Interferometric Images in Astronomy

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Interferometric Images in Astronomy
M. Busso

Introduction Historical and cultural
relevance of interferometry Motivations
Why interferometry supported also by
incompetents (like me) Technical issues Ho
w do we achieve interferometry and analyse its
data (a few examples for LBTI and VLTI)
Scientific rationale What can we do
reasonably and first with LBTI-VLTI?
Scuola Nazionale Tecnologie Astronomiche Napoli
Settembre 2000 M. Busso et al.
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Interferometry has been 200 years old in 2001!
In 1801 Thomas Young (1773 1829), English
physician and physicist (and many other things,
poet and archeologist among the others, he
translated the Rosetta stone!), made his famous
experiment of the double slit, which gave a
tremendous impulse to the ideas of the
oscillatory nature of light, in an epoch still
dominated by a mechanicistic scientific
immagination, based on particles (same years
Dalton and the notion of atom, recovered from
the thought of the Greek philosopher
Democritus). We are therefore in a good moment
to remember and apply through modern technology
Youngs lesson on interferometry!
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Interferometry in the scientific culture XIX
Century - 1

• The Fizeau experiment and later the
  Michelson-Moreley
  
• experiment, whose implications were not
  completely
  
• understood, stated the crisis of all theories
  involving
  
• fluids to explain unknown scientific
  propagations of
  
• waves and interactions (in this case they
  proved the non-
  
• existence of a luminifer aether).
• The theory on waves was proved through
  interferometry
  
• beyond any doubt.
• First astronomical applications were
  presented.
  

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Interferometry in the scientific culture XIX
Century - 2

• H. Fizeau (1819- 1896)
• E. Stephan (1837- 1923)
• 1868 Fizeau suggests the possibility of
  stellar
  
• interferometry.
• 1874 E. Stephan uses the Foucault telescope at
  the
  
• Marseilles Observatory to observe most stars
  down
  
• to 4th magnitude.
• 65 cm aperture separation.
• All stars produce distinct fringes.
• Concludes stars must have diameters much
  smaller
  
• than 0. 158 arcseconds.
• 1896 M. Hamy performs similar measurements at
  the
  
• Observatoire de Paris.

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Interferometry in the scientific culture XIX
Century - 3
Albert A. Michelson (1852- 1
931) 1878. Measures speed of light 200 times more
accurately than previous measurements
. 1880. Invents Interferential Refractometer 188
7. Michelson- Morley experiment. Light speed in
vacuum does not combine with Earths ve
locity (no aether). 1890. Describes mathematical
basis of stellar interferometry.
1891. Measures Jupiters moons.
1907. Receives Nobel Prize in physics (after
Einsteins Special Relativity Theory).
1920. Measures diameter of Betelgeuse with the
20 ft Interferometer.
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Interferometry in the scientific culture XIX
Century 4
Fizeau and Michelsons Experiments
(hence the names taken by the setups)
v c/n w(1-1/n2)
Interf. Di Sagnac
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Interferometry in the scientific culture XX
Century - 1

• F. G. Pease (1881- 1938)
• 50 ft Interferometer
• Designed and built by F. G. Pease (1931).
• Stellar diameter estimates by looking for the
  baseline
  
• where fringes disappeared.
• Probably subject to numerous problems
• - 38 cm mirrors produced speckled images.
• - Increased fringe motion at longer
  baselines.
  
• - Excessive vibrations.
• - Polarization mismatch between arms.
• - Results questioned (20 accuracy). Idea too
  good,
  
• time too early
• (Optical interferometry really successful only
  in 1960s)

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Interferometry in the scientific culture XX
Century - 2
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Motivations for interferometry in the XXI
Century - 1
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Problems with the atmosphere....

Wavefront deformations of size comparable with
the telescope size induce mainly tip-tilt, i.e.
random wandering of the diffraction-limited image
Smaller scale perturbations produce a speckle pa
ttern, which on integration results in the
quasi-Gaussian seeing-limited image
Adaptive optics improves the planarity of the
wavefront and stabilizes its propagation
direction, so that the two telescope beams can be
combined and the interferometric signal
integrated for long exposures
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Diffraction-limited images
The diffraction-limited image of an unresolved
source is
J1 Bessel J function of order 1
? observing wavelength
D telescope diameter
The image is - insensitive to a global phase var
iation of the incoming wavefront (tip)
- translated on focal plane for angular change in
its propagation direction (tilt)
Dominant image motion for small telescopes or
long wavelength
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Resolution and sensitivity

The Airy disk diameter is often used as an
indication of the telescope resolution
q 2.44 l /D (alternatively the Rayleigh
criterion is based on separation by ½ q
But actual achievement of diffraction-limited
performance depends critically on the performance
of advanced Adaptive Optics systems!
Normal telescopes are dominated by atmospheric
turbulence, degrading the wavefront quality and
therefore the image quality to order of 1
The Airy disk diameter of an 8 m telescope in K
band (2.2 ?m) is q 0.13. Further improvements
in resolution are possible -by building larger
telescopes (with Adaptive optics)
-by working in interferometry.
In order to retain high sensitivity, i.e. to
measure faint objects, large telescopes must be
used, but in view of the high cost and
technological problems, interferometry must ALSO
be applied (i.e. interferometry from large
mirrors).
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The Rayleigh criterion

Top 3D representation of the image at the bottom
(linear scale)
Left center to center separation corresponding
to a full Airy diameter Right separation corres
ponding to the Rayleigh criterion
Closer separations not appreciated by eye but
estimated by analytical approach in the case of
close binaries, the model can be based on
separation in angle and intensity
The Rayleigh criterion may be extremely critical,
in particular for more complex objects of
astrophysical interest nebulæ, jets, unresolved
structures, ... (right NGC 4438 from HST)
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Active vs Adaptive optics
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Resolving power and telescope size
i
The resolution achievable by an instrument can be
expressed in terms of the spatial frequencies
included in the observed image the telescope
aperture acts as a low-pass filter, with passband
D/l
The Point Spread Function (PSF) is the
diffraction limited image of a point-like object
but also the Fourier transform of the system
response function i.e. the Modulation Transfer
Function (MTF)
Implementation of larger diffraction-limited
telescopes provides smaller PSF, i.e. coverage of
a larger region in the frequency domain
Above MTF of a 8 m telescope (MTF large, PSF
small) Below MTF of a 1 m telescope (MTF small,
PSF large)
...identical except for the scale!
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Motivations for interferometry in the XXI
Century 2
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Motivations for interferometry in the XXI
Century 3

LONG BASELINE STELLAR INTERFEROMETERS - from JPL
Web pages Space Interferometry within NASA's O
rigin Programs The Jet Propulsion Laboratory (J
PL) is planning two space missions in near
future - SIM - Space Interferometry Mission
- 10 m baseline fixed structure. Primarily a
pointed astrometry mission, but also designed
with imaging capability. Scheduled for launch in
2006. - Space Technology 3 - a two element "fr
ee flyer" as a technology demonstration for TPF.
Scheduled for launch in 2005.
- Terrestrial Planet Finder - search for extra-s
olar planets. Currently in the pre-formulation
phase. Previously described at the Exploration of
Neighboring Planetary Systems (ExNPS) Homepage.
Possibly scheduled for launch in 2011.
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Optical interferometers working today.
LONG BASELINE STELLAR INTERFEROMETERS - from JPL
Web pages Operational Ground-Based Interferom
eters CHARA Array - Center for High Angular Res
olution Astronomy Array (Mount Wilson,
California GSU). COAST - Cambridge Optical Ape
rture Synthesis Telescope (MRAO, UK).
FLUOR - Fiber Linked Unit for Optical
Recombination (Obs. de Paris, France).
GI2T/REGAIN - Grand Interféromètre à 2 Télescopes
(Obs. de Calern, France). IOTA - Infrared-Optica
l Telescope Array (Whipple Obs, Arizona). Photo.
ISI - Infrared Spatial Interferometer (Mount Wil
son Obs., California). NPOI - Navy Prototype Opt
ical Interferometer (Lowell Obs., Arizona).
Photos. PTI - Palomar Testbed Interferometer (Mo
unt Palomar, California). SUSI - Sydney Universi
ty Stellar Interferometer (Narrabri, Australia).
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The Optical IR Interferometric System IOTA
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Interferometry Projects involving Italian
Institutes
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A few (very simple) technical issues
(VLTI has an analogous in Youngs two slit
experiment, made in 1801. Also to
The Michelson experiment Michelson
interferometer).
(This is similar to VLTI, NOT to LBTI
LBTI has fixed mirrors that act as masks
of a SINGLE telescope -- sB 0)
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LBTI A Large Masked Telescope (Fizeau
interferometer)
Pupil
PSF
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Implementation of VLTI delay line
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A few definitions

• The Frieds parameter r0 is the equivalent
  diameter of a telescope that would see
  diffraction limited images in the conditions
  assigned. It is 10-20 cm in normal seeing. The
  target of high resolution techniques is to make
  it as similar as possible to the outer scale of
  atmospheric convective eddies, L0, e.g. up to a
  few meters.
• The isoplanatic patch is the field over which the
  response of an optical system (or even of the
  atmosphere) is invariant.
  
• (Modulus of complex) Visibility of the fringes
  from an extended source is the
  
• ratio (Imax-Imin)/(ImaxImin), which for
  perfectly constructive interference (Imin 0)
  equals unity (and is otherwise between 0 and 1).
  
• The coherence (spatial or temporal) between two
  signals can be seen as the level at which fixed
  phase relations, e.g. overlapping of maxima and
  minima, is mantained (it is between 0 and 1).
• The Youngs period is the ratio Tl l /B (B
  baseline, i.e. 14.42m for LBTI)
  
• The max. number of fringes is DA/Tl (4.18 for
  LBTI, 3 are visible) DA is the Airy diameter,
  i.e. 2.44 l/D
  
• DA for a 8.4 dish at 2 mm is 131.55 mas Tl is
  31.48 mas. A minimum of 4 pixels
  
• for fringe requires pixels of 7.87mas. With
  pixels of 40 mm one needs an effective focal
  length of 1048m!!! A lot of relay optics may be
  required.

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Again some (boring) technical issues.
(it is complex)
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Types of interferometric combinations
Fizeau - homothetic combination
The beams from two telescopes are propagated
through the system as if a single telescope
observes the two wavefront sections - a full
image of the interferogram is produced on the
focal plane
LBT, low dilution interferometer - 3 fringes per
Airy disk
Michelson - non-homothetic combination
The compressed, afocal beams from two telescopes
are combined, e.g. by means of a semi-reflective
beam splitter, producing two intensity outputs
corresponding to current OPD the whole
interferogram is observed by progressive OPD scan
VLTI, high dilution interferometer - Fizeau
combination is impossible due to the very large
focal plane required
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What can be obtained in the two cases
Homothetic combination is practical only for
lower resolution interferometers, but it has the
multiplex advantage of simultaneous imaging of
all targets within its field of view - sampled
with the same baseline, set in hardware
An high resolution interferometers must observe
subsequently each point of the field, which is
easily done only in case of a reduced number of
objects, with not exceeding internal complexity
(multiple stellar systems, resolved stars, ...)
In any case, when observing an object with
complex morphology, it is necessary to
disentangle the target structure from the
observed data, modulated by the instrument
response function
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Fringe Tracking
ci
Even if the wavefront is corrected to an high
degree for the individual telescopes, the optical
path difference (OPD) is affected by
perturbations associated to atmospheric
turbulence - same source as seeing
The interferogram stabilization requires
detection of the perturbation and actuation of a
suitable correcting device (e.g. the delay line)
fringe tracking
As for adaptive optics, a sufficiently bright
reference source must be located close to the
scientific target, but this leads to limitations
- All artificial stars are resolved at interfero
meter scale natural sources required
- Few natural stars have sufficient brightness
poor sky coverage - Limiting magnitude is still
fairly high extra-galactic science not yet
accessible!
Improvements on sensitivity are expected from the
Keck and VLT interferometers, but a significant
advance is expected from LBT
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Observing reference and scientific targets
The VLTI and other high resolution
interferometers use two distinct instruments
- the Fringe Tracker detects OPD perturbations
and corrects the delay line - the science instru
ment integrates on the stabilized fringes of the
desired target
The differential delay line compensates for the
angular separation between science and reference
targets, resulting in a different external delay
The conditions for common perturbation and
correction are similar to the adaptive optics
requirements isoplanatic patch l-6/5
In particular, natural target density limits the
sky coverage (e.g. to 1-2)
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VLTI Setup
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The case of LBTI
The two telescopes are on the same alt-azimuthal
mount - no external delay is generated - no d
elay line required - always maximum baseline use
d - minimal internal optics - simultaneous lar
ge field observation
The resolution is quite appealing
fringe period in K band l / B 30 mas
The high degree of adaptive correction allows
combination of high quality wavefronts down
to the near-IR and possibly visible range
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A possible scheme for beam combination (MPIA)
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Tests on extended images
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LBT Point Source Sensitivity
What can we see ? 30 nJy, 2µm 10 s 1 Hour
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LBTI Expected resolution 1.
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LBTI Expected resolution 2.
37
LBTI Expected resolution 3.
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Scientific Targets LBTI VLTI 1.
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Scientific Targets LBTI VLTI 2.
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Scientific Targets LBTI VLTI 3.
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LBTI scientific key projects of easy execution
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References general - 2
References - from COAST Web pages 2
12. A. E. E. Rogers, H. F. Hinteregger, A. R. Wh
itney, C. C. Counselman, I. I. Shapiro, J. J.
Wittels, W. K. Klemperer, W. W. Warnock, T. A.
Clark, L. K. Hutton, G. E. Marandino, B. O.
Ronnang, O. E. H. Rydbeck, A. E. Niell, The
structure of radio sources 3C 273B and 3C 84
deduced from the "closure" phases and visibility
amplitudes observed with three-element
interferometers, Astrophysical Journal 193 pp 294
(October 1974) 13. T. J. Pearson and A. C. S. Re
adhead, Image formation by self-calibration in
radio astronomy, Annual Review of Astronomy and
Astrophysics vol 22 pp 97 (1984)
14. A. R. Thompson, J. M. Moran, G. W. Swenson
JR, Interferometry and synthesis in radio
astronomy, John Wiley and sons (1986)
15. T. J. Cornwell, The applications of closure
phase to astronomical imaging, Science vol 245 pp
263 (July 1989) 16. A. Labyrie, Interference frin
ges obtained on Vega with two optical telescopes,
Astrophysical Journal 196 pp L71 (March 1975)
17. M. Shao, D. H. Staelin, First fringe
measurements with a phase-tracking stellar
interferometer, Applied Optics 19 pp 1519
(1980) 18. D. F. Buscher, A thousand and one nigh
ts of seeing on Mount Wilson, SPIE Proceedings
vol 2200 pp 260 (March 1994) 19. J. E. Baldwin,
C. A. Haniff, C. D. Mackay, P. J. Warner, Closure
phase in high-resolution optical imaging, Nature
vol 320 pp 595 (April 1986)
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References Image Reconstruction
1. Bertero M., Boccacci P., 1998, Introduction to
Inverse Problems in Imaging (IOP Publishing, Bri
stol)
2. Correia S., Richichi A., 2000, AAS 141, 301
3. Bertero M., Boccacci P., Application of OS-EM
method to the restoration of LBT images, AAS 144
, 181-186 (2000)
4. Bertero M., Boccacci P., 2000, Image
Restoration Methods for the Large Binocular
Telescope (LBT), AAS - in press
Specific information on the LBT project
http//lbtwww.arcetri.astro.it
and related pages
Activity of the Astronomical Image Restoration in
Interferometry (AIRI) group web page http//d
irac.disi.unige.it/
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The End