Characterization of the error budget of the Alba-NOMiwxm.cells.es/docs/IWXM12_NICOLAS_05.pdf ·...
Transcript of Characterization of the error budget of the Alba-NOMiwxm.cells.es/docs/IWXM12_NICOLAS_05.pdf ·...
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Characterization of the error budget
of the Alba-NOM
Josep Nicolas, Juan Carlos Martínez
ALBA light source
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1. The bench
a. Motion metrology
b. Raytracing of the guidance induced error
c. Vibrations, noise and stability
2. The optics
a. Calibration using redundant-independent
datasets.
b. Optimization of the iris aperture.
3. One application
a. surface correction using few point forces
b. Exsitu vs Insitu
We aim to characterize the uncertainty of slope measurements obtained by the Alba-NOM,
contributed by stochastic effects and systematic errors:
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Resolution (linear) 1 nm
Resolution (angular) 41 nrad
Maximum sampling rate 5 kHz
Noise level ~0.1 nm RMS
Accuracy (linear) ±0.7p.p.m
Linearity (angular) ±0.5 μrad
The use of a differential interferometer allows an accurate characterization of themotion performance of the bench
0 5 10 15 20 25 30 35 40
-2
-1.5
-1
-0.5
0
0.5
1
x 10-3
time (s)
Am
plitu
de (
µm)
RenishawNoiseAndDrift015_HVACOFF.rtd
20 40 60 80 100 120 140 160 180
0.5
1
1.5
2
2.5
x 10-4
frequency (Hz)
Am
plitu
de s
pect
ral d
ensi
ty (
µm/H
z)
RenishawNoiseAndDrift015HVACOFF.rtd
0.1 nm
Time signal Spectrum
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Backlash Accuracy Repeatability Resolution
Position 100 nm 3.5 um 77 nm 20 nm
-1 -0.5 0 0.5 1 1.5 2
0
0.02
0.04
0.06
0.08
time (s)
Ste
p ( µ
m)
0 1 2 3 4 5 6
x 104
-2
-1.5
-1
-0.5
0
0.5
1
1.5
motor position (kec)
Y p
ositi
on e
rror
(µm
)
Resolution, a 40 nm step Positioning error
The use of a differential interferometer allows an accurate characterization of themotion performance of the bench
40 nm
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0 0.2 0.4 0.6 0.8 1 1.2
-4
-3
-2
-1
0
1
2
3
motor position (m)
Pitc
h er
ror
( µra
d)
0 0.2 0.4 0.6 0.8 1 1.2
2
4
6
8
10
motor position (m)
Yaw
err
or (
µrad
)
0 0.2 0.4 0.6 0.8 1 1.2
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
motor position (m)
Fla
tnes
s er
ror
( µm
)
Backlash Accuracy Repeatability
pitch 2 nrad 7.1 urad 200 nrad
yaw 390 nrad 10.1 urad 94 nrad
roll <115 nrad 6.1 urad <200 nrad
flatness 14 nm 1.1 um 42 nm
straightness 2 nm 2.1 um 47 nm
z
x
z
x
0 0.2 0.4 0.6 0.8 1 1.2
-1
-0.5
0
0.5
motor position (m)
Fla
tnes
s er
ror
( µm
)
Pitch Yaw Flatness Straightness
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-50 0 50-50
0
50
y
z
-50 0 50-50
0
50
y
z
-50 0 50-50
0
50
yz
Pitch Yaw Roll
Double pass raytracing of the scanningpentaprism is used to determine the influence ofguidance error on the measurement
-50 0 50-50
0
50
y
z
Flatness
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0 200 400 600 800 1000 1200-50
0
50
100
150
Position (mm)
trac
ing
erro
r (n
rad)
Roll - 0 nradPitch - 2 nrad
Yaw - 0 nrad
Straightness - 0 nrad
Flatness - 5 nrad
Position - 17 nradTotal - 17 nrad
Contribution of the guidance error to the LTP error
R = 100 m
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0 200 400 600 800 1000 1200
-200
-100
0
100
200εA=-0.50 mrad - 57 nrad
Position (mm)
trac
ing
erro
r (n
rad)
εA=-0.25 mrad - 34 nrad εA=+0.00 mrad - 17 nrad εA=+0.25 mrad - 23 nrad εA=+0.50 mrad - 45 nrad
Pentaprism error – R=100 m
0 200 400 600 800 1000 1200-100
-50
0
50
100
150
200
250
R=50 m 33 - nrad RMS
Position (mm)
trac
ing
erro
r (n
rad)
R=100 m 17 - nrad RMS
R=200 m 8 - nrad RMS
R=500 m 3 - nrad RMS
Different spheres
0 200 400 600 800 1000 1200-100
-50
0
50
100
150
200
250
R=50 m 11 - nrad RMS
Position (mm)
trac
ing
erro
r (n
rad)
R=100 m 6 - nrad RMS
R=200 m 3 - nrad RMS
R=500 m 1 - nrad RMS
Different spheres – Position LUT
0 200 400 600 800 1000 1200
-200
-100
0
100
200 roll=-2.00 mrad - 14 nrad roll=-1.00 mrad - 9 nrad roll=+0.00 mrad - 17 nrad roll=+1.00 mrad - 32 nrad roll=+2.00 mrad - 66 nrad
Position (mm)
trac
ing
erro
r (n
rad)
Pentaprism roll – R=100 m
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0 200 400 600 800 1000 1200
-200
-100
0
100
200εA=-0.50 mrad - 57 nrad
Position (mm)
trac
ing
erro
r (n
rad)
εA=-0.25 mrad - 34 nrad εA=+0.00 mrad - 17 nrad εA=+0.25 mrad - 23 nrad εA=+0.50 mrad - 45 nrad
Pentaprism error – R=100 m
0 200 400 600 800 1000 1200-100
-50
0
50
100
150
200
250
R=50 m 33 - nrad RMS
Position (mm)
trac
ing
erro
r (n
rad)
R=100 m 17 - nrad RMS
R=200 m 8 - nrad RMS
R=500 m 3 - nrad RMS
Different spheres
0 200 400 600 800 1000 1200-100
-50
0
50
100
150
200
250
R=50 m 11 - nrad RMS
Position (mm)
trac
ing
erro
r (n
rad)
R=100 m 6 - nrad RMS
R=200 m 3 - nrad RMS
R=500 m 1 - nrad RMS
Different spheres – Position LUT
0 200 400 600 800 1000 1200
-200
-100
0
100
200 roll=-2.00 mrad - 14 nrad roll=-1.00 mrad - 9 nrad roll=+0.00 mrad - 17 nrad roll=+1.00 mrad - 32 nrad roll=+2.00 mrad - 66 nrad
Position (mm)
trac
ing
erro
r (n
rad)
Pentaprism roll – R=100 m
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Although the amplitude of the vibration in the ground is 50 nm RMS, themeasurement on top of the NOM is 13 nrad RMS
0 50 100 150 200 250 300 350 400-0.4
-0.2
0
0.2
0.4
time (s)
Am
plitu
de (
µrad
)
20 40 60 80
0.1
0.2
0.3
0.4
0.5
0.6
frequency (Hz)
Am
plitu
de s
pect
ral d
ensi
ty (
µrad
/Hz)
NOM(pitch
betweenplatforms)
20 40 60 80 100
100
102
Frequency (Hz)
Am
plitu
de s
pect
ral d
ensi
ty (
nm/H
z)
20 40 60 80 1000.1
1
10
100
Frequency (Hz)
Spe
ctra
l Am
plitu
de (
nm R
MS
)13 nrad RMS in 6:40 min
Groundvibration(vertical)
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The use of redundant-independent measurements of a mirror allows to estimatethe slope error and the linearity error of the instrument
The resolution of the surface is limited
• Validity of the error model � short mirrors vs long mirrors
• Noise of each measurement
• Number of measurements
F. Polack, et al , Nucl. Instrum. Meth. Phys. Res. A 616 (2010) 207
0 50 100 150 2000
5
10
15
20
25
30
Measurement noise (nrad RMS)
Rec
onst
ruct
ion
erro
r (n
rad
RM
S) N = 20
0 10 20 30 40 500
5
10
15
20
25
30
Number of datasets
Rec
onst
ruct
ion
erro
r (n
rad
RM
S) σ = 50 nrad
Simulation: accuracy dependence on noiseSimulation: accuracy dependence on
number of datasets
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-6 -4 -2 0 2 4 6-10
-5
0
5
10
angle (mrad)
angl
e er
ror
( µra
d)
instrument angle error
roll A
roll B
-50 0 50-10
-5
0
5
10
position (mm)
slop
e ( µ
rad)
best fit surface slope
roll A
roll B
A 100 mm, R=75 m sphere has been used to cover 12 mrad range of the NOM.
Each reconstruction is based on 54 scans
Residual aberration + periodic subpixel interpolation error found for two differentroll positions of the pentaprism.
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• For small apertures uncertainty is limited by noise and repeatability
• For larger apertures, the error increases, mainly, due to the loss of lateral resolution
Measurements of the same mirror, using different iris apertures, all compared witha reference measurement at 3 mm iris
10-2
10-1
104
106
108
spatial frequency (mm-1)
PS
D (
nm3 )
3.0 mm
6.5 mm
3.5 4 4.5 5 5.5 6 6.50
0.1
0.2
0.3
0.4
0.5Error Contribution R = 20 m
aperture (mm)
Err
or (
µrad
RM
S)
Noise
RepeatabilityLateral Res.
Accuracy
Systematic error?
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-150 -100 -50 0 50 100 150-2
-1
0
1
2
3
4
Position (mm)
Res
idua
l Pro
file
(nm
)
Bent
Flat
In situ 0.045 µrad0.055 µrad
0.05 0.1 0.150
0.05
0.1
0.15
0.2
LTP error (µrad RMS)
achi
eved
slo
pe e
rror
( µra
d R
MS
)
Simulation of the achievable slopeerror with 2 actuators, as a functionof the measurement error.
Mirror figure measured by the pencil beam method matches the profile optimized to55 nrad at the Alba-NOM 2 years ago.
For whatever correction technique, accuracy of metrology is a limit to theachievable slope error
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Positioning error correction (LUT) and accurate pentaprism
allow reducing the bench induced error to the few
nanoradian
The usage of redundant-independent datasets allow an
accurate modeling of the optics induced error.
Using them, also allows reducing the iris aperture, to
increase spatial resolution preserving accuracy.
The measurements provided by the NOM are accurate
enough to optimize the mirror figure to nanometer accuracy
0 200 400 600 800 1000 1200
-200
-100
0
100
200εA
=-2.00 mrad - 14 nrad
Position (mm)
trac
ing
erro
r (n
rad)
εA=-1.00 mrad - 9 nrad εA=+0.00 mrad - 17 nrad εA
=+1.00 mrad - 32 nrad εA=+2.00 mrad - 66 nrad
10-2
10-1
104
106
108
spatial frequency (mm-1)
PS
D (
nm3 )
3.0 mm
6.5 mm
-150 -100 -50 0 50 100 150-2
-1
0
1
2
3
4
Position (mm)
Res
idua
l Pro
file
(nm
)
Bent
Flat
In situ
-6 -4 -2 0 2 4 6
-3
-2
-1
0
1
2
3
4
angle (mrad)
angl
e er
ror
( µra
d)
instrument angle error
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Thank you for your attention
Computing and Controls Zbigniew Reszela
Sergi blanch
Guifré CuníTiago Coutinho
Sergi Pusó
Algorithms Juan Campos (UAB)
Engineering Claude Ruget (CRC)Carles ColldelramRicardo Valcárcel
Jordi Iglesias
Technicians José FerrerDavid CalderónPablo Jiménez
Administration Laura Campos
XALOC beamline Jordi Juanhuix