Error budget for the PRIMA conceptual design review

1
Error budget for the PRIMA conceptual design
review

• Bob Tubbs, Richard Mathar, Murakawa Koji, Rudolf
  Le Poole, Jeff Meisner and Eric Bakker
• Leiden University and ASTRON

2
Executive summary

• Analysis work undertaken indicates that the
  design and operation of VLTI/PRIMA will have to
  be modified/improved in order to reach the goal
  of 10 µas accuracy. Key areas are
• Main delay line and VCM performance
• Fringe tracking with wavefront corrugations
• Dependence of spectral response on wavefront
  corrugations across AT apertures
• Systematic gradients above Paranal

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Executive summary

• Turbulence in the ducts and tunnels
• Accurate model for the refractive index of air
• Measurements of the difference in the colour of
  the correlated flux from each star
• Solutions to each of these problems must be found
  and tested to ensure that the 10 µas astrometric
  performance can be reached (in some cases
  solutions have already been suggested)

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Executive summary
The astrometric accuracy will be determined by
the accuracy with which errors can be compensated
it will thus depend on how well the VLTI can be
modelled, how accurately the refractive index of
air can be calculated, how accurately the
centroid wavelength of the observing band can be
measured, etc.
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Contents

• Interferometry introduction
• The need for an error budget
• Summary of principle contributions
• Error terms which must be reduced
• Potential problems
• Conclusions

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Interferometry

• Interferometers measure the correlated flux (a
  complex number) from one or more sources on one
  or more baselines
• The phase of the measured correlated fluxes is
  corrupted by atmospheric fluctuations
• These correlated fluxes are usually normalised
  according to the source brightness, giving
  visibilities

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Narrow angle interferometry

• If two stars lie within the isoplanatic
  separation angle then the correlated fluxes for
  the two stars are correlated with each other (the
  phases vary in harmony with each other)
• The phase of the cross-correlation is called the
  astrometric phase, and provides a measure of the
  separation between the stars
• Atmospheric errors can be eliminated by averaging
  this cross-correlation with time, if the stars
  are within one isoplanatic angle

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Narrow angle interferometry
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Coherent integration

• An additional benefit of narrow angle
  interferometry is that the phase of the
  correlated flux from a bright star can be tracked
  and used to correct fluctuations in the phase of
  a nearby fainter star
• This can allow long coherent integrations on the
  faint star, although it requires a bright primary
  star
• At K-band the improvement in limiting magnitude
  for the faint star is moderate (thermal
  background limitations)

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Need for error budget

• The target of 10 µas accuracy is very challenging
  (requiring a total differential OPD accuracy of
  10 nm, with individual contributions much smaller
  than this)
• For most of the path through the VLTI, the beams
  from the different stars are separated, passing
  through different air and reflecting off
  different mirrors

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Principle contributions

• The principle contributions can be separated into
  random, zero-mean effects and systematic effects
• The zero-mean random terms produce requirements
  on the integration times and stability of the
  instrument between repeated measurements
• The systematic effects can only be eliminated
  with a good understanding of the instrument and
  again through good instrument stability

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Zero-mean random terms

• 1st order atmospheric, dome and tunnel seeing
• Photon shot noise, thermal background and readout
  noise
• Signal loss due to phase and group delay tracking
  errors
• Vibrations (zero mean to 1st order)
• Polarisation effects (to 1st order)

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Zero-mean random terms

• Apart from VLTI internal seeing, the zero-mean
  random components of the OPD error will average
  out to the 10 nm level in 30-120 mins of
  observation, depending on the seeing and angular
  separation
• VLTI internal seeing is more problematic as it is
  applied separately to the two beams from each AT
• Measurements indicate that drifts of 1000s of nm
  occur on the timescales of beam switching

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Eliminating systematic terms

• Many of the systematic terms will be reduced
  using careful calibration procedures such as
• Regularly swapping the stellar beams using the AT
  derotator to eliminate systematic differences
  between the two beam paths after the derotator
• Monitoring the spectrum of the correlated flux
  from each star by using the FSUs as
  Fourier-transform spectrometers

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Eliminating systematic terms

• Additional checks on residual systematic terms
  can be performed such as
• Splitting the light from a single star in the
  image plane so that half of the light passes down
  the PS beam and half passes down the SeS beam
  (StS calibration mode)
• Repeated measurements of well known binary
  systems to check the system performance

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Remaining systematic terms

• The remaining systematic terms generally come
  from 2nd order effects or from combinations of
  multiple error terms, e.g.
• The combined effects of stellar colour and
  differential dispersion in the main delay line
• The combined effects of the differential offset
  of the beam footprints on the mirrors before the
  derotator and figuring errors in these mirrors

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Systematic terms

• The dependence of the spectral sensitivity of the
  FSUs on the seeing and STRAP performance (due to
  spatial filtering effects)
• The difference in the atmospheric refraction
  along the paths to the two different stars
• 2nd order effects on the phase measured at the
  FSU from seeing, photon shot noise and
  polarisation effects

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Stellar colour and dispersion

• If the correlated fluxes from the stars have
  different colours, then the differential OPD
  depends on the position of the main delay line
  (MDL) (Richard Mathar will discuss this)
• The colour of the correlated flux must be well
  known (the centroid wavelength for the
  observations must be known to 0.2nm either
  using the FSUs as Fourier transform
  spectrometers, or by measuring the stellar SEDs
  accurately and knowing the PRIMA instrument
  response very well)

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Beam walk before de-rotator

• This will only be significant on M4, which is
  very close to an image plane and before the
  de-rotator
• The beams from the two stars will reflect off
  different parts of this mirror, so that figuring
  errors at the 5 nm level will cause significant
  errors in the astrometry
• It may be necessary to map the figuring errors in
  the AT M4 mirrors at the nm level

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Spectral sensitivity of FSUs

• Image plane obstructions in the VLTI light beams
  make spectral throughput of the VLTI depend on
  the seeing, the atmospheric refraction and the
  STRAP performance
• Image plane obstructions include the FSU spatial
  filters and the star separator roof mirror when
  operating in StS calibration mode
• The spectral throughput must be accurately known
  for atmospheric dispersion corrections

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Spectral sensitivity of FSUs

• The StS roof mirror is the easiest component to
  describe here
• It acts as a Schlieren detector (knife edge)
  (Schlieren is a trick used by optics
  manufacturers to convert wavefront phase
  perturbations across the aperture into wavefront
  amplitude perturbations across the aperture,
  making them visible to the eye)
• The effect on the astrometric phase is also quite
  complicated and needs modelling

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Spectral sensitivity of FSUs
In order to investigate the effect of the StS
roof mirror, a simple simulation was undertaken
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Spectral sensitivity of FSUs
Adding atmospheric refraction
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Spectral sensitivity of FSUs
Spatial filtering
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Spectral sensitivity of FSUs

• The FSU spatial filter causes the spectral
  sensitivity to vary with the seeing and STRAP
  performance, and causing the centroid wavelength
  to fluctuate by 5nm RMS on short timescales
• The roof mirror causes the difference in spectral
  sensitivity to vary with the amount of
  atmospheric refraction when in StS calibration
  mode, producing a shift of up to 10 nm in the
  centroid wavelength of the observations (strongly
  dependent on the seeing)

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Other terms

• The difference in atmospheric refraction along
  the different beams will be discussed by Richard
  Mathar
• 2nd order effects on the phases measured will
  require further information about the FSU
  performance
• Additional terms are discussed in the error
  budget document

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Potential problems for PRIMA

• Potential problems which may prevent PRIMA from
  operating have been attached to the error budget
  workpackage. These include
• Difficulty in operating the VCMs due to problems
  with the delay line supports (also discussed by
  Rudolf Le Poole)
• Refractive index fluctuations in the delay line
  tunnel due to airflow (discussed by Rudolf Le
  Poole)

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Deformation of MDL tunnel

• The MDL Tunnel is built from 20m sections

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Deformation of MDL tunnel
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Deformation of MDL tunnel
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Deformation of MDL tunnel

• Currently this deformation prevents use of the
  VCMs
• The VCMs are essential to PRIMA astrometry
  (otherwise the beam walk on mirrors becomes
  large, leading to large OPD variations, and the
  pupil is not re-imaged in front of the DDL)
• This will be discussed in detail by Rudolf

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Refractive index fluctuations
Airflow in tunnels will be discussed by Rudolf
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Fringe tracking problems

• Numerical simulations indicate that fringe
  tracking may be unreliable with large apertures
  using the FSU design envisaged
• The principle problem relates to the break-up of
  the stellar images into speckles
• Each speckle has a different optical phase, and
  the speckle patterns are different in the
  different group delay tracking spectral channels

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Phase in the image plane
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Fringe tracking problems

• Even for an AT-size aperture, it may be necessary
  to average the group delay over many atmospheric
  coherence times in order to get a sensible
  number

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Fringe tracking problems

• The high frequency fringe motion is dominated by
  the effects of the image breaking up into speckles

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Fringe tracking

• The fringe tracking performance will be dominated
  by effects which can only be studied using
  numerical simulations
• It will be essential to incorporate the wavefront
  corrugations across the AT apertures in any
  modelling of PRIMA performance

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Conclusions

• A summary of some of the key terms in the error
  budget has been presented
• There are several potential problems which could
  halt the PRIMA astrometry project
• A number of areas require more detailed analysis,
  to determine whether error terms can be
  adequately compensated or not
• Numerical simulations will be required in order
  to estimate the fringe-tracking performance of
  PRIMA