1. Fringe tracking principles and difficulties F. Delplancke with help from J-B. le Bouquin, S. Ménardi, J. Sahlmann, N. Di Lieto... and many others

2. Plan Why do we need fringe tracking ? –Atmosphere –Phase and group delay co-phasing versus coherencing Fringe sensing methods –general –examples: FINITO and PRIMA FSU at the VLTI Some control theory: –fringe tracking is much more (difficult) than fringe sensing Problems and difficulties: –injection –vibrations –fringe jumps –longitudinal dispersion and star spectrum Conclusions

3. Atmospheric turbulence and piston issue piston turbulence Atmospheric turbulence cells distort the stellar wavefront Distortion over the pupil size is called turbulence –bad flux injection –tip/tilt or AO mandatory Global shift between the pupils is called piston –real-time fringe motion –small DIT mandatory

4. Fringes and Fringe-packet The fringe size is the wavelength of the light, so few  m in the near-IR –Precise instrumentation –Mechanical vibrations are “killers” When observing with a large spectral bandwidth, the fringe packet is small: –R=500   ~ 0.75mm –R=25   ~ 7.5  m Important to observe close to the zero-opd position sum of monochromatic fringes = real fringe packet opd (m) packet size  = R. fringe size:  m I ~ . cos(2  opd/ +  ) Definition and typical size

5. Effect of the atmosphere on VINCI data photometric channel 1 photometric channel 2 interferometric channel 1 interferometric channel 2 flux corrected fringes ~ Fourier transform of the fringes (linked to their visibility)

6. Effect on AMBER

7. OPD equalization as seen by AMBER and FINITO FINITO (R~5) AMBER (R~40) Opd = 0 fringes (what we want !) Opd = 2 fringes Opd = 5 fringes Opd = 15 fringes Opd = 30 fringes Important to observe close to the zero-opd position:  < 20  m opd opd White fringe

8. Coherencing / Cophasing Without fringe tracking –Good opd-model required –Short exposure required –Strong frame selection With coherencing –Fringe-packet centered –Short exposure required –Much more frames with fringes With cophasing –Fringes locked –Long exposure possible on AMBER opd Time (10s) No FinitoCoherencingCophasing

9. Fringe tracking methods

10. What shall we measure ? Position of the fringes: -local maximum = phase delay -maximum of the envelope = group delay Attention: group delay ≠ phase delay if propagation in air ! visibility amplitude SNR

11. How can we measure it ? Ideally, only 3 parameters: –local fringe position, phase  –envelope position GD –visibility  Period and fringe packet width are known (  source spectrum and transmissivity) So ideally 3 measurement points in OPD should be enough to fit the fringes In practice, one needs more points for robustness Methods to vary the OPD and measure the ABCD points: –mechanical scan of the OPD –multi-axial combination –separation of the beam and application of phase shifts to each beam with polarization effects without polarization effects –spectral dispersion I ~ . cos (2  GD). cos(2  opd/ +  ) A B C D

12. Temporal modulation scan the OPD on a controlled way (with an internal metrology): –in triangle –in sawtooth –... synchronize the detection with the scanning => 4 “bins” ABCD on each interferometric beam while scanning one fringe the phase is given by (if  =constant and in first approximation, w/o envelope effect)  = arctan (I k-1 / I k ) -  k where I k is the intensity in the bin at “moment” k, and  k is linked to the the center point of the modulation scan over several fringes to get the group delay prior normalization of the intensity is necessary

13. Multi-axial combination the 2 beams are combined with a small tilt between them => spatial modulation of the OPD cylindrical (anamorphic) optics to compress the PSF perpendicular to the modulation adaptation of the image scale to the fringe spacing and “binning” of ABCD into 4 different pixels similar formula as before D B -200-100 200 0.2 0.4 0.6 0.8 1 ~/D ~/B wavefront 1 wavefront 2 observation plane OPD

14. Spatial modulation Dividing both beams into 4 beams via –bulk optics –integrated optics Applying phase shifts of 0º, 90º, 180º and 270º to each beam via –polarizing / non-polarizing methods Make the beam combination Send to 4 different detectors Synchronised detection => measurement of the points ABCD, not anymore the bins The phase is given by (if perfect system):  = arctan ( A-C / B-D) Advantage: –synchronous measurement of ABCD –no “cross-talk” between variable OPD and temporal measurement Disadvantage: –variable OPD during exposure => blurs the fringes (reduced visibility) –detection on 4 different pixels => photometric calibration more difficult 0 90 180 270 ABCD Telescope 1Telescope 2

15. Spectral dispersion Can come in addition to the previous methods Used to measure the group delay Each ABCD measurement is dispersed in wavelength Wavelengths are binned into pixels Measurement of one phase per wavelength bin Group delay is a combination of the phases at each wavelength assuming a certain profile of the air refractive index with wavelength Zero group delay = –where all phase delays are equal (no air, no dispersion) –where the phase delay differences are minimised (with dispersion) opd

16. FINITO Fringe sensor for Interferometry NIce - TOrino

17. ACU FINITO principle 1 0 2 0+1 0+2 Only 2 pairs are combined: fringes 1+2 are not measured Use 3 telescopes –Only 2 baselines are measured No real spectral resolution –Complete H band –R ~ 5 Temporal combination (scan) Spatial Filtering Real-Time Photometry FMU: opd IRIS error vectors

18. FINITO principle (2) –Phase Delay = OPD mod Measured on each 1 scan High frequency (up to 2kHz / 500Hz) Low noise Small range ( ) –Group Delay or Coherence = “white” fringe position Measured on the total scan (~5 to 10 ) Low frequency (up to 50Hz) Higher noise Large range (10 ) for fringe jump detection & correction

19. FINITO Metrology 3-way BC H-band 3-way beam-combiner

20. PRIMA FSU Phase-Referenced Imaging and Micro-arcsecond Astrometry Fringe Sensor Unit

21. FSU principle Static phase modulation through polarization => –ABCD algorithm for the Phase Delay –spectral dispersion (5 channels) for the GD K-band (less sensitive to turbulence) Spatial filtering by mono-mode fibers + piezo-controlled tip-tilt mirrors for injection stabilization and optimization (FINITO like) detector 256x256 white 1pix spectrum 5pix

22. Fringe Sensor Units Alcatel-Alenia Space inTurin

23. Fringe tracking test bench Relay optics MARCEL FSUB FSUA Delay line simulators Phase screens

24. FSU cryostat before after

25. Fringes during calibration Additional use of the testbed: –Study of the effect of tip-tilt jitter and of higher-order aberrations. –Test of the long term stability of the FSU. –Implementation of (d)OPD controller with phase and group delay tracking. –Test of VTK (vibration tracking) algorithms before implementation in Paranal. –Test of PRIMA control software, architecture and templates.

26. Closing the loop (indicative numbers: only the ratio is important) frequency [Hz] 10 -1 10 0 10 1 10 2 attenuation magnitude [dB] 0 -10 -20 -30 -40 10

27. Group delay stability specification 1 FSU: bias < +/- 5nm in 30 min specification 2 FSUs: differential bias < +/- 10nm in 30 min dewar refills with liquid nitrogen

28. Some FSU performances FSU intrisic noise = 4 x fundamental limit (perfect FSU) = 0.06nm / √Hz Group delay bias and stability just in specifications - to be improved FSU OPD rejection curve is according to model Sensitivity to tip-tilt: –due to the relative misalignment of the 4 fibers (ABCD) –cross-coupling tip-tilt - piston: for STRAP residuals, no piston, the measured “piston” is 75nm in open loop, 200nm rms in closed loop ! for residuals typical of IRIS Fast Guiding, the measured piston is 50nm rms in OL and 85nm rms in CL corresponding increase of the closed loop residuals with atmospheric piston very important to start with a good initial centering on fibers: an 0.5FWHM starting error mutliplies the residuals by 2 ! Weak impact of high order WFE (MACAO residuals) Atmospheric piston rejection: –for high flux, currently limited by main delay lines pure delay (2ms) Telescope vibrations between 10 and 100Hz are very annoying (amplified)

29. Some control theory or fringe tracking is much more than fringe sensing

30. Fringe tracking control loop real residuals measured residuals frequency OPD PSD Kolmogorov spectrum frequency rejection [dB] transfer function 0 dB frequency OPD PSD white noise frequency OPD PSD residuals = Kolmogorov spectrum * transfer function + noise

31. Fringe tracking on the FSU Fringe tracking a bright object with Auxiliary Telescopes PRIMA FSU running @ 4 kHz Total pure loop delay 3 ms (Delay line + OPDC + FSU) Delay line model from Nov 2004 measurements Disturbance as recorded during AT FINITO fringe tracking run (AT_sky_close_11.dat 2006-03-31T07:47:02) n Approximately 63% of the residual energy is above 20 Hz n Approximately 45% of the residual energy is between 20-100 Hz n Total estimated residuals = 127 nm rms up to 1 kHz.

32. Pure delay in control loops Pure delay digital (discrete) control: –integration time of the detector T int : most of our sensors are based on integrating detectors pure delay of half the integration time integration time is imposed by star magnitude –sampling time of the controller: d igital control systems have at least one sample of pure delay 200 Hz → 5 ms loop delay, just due to sampling… –“propagation” time in the loop: any system that delays the transmission of the signal electronic systems, computation time... Minimum pure delay = 0.5 * integration time of the detector + 1 sampling time Any additional delays stack up and kill performance

33. Effect of a pure delay The phase response (at low frequency) of pure delay e -s Δ T can be approximated by 1/(1+s Δ T), namely a 1 st order low pass filter with cut off frequency 1/(2 πΔ T). For example, the phase response of a 5 ms delay is equivalent to that of a 31.83 Hz low pass filter. –Negligible loop performance improvement by pushing the actuator dynamic beyond 3 times that (~95 Hz) –Negligible loop performance reduction due to delay if the actuator is slower than 3 times that (~10.5 Hz). How to optimize a fringe tracking system ? Rule of thumb: –find the maximum frequency that you want to correct f = 1Hz –you want a bandwidth BW that is at least 10 times higher (indeed a BW of 10 Hz means that 10 Hz is not corrected anymore) = 10 Hz –use actuators faster than 10 * BW = f actuator > 100 Hz –reduce the delay to 1/3 * 1/f actuator = 3 ms –get a sensor measurement frequency that is compatible with this –run the control loop faster that all that > 1 kHz –no need to push too much on one of these if the others are limiting

34. Effect of pure delay

35. Systems with low SNR If W is the measurement noise, A the disturbance, H the closed loop response (or gain) and S=(1-H) the closed loop sensitivity, then Measured OPD = S (A + W) = SA + SW On the other hand, Real OPD = SA – HW Therefore due to the relatively high level of noise (faint object), the difference between the measured and real controller residuals is not negligible: Measured - Real = (S + H) W Recall S is low at low frequency, while H is low at high frequency…. frequency sensitivity [dB] sensitivity S 0 dB frequency attenuation [dB] closed loop gain H 0 dB

36. FINITO mode switching First close the loop in coherencing: –SNR threshold is the same on every target (and is small) –better sensitivity to find and follow the fringes When packet is centered, try to close in co-phasing mode: –always close the co-phasing mode near the packet center When SNR becomes small, switch back to coherencing mode, before looking for the fringes: –very few fringe search –fringes are always present in the scientific camera

37. Problems and difficulties vibrations injection dispersion resolution

38. Telescope vibrations What has been tested: –MACAO fans = critical –NACO rotation angle = small –enclosure tracking far from zenith = nothing –enclosure tracking at zenith = critical –enclosure pumps = nothing –UTs air-exchanger = small –pumps for eletronics cooling = significant –pumps for hydraulic pads = significant –closed-cyclo-coolers of other instruments = MAJOR Still under investigation –other UTs should be investigated (other instruments) –performances not easily repeatable, looks dependent on the environment (wind?) Most vibrations are in the “critical” zone of the control loop: –20-100 Hz => amplification CRIRES ON = 1000nm CRIRES OFF = 320nm

39. Vibration remedies Accelerometers on vibrating mirrors –1 to 3 per mirror –derive piston from measurement –feed it directly to the piezo controlling the OPD without passing by a control loop (no feedback) Vibration tracking algorithm –frequencies of vibrations are almost fixed & known (by experience) –tune “lock-in” filters around these frequencies –measure phase and amplitude of the vibrations in the residual measurements of the fringe sensor –make a slow closed loop to adapt the parameter (frequency) of the lock-in filters if frequency drifts –works for up to ~ 10 different frequencies Active / passive damping of vibrations Laser metrology

40. Vibration tracking (VTK)

41. Injection into fibers Injection stability: –Use of monomode optical fibers as spatial filter => wavefront corrugations and tip-tilt are transformed into photometric fluctuations –Strehl ratio is not stable at 10 ms timescales –To measure fringes with enough accuracy for fringe tracking, one needs ~ 100 photons at any moment

42. Remedies to bad injection Solutions:  optimize adaptive optics for minimum Strehl not for the average one  fast & optimized tip-tilt sensing close to the instrument  optimize injection before starting with beam position modulation  optimize injection during tracking with small beam modulation  laser metrology for tip-tilt  accept a not-perfect fringe lock ? BTK = Beam TracKing

43. Effects of dispersion Transversal & longitudinal dispersion Fringe tracking and observation at different Air index of refraction depends on wavelength => –phase delay ≠ group delay –group delay depends on the observation band –fringe tracking in K does not maintain the fringes stable in J / H / N bands Air index varies as well with air temperature, pressure & humidity –overall air index dominated by dry air –H 2 O density varies somewhat independently –H 2 O effect is very dispersive in IR (between K and N) Remedy: spectral resolution & good modeling

44. Refractive index of water vapor (©R. Mathar) [THz] [µm] 631.5215 K-band N-band H-band L-band

45. Dispersive effect between (and within) bands due to 0 – 600 mole/m^2 of additional dry air. (= 20 meter delay-line offset) (©J. Meisner) Note that dispersion from dry air increases rapidly at short wavelengths (Tracking at the group-delay in K band)

46. Water Vapor dispersion, with phase-tracking at K band 0 – 5 moles/m 2 (typical p-p value due to atmosphere) ( ©J. Meisner)

47. Water Vapor dispersion, with phase-tracking at K band 0 – 5 moles/m^2 (typical p-p value due to atmosphere) ( ©J. Meisner)

48. MIDI observation: OPD and water vapor (©J. Meisner)

49. Keck’s results of dispersion extrapolation ( ©C. Koresko): estimated phase delay at 10µm vs. measured phase delay

50. Resolution All previous considerations / simulations are assuming that the star is not resolved => visibility = 1 In practice, V can be lower than 1 Effects: –reduces the signal to noise ratio –introduces a phase bias if the object is not centro-symmetric It can be a problem e.g. for an-axis fringe tracking of objects to be observed at 10µm

51. Current fringe tracking concept at the VLTI

52. FINITO concept on the ATs IRIS = Infra-Red Image Sensor = tip-tilt sensor Sends tip-tilt corrections to fast piezo-driven tip-tilt mirrors in front of FINITO fiber injection = IFG = IRIS Fast Guiding Finito piezo IRIS IFG + OPDC + BTK Modulation of the beam pointing on the fiber, for better centering = BTK = Beam TracKing

53. FINITO on the UTs : the control version 2.0 ! Needs the “dream team”: P. Haguenauer, Ph. Gitton, N. di Lieto, J-B. le Bouquin, S. Morel (B. Bauvir, H. Bonnet) Finito Vib.Tracking algorithm piezo accelerometers (manhattan) IRIS IFG + BTK + OPDC + Manhattan 2 + VTK

54. FINITO performance

56. Summary: what is important? Good injection (stabilisation) into the fibers is essential Photometric channels are an asset Spectral dispersion is a compromise: –better reliability (sturdiness) –lower sensitivity to star spectral type –lower sensitivity (limiting magnitude) Better stability is obtained if injection into the fibers happens before the beam combination (not possible on FSU due to metrology) Thermal & vibration stability of the system has to be carefully studied Motorised alignment is an asset Accurate knowledge / measurement of the atmospheric dispersion is needed to stabilise fringes at another wavelength Test, test, test and test in the laboratory before going on sky Fringe tracking is much more than fringe sensing: –proper management if fringe / flux losses –top performance to be balanced by reliability, sturdiness, operability –highly dependent on atmosphere quality => many parameters influence the performance, difficulty to give “one “ number