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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
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
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)
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.
Contents
•Interferometry introduction
•The need for an error budget
•Summary of principle contributions
•Error terms which must be reduced
•Potential problems
•Conclusions
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
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
Narrow angle interferometry
Primary star
UT1 PS
UT2 PS
Secondary star
UT1 SeS
UT2 SeS
Optical correlation
at VLTI (but
numerical at
radio
interferometers)
Numerical correlation
Output with phase which is stable to within
one radian rms (phase of the output is the
astrometric phase)
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)
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
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
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)
Zero-mean random terms
•Apart from VLTI internal seeing, the zeromean 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
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 Fouriertransform spectrometers
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
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
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
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)
Beam walk before de-rotator
•This will only be significant on M4, which is
very close to an image plane and before the derotator
•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
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
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
Spectral sensitivity of FSUs
In order to investigate the effect of the StS roof
mirror, a simple simulation was undertaken
Spectral sensitivity of FSUs
Adding atmospheric refraction
Spectral sensitivity of FSUs
Spatial filtering
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)
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
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)
Deformation of MDL tunnel
• The MDL Tunnel is built from 20m sections
Deformation of MDL tunnel
Deformation of MDL tunnel
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
Refractive index fluctuations
Airflow in tunnels will be discussed by Rudolf
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
Phase in the image plane
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
Fringe tracking problems
•The high frequency fringe motion is
dominated by the effects of the image breaking
up into speckles
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
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