Download From direct interferometry imaging to intensity interferometry imaging F. Malbet CNRS/Caltech

From direct interferometry imaging
to intensity interferometry imaging
F. Malbet
CNRS/Caltech
Workshop on Stellar Intensity Interferometry
29-30 January 2009 - Salt Lake City
Principle of direct interferometry
A
B
IAB
IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB
IAB = I0 (1 + VAB cos φAB)
if IA = IB = I0/2
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Principle of direct interferometry
A
B
Visibility
amplitude
V(u,v)
Visibility
phase
Φ(u,v)
IAB
IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB
IAB = I0 (1 + VAB cos φAB)
if IA = IB = I0/2
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Spatial coherence
• Each unresolved element of the image
produces its own fringe pattern.
• These elements have unit visibility and a
phase corresponding to the location of the
element in the sky.
• The observed fringe pattern from a
distributed source is the intensity
superposition of these individual fringe
pattern.
• This relies upon the individual elements of
the source being “spatially incoherent”.
• The resulting fringe pattern has a
modulation depth that is reduced with
respect to that from each source
individually, called object visibility
• The positions of the sources are encoded
in the resulting fringe phase.
Visibility = Fourier transform of
the brightness spatial distribution
Haniff (Goutelas, 2006)
Zernicke-van Cittert theorem
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Visibility
Visibilities
Projected baseline (m)
Uniform disk
Projected baseline (m)
Projected baseline (m)
Binary with unresolved
components
Binary with resolved
component
For a resolved source, given a simple model (uniform disk, Gaussian, ring,...),
there is a univoque relationship between a visibility amplitude and a size.
However this size is very dependent on the input model
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Imaging process
We start with the fundamental relationship between the visibility
function and the normalized sky brightness:
Inorm(α, β) =
∫ V(u, v) e
+i2π(uα + vβ)
du dv
In practice what we measure is a sampled version of V(u, v), so the image
we have access to is to the so-called “dirty map”:
I(α, β) =
∫ S(u, v) V(u, v) e
+i2π(uα + vβ)
du dv
= Bdirty(α, β) * Inorm(α, β) ,
where Bdirty(α,β) is the Fourier transform of the sampling distribution, or
dirty-beam.
The dirty-beam is the interferometer PSF. While it is generally far less
attractive than an Airy pattern, it’s shape is completely determined by the
samples of the visibility function that are measured.
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Actual image reconstruction
A
100
0
-200
2
7500K
1
0
-1
70
00
K
-2
-300
300 200 100 0 -100 -200 -300
East (m)
B
High-Fidelity Image
2
1
0
1
0
-1
-2
East (milliarcseconds)
700
0K
-1
-2
2
0K
750
-100
Altair Image Reconstruction
North (milliarcseconds)
CHARA UV Coverage
8000K
North (m)
200
S2-W1
S2-W2
S2-E2
W1-W2
E2-W1
E2-W2
North (milliarcseconds)
300
Convolving
Beam (0.64 mas)
2
1
0
-1
-2
East (milliarcseconds)
the Fourier UV coverage for the Altair observations, where each point represents the
Figure
A) shows
intensity
(λ = 1.65µm) created with the MACIM/MEM
one pair of CHARA telescopes (S2-E2-W1-W2) (31).
The 2:
dashed
ellipse the
shows
the image of the surface of Altair
2
method
ptical aperture of 265×195 meters oriented alongimaging
a Position
Angle using
of 135a◦ uniform
East of brightness elliptical prior (χν = 0.98). Typical photometric errors in the imag
Image of the surface of Altair with CHARA/MIRC
correspond to ±4% in intensity. B) shows the reconstructed image convolved with a Gaussian beam of 0.64 ma
corresponding to the diffraction-limit of CHARA for these observations. For both panels, the specific intensitie
at 1.65µm were converted into the corresponding blackbody temperatures and contours for 7000K, 7500K, an
Monnier et al. (2007)
8000K are shown. North is up and East is left.
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Imaging issues independent of interferometric process
•UV sampling, i.e. the number of visibility data ≥ number of filled pixels in the
recovered image:
N(N-1)/2 × number of reconfigurations ≥ number of filled pixels.
•UV coverage, i.e. the distribution of samples, should be as uniform as possible:
•The range of interferometer baselines:
•
•
Bmax/Bmin, will govern the range of spatial scales in the map.
No need to sample the visibility function too finely: for a source of maximum extent θmax,
sampling very much finer than Δu ∼1/θmax is unnecessary.
•Field of view is limited by:
- FOV of individual telescopes
- Vignetting of optics
- Coherence length. The interference condition OPD < λ2/Δλ must be satisfied for all field
angles. Generally
FOV ≤ [λ/B][λ/Δλ].
•Dynamic range: the ratio of maximum intensity to the weakest believable intensity in
the image. Several × 100:1 is usual.
DR ∼ [S/N]per-datum × [Ndata]1/2
•Fidelity: Difficult to quantify, but clearly dependent on the completeness of the Fourier
plane sampling
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Practical issues
- What is in the black box ? telescopes, optical train, delay
lines, optical switches, fibers, detectors...
- Combining directly the photons is challenging in
particular at optical wavelength
- Instantaneous variables are integrated over time, over
wavelength, over spatial frequencies
- Main sources of perturbations:
•
•
Atmosphere: spatial and temporal fluctuations of wavefront
•
•
•
Photon detection: photon noise, read-out noise, dark current, cosmetics
Individual elements of infrastructure: displacements (tip-tilts, optical
path, piston), vibrations, drifts
Polarization: light is naturally polarized
Human action
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The telescopes
The delay
lines
The
instrument
Issues specific to direct interferometry
• Atmosphere disturbance due to the fluctuations of the
refractive index n(P,T,λ)
•
transverse atmospheric refraction
•
longitudinal dispersion
loss of throughput
loss of system visibility in broad band
operation
• wavefront corrugation
loss of throughput or visibility, need to
operate fast enough to freeze the turbulence
•
piston
need to operate fast enough to freeze the fringes
• All these effects reduce the performance and sensitivity of
interferometers.
2
Sensitivity
is
proportional
to
NV
in
photon
rich
regime
or
NV
•
in photon starved regime.
10
How to overcome atmospheric perturbations?
- Atmospheric dispersion compensator (ADC):
- Made of pair of prisms to control the spectral dispersion
- Beam stabilization (wavefront sensor + actuator):
- Tip-tilt correction → angle tracker
- Adaptive optics: requires a deformable mirror
- Reducing the pupil size
- Fringe tracking:
- fringe sensor to act on delay line actuator
- Spatial filtering:
- pinhole or single mode fiber
- photometric calibration
- Detectors:
- low read-out noise detectors, ideally photo counting ones.
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But new subsystems can introduce new pertubations
- When complexity increases, number of sources of
perturbations too!
- Reliability becomes also an issue when the number of
subsystems increases (e.g.VLTI)
- Collectors: guiding, active optics
- Beam routing: 32 motors
- Adaptive optics: wavefront sensors, deformable mirrors, real-time
-
control, configuration
Delay lines: carriage trajectory, 3 translation stages, metrology,
switches,
Beam stabilisation: variable curvature mirrors, image and pupil
sensors (ARAL/IRIS), sources (LEONARDO)
Fringe tracking: fringe search, group delay, phase tracking, locks
Beam combination: spectral resolution, spatial filtering, atmospheric
dispersion, polarization, detection
Control software: 60 computers, 750000 lines of code as for 2004
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a few results
1996
Capella
1996
Betelgeuse
Mizar
2004
Capella
2000
2007
2007
Θ1 0ri C
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Promising results in other domains
0.0479
data
1.0
0.0431
0.0383
0.0335
10
0.5
0.0287
0
0.0
0.0
0.024
0.5
1.0
10+7
1.5
spatial frequencies
50
0.0192
data
−10
0.0144
0.00958
−20
0.00479
0
20
10
0
−10
mira
closure phase (deg)
relative δ (milliarcseconds)
20
squared visibilities
mira
0
−50
−20
relative α (milliarcseconds)
−0.5
0.0
0.5
Hour angle
Renard, Malbet, Thiébaut & Berger (SPIE 2008)
Work in progress...
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Depends on dust grains size and distribution
Promising results in other domains
If inclined disk: asymmetries (skewness) depending on dust
characteristics
Closure phase is a powerful observable to probe such asymmetries
[Monnier et al. 2006]
0.0479
data
1.0
0.0431
0.0383
0.0335
10
0.5
0.0287
0
0.0
0.0
0.024
0.5
1.0
10+7
1.5
spatial frequencies
50
0.0192
data
−10
0.0144
0.00958
−20
0.00479
0
20
10
0
−10
mira
closure phase (deg)
relative δ (milliarcseconds)
20
squared visibilities
mira
0
−50
−20
relative α (milliarcseconds)
−0.5
0.0
0.5
Hour angle
Renard, Malbet, Thiébaut & Berger (SPIE 2008)
Work in progress...
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Intensity interferometry prospects?
• Phase: can it be measured?
• UV coverage: number of telescopes and baselines?
• operation: imnune to atmosphere effects?
• astrophysical topics: different phenomena?
• wavelength of operation: visible, UV, X-ray?
• spectral resolution: for free?
• sensitivity: gain compared to Hanbury Brown & Twiss
interferometer ?
Interest in Intensity Interferometry is driven by the imaging
capabilities.
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