Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.atnf.csiro.au/whats_on/workshops/synthesis2001/material/opticalint_extra.pdf Дата изменения: Tue Jan 15 06:16:17 2002 Дата индексирования: Wed Dec 26 14:02:16 2007 Кодировка: Поисковые слова: earth's atmosphere

Optical interferometry
Tim Bedding (Univ. of Sydney)
1. Introduction to high-resolution optical astronomy 2. Basics of two-aperture interferometry 3. Basics of multi-aperture interferometry 4. Summary of interferometer projects 5. Main science targets 6. Special topics See also "Introduction to Interferometry", http://xxx.lanl.gov/abs/astro-ph/9609092


1. Introduction to high-resolution optical astronomy Definitions: High (spatial) resolution: ability to see fine detail Optical and infrared wavelengths: 300 nm to 20 m

What limits our ability to get high resolution? 1. Wave nature of light 2. Ear th's atmosphere


Wave nature of light Consider a perfect space telescope: A point source produces an Airy pattern (1) where ­ is (approximately) the width of the image, called the `angular resolution' ­ ­ is the wavelength is the diameter of the telescope aper ture


Cause of Airy pattern: interference between par ts of the wavefront that arrive at different par ts of the aper ture (note dependence on wavelength) Each point on the source produces an Airy pattern. These overlap, degrading the fine detail. High resolution (smaller ) requires shor ter wavelengths and/or larger aper ture: Visible Near IR Mid IR (0.4­1 m) (1­5 m) (10­20 m) m 18 mas 77 mas 400 mas m 4 mas 6 mas 30 mas Note: mas = milliarcsec


The Earth's atmosphere Effects on the wavefront: On the ground, our perfect telescope produces stellar images 0.5­1 arcsec in diameter (seeing disk) Why? Wavefront gets distor ted by variations in refractive index in atmosphere (c.f. crumpled piece of paper). 1 arcsec seeing disk at 500 nm implies cm. Call this . is (approximately) the typical size over which the wavefront is `flat'. Note that `flat' is measured relative to the wavelength, so (actually, ) To be precise, is the distance over which the rms wavefront variation is 1 radian.


The Earth's atmosphere (cont.) Variations with time: The wavefront shape changes, but the dominant effect is that the whole pattern blows past the telescope with windspeed . The `coherence time' is (approximately) the time for the pattern to move sideways by distance . For example: m/s and cm gives ms.

High-resolution astronomy demands sampling faster than .


Methods of overcoming the atmosphere for single telescope: Adaptive optics: correct wavefront in real time Fast imaging: rapid sampling of the image, followed by post-processing to extract high-resolution information (`speckle interferometry')

But we are still limited by the wave nature of light (Airy diffraction pattern). To reach even higher resolution, we use interferometry: To make very big, we combine light from separate telescopes. Do not get real images directly, but we do get information on spatial scales corresponding to (where = baseline length).


2. Basics of two-aperture interferometry Combining light from two separate aper tures produces fringes (Young's double-slit experiment). The fringe visibility is defined as (2) Note that measures the fringe contrast, and lies between zero (no fringes) and one (full contrast).
1 V

V=1

V=0.5

V=0

0

baseline (m)

The measured is usually divided by from a point source to calibrate atmospheric and instrumental effects. The calibrated fringe visibility contains information about the source: low means the source is par tially resolved. The reason is that each par t of the source produces its own fringe pattern, but these all have slightly different phases and tend to wash out.


To be precise, measures the amplitude of the Fourier component of the source at the spatial frequency being sampled by the interferometer ( ). In other words, the visibility curve ( versus baseline) is the amplitude of the Fourier Transform of the source (the van Citter t­Zernike Theorem). The `phase' of the fringes (can be thought of as the sideways position on the detector) contains information about the source (the Fourier phase), but the measurement is dominated by atmospheric fluctuations. To measure all spatial scales on the source, use various baselines plus Ear th rotation to cover the so-called plane.


Interferometers measure fringes! To get good fringes: ­ the path lengths must be (nearly) equal. ­ the wavefronts must be (nearly) flat ­ the spectral resolution must be high enough ­ temporal sampling must be fast enough ­ the source must be (nearly) unresolved Main elements of an interferometer: ­ aper tures ­ tip-tilt correction on each aper ture (or higherorder adaptive optics) ­ delay line (with optional fringe tracking) ­ fringe detection and measurement


delay


3 Basics of multi-aperture interferometry Why use more than two aper tures? Faster coverage of different baselines (called coverage). Several baselines can be measured simultaneously, and aper tures form baselines. The ability to measure closure phases (see below). The possibility of baseline bootstrapping (see later).


Closure phases How can we construct an image? Recall that fringe visibility ( ) gives the amplitude of the Fourier transform of the source. To reconstruct an image using the inverse Fourier transform, we also need phases. In principle, the phase (position) of the fringes gives this information, but the measured phase is badly corrupted by the atmosphere. With three aper tures, the three sets of fringes move due to the atmosphere, but their relative positions contain information about the source phase.

3 1 2


Closure phases (cont.) The algebraic sum is called the closure phase. It is completely unaffected by atmospheric fluctuations and therefore is a proper ty of the source. For example, the closure phase of a symmetric source is always either 0 or 180 . By measuring closure phases of the source on various baseline triangles, we can use `self-calibration' methods to reconstruct an image.


4. Summary of interferometer projects No longer operating (incomplete list): Intensity Interferometer (1964-1976) ґ ` ` ґ I2T (Interferometre a 2 Telescopes; 1974­1987) Mark III (1986­1993)

Operating: ґ ` ` ґ GI2T (Grand Interferometre a 2 Telescopes). SUSI (Sydney University Stellar Interferometer) COAST (Cambridge Optical Aper ture Synthesis Telescope) ISI (Infrared Spatial Interferometer) FLUOR (Fiber Linked Unit for Optical Recombination) IOTA (Infrared-Optical Telescope Array) NPOI (Navy Prototype Optical Interferometer)
http://huey.jpl.nasa.gov/olbin/


PTI (Palomar Testbed Interferometer) CHARA (Center for High Angular Resolution Astronomy)

Under Construction: Keck Interferometer VLTI (Very Large Telescope Interferometer) LBT (Large Binocular Telescope) MIRA-II (Mitaka IR Array)


5. Main science targets for optical/IR interferometry Visibility measurements and imaging: Stellar angular diameters and effective temperatures Binary star orbits Stellar surface structure Star formation and early stellar evolution Be stars (B stars with excretion disks) AGB stars (red giants) The Galactic Centre Active Galactic Nuclei


Narrow-angle astrometry (dual-feed interferometer): Parallaxes and proper motions Indirect detection of low mass stars, brown dwarfs and extra-solar planets Direct detection of brown dwarfs and `hot' Jupiters (two-colour)

Nulling: Characterization of exo-zodiacal dust. Direct imaging of extra-solar planets (space missions)


6. Special topics 6.1 Thermal infrared 6.2 Wide-angle astrometry 6.3 Narrow-angle astrometry 6.4 Nulling 6.5 Adaptive optics and laser guide stars in interferometers 6.6 Space interferometry projects


6.1 Thermal infrared (5­20 m): The dominant noise source is thermal emission from the instrument and sky. So far, ISI has done heterodyne interferometry at 11 m with two aper tures. Signal-to-noise scales as , so big telescopes have a huge advantage: VLTI (MIDI) will combine four 8-m telescopes; Keck will combine two 10-m telescopes. Science targets are: AGB stars; AGN; direct detection of brown dwarfs and hot Jupiters; exo-zodiacal light


6.2 Wide-angle astrometry: Done by Mark III (closed down), NPOI and SIM Aim is to maintain the Hipparcos reference frame Accuracy is 2 mas over large angles, but requires a very stable baseline (accurate laser metrology)


6.3 Narrow-angle astrometry: Requires a dual-feed system to observe two stars simultaneously, plus an extra delay line (PTI; VLTI/PRIMA; Keck). Use the differential delay to measure the phase difference between the two stars. This gives their separation on the sky to about 20 arcsec.


A dual-feed system can also be used for phasereferenced interferometry: Measure the atmospheric delay on the brighter star, and use this to track fringes on the fainter star (`co-phasing'). This allows extended coherent integration of fringes on the fainter star. Another trick is two-colour phase-referenced interferometry: Observe one star at two wavelengths and use narrow-angle astrometry to measure the shift in photo-centre as a function of wavelength. This method will be used with the Keck Interferometer to detect hot Jupiters.


6.4 Nulling: Proposed by Bracewell (1979) as a means of detecting extrasolar planets Demonstrated with the MMT by Hinz et al. (1998). In SIM, the beam combiners will introduce an achromatic 180 phase shift in one of the interferometer arms by polarization inversion, thus eliminating the light from a point source that is located at the phase center. Science applications: direct detection of exoplanets; determining the spatial extent of stars, supernova shells, etc., by measuring the light leakage around the phase centre.


6.5 Adaptive optics and laser guide stars in interferometers: AO can be used to flatten the wavefront across individual aper tures (e.g., big telescopes of VLTI and Keck). This AO correction can be helped by laser guide stars. A conventional laser guide star is too big for use as an interferometer reference source (about 1 arcsec). Two interfering laser beams would produce fine fringes on the sky. These could be used as an interferometer reference source. The interferometer could track fringes on the laser source, allowing long integration on a faint target.


6.6 Space interferometry projects Main difference from ground-based is the absence of atmosphere. Thus, and become very large. There will still be slow variations from vibrations, etc. The NASA Origins Program (through the Jet Propulsion Laboratory) includes a series of space interferometers: ­ Space Technology 3 (ST3) ­ Space Interferometry Mission (SIM) ­ Terrestrial Planet Finder (TPF) ­ Planetary Imager (PI) There is an ESA proposal for `InfraRed Space Interferometry Mission' DARWIN.