
photodiode detecting the transmitted and reflected radiation
(Optodiode Corporation, model AXUV100HYB1) includes
a high vacuum compatible current-to-voltage converting
low noise amplifier. For the measurement presented in this
paper, the amplifier was not used and the current from the
photodiode was read directly with a picoammeter (Keithley
model 6487/E). The program also collects relevant data from
the server computers, such as ring current, monochromator
setting, and undulator gap and phase. During data acquisition,
we also measured the photocurrent from a fine electroformed
Au mesh in the beam path, providing a reference signal for
normalizing the data. A big advantage of integrating all devices
within the same program is that the alignment procedure
described previously can be performed autonomously by the
computer so that it gradually iterates towards the position with
optimal signal on the photodiodes. However, a final interface
is now being developed in the TANGO33
environment which is
the standard control architecture for the MAX IV Laboratory.
III. EXPERIMENTS AND DISCUSSION
The polarimeter was commissioned at beamline I1011
at MAX-II synchrotron in Lund. The beamline is described
in more detail in Ref. 16. Shortly, the beamline is based on
a plane grating monochromator illuminated with collimated
light. The source is an APPLE-II type undulator1
which
allows symmetric movements of the two movable sub-
girders, providing circularly polarized light (left and right),
and horizontally and vertically linearly polarized light. In
addition, the undulator was characterized in a magnetic
bench after delivery. Those measurements, together with
calculations based on the magnetic modeling, provide good
initial values for the phase shifts for vertical linear polarization
and circularly polarized light at any desired energy. The first
harmonic of the undulator radiation can be used in all modes
at around 400 eV, and we chose the resonance based Sc/Cr
multilayer pair for the initial tests at this beamline, the Sc 2p
edge being very close to that energy.
The beamline has a focal spot of about 150 µm × 800 µm
(vertical × horizontal, measured as full width at half-
maximum, FWHM) with low divergences located 300 mm
from the exit slit. Due to physical space constraints, we placed
the polarimeter downstream, ca. 1570 mm from the nominal
focus. The beam size there is about 2 mm × 1 mm (FWHM)
and in this case, the front pinhole Ø2 mm was used to both
limit the beam size and to guarantee that the beam hits only
optically active areas in both multilayers and detector.
Photon energy and multilayer angles of operation were
defined based on the optical properties of the multilayers.
The freestanding Sc/Cr transmission multilayer shows a
sharp drop in transmitted intensity at a photon energy
corresponding to Sc 2p edge at 398.49 eV.34
We used this for
calibrating the photon energy and performed the experiments
at hν = 398.0 eV, slightly below the Sc 2p ionization threshold.
The parameter to be optimized in this multilayer is the phase
shift between incoming s and p polarization components,
which is desired to be as close as possible to 90◦
. In general,
the highest phase shift occurs at threshold, but the transmission
is also smallest there. In this sense, the chosen photon energy
allows for higher transmission at the expense of the phase shift.
The incidence angle of the transmission multilayer relative to
the photon beam was set to 36.0◦
(angles here are always given
relative to the optical surface). The highest theoretical phase
shift according to simulations35
(see Fig. 2) is actually slightly
above 36◦
, but again the transmission is reducing rapidly with
increasing angle.
The reflection multilayer is operated in the Bragg angle,
which for hν = 398.0 eV is at 37.5◦
. In this case, it is desirable
to maximize the ratio Rs/Rp, where an ideal analyzer would
reflect only the s-polarized component of the light, the ratio
then being infinite. For this multilayer, the above mentioned
angle results in Rs/Rp being ca. 10, as depicted in Fig. 2.
The data analysis is done by fitting the theoretical inten-
sity curve I(α, β) to the experimental intensities Iexp(α, β),
measured at N different pairs of (α, β). The theoretical curve
in turn is derived by using Müller matrices36
and is given by
I(α, β) = K (c0 · S0 + c1 · S1 + c2 · S2 + c3 · S3) , (1)
FIG. 2. Simulated grazing incidence angle scan for (a) phase shift in the
Sc/Cr analyzer and (b) reflectances Rs and Rp in the Sc/Cr polarizer.
19:48:38

where S0, S1, S2, S3 are the Stokes parameters. K is a scaling
factor that depends on optical parameters and on the efficiency
of the detector, both being energy dependent but without
depending on the angles α and β. The parameters c0,c1,c2,
and c3 are functions of the rotation angles α and β, and they
are given by
c0 = 1 + cos (2β − 2α) × cos (2ψt) cos (2ψr) ,
c1 = − cos (2α) × cos (2ψt)
−
1
2
sin (4α) sin (2β) × cos (2ψr)

1 − sin (2ψt) cos (δt)

−cos (2α)2
cos (2β) × cos (2ψr)
−sin (2α)2
cos (2β) × cos (2ψt) sin (2ψr) cos (δt) ,
c2 = − sin (2α) × cos (2ψt)
−
1
2
sin (4α) cos (2β) × cos (2ψr) [1 − sin (2ψt) cos (δt)]
−sin (2α)2
sin (2β) × cos (2ψr) ,
−cos (2α)2
sin (2β) × cos (2ψt) sin (2ψr) cos (δt) ,
and
c3 = − sin (2β − 2α) × sin (2ψt) cos (2ψr) sin (δt) .
The parameters ψt and ψr are related to the optical parameters
of the multilayers by tan ψt = tp/ts and tan ψr = rp/rs, where
tsp and rsp are the s and p coefficients of transmission
and reflection. δt is the phase shift due to the transmission
multilayer.
The Stokes parameters are directly connected to degree
or linear polarization, PL, and degree of circular polarization,
PC as
PL =

S2
1 + S2
2/S0 and
PC = |S3|/S0.
With these notations, the degree of polarization, P, is simply
P =

P2
L + P2
C.
The fitting procedure is based on minimizing the value of
1
N
N
n=1
|Iexp(α,β)n−I(α,β)n|
Iexp(α,β)n
by varying the fitting parameters. In
the current case, the fitting parameters are the values of the
Stokes parameters and the optical constants of the multilayers.
However, initial analysis showed that the results of the fitting
procedure are quite sensitive to the initial values of the fitting
parameters, and often the fitting procedure converges to unre-
alistic values. In fact, this is a well known problem intrinsic to
any non-linear fitting.37
In the current case, this was solved by
brute force: the procedure was ran several times (≈100) with
random initial values. The results with small fitting errors
(as defined by the function above) are then used as the final
results. In addition, this method ensures that the results are not
sensitive to any particular choice of initial parameters.
There is however some ambiguity in this fitting procedure
regarding the signs of the Stokes parameters, which in turn
represent different states of polarization. This can be observed,
for instance, for the S3 parameter: Equation (1) shows that the
product (±|S3|)(∓| sin δt|) has the same result no matter which
of the two combinations of signs is used. In practice, this means
that the sign of S3 can only be determined if one knows the sign
of sin δ3. Similar reasoning is valid also for S1 and S2, where
the question is whether tp/ts > 1 or tp/ts < 1, and whether
rp/rs > 1 or rp/rs < 1. Fortunately, those conditions are easy
to deduce based on general optical properties, without any
detailed knowledge about the multilayers. In this case, we have
tp/ts > 1, rp/rs < 1, and δ3 > 0 and these conditions could
then be used as boundary condition for the fitting procedure.
Another approach is to solve the optical parameters of the
polarimeter by using linearly polarized light, and then using
these values as constants in the fitting procedure for circularly
polarized light.24
Three datasets at different polarization states were
collected at beamline I1011. The undulator was tuned
for horizontally, vertically, and circularly polarized light,
respectively. Experimental values and the fitted function
of one full dataset are shown in Fig. 3(a) for horizontal
FIG. 3. (a) Experimental data (dots) and the fitting curve. In principle, the values for α > 180 and β > 180 are redundant and are collected in order to avoid
(and check for) misalignment problems. In this sense, the uneven interval in experimental data for α > 180 is a balance between data quality and acquisition
time (with the temporary control software, the dataset was recorded in about 5 h). (b) Part of the dataset presented in (a) for horizontal linearly polarized light
and a similar subset of data for vertical linear polarization. It can be noted that the peak intensities are similar for any pair of β and β +180◦, which shows that
the instrument is well aligned.
19:48:38

TABLE III. Normalized Stokes parameters, s1,2,3, obtained for 398.0 eV by
using Sc/Cr multilayers. The undulator phase was set to zero for horizontal
linearly polarized light, 0.5 for vertical linear polarization, and 0.35 for circu-
larly polarized light. The last column shows the contribution of unpolarized
light.
Undulator tuning s1 s2 s3 1-P
Linear horizontal 0.99 0.04 0.04 0.01
Linear vertical −0.97 0.14 0.03 0.02
Circular 0.05 0.06 1.00 0.00
linearly polarized light. Figure 3(b) shows two subsets of
such experiments: one extracted from the dataset presented in
Fig. 3(a) and the other one from a similar dataset recorded for
vertical linearly polarized light.
Table III shows the results of the three datasets collected
at beamline I1011. The results show high values for the
degree of linear (or circular) polarization. This is in agreement
with results from other experiments: the beamline has been
used mostly for magnetic circular dichroism experiments over
several years and according to spectroscopic measurements,
the degree of circular polarization has been found to be
high, indicating that the undulator and the beamline are well
aligned relative to the electron beam and the photon beam,
respectively. All results are obtained by using first harmonic
of undulator radiation, without any filters for higher order
radiation, and the results may be affected by that. On the other
hand, the polarimeter was placed relatively far away from the
nominal focal plane of the beamline, and contributions from
any off-axis radiation should be reduced significantly. The
result for circularly polarized light, S3 = 1.00, is surprising,
being so close to unity. Nevertheless, that is a result based
on fitting, and although the normalized Stokes parameters are
limited to values less than one, the results stayed below that
limit consistently.
Regarding the values obtained for the optical parameters,
the theoretical curve I(α, β) has a linear dependence on the
Stokes parameters but a rather complex relation to the optical
parameters.38
This makes any error propagation analysis and
evaluation of the quality of the values obtained for the optical
constants difficult. To overcome that, it is necessary to perform
more systematic experiments at several different polarization
states and photon energies. Nevertheless, the values obtained
for the optical constants are consistent when comparing the
different datasets. Finally, although outside of the scope of
the initial tests of this instrument, the statistical analysis of
the present results indicates that errors for the Stokes
parameters and optical parameters at this single photon energy
are below, or around, one percent.
IV. CONCLUSIONS
A user-friendly instrument for high precision polarimetry
diagnosis of soft-X-ray synchrotron radiation is presented.
Results obtained show that relying on increased accuracy in
manufacturing allows to build instruments with complicated
yet smooth movements. During the commissioning phase, we
have used small angular steps (mainly in β). These steps
can be made bigger with little effect in the final result, but
further studies are necessary in order to find a good balance
between the number of points and the quality of the fit.
This would decrease the acquisition time and the effect of
the usually troublesome normalization using the intensity
of the monochromatic photon beam. Development of final
control software will also permit to run the instrument in more
sophisticated ways, e.g., with constant offset between α and
β, which at present is tedious.
ACKNOWLEDGMENTS
This project was fully supported by the Swedish Research
Council with a Grant No. VR 822-2010-5862. We like to
acknowledge TOYAMA for a very fruitful collaboration,
especially Dr. Hisataka Takenaka for sharing his expertise
about multilayers, and Kazuteru Akiyama for instrument
design as well as Dr. Carl Richardson and Mr. Noboru
Kamachi for the installation work at MAX IV Laboratory.
We also thank Dr. Mike MacDonald for advice in the initial
stage of the project and Dr. Andreas Gaupp for his suggestions
at the later stage.
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