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synchrotron light source

Characterization of the error budget

of the Alba-NOM

Josep Nicolas, Juan Carlos Martínez

ALBA light source

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synchrotron light source

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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synchrotron light source

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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synchrotron light source

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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synchrotron light source

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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synchrotron light source

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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synchrotron light source

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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synchrotron light source

-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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synchrotron light source

• 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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synchrotron light source

-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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synchrotron light source

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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synchrotron light source

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