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Absolute distance metrology:- sweeping wavelength

- frequency comb referenced 2 interferometric system

P. Pfeiffer* L. Perret** N. Schuhler***

* Université de Strasbourg** Université de Strasbourg Sagem*** Europeen Southern Observatory

European Southern ObservatoryInstrumentation Procédés Photoniques

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■ Wavelength sweeping Absolute Distance Metrology ● Signal processing● Tunable laser source● Non-linearities of the tuning speed

Outline

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■ Distance : 0 - 30m

■ 2 or more targets simultaneously

■ Accuracy, resolution: some ppm

■ Portable

■ 10 maesurements per second

■ Cost

ADM with wavelength sweeping

N. Pfeiffer L. Perret UdS

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Tunable Laser

PDmeasPDref

Reference Interferometer

Object Interferometer Target A

ISO

Target B

SC

Experimental Setup

ref

obj

b

b

ref

obj

f

f

L

L

2 i

b

Lf

i

sweeping speed

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Tunable wavelength laser

External Cavity Laser Diode

Coherence length >> 1kmCentral wavelength ~ 1.5µmContinuous tuning range up to ~ 5nmSweeping speed up to 40nm/s Large ranges and high sweeping

speeds without mode hopping to reduce error magnifications.

N. Pfeiffer L. Perret UdS

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Tunable laser source

External cavity laser diode:– Littman Metcalf configuration – Littman Shoshan configuration

-500 -400 -300 -200 -100 0 100 200 300 400 5000

1

2

3

4

5

6

7

8

9

10

xt [µm]

Tai

lle d

e l'a

ccor

d co

ntin

u [n

m]

N. Pfeiffer L. Perret UdS

Lentille

Réseau

Miroir

M'

na

xt

xl

Diode Laser

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Autoregressive method

Frequency resolution for N samples: N- 3/2

AR Burg method Sensitive to non-

linearities of the the sweeping speed

Fourier Transform technique

Eliminates low frequencies like drifts

Fringe processing

N. Pfeiffer L. Perret UdS

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Fringe processing

Spectral filtering Gaussian filter

Blackman

window

Fast Fourier Transform

I(t) = a(t)+b(t) cos(I(t) = a(t)+b(t) cos((t)(t)))I(t) = a(t)+1/2[b(t) e I(t) = a(t)+1/2[b(t) e ii(t)(t)+ b+ b**(t) e (t) e -i-i(t)(t)]]

A(f)A(f)BB**(-(f+f(-(f+fss)))) B(f-fB(f-fss))

Inverse Fourier Transform

1/2[b(t) e 1/2[b(t) e ii(t)(t)] ]

Extraction of the instantaneous frequency

dt

tdtfb

)(

2

1)(

1

N. Pfeiffer L. Perret UdS

2

3 4

5

99

Target A at 2.2m Target B at 8m

6 records/pos.

sweeping speed 20nm/s.

1000 1050 1100 1150 1200

0.187444

0.187446

0.187448

0.18745

0.187452

0.187454

0.187456

0.187458

0.18746

Target A increment from 2.2m [µm]

Fre

quen

cies

rat

io

Relative Uncertainty at 1 : 1.2e-006

FTT results for 1017 samples

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Non-linearities in wavelength sweeping

Results in an overlap of spectral peaks in the multi-target configuration.

8140 8160 8180 8200 8220 8240 8260 8280 8300-2000

-1000

0

1000

2000Object (red) & Reference (blue) signals

Sample number

Am

plit

ud

e (

raw

da

ta)

0 1 2 3 4 5 6 7

x 104

0

0.5

1

1.5

2

x 108 Object Spectrum

Frequency (Hz)

PS

D

Variations in fringes size

Spectral modulation

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Extracted instantaneous beat frequency

dt

tdtfb

)(

2

1)(

0.07 0.08 0.09 0.1 0.11 0.12 0.133.5

4

4.5

5

5.5

6

x 104

Time [s]

Inst

anta

neou

s be

at fr

eque

ncy

[Hz]

Sweeping speed

0 0.02 0.04 0.06 0.08 0.1 0.12 0.1412

14

16

18

20

22

24

26

28

30

Time (s)S

wee

pin

g s

pee

d (

nm

/s)

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Quasi-periodical variation of the beat frequency.

FFT analysis and reconstruction through sinusoidal signals.

ttt nl 00

iiif tfmAmt 2sin0

Modeling parameters:

mf : modulation rate

Ai : component’s weight (normalized)

fmi : component’s frequency

φi : component’s dephasage

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Periodical non-linear influence

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7

8

9x 10

-6

Err

or b

etw

een

sim

ulat

ed a

nd th

eore

tical

rat

ios

Distance increment from 2m (mm)

Simulation of different wavelength sweeps

Linear sweep

10nm/s model (5 components)

+ Single sinusoid : mf=2.2e-4fm=94.5Hz

Single sinusoid : mf /2fm /2

Single sinusoid : mf x2fm x2

Optimal sinusoidal modulation

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• Reduces by a factor 20 the mean error (increases precision)

• Reduces by a factor 1000 the error dispersion (increases resolution)

… compared to a linear sweep.

Averaging of the instantaneous frequency ratio minimizes errors due to FFT limited resolution.

However, modulation still introduces peak overlapping in a multi-target configuration…

N. Pfeiffer L. Perret UdS

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Frequency comb referenced two wavelength interferometry

N. Schuhler

ADM Laser system form the VLT at Paranal

European Southern Observatory

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Frequency comb stabilized 2 wavelength laser interferometry for ADM● Absolute frequency stabilization of PRIMET Nd:YAG

laser● Two wavelength laser source● Calibration of the system

Outline

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Phased Reference Imaging and Micro-arcsecond Astrometry

facility

LASBOPD

2 objects generate 2 fringe patterns related through:

where:

B is the baseline;

S the angular separation of the two objects;

A noise due to the atmosphere;

phase which depends on the nature of the object (0 for a point like source);

L instrumental noise (vibrations, internal turbulence). OPD

OPD

LASBOPD

N. Schuhler ESO

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Specifications

The detection of Exo-planet with PRIMA in astrometric mode requires 10 as accuracy over several years.

Observable: differential optical path difference between to Michelson interferometers, OPD Propagation distance: <500 m OPL for an interferometer: <250 m Maximum OPD: 60 mm Accuracy: 5 nm (relative accuracy ~ 10-8) Resolution: 1 nm Measurement:time <30 min Sampling frequency: >8 kHz

N. Schuhler ESO

Proposed solution

Incremental interferometry for the ultimate resolution

2 wavelength interferometry for increasing the NAR

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Architecture

Two heterodyne interferometers : Nd:YAG laser at = 1.319 m; Frequency shifting by Acousto-Optic Modulators; Electronic differential phase measurement (superheterodyne

phasemeter) (IMP Neuchatel)

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Error and Non Ambiguity Range

m: fringe order

M: fringe number

f(m): fractional part: phase (-<<)

222

)(2

MmfMmOPD

N. Schuhler ESO

OPDOPD

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Error on OPD due to the wavelength uncertainty:

Differential OPD measured:

22

refscrefsc OPDOPDOPD

88 101060

5

mm

nm

OPD

OPD

Non Ambiguity Range:

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Stabilization of the Nd:YAG

P(49)6-6

Nd:YAGI2EOM

PPLN Lock-in

Amplifier

CANPICNA

T Pz 25%

75%To the interferometers

Pound-Drever-Hall method applied to a frequency doubled Nd:YAG, the frequency reference is an I2 transition at 659.5nm

+PICNA

N. Schuhler ESO

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Residual error in closed loop

N. Schuhler ESO

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Measurements with an optical frequency comb

• Self-referenced optical frequency comb based on a fibered fs pulsed laser at the• Max Planck Institute for Quantum Optics (MPQ Munich, Germany)• Provides thousand of modes separated by 100 MHz over one octave (1m -2m)• Reference radio frequency signal (10 MHz) derived from a cesium atomic clock • Relative inaccuracy on the frequency of one mode of the comb < 10-12

• Frequency of Nd:YAG is deduced from the beat signal with one mode of the comb

nr

0

nr +0

I()

0

Nd:YAG

N. Schuhler ESO

rep

2(nr

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Peak-to-valley = 1.45 MHz Standard deviation = 226 kHz

Measurements with an optical frequency comb (3)

The discrepancy is due to: the error in the calibration of the error signal; detection noise.

N. Schuhler ESO

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Absolute frequency stabilization of PRIMET Nd:YAG laser

ConclusionUse of the temperature of the laser cavity to enable long-term (weeks) locking; Full automation of the laser frequency stabilization; Accurate characterization of the system performance by the use of a self-referenced optical frequency comb (with the help of MPQ) as an independent sensor :

locking frequency 0 = 227 257 330 623 020 Hz ± 94 kHz; frequency noise (rms) over bandwidth 5 mHz- 8 kHz : <2.27

MHz (PRIMET specifications); Demonstration that the system performance are limited by detection noise; Demonstration that the laser frequency cannot be calibrated with an accuracy better than 10-8 by comparison with a commercial HP interferometer

The system will be tested in Paranal with a self-referenced frequency comb from Menlo Systems.

N. Schuhler ESO

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Principle of two-wavelength interferometry

Multiple-wavelength interferometry (Benoit 1895) with the excess fraction method Synthetic wavelength technique for two-wavelength laser interferometry (Wyant in 1971)

A Michelson interferometer is used with two wavelength simultaneously:

2211

OPD

is the synthetic wavelength

The NAR of the system is /2

≈ 90 µm ↔ ≈ 20 nm

2222

OPD

222

1

2

21

21

21

OPD

N. Schuhler ESO

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Architecture of the source

Comb modes

1=c/1 2=c/2

rep

=c/=2-1=Nrep

to the interferometer

Absolute frequency

stabilization System1

fs laser (with stabilized repetition rate)

Beat detection + PLL

to the interferometer

Beat detection + PLL

2

ECLD tunable

Two lasers can be stabilized on different modes of the comb to generate a custom and highly stable synthetic wavelength: m < L < md/ < reference radio signal (10-12 GPS based clock)

N. Schuhler ESO

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Architecture of the prototype

10 MHz source with accuracy < 10-11

Fs-laser

TC 1500 Menlo Systems

AOM

+40.65MHz

AOM

+40.45MHz

AOM

-40MHz

1

2

2 + 650 kHz1 + 450 kHz

Nd:YAG

Lightwave 125

1.319 m

ECLD

Thorlabs Intun 1300

1.300 m

1319 ± 2.5 nm

BD

PLL

1

2

BDPLL1300 ± 2.5 nm

gratings

N. Schuhler ESO

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Performances of the prototype

10-1135 Hz~3.3 THzECLD-Nd:YAG

0.5×10-71 Hz20 MHzBeat signalECLD/Comb

0.5×10-1010 mHz20 MHzBeat signalNd:YAG/comb

10-111 mHz100 MHzRepetition rate

Relative instability

Instability (peak-to-valley)

Mean frequencySignal

Nd:YAG ECLDrep=100MHz

=N×rep~3.3THz

fb=20MHz

fb=20MHz

The relative stability of the synthetic wavelength in vacuum is 10-11.

N. Schuhler ESO

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Set-up for the calibration of in air

2-wavelength

Light source

Reference

Interferometer

Phasemeter

BS

PBS

probe

reference

2~1.30 m

1=1.319 m

LP

ref=0.633 m Translation stage

corner cube

N. Schuhler ESO

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Result of the calibration of

Slope=139.541582 rad/mm=90.054666 mTaking into account the dispersion:=3.32899949 ±0.00000067 Thz 33290 modes of the comb

Residuals:=22 mrad=2/285

OPD

=160 nm<1/2

N. Schuhler ESO

Merci de votre attention

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