Fringe Tracking with FINITO

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Fringe Tracking withFINITO PRIMA

• Gerard van Belle
• PRIMA Instrument Scientist
• 5 Nov 2008

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Food for Thought

• There aint no such thing as a free lunch1 R.
  A. Heinlein
• 1Often abbreviated as TANSTAAFL, from The Moon is
  a Harsh Mistress, 1966

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Food for Thought

• Whats for lunch?
• ? ultra-high-resolution astronomy easily 2
  orders of magnitude beyond conventional
  techniques
• The price?
• ? sensitivity
• ? TANSTAAFL turns up pretty much everywhere else
  in interferometry, too

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The Perfect Fringe Tracker(from the observers
point of view)

• Looks remarkably similar to the perfect AO system
• This is not the case (as is true with AO)
• As always, understanding your instrument is
  important to understanding your data
• Hence, this talk

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Michelson Interferometer
Star is at infinity
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Fringe Visibility

• Constructive destructive interference of light
• Fringe contrast or visibility
• Calibration issues
• Detector linearity
• Zero point measurement
• Noise characterization

Actual starlight fringes from IOTA - ? And Photo
credit R.R. Thompson
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Interferometer responseversus delay

• Bandwidth averaged point-source response
• bandpass of wavenumber center s0, width d0, delay
  ?

White light fringes for broadband K-band flux
versus delay line position
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Fringe Quadratures

• Can zoom into central fringe and take 4
  consecutive samples
• Quadratures
• Converts easily to fringe phase, amplitude
• Note assumes flux steady, 90 ABCD separation

A
B
C
D
Flux versus OPD Zoom into central part of fringe
for ABCDs (Shao et al 1988), Wyant 1975)
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Temporally Modulated Fringes

• Delay line driven back forth over zero OPD
• ABCD samples taken during scan
• Non-zero f indicates drift from zero OPD
• FINITO approach (also PTI, MkIII interferometers)

OPD versus Time
Flux versus Time
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Temporal Fringes in Practice

• Fringe-scanning modulation, implemented
  temporally on delay line
• Sawtooth waveform to minimize number of reads per
  frame
• Retrace occurs during array settling time
• Single-pixel reads A, B, C, D ¼-wave intensity
  bins computed as
• A a - z, B b a, etc.
• Let X A - C, Y B - D,
• N ABCD

Colavita 1999
A
B
C
D
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Optical Modulation of Fringes

• Two outputs from beam combiner split in two
• Makes use of fact that beam combiner has two
  outputs
• Four matched phase retarders ? ABCD
• PRIMA approach

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Relative merits of modulation approaches

• Temporal modulation
• ABCD samples get ¼ of coherence time
• 100 of flux for each sample
• SNR lower because
• Tip-tilt errors are non-common-mode
• Stroke of OPD must be linear / non-wandering
• Hard to generate perfect sawtooth

• Optical modulation
• Each ABCD sample integrated for a full coherence
  time
• Flux split 4 ways
• SNR lower because
• Alignment difficult
• Susceptible to imperfections in optics such that
  ?f?90

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Effects of FT Errors on V2

• Comparison of V2 measures for two stars
• 51 Peg
• HD215510
• Four separate nights
• Objects close in time, on sky
• Raw V2 shows lots of scatter
• Yet data move synchronously
• Excursions due to instrumental, environmental
  factors

Boden et al (1988)
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Typical Observing Program

• Calibration star (calibrator) - target -
  calibrator
• Bracket the target with unresolved sources on
  both sides
• Not required but strongly recommended
• Time dependence of atmosphere, instrument
• Evolving targets
• Can appear change with baseline projection, time,
  wavelength
• Calibrator - target - calibrator - resolved
  calibrator
• Choose a secondary resolved object (check star)
  not expected to evolve

7 Apr 2008
G van Belle - Supergiant Diameters
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Visibility Function

• For a uniform disk, visibility matches
• B is the projected baseline
• q is the stellar disk size
• l is the instrumental wavelength
• Baseline, wavelength known
• Can solve for q
• Use V2 instead of V
• Unbiased estimator of visibility
• See Colavita (1999)
• Important consideration fringe trackers have a
  hard time operating past 1st zero

where
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An Aside True Resolution of Optical
Interferometry

• Single aperture resolution limit usually quoted
  as 1.22 x ?/D
• This is the somewhat arbitrary Airy limit
• Others, such as Sparrow, Dawes, etc. exist
• Optical interferometry resolution limit often
  quoted as the corresponding ?/B
• But, for optical interferometer, we can work much
  higher up on visibility curve
• If sufficient measurement precision is provided
• Example for a 110m baseline at K-band
• Can get down to 0.70mas size measurements with
  sV20.015
• NB. This is hard to do
• Corresponds to 0.17 x ?/B

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Visibility Function Calibrators

• Atmospheric and instrumental effects reduce
  system V2
• Observe unresolved sources to establish system
  response
• Use an estimate of size
• Assume V2 gains are equal
• Gain factor is analogous to Strehl ratio
• Flattening portion of visibility function ?
  errors in calibrator size do not translate into
  errors in system V2
• Need to account for partial resolution of
  calibrators
• Predicted size bias can bias the normalization
• See van Belle van Belle (2005)

7 Apr 2008
G van Belle - Supergiant Diameters
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Practical Considerations

• Many operational considerations to think about
  when actually using fringe trackers
• Generally where reality intrudes upon theory
• Atmosphere, astrophysics, quirks of
  instrumentation, etc.
• Already seen with typical observing program of
  cal-trg-cal
• Shall be abbreviated PC henceforth

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PC (Unknown) Binary Stars

• Binaries are interesting targets for
  interferometry
• Can be problematic for
• Fringe tracking
• Use as calibrators
• Two regimes
• Separated fringe packet (illustrated)
• Overlapping FP
• Need to be very careful with calibrator selection
• Interferometers are great a discovering
  heretofore unknown binaries
• Remember, 3 out of every 2 stars is a binary

Dyck Benson Schloerb 1995
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PC Resolved Targets Impact FT Sensitivity

• True for stars of large angular size, binary
  stars
• As interferometer separates light from either
  side of scene, fringes smear
• Reduction of contrast ? reduction of FT
  sensitivity
• SNR of FT goes as NV or NV2 depending on regime
• Fortunately, for most resolved stars, as V2
  drops, N goes up

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Correlated Flux Magnitude

• Defined as
• where V is the (expected) object visibility
• Example K2 giant with V6, K4 on B100m
  baseline
• Rough angular diameter prediction from V-K
  (van Belle 1999) ? 2.1 mas
• Visibility prediction for 2.1 mas object on a
  100m baseline V0.76
• Thus, Kcorr4.3

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PC a priori Angular Size Knowledge

• Useful to know estimate of angular size of target
  prior to observing
• For observation planning
• Necessary information for proper use of
  calibrators
• Simple V-K or other surface brightness proxy
  (eg. van Belle 1999)
• Better SED fitting
• Best make the actual measurement

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PC Multiple Baselines with FINITO/AMBER

• AMBER can see 3 baselines at once
• Can leverage this to get high-resolution
  information (past 1st zero) on target
• Example B0-E0-H0
• B40,48,88m
• Fringe track on 2 short baselines, get data on
  3rd long one
• Baseline bootstrapping
• Not an offered triple

Dotted lines bracket 7.0, 8.2 mas
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PC Group Delay Tracking
Sirius

• Group delay tracks envelope of fringe pattern
• Does not suffer from fringe hopping (wrapping
  errors)
• Instrumental effects can introduce dispersion
  that shift the GD peak from the PD peaks
• GD tracking allows for incoherent addition of
  frames ? greater sensitivity
• Poorer data quality

Delay ?
V806 Cen
Delay ?
Fig. 3 from Meisner 2001 VINCI-VLTI observations
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Capabilities Now

• AMBER / MIDI
• Two main current workhorse instruments of VLTI
• FINITO feed of AMBER / MIDI (as advertised in the
  P83 call)
• UTs
• ATs
• PRIMA
• First fringes in Sept 2008!
• Capabilities unproven (at present)
• Still undergoing commissioning

STS1 Install on AT4
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AMBER Limiting Magnitudes and Performances

• Concerning the limits in sensitivity, these
  depend on a large number of factors
• The type of telescopes, can be either UTs or ATs
• vibration environment of each
• The chosen spectral resolution
• low (LR), medium (MR) and high (HR) resolution
• Environmental constraints such as seeing, and
  atmospheric transparency
• The use of the active fringe tracking (using
  FINITO)
• Why fringe track? ? Significant improvement in
  data quality

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AMBER Sensitivity

• FINITO improves AMBER performance when conditions
  permit
• Low airmass, nearby (or self-)phase reference
• Computed for DIT25ms. Visibility calibration
  of longer DIT is not guaranteed.
• Computed for DIT100ms. Reduced by 0.7mag and
  1.5mag for DIT of 50ms and 25ms respectively.

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Wait a second

• Hey, those UT numbers dont look much better than
  AT numbers!

• 8.2-m versus 1.8-m telescope
• Factor of 20.7 in flux(!) 3.3 magnitudes
• Remember TANSTAAFL?
• Atmosphere restricts improvement in flux to less
  than D2
• Vibrations of UT are pretty unforgiving

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Future Capabilities

• Dual-Object Interferometry with PRIMA
• Astrometry
• Phase referencing
• Faint object science
• Future real soon now
• PRIMA currently undergoing commissioning

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Dual Star Astrometry
Primary Star
Secondary Star
Objective ground-based astrometric detection of
exo-planets 10 - 50 mas _at_ VLTI

• Primary star
• Used to phase individual apertures
• Used to co-phase the interferometer
• Secondary star
• Used as positional reference for primary star
• Delay line difference
• Observable proxy for angular separation between
  stars
• Angular separation reflects periodic reflex
  motion of stars due to planetary companions
• For exo-planet reflex detection
• 10s of mas (O(10-11 rad))

Delay Lines
Delay Lines
Beam Combiners
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Dual-Object Phase Referencing

• Objective long synthetic coherence time for
  faint-object detection
• Fundamentally enabled by dual-beam optical design
  of PRIMA
• Phase referenced interferometry the analog of
  single-aperture AO
• Fringe tracking piston correction signal on one
  object is used to correct the piston on a second,
  nearby (isoplanatic separation) object
• Required for VLTI and KI faint-object
  interferometry
• Demonstrated at PTI
• Phase error with and without loop closed between
  the two fringe trackers
• Two data segments taken within 200 s of each other

Lane Colavita 2003
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Bibliography

• Boden, A.F., et al., 1998, Visibility
  calibrations with PTI, Proc. SPIE, 3350, 872
• Colavita, M.M., 1999, Fringe visibility
  estimators for the PTI, PASP, 111, 111
• Meisner, J., 2001, Fringe tracking and group
  delay tracking methods for MIDI, Proc. 36th
  Liege International Astrophysical Colloquium
• Shao, M., et al., 1988, The Mark III Stellar
  Interferometer, AA, 193, 357
• Van Belle, G.T., 1999, Predicting Stellar
  Angular Sizes, PASP, 111, 1515
• van Belle, G.T. van Belle, G., 2005,
  Establishing Visible Interferometer System
  Responses Resolved and Unresolved Calibrators,
  PASP, 117, 1263
• Wyant, 1975, J.C., Use of an AC heterodyne
  lateral shear interferometer with real-time
  wavefront correction systems, App. Opt., 14, 2622