1 absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric...
TRANSCRIPT
![Page 1: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/1.jpg)
1
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
![Page 2: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/2.jpg)
2
■ Wavelength sweeping Absolute Distance Metrology ● Signal processing● Tunable laser source● Non-linearities of the tuning speed
Outline
![Page 3: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/3.jpg)
3
■ 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
![Page 4: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/4.jpg)
4
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
![Page 5: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/5.jpg)
5
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
![Page 6: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/6.jpg)
6
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
![Page 7: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/7.jpg)
7
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
![Page 8: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/8.jpg)
8
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
![Page 9: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/9.jpg)
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
![Page 10: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/10.jpg)
10
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
![Page 11: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/11.jpg)
11
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)
![Page 12: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/12.jpg)
12
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
![Page 13: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/13.jpg)
13
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
![Page 14: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/14.jpg)
14
• 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
![Page 15: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/15.jpg)
15
Frequency comb referenced two wavelength interferometry
N. Schuhler
ADM Laser system form the VLT at Paranal
European Southern Observatory
![Page 16: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/16.jpg)
16
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
![Page 17: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/17.jpg)
17
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
![Page 18: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/18.jpg)
18
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
![Page 19: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/19.jpg)
Proposed solution
Incremental interferometry for the ultimate resolution
2 wavelength interferometry for increasing the NAR
19
![Page 20: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/20.jpg)
20
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)
![Page 21: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/21.jpg)
21
Error and Non Ambiguity Range
m: fringe order
M: fringe number
f(m): fractional part: phase (-<<)
222
)(2
MmfMmOPD
N. Schuhler ESO
OPDOPD
22
Error on OPD due to the wavelength uncertainty:
Differential OPD measured:
22
refscrefsc OPDOPDOPD
88 101060
5
mm
nm
OPD
OPD
Non Ambiguity Range:
![Page 22: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/22.jpg)
22
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
![Page 23: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/23.jpg)
23
Residual error in closed loop
N. Schuhler ESO
![Page 24: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/24.jpg)
24
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
![Page 25: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/25.jpg)
25
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
![Page 26: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/26.jpg)
26
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
![Page 27: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/27.jpg)
27
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
![Page 28: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/28.jpg)
28
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
![Page 29: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/29.jpg)
29
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
![Page 30: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/30.jpg)
30
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
![Page 31: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/31.jpg)
31
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
![Page 32: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/32.jpg)
32
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
![Page 33: 1 Absolute distance metrology: - sweeping wavelength - frequency comb referenced 2 interferometric system P. Pfeiffer* L. Perret** N. Schuhler*** * Université](https://reader030.vdocuments.us/reader030/viewer/2022032604/56649e605503460f94b5aa41/html5/thumbnails/33.jpg)
Merci de votre attention
33