[PPT] - From direct interferometry imaging to intensity interferometry PowerPoint Presentation

SLIDE 1

From direct interferometry imaging to intensity interferometry imaging

F. Malbet

CNRS/Caltech

Workshop on Stellar Intensity Interferometry 29-30 January 2009 - Salt Lake City

SLIDE 2

Principle of direct interferometry

2

IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB IAB = I0 (1 + VAB cos φAB) if IA = IB = I0/2

A B

IAB

SLIDE 3

Principle of direct interferometry

2 Visibility amplitude V(u,v) Visibility phase Φ(u,v)

IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB IAB = I0 (1 + VAB cos φAB) if IA = IB = I0/2

A B

IAB

SLIDE 4

Spatial coherence

3

Zernicke-van Cittert theorem Visibility = Fourier transform of the brightness spatial distribution

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.

Haniff (Goutelas, 2006)

SLIDE 5

Visibilities

4

Uniform disk 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

Visibility Projected baseline (m) Projected baseline (m) Projected baseline (m)

SLIDE 6

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.

5

SLIDE 7

Actual image reconstruction

6

300 200 100

100 -200 -300

East (m)

300
200
100

100 200 300 North (m)

CHARA UV Coverage

S2-W1 S2-W2 S2-E2 W1-W2 E2-W1 E2-W2

2 1

1
2

East (milliarcseconds)

2
1

1 2 North (milliarcseconds)

Altair Image Reconstruction

7 K 7500K 8000K

2 1

1
2

East (milliarcseconds)

2
1

1 2 North (milliarcseconds)

High-Fidelity Image

7000K 7500K

Convolving Beam (0.64 mas)

A B

Monnier et al. (2007)

Image of the surface of Altair with CHARA/MIRC

SLIDE 8

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

7

SLIDE 9

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
Individual elements of infrastructure: displacements (tip-tilts, optical

path, piston), vibrations, drifts

Photon detection: photon noise, read-out noise, dark current, cosmetics
Polarization: light is naturally polarized
Human action

8

SLIDE 10

SLIDE 11

The telescopes

SLIDE 12

The delay lines

SLIDE 13

The instrument

SLIDE 14

Issues specific to direct interferometry

Atmosphere disturbance due to the fluctuations of the

refractive index n(P,T,λ)

transverse atmospheric refraction ⇒ loss of throughput
longitudinal dispersion ⇒ loss of system visibility in broad band
peration
wavefront corrugation ⇒ loss of throughput or visibility, need to
perate 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.

Sensitivity is proportional to NV in photon rich regime or NV2

in photon starved regime.

10

SLIDE 15

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.

11

SLIDE 16

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

12

SLIDE 17

a few results

13

Capella Mizar Betelgeuse Capella Θ1 0ri C

1996 1996 2000 2004 2007 2007

SLIDE 18

Promising results in other domains

0.0 0.5 1.0 1.5 10+7 0.0 0.5 1.0

spatial frequencies squared visibilities

data mira −0.5 0.0 0.5 −50 50

Hour angle closure phase (deg)

data mira

−20 −10 10 20 −20 −10 10 20 0.00479 0.00958 0.0144 0.0192 0.024 0.0287 0.0335 0.0383 0.0431 0.0479

relative α (milliarcseconds) relative δ (milliarcseconds)

Renard, Malbet, Thiébaut & Berger (SPIE 2008)

Work in progress...

14

SLIDE 19