Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Laboratoire nationalLaboratoire nationalde métrologie et d’essais
T d d i i f R i f hToward a determination of RK in term of the new LNE calculable cross capacitor
O. Thévenot, L. Lahousse, C. Consejo, F. Piquemal (LNE, France)id l ( )J. David, S. Leleu (ENSAM, France)
SummarySummary
IntroductionThe SI electrical base unit - Ampere definition Filiation of the electrical unitsDetermination of RK
Part 1 - Thompson Lampard calculable capacitorPart 1 Thompson Lampard calculable capacitorPresentationMise en pratique at LNEL t lt i 2000Last results in 2000
Part 2 – Present developmentspDedicated measurement apparatusFabrication of a new set of electrodesDesign of the new LNE Thompson Lampard calculable capacitorDesign of the new LNE Thompson Lampard calculable capacitor
Conclusion
The SI electrical base unit : the ampereThe SI electrical base unit : the ampere
The ampere is that constant current which, if maintained in two straight parallelconductors of infinite length, of negligible circular cross-section, and placed 1 m apartin vacuum, would produce between these conductors a force equal to 2.10-7 newtonin vacuum, would produce between these conductors a force equal to 2.10 newtonper metre of length.
This force has for expression : F = (µ0/2π)⋅(I 2/d)
µ0 = 4π 10-7 N/A2 (permeability of free space)µ0 (p y p )
The SI definition of the ampere gives simultaneously those of the vacuum impedance :Z (Z 377 Ω)Z0 = µ0 ⋅ c (Z0 ≈ 377 Ω)
and the vacuum permittivity :
ε0 = 1/(µ0 ⋅ c2 ) (ε0 ≈ 8.85 pF/m)
Realization chain of the electrical unitsRealization chain of the electrical units
ohm
henryvolt
ampere
µofarad
Mechanical units
coulomb
Filiation of the electrical units definition
ohmfarad
µo
coulomb ampere
M h i lvolt
henry
Filiation of the realisations
Mechanical units
Filiation of the realisations
Determination of Determination of RRKK at LNE : at LNE : linking the ohm to the faradlinking the ohm to the farad
METREcapacitorCalculable
γ= επ0 ln pF/m2
5-1
QHE
HR (i)=RKi
hi.e2
METREcapacitorCalculable
γ= επ0 ln pF/m2
5-1
QHE
HR (i)=RKi
hi.e2HR (i)=
RKi
hi.e2
Two-terminal paircapacitance bridge i = 2
12
345
and αh/e2h/e2h/e2
Two-terminal paircapacitance bridge i = 2
12
345
Calibration center
200 Ω
1, 10 et 100 pF 100 ΩCalibration center
200 Ω
1, 10 and 100 pF 100 Ω
Four-terminal paircapacitance bridge
Four-terminal paird t b id
CCC
200 Ω
Ω10 kor100 à 1000 pF
1000 à 10000 pF
Four-terminal paircapacitance bridge
Four-terminal paird t b id
CCC
200 Ω
Ω10 kor100 to 1000 pF
1000 to 10000 pF quadrature bridge
DC
1000 à 10000 pF
DR
40kΩ20kΩ101 600 Hz
800 Hz400 H
R( ).C. =1ω ω
quadrature bridge
DC
1000 to 10000 pF
DR
k40kΩ20
kΩ101 600 Hz
800 Hz400 H
R( ).C. =1ω ω
SECOND
ACCoaxial
calculableresistor
DCDC kΩ40400 HzSECOND
ACCoaxial
calculableresistor
DCDC kΩ40400 Hz
… and checking R… and checking RKK =h/e=h/e22
2 0
Determination of Determination of RRKK in National Metrology Institutesin National Metrology Institutes
N P L 1 9 8 8 C S IR O 1 9 8 9
B N M 1 9 9 3 1 5
1 0 -8
C S IR O 1 9 9 7
N IS T 1 9 9 7
B N M 2 0 0 0
5
1 0
N IS T 1 9 8 9
0
5
R k -9 0
C o d a ta 9 8
N IM 1 9 9 5 1 0
-5
-1 0
BNM 1986 RK-90 = 25 812.807 Ω
-1(R )α-1(RK)
SummarySummary
IntroductionThe SI electrical base unit - Ampere definition Filiation of the electrical units
Part 1 - Thompson Lampard calculable capacitorPresentationPresentationMise en pratique at LNELast results in 2000
Part 2 – Present developmentsDedicated measurement apparatusDedicated measurement apparatusFabrication of a new set of electrodesDesign of the new LNE Thompson Lampard calculable capacitor
Conclusion
The Thompson Lampard calculable capacitor The Thompson Lampard calculable capacitor
Assume four electrodes of infinite length, separated by a null thickness
The Lampard theorem
Assume four electrodes of infinite length, separated by a null thickness insulator, delimiting a volume perfectly cylindrical :
γ1-3 and γ2-4 : lineic capacitances (pF/m)
1 e(-π/ε)γ1-3 + e(-π/ε)γ2-4 =1
γ1-32γ 2-4
In a case of a symmetrical arrangement :
3
4 ...953.12ln0 ≅=π
εγ pF/m
Lampard D G IEE 104C (1957) 271 280Lampard D.G, IEE, 104C (1957) 271-280
The Thompson Lampard calculable capacitor The Thompson Lampard calculable capacitor
The Lampard theorem is valid only for a uniform field repartition (out of
Infinite lenght of the electrodes
The Lampard theorem is valid only for a uniform field repartition (out of extremity effect)
1
3 and 4450 mmC1=L1γ + extrδ
1
3 d 43 and 4L1
1=L2γ + extrδC2
[ 3/8 pF for 138.25 mm ]3 and 4
L2
∆ γC=C - C = (L - L )1 12 2
[ / p ] L2
The Thompson Lampard calculable capacitor The Thompson Lampard calculable capacitor
Null thickness inter-electrodes insulator
112
=
=
k
πα1
2
2
4
∆z α2
2
∆
≈∆
=
=
zz
CC
k
δ
3
4
α
34 zC
0→= απα
∆z
210
It can be demonstrated that the errordue to the non null thickness of the
l f f l
,1
0,
∞→=
→=
nn
k
nαα
34α=0insulator,δ, varies as a function of angle,
α, between the electrodes’ tangents, attheir contact to the insulator (ofthi k ∆ )
0≈
∆
≈∆
=n
zz
CCδ∆z
thickness ∆z)
The Thompson Lampard calculable capacitor The Thompson Lampard calculable capacitor
Mise en pratique
• For a 4 electrodes system :
211expexp
0
24
0
13 =
−+
−
επγ
επγ
theorem :
34γ24
γ13 measurement : K= γ1-3 / γ2-434
The capacitance variation allows to calibrate
tare: 1,25 pF
10AT2quad.
(for LVb)
1 pF
baMobile guarda : in
ωtare: 1,25 pF
10AT2quad.
(for LVb)
1 pF
baMobile guarda : in
ω
Cx=ki.∆LγijC i t ti
The capacitance variation allows to calibrate a capacitance Cx :
7 or 0 D
-1
phase
inj.1pF
wagner
bab : out
7 or 0 D
-1
phase
inj.1pF
wagner
bab : out
This kind of standard has been developped in different NMIs (NMIA, PTB, BNM, NPL, NIST )
Comparison system ratioLVb or 10 pFLVb or 10 pF
NIST…)
The Thompson Lampard calculable capacitor The Thompson Lampard calculable capacitor
Lampard theorem extension
N. Elnekavé (BNM, 1973): Capacitor with 5 electrodes 1N. Elnekavé (BNM, 1973): Capacitor with 5 electrodes
exp (-π(γ13+γ14)/ε0) + exp (-πγ25/ε0) = 1
f f
25γ25
γ13
γ14
In case of a perfect symmetryγ = (ε0/π)⋅ln[2/(√5-1)] F/m = 1. 356 235 626 … pF/m 34
Circular permutation 5 Lampard configurations
( )4,13,11 γγ +∆= LkCx These 5 equations are successively associate with the 5 possible Lampard relations :
( )3,52,55
...γγ +∆= LkCx
The resolution of this 6 equations system gives the values and the C to C values of C
( )( )[ ] ( )( )[ ] 1expexp 4,103,2,0 =−++− ⊕⊕⊕⊕ iiiiii γεπγγεπ
The resolution of this 6 equations system gives the γi,j values and the C1 to C5 values of Cx
The French Thompson Lampard calculable capacitor The French Thompson Lampard calculable capacitor
Movable guard (diam. 50 mm)
MotorCylinder 1 (450 mm) 12
Cylinders 3+42
34
5γ 2γ
PTFE h
PTFE shoe(fixed on the frame)Guard
(fixed on the electrodes)
1
25
« Spike » 34
PTFE shoe(fixed on the movable guard)
Interferometer34Screen
Diam. 75.5 mmUsable length ≈ 138.25 mm∆C ≈ 0.375 pF∆C ≈ 0.375 pF
Standard uncertainty : 3.8 10-8
G. Trapon et al, Metrologia, 40 (2003) 159-171
Determination of Determination of RRK K in 2000in 2000
Uncertainty components 1σ relative
RK=RK-90(1+4.1 10-8) (1σ=5.3 10-8)
Uncertainty components 1σ relative
uncertainty x 108
Laser wavelenght 0.003
Air refractive index 0 013Air refractive index 0.013
Laser alignment 0.09
Defect of the movable corner cube reflector 0.02
Deformation of the pentagon 0 02
Fabrication of a new standard in ti l iti
Realisation of a new set of electrodesDeformation of the pentagon 0.02
Cylindrical defect 2.4
Efficiency of the movable guard 0.2
Lateral shifting of the spike 3
New ratio transformers
vertical positionLateral shifting of the spike 3
Bridge ratio (used 5 times) 1.5
Injection signal 0.3
Bridge coaxiality defect 0 5 New ratio-transformersBridge coaxiality defect 0.5
Loading 0.3
Voltage effect (10 pF, 100 pF, 1000 pF) 1.0
10 nF connection effect 0 310 nF connection effect 0.3
Frequency (quad bridge) 0.02
Resistor frequency effect 1.5
DC QHE 0 3
New optimized coaxial calculable resistors and resistance transfer standards for quad. bridge (already available)
G. Trapon et al, Metrologia, 40 (2003) 159-171
DC QHE 0.3
Total type B uncertainties 4.6available)
SummarySummary
IntroductionThe SI electrical base unit - Ampere definition Filiation of the electrical units
Part 1 - Thompson Lampard calculable capacitorPresentationPresentationMise en pratique at LNELast results in 2000
Part 2 – Present developmentsDedicated measurement apparatusDedicated measurement apparatusFabrication of a new set of electrodesDesign of the new LNE Thompson Lampard calculable capacitor
Conclusion
Objective: total uncertainty ≤ 1 10-8
Present improvements Present improvements
Objective: total uncertainty ≤ 1 10-8
Realisation of a new set of electrodes∆(rect. + diam.)< 0.1µm 5 10-9 (instead of 2.4 10-8)
Dedicated measurement apparatusMeasurement of the cylindricality defect of the new set of electrodes
New Thompson-Lampard calculable capacitor :New Thompson Lampard calculable capacitor : 5 electrodes in vertical positionLateral shifting of the movable guard < 50 nm 5 10-9 (instead of 3 10-8)P iti i f th l t d b tt th 100Positionning of the electrodes better than 100 nm
Improvements of the measurement chainConstruction of new ratio transformers
target uncertainty on ratio calibration ≈ 1 10-9
Fabrication of new calculable resistors (1 kΩ Haddad type) and transfer standards (10, 12.9, 20 and 40 kΩ) for quadrature bridge( , , ) q g
Fabrication of a new set of electrodesFabrication of a new set of electrodes
Dedicated Measurement DeviceDedicated Measurement Device
Objective : Measurement of the straightness and the parallelism of the generating lines of the future electrodes with an uncertainty lower than 25 nm
Key elements of the device :
• based on the dissociated metrologicalPortal structure
principle
• designed to respect the Abbe principle
Portal structure
Chain of solids
• two vertical references (in red) are thestraightness reference
• a mobile plate (in purple) with 8
Mobile plateElectrode under
test
a mobile plate (in purple) with 8capacitive sensors : 4 sensors measure thereference cylinders information ofposition, 4 sensors measure the electrode
Referencecylinders
Sensors support ring
p ,
• a second mobile plate (in green)supports the first one without transmittingany deformation this plate can go up and
Metrological chain
any deformation, this plate can go up anddown along the electrode.
Fabrication of a new set of electrodesFabrication of a new set of electrodes
Dedicated Measurement DeviceDedicated Measurement Device
Objective : Measurement of the straightness and the parallelism of the generating lines of the future electrodes with an uncertainty lower than 25 nm
Key elements of the device :
• based on the dissociated metrological
Portal structurePortal structure
principle
• designed to respect the Abbe principle
Mobile frame
Sensors support ring
Mobile frame
Sensors support ring
• two vertical references (in red) are thestraightness reference
• a mobile plate (in purple) with 8Electrode under testElectrode under test
a mobile plate (in purple) with 8capacitive sensors : 4 sensors measure thereference cylinders information ofposition, 4 sensors measure the electrode
Reference cylindersReference cylindersp ,
• a second mobile plate (in green)supports the first one without transmittingany deformation this plate can go up andany deformation, this plate can go up anddown along the electrode.
Cylindricality dedicated measurement device Cylindricality dedicated measurement device
Straightness measurement of the present standard reserve electrode
straightness of generating line 90 °
0.2
0.3
90
100
-0.2
-0.1
0
0.1
0 50 100 150 200 250 300 350 400 450
tnes
s (µ
m)
50
60
70
80
d de
viat
ion
nm)
-0.6
-0.5
-0.4
-0.3
stra
ight
10
20
30
40
stan
dard (n
straightnessstandard deviation
-0.7Tz (mm)
0
Measurement of the same generating lineduring 12 hours with a 1 mm step (8 forth
Cylindricality measurement (withoutconicity defect) with a 2,5 mm and 2,5 °
and back runs)y ) , ,
steps. The measurement was performedduring 30 hours (4 forth and back runs)
Fabrication of a new set of electrodesFabrication of a new set of electrodes
Fabrication of a new set of electrodesFabrication of a new set of electrodesThe new set of electrodes is made of amagnetic stainless steel (grade 1.4539)
Dimensions : diameter 75.5 mm, length : 450 mm
After grinding the cylindricality defect is about 1,5 µm
To reduce this defect to a value close to 100 nm, the cylinders are manually lapped and polishedpolished
Fabrication of specific lapping-toolThe best results were obtained with grinding-tool made of corundum (abrasive) with shellac and rosinmade of corundum (abrasive) with shellac and rosin for bonding. The tool is shaped to fit the cylinders.
Fabrication of a new set of electrodesFabrication of a new set of electrodes
First resultsFirst results
After the grinding stage After 30 hours of lapping
Straightness defect +/ 0 8 µm Straightness defect +/ 0 15 µmStraightness defect ∼+/- 0,8 µm Straightness defect ∼+/- 0.15 µm
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Main characteristics :
5 electrodes in vertical position 75 5 mm- 5 electrodes in vertical position, 75.5 mmdiameter, 450 mm long, with straightnessdefects < 0.1 µm (polishing process inprogress) amagnetic stainless steelprogress), amagnetic stainless steel
- Integrated device to control electrodes relativepositionposition
- Independent micrometric adjustment of theelectrodes position coupled with a maintainp psystem
- Cross section cylindricality quality is used toy y q yguarantee the movable guard lateral position
Positionning the electrodes
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Positionning the electrodes
cylindricality defects < 0.1 µm
Bidimensional micrometric adjustment with flexure leaves
Clamp fixe position designed to not disturbClamp fixe position, designed to not disturb previous adjustment
Clamp
Linking part
Xdj t t
Reduction lever
PivotX
Yadjustment system without clearance
Ultra-fine adjustement screw
Flexure stageLampard
Flexure stage
Bidimensional positioning system
structure
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Control the distance inter-electrodes Two axis carrier
Integrated and removable measurement system :ten capacitive sensors on a non-shrinking plateindexable in 5 positions each sensor can
Control the distance inter electrodes Two axis carrier
pmeasure the 5 cylinders.
This plate measure straightness of outsideelectrodes This information combined to theelectrodes. This information combined to thegeometry knowledge coming from the dedicatedmeasurement apparatus allows to know the crosssection geometry
Capacitive sensor
section geometry. Non-shrinking plate
Lampard structure
Ultra-fine adjustement screw
structure
Capacitive sensor in the same vertical plane of the micrometric screw
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Control the distance inter-electrodes Two axis carrier
Integrated and removable measurement system :ten capacitive sensors on a non-shrinking plateindexable in 5 positions each sensor can
Control the distance inter electrodes Two axis carrier
pmeasure the 5 cylinders.
This plate measure straightness of outsideelectrodes This information combined to theelectrodes. This information combined to thegeometry knowledge coming from the dedicatedmeasurement apparatus allows to know the crosssection geometry
Capacitive sensor
section geometry. Non-shrinking plate
Lampard structure
Ultra-fine adjustement screw
structure
Capacitive sensor in the same vertical plane of the micrometric screw
The movable guard
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
The movable guard
Sleeve bearing mounted in a double cardan
G id bGuidance bars
Support plate of theMetrological framenon-shrinking structure
Support plate of the measurement device
Metrological framenon-shrinking structurenon shrinking structure + guidance bars
The movable guard Rigid structure
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
The movable guard
Drive screws
Rigid structure frame
Guidance bars Driving plate
Metrological frame
Metrological framenon-shrinking structurenon shrinking structure
Support plate of theSupport plate of the measurement device
Metrological frame implented in the rigid structure frame
The movable guard
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
The movable guardThe movable guard
Flexure stage
The movable guard
Driving plate
Metrological frame
Movable guard
Metrological framenon-shrinking structure
Metrological frame implented in the rigidnon shrinking structure implented in the rigid
structure frame
Integration of the movable d i th t l i l fguard in the metrological frame
The movable guard
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Ri id t tThe movable guard Rigid structure frame
5 PTFE shoes fixed on
Driving plate
5 PTFE shoes fixed on the structure
Metrological frame
5 PTFE shoes fixed on the guard end
Lampard structure
Lampard structure
Expected quality of guide better than 100 nm
Prolongations of the electrodes with same diameter but with larger cylindricity defects
New mechanical design of the LNE cross calculable capacitorNew mechanical design of the LNE cross calculable capacitor
Prolongations of the electrodes with same diameter but with larger cylindricity defectsare expected to extend the usable lenght from 200 mm to 400 mm
Capacitance variation between 0.3 and 1 pF
CmExpected linearity
CmExpected linearity
50 500 650
Usable lenght > 380 mm
50 500 650
Usable lenght > 380 mm
500
Electrodes + ends
Linearity measured
500
Electrodes + ends
Linearity measured1 ppm
End effects
Linearity measured in 2000
Usable lenght = 200 mm
1 ppmEnd effects
Linearity measured in 2000
Usable lenght = 200 mmElectrodes prolongation
0Length (mm)
250 450Electrodes
0Length (mm)
250 450Electrodes
SummarySummary
IntroductionThe SI electrical base unit - Ampere definition Filiation of the electrical units
Part 1 - Thompson Lampard calculable capacitorPresentationPresentationMise en pratique at LNELast results in 2000
Part 2 – Present developmentsDedicated measurement apparatusDedicated measurement apparatusFabrication of a new set of electrodesDesign of the new LNE Thompson Lampard calculable capacitor
Conclusion
ConclusionConclusion
The new LNE cross calculable capacitor has the objective to make a direct determination of RK in the SI in the next two years with an uncertainty of about 1 2 10-81∼2 10 8
This experiment will contribute to the knowledge of constants, in particular to test the relation RK =h/e2, and take part to the discussion on revising the SI based ontake part to the discussion on revising the SI based on fundamental constants.
If h, e… are fixed in a « near » future, this measurement chain will contribute to the determination of constants that might become floating like µ0, ε0, Z0
Thank you
Effect of the tilt of one electrodeEffect of the tilt of one electrode
Influence coefficient : -0.16 µF.F-1.µrad-1−α αbar 1
Residual cylindricity defect : 3.5 µrad
Corresponding relative error : -59 10-8bars 3 and 4
frame
movable guard
1000 20
0
500
γ5,2
γ3,5
γ2,4
γ i,j relative variations × 10 6
0
10 Cm relative variation × 106
1000
-500γ1,3
γ4,1
-30
-20
-10
-100 -50 0 50 100 150-1000
-100 -50 0 50 100 150 30
Tilt of electrode n°1 ( α, in µrad)
The French Thompson Lampard calculable capacitor The French Thompson Lampard calculable capacitor
Compensation for the residual cylindricality defect
Influence of the “spike” length and diameter on ∆Cm/Cm, for 750 µrd tilting of electrode n°1
The influence coefficient(about 2 10-7/µrd) is reducedby a factor ≥ 25 The effect of
∆Cm/Cm×106
by a factor ≥ 25. The effect ofthe residual cylindricalityimperfections (about 3 µrad)i t k i t tis now taken into account as a2.4 10-8 uncertainty (1σ) withthe spike in place.
Length / mm
Diameter / mmDiameter / mm
Movable guard displacementMovable guard displacement
Variation of the extremity effect between the two
1 1
25
β
measurements
( ) − 2130 πβCCi
3+4
α 2
3 4
5
A B ( )
−+−=
521cos3.0 πβα i
CCC
m
miA B
400
500
) 0-6
A lateral displacement of 5 µm leads to a defect of 6 10-7100
200
300
mea
n va
lue
(ppm
C1C2C3m
mea
n va
lue
/10
PTFE shoes guidance system
Lateral displacement < 0.3 µm-200
-100
0
Dev
iatio
n fr
om m C3
C4C5
ve d
evia
tion
from
Corresponding uncertainty : 3 10-8-400
-300
-1000 -500 0 500 1000 1500
Axis tilting of movable guard (µrd)
DR
elat
iv
Axis tilting of movable guard / µrad
Fabrication of a new set of electrodesFabrication of a new set of electrodes
Objective : Measurement of the straightness and the parallelism of the generatingObjective : Measurement of the straightness and the parallelism of the generating lines of the future electrodes with an uncertainty lower than 25 nm
CrossheadCrosshead Classical structure
Slider ZTruck Y
Crossheadguide Z
Sensor
Slider ZTruck Y
Crossheadguide Z
Sensor
Metrological chain of a 3D measurement deviceof serial architecture : the final precision
Classical structure
Portal X
DUTCrosshead
guide Y
Sensor
LayingsystemPortal X
DUTCrosshead
guide Y
Sensor
Layingsystem
pdepends on each element defects. Guidingdefects and solids flexibility add entirely
This kind of structure is not appropriate
The dissociated metrological structure
Portal XFrame
Crossheadguide X
Portal XFrame
Crossheadguide X
Slider ZCrosshead
guide Z Slider ZCrosshead
guide Z
This kind of structure is not appropriate with the target uncertainty
The dissociated metrological structureTruck Y
Slider Z
Sensor
C h dMetrological
Kinematic coupling
Truck Y
Slider Z
Sensor
C h dMetrological
Kinematic coupling The « dissociated metrological structure » consists
in separating the metrological chain, wich assumesDUT
FramePortal X
Layingsystem
Crossheadguide Y
links
DUT
FramePortal X
Layingsystem
Crossheadguide Y
linksp g g ,
the metrological reference, from the solids chain,wich assumes displacement, positioning andsupport of the sample. The link between them is
Crossheadguide XCarrier
structure Crossheadguide XCarrier
structuremade by a kinematic coupling
Cylindricality dedicated measurement device Cylindricality dedicated measurement device
The metrological mobile plateRotating sensors
support ringSensors support (x4)
In situ calibrating system (that can be taken appart)
• 8 capacitive sensors
• Sensors 1,2,3,4 mobile
Sensors support plate
Rotating sensorssupport ring
A
Sensors support plate
Rotating sensorssupport ring
A
The metrological mobile plate
Sensors 1,2,3,4 mobile plate position in the plane (reference)
S A B C D thC
BD
D
1
2
4
3
O
C
BD
DD
1
2
4
3
O
Rotating ring with sensors A,B,C,D
• Sensors A,B,C,D on the rotating support electrodes generating lines measurement
S lib ti
LAMPARDcylinder
Reference cylinder 1
Reference cylinder 2
LAMPARDcylinder
Reference cylinder 1
Reference cylinder 2
Sensors calibration
systemsystemSensors supporting
system Active sensor Sensor working situationMovingparts Transfer
Sensor working situationMoving parts Transfer capacitive
sensor
In-situ sensor calibrationsensor working situation
Flexible leaves carrier
Lampard cylinder
Lampard cylinder
Calibration of the calibrating device
Fixedparts Piezoelectricactuator
Laser interferometer
Piezoelectric actuatorFixed parts
Capacitive sensors
The sensors made by FOGALEnanotech :
Type MCC10EC
Active surface area : diam 5.5 mm
The sensors are calibrated on a 40 µm range, they are located at 300 µm from the electrode surface, the uncertainty on their calibration is ~10 nm Measuring range : 200 µm, bandwitch 0-10 kHz
Thermal drift : < 0.005% - Resolution ~ nm
the uncertainty on their calibration is ~10 nm
Cylindricality dedicated measurement device Cylindricality dedicated measurement device
Calibration of the machine straightness
Machine straightness2
2.5
Calibration of the machine straightness
salsalsalAA
salsalsalsalsalAAAA
salsalsalAA
salsalsalsalsalAAAA
salsalsalAA
salsalsalsalsalAAAA
Before reversal
0 5
0
0.5
1
1.5
µm
Defaults elimination by reversal
lllafter reversal
lllllafter reversal
lafter reversal
BD
C
BD
C
BD
C
BD
C
BD
C
BD
C
lllafter reversal
lllllafter reversal
lafter reversal
BD
C
BD
C
BD
C
BD
C
BD
C
BD
C
lllafter reversal
lllllafter reversal
lafter reversal
BD
C
BD
C
BD
C
BD
C
BD
C
BD
C
After reversal
-2
-1.5
-1
-0.5
0 50 100 150 200 250 300 350 400 450
mm
RxRy
salsal
A
B
C
D
sal
A
B
C
D
salsalsalsal
A
B
C
D
sal
A
B
C
D
A
B
C
D
sal
A
B
C
D
C
D
A
B
salsal
A
B
C
D
sal
A
B
C
D
salsalsalsal
A
B
C
D
sal
A
B
C
D
A
B
C
D
sal
A
B
C
D
salsal
A
B
C
D
sal
A
B
C
D
salsalsalsal
A
B
C
D
sal
A
B
C
D
A
B
C
D
sal
A
B
C
D
C
D
A
B
mm
straightness of generating line 90 °
0.2
0.3
90
100
Measurement of the
Result of electrode straightnessAAAAAACAAAAAAAAAAAAC
-0.4
-0.3
-0.2
-0.1
0
0.1
0 50 100 150 200 250 300 350 400 450
raig
htne
ss (µ
m)
30
40
50
60
70
80
anda
rd d
evia
tion
(nm
)
straightnessstandard deviation
Measurement of thesame generating lineduring 12 hours witha 1 mm step (8 forthand back runs)
-0.7
-0.6
-0.5
Tz (mm)
st
0
10
20 sta and back runs)
Cylindricity measurement (without conicitydefect) with a 2,5 mm and 2,5 ° steps. The
f d dMeasurement of one electrode of the present
measurement was performed during 30hours (4 forth and back runs)
Measurement of one electrode of the present standard
Length measurement of the movable guard displacementLength measurement of the movable guard displacement
Laserisolator
moving
fixed retroreflector
Electrode n°1opt.
4 l t Michelson interferometerretroreflector
4 quadrants
g
Vacuum Electrodes n°3 and 4
λ/
detector
4 plate Michelson interferometer
Iodine stabilized He-Ne laser
P1 D1P2
D2
polarisingfilter
photodiode
λ=633 nm
(0,3 µm / fringe)
[ 2 10 / f i-6
Uncertainty components :
- Laser wavelength : 3 10-11p [ 2.10 / fringe
for 138 mm ]
adjustment of gains
- Laser alignment : 20 µm over 230 mm : 9 10-10
and offsets - Air refractive index : pressure in the cross section of the standard < 0,05 Pa :
1.3 10-10
Fringe counterPhasemeter
3 0
- Counting : type A
Oscillo.