laboratoire nationallaboratoire national de métrologie et d’essais · 2008. 12. 10. ·...

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 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


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)


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…)


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




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.


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


Mobile frame


• 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 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.


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


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


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


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


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


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


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


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




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


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


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


LAMPARDcylinder



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


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.

laboratoire nationallaboratoire national de métrologie et d’essais · 2008. 12. 10. ·...

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