1. 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 Observatory Instrumentation Procédés Photoniques

2. 2 ■Wavelength sweeping Absolute Distance Metrology ●Signal processing ●Tunable laser source ●Non-linearities of the tuning speed Outline

3. 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

4. 4 Tunable Laser PDmeas PDref Reference Interferometer Object Interferometer Target A ISO Target B SC Experimental Setup  sweeping speed

5. 5 Tunable wavelength laser  External Cavity Laser Diode Coherence length >> 1km Central wavelength ~ 1.5µm Continuous tuning range up to ~ 5nm Sweeping speed up to 40nm/s  Large ranges and high sweeping speeds without mode hopping to reduce error magnifications. N. Pfeiffer L. Perret UdS

6. 6 Tunable laser source  External cavity laser diode: –Littman Metcalf configuration –Littman Shoshan configuration N. Pfeiffer L. Perret UdS Lentille Réseau  Miroir M'   nana  xtxt xlxl Diode Laser

7. 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

8. 8 Fringe processing Spectral filtering Gaussian filter Blackman window Fast Fourier Transform I(t) = a(t)+b(t) cos(  (t)) I(t) = a(t)+1/2[b(t) e i  (t) + b * (t) e -i  (t) ] A(f) B * (-(f+f s )) B(f-f s ) Inverse Fourier Transform 1/2[b(t) e i  (t) ] Extraction of the instantaneous frequency 1 N. Pfeiffer L. Perret UdS 2 34 5

9. 9 9 Target A at 2.2m Target B at 8m 6 records/pos. sweeping speed 20nm/s. FTT results for 10 17 samples

10. 10 Non-linearities in wavelength sweeping Results in an overlap of spectral peaks in the multi-target configuration. Variations in fringes size Spectral modulation

11. 11 Extracted instantaneous beat frequency Sweeping speed

12. 12 Quasi-periodical variation of the beat frequency. FFT analysis and reconstruction through sinusoidal signals. Modeling parameters:  m f : modulation rate  A i : component’s weight (normalized)  f mi : component’s frequency  φ i : component’s dephasage

13. 13 Periodical non-linear influence Simulation of different wavelength sweeps Linear sweep 10nm/s model (5 components) + Single sinusoid : m f =2.2e-4 fm=94.5Hz Single sinusoid : m f /2 fm /2 Single sinusoid : m f x2 fm x2 Optimal sinusoidal modulation

14. 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

15. 15 Frequency comb referenced two wavelength interferometry N. Schuhler ADM Laser system form the VLT at Paranal European Southern Observatory

16. 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

17. 17 Phased Reference Imaging and Micro-arcsecond Astrometry facility 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  N. Schuhler ESO

18. 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

19. Proposed solution  Incremental interferometry for the ultimate resolution  2 wavelength interferometry for increasing the NAR 19

20. 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)

21. 21 Error and Non Ambiguity Range m: fringe order M: fringe number f(m): fractional part  : phase (-  <  <  ) N. Schuhler ESO Error on  OPD due to the wavelength uncertainty: Differential OPD measured: Non Ambiguity Range:

22. 22 Stabilization of the Nd:YAG P(49)6-6 Nd:YAG I2I2 EOM PPLN Lock-in Amplifier CAN PI CNA T Pz 25% 75% To the interferometers Pound-Drever-Hall method applied to a frequency doubled Nd:YAG, the frequency reference is an I 2 transition at 659.5nm + PI CNA N. Schuhler ESO

23. 23 Residual error in closed loop N. Schuhler ESO

24. 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 (1  m -2  m) 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 n r   0  n r + 0 I( ) 0 Nd:YAG N. Schuhler ESO rep 2(n r   

25. 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

26. 26 Absolute frequency stabilization of PRIMET Nd:YAG laser Conclusion Use 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

27. 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:  is the synthetic wavelength The NAR of the system is  /2  ≈ 90 µm ↔  ≈ 20 nm N. Schuhler ESO

28. 28 Architecture of the source Comb modes 1 =c/ 1 2 =c/ 2 rep  =c/ = 2 - 1 =N rep to the interferometer Absolute frequency stabilization System 1 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 < m d / < reference radio signal (10 -12 GPS based clock) N. Schuhler ESO

29. 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 kHz 1 + 450 kHz Nd:YAG Lightwave 125 1.319  m ECLD Thorlabs Intun 1300 1.300  m 1319 ± 2.5 nm BD PLL 1 2 BD PLL 1300 ± 2.5 nm gratings N. Schuhler ESO

30. 30 Performances of the prototype 10 -11 35 Hz~3.3 THz ECLD - Nd:YAG 0.5×10 -7 1 Hz20 MHzBeat signal ECLD/Comb 0.5×10 -10 10 mHz20 MHzBeat signal Nd:YAG/comb 10 -11 1 mHz100 MHzRepetition rate Relative instability Instability (peak-to-valley) Mean frequencySignal Nd:YAG ECLD rep =100MHz  =N× rep ~3.3THz f b =20MHz f b =20MHz The relative stability of the synthetic wavelength in vacuum is 10 -11. N. Schuhler ESO

31. 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

32. 32 Result of the calibration of  Slope=139.541582 rad/mm  =90.054666  m Taking 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

33. Merci de votre attention 33