Mirrors and gratings
Daniele Cocco
Sincrotrone Trieste -Italy
ICTP School on Synchrotron Radiation and Application
May 2006, Trieste, Italy
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Refraction index
refractive index
µ=1−δ−iβ
δ=(e2λ2/2πmc2)|N+ΣHNH[λ/λH]2ln[λH2/λ2-1] |
δ (unit decrement) related to the speed in the medium
β related to the absorption
N=electron density (1023-1024 el./cm3)
λH=adsorption edge’s wavelength
λ far from λH δ=Ne2λ2/2πmc2
β=λµl/4π
the
µl=linear absorption coefficient
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HXR lens
i
i
γ
γ
S
n>1
n<1
Fermat’s principle
n>1
S
n<1
1
1
1 2
≈ (1 − δ − 1) ⋅ < 0
= (n − 1) +
f
R
R1 R2 I
δ=
δ ≈ 10 −4
the
I
Ne 2 λ2
≈ 10 −2 − 10 −4
2πmc 2
HXR f ≈ 1m
if
R ≈ 1mm
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HXR berillium lens
S
n<1
I
δ ≈ 10−4
the
HXR f ≈ 1m
if
R ≈ 1mm
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Refraction index
i
i
n>1
n<1
Material
Snell’s law: cosγ=cosi/n
Pentadecane (oil)
Glass
Aluminum oxide
Gold
γ=0 n=cosic
ic critical angle: total external reflection
sinic
γ
γ
i=5o:
=λ(e2N/πmc2)1/2
λc(min)=3.333.10-13 N-1/2 sinic
Density
N
(g/cm3) (electron/cm3)
0.77
7x1022
2.6
78x1022
3.9
115x1022
19.3
466x1022
λmin
nm
64.1sini
37.9sini
31.2sini
15.4sini
λminglass=3.3nm=375 eV
λmingold=1.34nm=923eV
shorter wavelength needs smaller angles of incidence
Materials with higher density (i.e. higher atomic weight)
have higher reflectivity
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Mirror reflectivity
θ
Gold
1.0
1
reflectivity
0.8
0.6
o
o
2
0.4
o
3
0.2
20
10
o
5
o
o
0.0
0
500
the
1000
Photon energy (eV)
1500
2000
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Mirror reflectivity
θ=2o
θ
1.0
1.0
1.0
Fused Silica
Ni
0.4
0.4
0.2
0.0
0.0
500
1000
1500
Photon energy (eV)
2000
2000
0
0.6
0.4
0.2
0.2
0.0
0.0
0
500
1000
1500
Photon energy (eV)
the
2000
2000
Au
0.8
reflectivity
0.4
500
1000
1500
Photon energy (eV)
1.0
Al
0.8
reflectivity
0.6
0.4
0.0
500
1000
1500
Photon energy (eV)
1.0
C
0.8
0.6
0.2
0
1.0
reflectivity
0.6
0.2
0
reflec tivity
0.6
SiC
0.8
0.8
reflectivity
reflectivity
0.8
0.6
0.4
0.2
0.0
0
500
1000
1500
Photon energy (eV)
2000
0
500
1000
1500
Photon energy (eV)
2000
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Figure errors
θ
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Figure errors
σ
2σ
r'
θ
∆s'=2 r'σ
10
vertical position (µm)
5
s' = √(Ms)2 + (2 r'σ)2
0
-5
-10
-10
-5
0
5
10
horizontal position (µm)
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Figure errors
σ
2σ
r'
θ
50
50
Distance mirror-image = 1m
Slope error contribution FWHM (µm)
Slope error = 2.5 µrad
Slope error contribution FWHM ( µm)
∆s'=2 r'σ
40
30
20
10
40
30
20
10
0
0
0
2
4
6
8
10
0
Distance mirror-image (m)
the
2
4
6
8
10
Slope error [rms] (µrad)
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Slope errors (tangential)
Typical manufacturer capabilities (SESO, ZEISS, Winlight, Jobin Yvon)
Length
Spherical/flat Up to 500 mm < 0.5 µrad
1-2 µrad
Spherical/flat > 500 mm
Up to 500 mm < 1 µrad
Toroidal
> 1 µrad
Toroidal
> 500 mm
Aspherical
Up to 500 mm 2 µrad
Aspherical
> 500 mm
the
10
50
rms errors
3-5 µrad
Distance mirror-image = 1m
1m
Slope error contribution FWHM (µm)
Shape
40
8
30
6
20
4
10
2
0
0.0
0
2 0.5
4
1.0
6
1.5 8
2.0
10
Slope error [rms] (µrad)
(µrad)
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Focal property
Object
r
r’
θ
Image
Image
Object
Tangential focusing
Sagital focusing
Term F20 of the optical path function
(1/r+1/r’)cosθ/2=1/R
spherical mirror
Term F02 of the optical path function
(1/r+1/r’)/(2cosθ)=1/R cylindrical/toroidal mirror
image
σt
θ
σs
2σt
r'
∆s't=2 r'σt
∆s's=2 r' cosθ σs
cosθ
sinθ
θ
Mirror surface
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Slope error effect
Object
r
r’
θ
Image
Image
Object
Tangential focusing
Sagital focusing
Slope error contribution FWHM ( µm)
20
Distance mirror-image = 1m
15
Typical value ~ 5µrad
10
∆s't=2 r'σt
5
∆s's=2 r' cosθ σs
0
2
4
6
8
10
Slope error [rms] (µrad)
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Final focus (F30-F03-F12 …..)
source 80 µm vertical; r=4000 mm r´=400 mm (10:1) θ=88o
Beam divergence 100X100 µrad
-25
0
25 -25
0
-60
25 -25
-3
-40
-60
-25
0
-3
x10
0
-3
x10
0
-20
-40
-60
25 -25
the
0
-3
x10
-20
-20
-40
-60
0
-3
x10
25 -25
0
-3
x10
0
-20
-20
-40
-60
-20
-40
-60
25 -25
0
-3
x10
25
0
-3
x10
25
20
0
0
-3
x10
-60
25 -25
20
0
25 -25
-60
0
-3
x10
20
0
25 -25
-60
25 -25
20
vertical spot (µm)
vertical spot (µm)
vertical spot (µm)
20
-20
vertical spot (µm)
-60
-3
0
-20
20
0
Elliptical
Cylinder
Spherical
Elliptical
Cylinder
-40
-40
No slope errors-40 No slope errors-40 1µrad slope errors
5µrad slope errors
5µrad slope errors
x10
x10
Beam divergence
500X500
µrad
20
0
vertical spot (µm)
-60
-20
20
vertical spot (µm)
Spherical
No slope errors-40
0
vertical spot (µm)
-40
-20
20
vertical spot (µm)
-20
20
0
vertical spot (µm)
0
vertical spot (µm)
20
vertical spot (µm)
vertical spot (µm)
20
0
-3
x10
0
-20
-40
-60
25 -25
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Mirror defects
Slope errors = every deviation from the ideal surface with period larger then ~ 1,2 mm
Typical definition is µrad or arcsec rms.
Alternative definition is λ/10 or λ/20 and so on… P-V or rms
used for normal incidence mirror or “poorer” quality mirrors
Roughness = every deviation from the ideal surface with period smaller then ~ 0.5-1 mm
Typical definition is Årms.
Alternative definition is surface quality 20-10 or 10-5 (scratch-dig)
used for normal incidence mirror or “poorer” quality mirrors
A dig is nearly equal in terms of its length and width. A scratch could be much longer then width
20-10 means 20/1000 of mm max scratch width 10/100 mm max dig dimension
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Roughness
I = I 0e
4πσ sin ϑ 2
−
λ
2
1 n
[s ( x ) − s ( x )]
σ=
n x =0
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Power spectral density
Slope errors
(SF<0.5-0.2 mm-1)
Roughness (SF>1mm-1)
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Power spectral density
1 mm
10 mm
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Roughness
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Roughness
Intensity reduction (%)
10
10 Å rms
1
3 Å rms
0.1
0.01
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Photon energy (eV)
Shape
Spherical/Flat
Toroidal/aspherical
Roughness (Å)
3 standard 1 best
5 standard 3 best
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Beamline layout
Prefocusing section:
Adapt the source to the monochromator requirements
Adsorb the unwanted power radiation
Horizontal focusing
Vertical focusing
HFM
VFM
Exit slit
Monochromator
Entrance slit
Pin hole
Prefocusing
Side view
Deflection mirror
Monochromator:Select the proper photon energy
Top view
Refocusing section: Adapt the spot shape at the necessity of the experiment
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Basic lattice structure
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Basic lattice structure
Intens ity (photons /sec)
Undulator
2.0x10
15
1.5
1.0
0.5
0.0
200
400
600
800
1000
Photon Energy (eV)
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Basic lattice structure
λ∝
∆λ
1
1
∝
≥
λ
nN n(80 )
λu B 2
E2
σ∝
1
1/ 2
L
40 µrad
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Sources
ehν
Horizontal
Vertical
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Thermal deformation
Horizontal
Vertical
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Mechanical and thermal properties of some mirror materials
Density Young’s modulus Thermal Thermal
Figure of
expansion conductivity merit
Fused silica
Zerodur
Silicon
SiC CVD
Aluminum
Copper
Glidcop
Molybdenum
the
gm/cc
2.19
2.53
2.33
3.21
2.70
8.94
8.84
10.22
GPa
73
92
131
461
68
117
130
324.8
(α) ppm/oC
0.50
0.05
2.60
2.40
22.5
16.5
16.6
4.80
(k) W/m/oC
1.4
1.60
156
198
167
391
365
142
k/α
2.8
32
60
82
7.42
23.7
22
29.6
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Silicon mirrors
m
600
m
110 mm
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Side cooling
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Side cooling
Image
Object
Sagital focusing
image
σs
mirror deformation (nm)
∆s's=2 r' cosθ σs
70
60
50
40
30
20
10
0
300
250
200
150
100
50
0
mirror position (mm)
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Internal cooling mirror
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Internal cooling mirror
Vacuum flanges
Joystick connection
50
500
120
residual height (nm)
80
30
300
20
200
14 µm
10
2.7 µrad
100
400
height difference (nm)
Slope error contribution FWHM (µm)
Distance mirror-image = 1m
40
7 100
µm
0
40
20
1.4 µrad
0
-20
-40
-60
0
0
60
-80
0 2
4100
6
200 8
10
Slope
error
[rms] (µrad)
mirror
position
(mm)
the
0
100
200
mirror position (mm)
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Induced slope errors for 400 W source
3GeV Synchrotron source
6.6 cm period undulator Kmax=5.7
BL6.1
glidcop
1.5o grazing incidence
1.5o grazing incidence
∆h=17µm slope 26 µrad
the
∆T=7.7o
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Induced slope errors for 400 W source
Density Young’s modulus Thermal
Thermal
Figure of
expansion conductivity merit
Silicon
SiC CVD
Aluminum
Copper
Glidcop
Molybdenum
Invar 36
Glidcop
SuperInvar
gm/cc
2.33
3.21
2.70
8.94
8.84
10.22
9.05
8.13
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GPa
131
461
68
117
130
324.8
141
145
(k) W/m/oC
(α) ppm/oC
2.60
156
2.40
198
22.5
167
16.5
391
16.6
365
4.80
142
0.5
10.4
Molybdenum
0.06
10.5
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k/α
60
82
7.42
23.7
22
29.6
20.8
210
∆T=13.3o
17
Induced slope errors for 400 W source
Density Young’s modulus Thermal
Thermal
Figure of
expansion conductivity merit
gm/cc
2.33
3.21
2.70
8.94
8.84
10.22
9.05
8.13
-4
∆h=9µm
-6
-8
Tangential deformation
Glidcop
Molybdenum
-10
-12
∆h=17µm
-14
(k) W/m/oC
156
198
167
391
365
142
10.4
10.5
(α) ppm/oC
2.60
2.40
22.5
16.5
16.6
4.80
0.5
0.06
80
GPa
131
461
68
117
130
324.8
141
145
Induced slope error (µrad)
Mirror deformation ( µm)
Silicon
SiC CVD
Aluminum
Copper
Glidcop
Molybdenum
Invar
0 36
SuperInvar
-2
-16
60
k/α
60
82
7.42
23.7
22
29.6
20.8
210
Tangential induced slope errors
Glidcop 26 µrad
Molibdenum 16.4 µrad
40
20
0
-20
0
50 the
100
mirror position (mm)
0
20
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150
40
60
80
100 120
mirror position (mm)
140
160
Induced slope errors for 400 W source
Density Young’s modulus Thermal
Thermal
Figure of
expansion conductivity merit
Silicon
SiC CVD
Aluminum
Copper
Glidcop
Molybdenum
Invar 36
SuperInvar
gm/cc
2.33
3.21
2.70
8.94
8.84
10.22
9.05
8.13
(α) ppm/oC
2.60
2.40
22.5
16.5
16.6
4.80
0.5
0.06
GPa
131
461
68
117
130
324.8
141
145
!!"
$
'(
) *
!!" #$
% ! &
#'
"
% !+! #'
&&
the
(k) W/m/oC
156
198
167
391
365
142
10.4
10.5
k/α
60
82
7.42
23.7
22
29.6
20.8
210
#
!"
!"&
#
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Induced slope errors for 400 W source
Density Young’s modulus Thermal
Thermal
Figure of
expansion conductivity merit
gm/cc
8.84
10.22
8.13
Glidcop
Molybdenum
SuperInvar
(α) ppm/oC
16.6
4.80
0.06
GPa
130
324.8
145
(k) W/m/oC
365
142
10.5
k/α
22
29.6
210
0
∆h=4µm
Mirror deformation ( µm)
-4
-6
-8
-10
∆h=9µm
Tangential deformation
Glidcop
Molybdenum
Super Invar
-12
80
Induced slope error ( µrad)
-2
Tangential induced slope errors
Glidcop 26 µrad
Molibdenum 16.4 µrad
Super Invar 9.15 µrad
60
40
20
0
-14
∆h=17µm
-16
0
50
100
mirror position (mm)
the
-20
150
0
20
40
60
80
100 120
mirror position (mm)
140
160
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SuperInvar
Density Young’s modulus Thermal
Thermal
Figure of
expansion conductivity merit
Glidcop
Molybdenum
SuperInvar
gm/cc
8.84
10.22
8.13
GPa
130
324.8
145
(α) ppm/oC
16.6
4.80
0.06
∆h=6µm
the
(k) W/m/oC
365
142
10.5
k/α
22
29.6
210
∆T=130o
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Carbon contamination
Effect of the contamination:
Strong adsorption at the carbon edge (≈270 eV)
Reduction of reflectivity due to enanchment of the surface roughness
general deterioration of the surface
250 eV
the
260 eV
270 eV
280 eV
290 eV
300 eV
310 eV
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Carbon contamination and cleaning
Contamination process:
Hydrocarbons adsorbed by the surface
Cracking induced by the incoming radiation
Formation of graphitic carbon layer (mixed C coumpond)
M
irr
or
su
rfa
ce
Effect of the contamination:
Strong adsorption at the carbon edge (≈270 eV)
Reduction of reflectivity due to enanchment of the surface roughness
general deterioration of the surface
the
UV lamp discharge
+ 300-500 V (DC)
I 100 mA-1A
P 0.5-1 mbar O2
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Other contamination
Effect of the contamination:
Strong adsorption at the O/Cr edge
Reduction of reflectivity due to enanchment of the surface roughness
general deterioration of the surface
-3
40x10
0.4
536.2 eV
571 eV
Intensity (a.u.)
542.8 eV
20
CO contamination
0.3
Cr contamination
578 eV
0.2
0.1
10
510
520
530
540
500
550
520
the
540
560
580
600
Photon Energy (eV)
Photon Energy (eV)
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Soft X-ray monochromators
Horizontal focusing
Vertical focusing
HFM
VFM
Exit slit
Monochromator
Entrance slit
Prefocusing
Side view
Deflection mirror
Monochromator:Select the proper photon energy
Pin hole
Intensity (a.u.)
30
Top view
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Diffraction grating
Micro
wave
I.R.
Visible U.V. Soft
X-ray
Hard
X-ray
limit ~ 1-2 keV ( 1 nm)
Micro
wave
d sin
(α)
d
Visible U.V.
I.R.
Soft
X-ray
Hard
X-ray
Internal Orders (+)
)
(β
si n
α
d
β
Zero order
External Orders (-)
nλ = d (sin (α ) − sin (β ))
d
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Gratings profiles
θ
γ
h
Blaze profile
Blaze condition
w
Laminar profile
Blaze gratings:
higher efficiency
Laminar gratings:
Higher spectral purity
Higher resolution
Blaze angle=(α+β
)/2
angle=(α+β)/2
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1λ
nnλ = d (sin (α ) − sin (β ))
2 2λ
22
Gratings profiles
θ
γ
w
h
Blaze profile
Laminar profile
50
10
ord)
Laminar grating
Blaze grating
Laminar grating
Blaze grating
nd
8
Relative efficiency (1 ord/2
6
st
Grating efficiency (%)
40
30
20
10
4
2
0
200
400
600
800
200
Photon energy (eV)
400
600
800
Photon energy (eV)
nλ = d (sin (α ) − sin (β ))
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Gratings profiles
θ
γ
w
h
Blaze profile
Laminar profile
5
10
o
γ=90 gd=2400 l/mm
200 eV
800 eV
4
Efficiency (%)
Efficiency (%)
8
6
4
3
2
1
2
0
W=60% gd=2400 l/mm
200 eV
800 eV
0
1
2
3
4
5
6
7
8
blaze angle (θ) (deg)
the
5
10
15
20
groove height (nm)
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Diffraction grating production
Mechanical ruling blaze profile
Holographically recording
the
smaller blaze angles; higer efficiency
laminar and blaze profile (large blaze angle)
higher groove density; lower spacing disomogeneity
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Mechanically ruled grating
Mechanically ruled (CARL ZEISS Grating Ruling Engine GTM6)
GTM6) with blazed profile down to 0.50.5-0.7o
Diamond tool
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Holographical grating
Exposure
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Development
Ion etching
Photoresist
removal
Coating
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Holographical grating
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25
Gratings profiles
θ
γ
w
h
Blaze profile
Laminar profile
5
10
o
γ=90 gd=2400 l/mm
200 eV
800 eV
Efficiency (%)
4
6
4
3
2
W=60% gd=2400 l/mm
200 eV
800 eV
1
2
0
0
1
2
3
4
5
6
7
8
5
the
10
15
20
groove height (nm)
blaze angle (θ) (deg)
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Shallow blaze gratings
2500 eV
14
13
θ
γ
Micro
wave
I.R.
Visible U.V. Soft
X-ray
Hard
X-ray
Blaze profile
12
11
10
10
9
o
γ = 9 0 g d = 2 4 0 0 l/m m
200 e V
800 e V
8
8
7
Efficiency (%)
Efficiency (%)
8
6
6
5
4
4
3
2
2
1
0
0.4
0.8
1 1.2
1.6
2.0
2
3
4
5
6
7
8
b la z e a n g l e ( θ ) ( d e g )
the
abdus salam
international centre for theoretical physics
26
Shallow blaze angle grating realization
• Thermal evaporation of Gold
on the Si substrate (plus Cr
binding layer)
• Grooves formed by plastic
deformation of the ruling layer
Mechanically ruled by the CARL
ZEISS Grating Ruling Engine GTM6
Diamond tool
Gold (Cr) layer
Si substrate
the
abdus salam
international centre for theoretical physics
Shallow blaze angle grating realization
+
+
+
+
+
+
the
+ +
+
+
+
+
+
+ +
+
+
+
+
+
+
+ +
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+ +
+
+
+
+
+
+
• Thermal evaporation of Gold
on the Si substrate (plus Cr
binding layer)
• Grooves formed by plastic
+ deformation of the ruling layer
+
+ •Realization of low micro+
roughness blaze grating with
+ +
20<gd<5000 l/mm and down
to 1.5o of blaze angle
•Ar+ ion etching (200 mm
diameter collimated beam)
abdus salam
international centre for theoretical physics
27
Shallow blaze angle grating realization
+
+
+
+
+
+
the
+ +
+
+
+
+
+
+ +
+
+
+
+
+ +
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+ +
+
+
+
+
+
+
+
• Thermal evaporation of Gold
on the Si substrate (plus Cr
binding layer)
• Grooves formed by plastic
deformation of the ruling layer
•Realization of low micro+
roughness blaze grating with
+
+
+ 20<gd<5000 l/mm and down
+ + to 1.5o of blaze angle
•Ar+ ion etching (200 mm
diameter collimated beam)
• Ar+ ion etching rate on gold
much larger then on Silicon
•An angle reduction of a factor
3 (even higher if Ar+ + O+ is
used) can be achieved by this
technique
•Roughness and anti blaze
angle are also reduced.
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international centre for theoretical physics
Our grating
Plane substrate 600 l/mm gold coated
80X5 mm useful area, blaze angle 0.4o
the
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international centre for theoretical physics
28
Expected performance
25
1300 eV
1000 eV
1600 eV
20
Grating efficiency (%)
770 eV
15
600 eV
2000 eV
3000 eV
10
400 eV
3500 eV
5
4000 eV
0
170
171
172
173
174
175
176
177
178
179
Included angle (deg)
the
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Grating’s equations
α
r
r`
β
Optical path function
F100 = −nλD0 + (sin α − sin β )
grating equation
cos 2 α cos α cos 2 β cos β
F200 = −
+
−
R
r'
R
r
tangential focus
cos 2 α cos α sin α cos 2 β cos β
F300 = −
+ −
R r
R
r
r′
the
sin β r′ primary coma
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international centre for theoretical physics
29
Rowland condition
Rowland Circle
r =Rcos
r'=Rcos
Grating
F200 =F300 =0
Source
Rgrating=2Rrowland circle
cos 2 α cos α cos 2 β cos β
F200 = −
+
−
R
r'
R
r
tangential focus
cos 2 α cos α sin α cos 2 β cos β
F300 = −
+ −
R r
R
r
r′
the
sin β r′ primary coma
abdus salam
international centre for theoretical physics
Plane/spherical grating monochromators
cos 2 α cos α cos 2 β cos β
F200 = −
+
−
R
r'
R
r
F100 = −nλD0 + (sin α − sin β )
r
α
β
r`
Mantain fixed source and image in position and direction
the
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international centre for theoretical physics
30
Plane/spherical grating monochromators
F100 = −nλD0 + (sin α − sin β )
Entrance slit/source
the
cos 2 α cos α cos 2 β cos β
F200 = −
+
−
R
r'
R
r
t
gra
ne
pla
/
l
ica
her
Sp
r
irro
em
n
a
Pl
ing
Exit slit/image
θmirror=(α+β)/2
abdus salam
international centre for theoretical physics
Plane/spherical grating monochromators
Entrance slit/source
t
gra
ne
pla
/
l
ica
her
Sp
r
irro
em
n
a
Pl
ing
Exit slit/image
h mirror axis ~ h/2 grating center
the
abdus salam
international centre for theoretical physics
31
Plane/spherical grating monochromators
t
gra
ne
pla
/
l
ica
her
Sp
r
irro
em
n
a
Pl
Entrance slit/source
the
ing
Exit slit/image
abdus salam
international centre for theoretical physics
Spherical grating monochromator efficiency
40
Efficiency (%)
35
30
25
20
15
10
5
0
0
200
400
the
600
800
1000
1200
1400
1600
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international centre for theoretical physics
32
Resolving power
CCD vertical position (µm)
40
Source
Grating
Exit slit
20
10 µm
0
-20
-1.0
-0.5
0.0
0.5
Exit slit
r
rro
mi
e
n
Pla
Entrance slit
Intensity (a.u.)
1.0
ing
grat
ical
r
e
h
Sp
1.0
Photon Energy (eV)
FWHM = 1.6 meV
0.8
0.6
0.4
0.2
0.0
44.998
44.999
45.000
45.001
45.002
Photon Energy (eV)
the
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international centre for theoretical physics
Resolving power
Nkλ = sin(α ) − sin(β )
∂λ cos(α )
=
Nk
∂α ∆α =
s
r
∆λentrance =
∂λ cos(β )
∂β = Nk
∆β =
s′
r′
∆λexit =
smaller are s and s´,
smaller will be the bandpass
s ⋅ cos(α )
Nkr
entrance slit contribution
s ′ ⋅ cos(β )
Nkr ′
exit slit contribution
Resolving power = E/∆E
Exit slit
r
irro
em
n
a
Pl
Entrance slit
Intensity (a.u.)
1.0
ing
grat
rical
e
h
p
S
Note: the angular precision of the grating rotation have to allow
the energy selection i.e. 0.2-0.3 µrad
the
FWHM = 1.6 meV
0.8
0.6
0.4
0.2
0.0
44.998
44.999
45.000
45.001
45.002
Photon Energy (eV)
45/0.0016 ≈ 28000
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international centre for theoretical physics
33
Resolving power
Typical Spherical grating monochromator resolving power
the
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international centre for theoretical physics
Resolving power
+50-250 V
Typical Spherical grating monochromator resolving power
Photon in
Gas inlet
Gaussian Width
FWHM: 34 ± 3 meV
I(nA)
Experimental Data
Fitted Data
4
N2 1s
E/∆
∆E > 11000
Intensity (arb. units)
3
2
1
the
400.5
401.0
abdus salam
Photon Energy [eV]
international centre for theoretical physics
401.5
402.0
34
Resolving power
+50-250 V
Typical Spherical grating monochromator resolving power
Photon in
Gas inlet
I(nA)
0.45
2p
3/2
-> 3d
2p
1/2
-> 3d
4d
0.40
Ar L2,3
0.35
Intensity (arb. units)
5d
6d
4d
5d
0.30
6d
2p
3/2
-> 4s
2p
0.25
1/2
-> 4s
7d
0.20
0.15
the
244
245
246
247
248
249
250
abdus salam
Photon Energy [eV]
international centre for theoretical physics
Resolving power
+50-250 V
Typical Spherical grating monochromator resolving power
Photon in
Gas inlet
I(nA)
Ne K-shell
excitations
10
1s -> 3p
Intensity (Arb.Un.)
8
R ≅ 8500
6
4p
4
5p
2
0
866
the
867
868
869
870
871
Photon energy (eV)
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international centre for theoretical physics
35
Resolving power
+50-250 V
Typical Spherical grating monochromator resolving power
Photon in
Gas inlet
I(nA)
CO: O 1s → Π*
R ≅ 8000
the
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international centre for theoretical physics
Magnification
s’=image dimension
s=source dimension
Grating
M (λ ) =
Nkλ = sin (α ) − sin (β )
M (λ ) =
the
s′
s
∂λ cos(α )
=
Nk
∂α ∆α =
s
r
∂λ cos(β )
=
Nk
∂β ∆β =
s′
r′
s ′ r ′ cos(α )
=
s r cos(β )
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international centre for theoretical physics
36
Groove errors
Ghosts & Stray Light
dg
Random imperfections
Periodic imperfections
nλ
sin β = sin α −
d
nλ
sinβg= sinα −
dg
nπ δ d
I g = I 0 d
2π sinβ δd I = I 0 exp − λ
2
δd
Maximum deviation
from the ideal d-spacing
the
rms deviation
from the ideal d-spacing
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international centre for theoretical physics
Variable line space grating
D(x) = D0 + D1x + D2 x 2 + D3x 3 + ⋅⋅⋅⋅
Groove density D varies along the grating surface:
2
2
F200 = 1 − nλD1 + cos − cos + cos − cos
2
R
r'
R
r
2
F300 = − 1 n D2 + 1 cos − cos
3
R
2 r
sin
r
2
+ cos − cos
R
r′
sin
r′
x
FM00 = −cM n DM + K M00
Reduction of higher order aberrations
Increasing of focusing property of spherical gratings
Focusing plane gratings
Constant demagnification ratio of plane VLS monochromators
the
abdus salam
international centre for theoretical physics
37
Spherical Variable line space grating
Spherical
(VLS) grating
Entrance
Slit
Exit
Slit
r
Plane Mirror
2
F300 = − 1 n D2 + 1 cos − cos
3
2 r
R
sin
r
200eV
20
0
-20
-40
∆=300µrad
D0=3000 l/cm
2
D1=0 l/cm
3
D2=0 l/cm
∆=100µrad
D0=3000 l/cm
2
D1=0 cm
3
D2=0 l/cm
-80
sin
r′
70eV
0
-60
2
+ cos − cos
R
r′
20
Dispersion direction (µm)
Dispersion direction (µm)
r'
Side View
∆=300µrad
D0=3000 l/cm
2
D1=0 cm
3
D2=-0.15 l/cm
-20
-40
∆=300µrad
D0=3000 l/cm
2
D1=0 l/cm
3
D2=-0.15 l/cm
∆=300µrad
D0=3000 l/cm
2
D1=0 l/cm
3
D2=0 l/cm
-60
-80
-100
-0.5
0.0
0.5
1.0
1.5
2.0
-0.5
2.5
0.0
the
0.5
1.0
1.5
Sagital direction (cm)
Sagital direction (cm)
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international centre for theoretical physics
Variable line space grating
D(x) = D0 + D1x + D2 x 2 + D3x 3 + ⋅⋅⋅⋅
Groove density D varies along the grating surface:
2
2
F200 = 1 − nλD1 + cos − cos + cos − cos
2
R
r'
R
r
2
F300 = − 1 n D2 + 1 cos − cos
3
R
2 r
sin
r
2
+ cos − cos
R
r′
sin
r′
x
FM00 = −cM n DM + K M00
Reduction of higher order aberrations
Increasing of focusing property of spherical gratings
Focusing plane gratings
Constant demagnification ratio of plane VLS monochromators
the
abdus salam
international centre for theoretical physics
38
Spherical VLS spectrometer (ComIXS)
D(x) = D0 + D1x + D2 x 2 + D3x 3 + ⋅⋅⋅⋅
Groove density D varies along the grating surface:
2
2
F200 = 1 − nλD1 + cos − cos + cos − cos
2
R
r'
R
r
2
F300 = − 1 n D2 + 1 cos − cos
3
2 r
R
sin
r
2
+ cos
r′
− cos
R
sin
r′
x
If distance source-grating and angle of incidence are kept constant i.e.
R = cosr
2
F200 = 1 − nλD1 + cos − cos
2
R
r'
α
r
the
= 0
r'= f ( ),D1 r`
β
abdus salam
international centre for theoretical physics
rgy
ne
rE
we
Lo
D
CC
Spherical VLS spectrometer (ComIXS)
70
60
50
40
eV
100
30
Y (cm)
Beamline focus
Spectrometer Source
20
10
Source
r
-50
1200 eV
VLS
grating
0
50
0
100
150
200
250
300
X (cm)
D 1=0
D 1=400 l/cm2
cos 2
cos
F200 = 1 − nλD1 + −
2
r'
R
the
D 1=800 l/cm2
D 1=1200 l/cm2
D0=19200 l/cm
r=63 cm
R≈14 m
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international centre for theoretical physics
39
rgy
ne
rE
we
Lo
D
CC
Compact Inelastic X-ray spectrometer
ComI S
Distance sample grating (cm)
Distance grating CCD (cm)
63
variable
Angle of incidence(deg)
radius of curvature (cm)
Beamline focus
Spectrometer Source
Y (cm )
8
HEG
Energy range (eV)
25-200
100-1200
D0 (l/cm)
4800
19200
D1 (l/cm2)
200
800
7.5
30
3
D2 (l/cm )
40 eV direction
35
160
45
200
55
240
70
340
105
500 135
6
4
1432.7
LEG
25
120
42
87.48
CC
Dp
l an
e
500 eV direction
580
155
660
175
740
195
820
215
900
235
1000
Zero order direction
2
41.4
41.6
41.8
42.0
42.2
42.4
42.6
42.8
X (cm )
the
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Plane VLS grating
Groove density D varies along the grating surface:
2
2
F200 = 1 − nλD1 + cos − cos + cos − cos
2
R
r'
R
r
2
F300 = − 1 n D2 + 1 cos − cos
3
R
2 r
sin
r
2
2
F200 = 1 − nλD1 + cos + cos
2
r
r'
2
+ cos − cos
R
r′
sin
r′
x
A plane grating can focus!
2 sin cos 2
F300 = − 1 n D2 + 1 sin cos
+
3
2 r2
r ′2
D(x) = D0 + D1x + D2 x 2 + D3x 3 + ⋅⋅⋅⋅
F100 = −nλD + (sin α − sin β )
β
sin β = sin α − nλD
D> ; β<
D< ; β>
the
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international centre for theoretical physics
40
Plane VLS grating (nanospectroscopy)
gs
tin
gra
S
VL
Exit slit
Entrance slit
3
30x10
Resolving Power
vls
sgm
20
170
165
Included angle
vls
sgm
160
155
0
200
15
400
600
800
1000
Photon energy (eV)
10
0
0
200
400
600
800
1000
Photon energy (eV)
Demagnification factor
2.0
5
1.8
1.6
1.4
1.2
1.0
vls
sgm
0.8
0.6
0
200
400
600
800
1000
Photon energy (eV)
the
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Microfocusing
Demagnification 120X20
Horizontal focusing
Vertical focusing
HFM
Exit slit
Monochromator
Entrance slit
Prefocusing
Side view
2 X 2 µm2
mrad2
VFM
Accepted divergence 1X1
Deflection mirror
240 X 40 µm2
Pin hole
Resolving Power
25
175
Included angle (2θ) (deg)
r
irro
em
n
a
Pl
Top view
the
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international centre for theoretical physics
41
Kirkpatrick Baez configuration
(1/r+1/r’)cosθ/2=1/R
the
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Microfocusing
3
-4
-6
-8
0
1000
2000
3000
4000
5000
6000
-10
-12
-14
Changing S
-16
0
50
100
150
200
250
300
Profile variation (µm)
Profile variation (µm)
0
-2
0
2000
4000
6000
8000
10000
12000
14000
16000
2
1
0
-1
Changing ∆S
-2
0
50
Position (mm)
the
100
150
200
250
300
Position (mm)
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international centre for theoretical physics
42
Microfocusing
Vertical intensity profile (a.u.)
Horizontal intensity profile (a.u.)
Sample tilted by 76o
2500
2000
1500
1000
FWHM=7µm
500
-10
-5
0
5
10
2500
FWHM=2µm
2000
1500
1000
500
0
-10
Position (µm)
the
2X7 µm2
Flux 1x1013 ph/sec
-5
0
5
10
Position (µm)
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international centre for theoretical physics
Mechanical bender (ESRF)
micro-fluorescence & micro-diffraction (HXR)
To picomotors
Bending system
The mirror must be shaped according to the required working distance and angle of incidence
constant thickness but linear width variation.
Open clamping system to let the beam pass trough
Picomotors for the bending driving system (2 for each mirror)
Two different moments are applied at the end of the flat polished substrate
the
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43
Mechanical bender (ESRF)
the
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international centre for theoretical physics
EUV and soft x-ray optics
Homogeneous spot
1.0
F
gb
si n
u
c
o
eam
Y (cm)
0.5
0.0
-0.5
-1.0
-1.0
the
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international centre for theoretical physics
-0.5
0.0
0.5
1.0
X (cm)
44
EUV and soft x-ray optics
Homogeneous spot
0
-20
-30
-40x10
-6
Residual slope=1.3 µrad
Shape error: 27 nm rms 77 nm P-V
0
50
100
150
x (mm)
200
250
300
1.0
0.5
F
gb
si n
u
c
o
Y (cm)
profile (mm)
-10
eam
0.0
-0.5
-1.0
-1.0
the
-0.5
0.0
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international centre for theoretical physics
0.5
1.0
X (cm)
Piezoelectric Bimorph mirrors
R. Signorato (ACCEL)
J.J. Fermé S.E.S.O.
Thin metallic electrode (deposited)
Inert plate (optical material)
Piezo ceramic
VD
Optical surface polished after gluing
Second optical surface available
the
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international centre for theoretical physics
45
Piezoelectric Bimorph mirrors
Dimension: from 150 mm (single element) to 1400 mm.
Radius variation: 370 m (+1500V) to 2300 m (-1500V)
Stability: ∆R/R≅0.8% on 1 day scale
∆R/R≅2.0% on 10 day scale
the
abdus salam
international centre for theoretical physics
Metrology
Request of higher performance
!
t
Request of better mirrors
re i
Better results
tb
ble
ea
to
asu
me
s
Production
muof better mirrors
u
Yo
the
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international centre for theoretical physics
46
Metrology laboratory
Clean room class 1000 (BIOAIR)
Micromap Promap 512
o
Thermostabilised room (∆T= 0.1 rms)
WYKO RTI 4100
Long trace profiler (LTP II)
Purchased in 2002
3D surface topography
Purchased in 1991
Several in house modification
2D direct slope measurement
Reichert POLIVAR 2 MET
Purchased in 1992
Roughness measurement
Good repeatability and
precision (better then 1Å rms)
the
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Long trace profiler (LTP)
16
x10
3
12
Laser beam
8
FTL
SU
T
4
0
Linear
array
detector
Reference
Surface under test
ce 600
400
renCCD pixel
e
f
Re
200
800
90o
the
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international centre for theoretical physics
47
Long trace profiler (LTP)
Control of environmental conditions
-Thermalisation of the laboratory
-Absence of air turbulence
-Remote control measurement
-Stable supports
2
0.61 µ rad
0.63 µrad
1
0 .6 9 µ r a d
0.68 µ rad
0
0 .6 2 µ r a d
0 . 65 µ r a d
M e a n s lo p e = 0 . 6 5 µ r a d
∆ m a x= 0 . 0 5 µ r a d
-1
0 . 64 µ r a d
0
50
100
150
200
m i r r o r le n g th ( m m )
the
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international centre for theoretical physics
Groove density measurement
OH
Internal Orders (+)
α β
α
Zero order
External Orders (-)
2 sin(α)=nλ/d
tin
ra
G
d
δβ=0.5 µrad
st
1 diffraction order
nd
2 diffraction order
-5
10
-6
10
g
10
d-spacing error (nm)
10-4
groove density error (δ k/k)
residual slope (µ rad)
3
δβ=0.5 µrad
1
0.1
0.01
-7
10
0.001
5
10
15
3
20x10
0
groove density (l/cm)
the
5
10
15
20
3
25x10
groove density (l/cm)
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international centre for theoretical physics
48
WYKO RTI 4100
3D measurement of optical surfaces
λ/100 precision
λ/2000 repeatability
Laser collimated beam
am
Be
l
sp
e
itt
Surface under test
Surface under test
Accessories
Transmission spheres
f /1.5 for sagittal radii and NI mirrors with R<1 m
f /24.8 diverger for NI mirrors with R>2 m
r
Partially reflective
transmission flat (or sphere)
To CCD
the
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Roughness measurment (Micromap Promap)
Precision 0.5 Å rms
Spatial frequency:
1 µm-1 to 1 mm -1
the
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49
AFM measurement
the
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AFM measurement
4
3
Height (nm)
2
1
0
-1
-2
-3
-4
-5
0
500
1000
1500
2000
2500
3000
3500
4000
Grating position (nm)
the
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4500
5000
5500
6000
6500
Best fit:
blaze=0.4° antibleze=1.34°
50