Mem. S.A.It. Suppl. Vol. 2, 194c© SAIt 2003

Memorie della

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Optical interferometry | A brief introduction

Markus Scholler

European Southern Observatory, Casilla 19001, Santiago 19, Chile

May 31, 2003

Abstract. Optical interferometry is an evolving field that in the current decadewill become a tool for a wider astronomical community. We take a look at theprinciple underlying interferometry, introduce the key elements of an interfero-meter with examples from the VLT Interferometer, explain some constraints forinterferometric observations and give an overview about the science which canbe done with optical interferometers. While on this path we will try to illustrateseveral terms which are widely used by interferometrists.

Key words. Optical Interferometry, Very High Angular Resolution

1. Introduction

Interferometry between separate telescopesgives access to angular resolution whichis much better than any single telescopecan deliver. Interferometry is routinely op-erating at radio wavelengths since about30 years, combining telescopes on differentcontinents and even in space. During thesame period optical interferometry wentthrough a phase of definition and test-ing of the technology needed and pro-duced science results regularly throughoutthe 1990s. The current implementation oflarger facilities will bring optical interfer-ometry into the astronomical mainstream.

There are ten optical interferome-ters in operations today: CHARA (tenBrummelaar et al. 2003), COAST (Haniffet al. 2003), GI2T (Mourard et al. 2003),IOTA (Traub et al. 2003), Keck (Colavita& Wizinovich 2003), MIRA (Nishikawa2003), NPOI (Mozurkewich et al. 2003),PTI (Lane et al. 2003), SUSI (Tango

2003) and VLTI (Glindemann et al. 2003).Several more went out of service. Althoughthey are very different in their design(e.g. they have telescope sizes between afew cm and more than 10 m), the wave-length regime they operate in (between400,nm and 20,µm), the modes of opera-tion (pure visibility measurements, closurephases, phase referencing, wide and nar-row angle astrometry, nulling), they all uti-lize the same underlying physical principlesand use similar hardware. When we talkabout optical interferometers in this paper,we think of interferometers which work atvisible, near- or mid-infrared wavelengthsand make a direct detection of fringes.

For a good overview about the sta-tus of optical interferometry in general,the reader is referred to Quirrenbach(2001) and for the historic context toShao & Colavita (1992). An introduc-tion into the key technology of opti-cal interferometers has recently been pre-sented by Scholler (2003). Information on

Markus Scholler: Optical interferometry — A brief introduction 195

projects and resources within stellar in-terferometry can be found in the OpticalLong Baseline Interferometry News underhttp://olbin.jpl.nasa.gov/.

2. Interferometers and interference

Optical interferometry – the coherent com-bination of the light from several telescopesat visible or infrared wavelengths – offersangular resolution far superior to that of asingle aperture.

The angular resolution capabilities ofan optical element are determined by itsdiameter D and the wavelength λ throughλ/D. With a 10,cm telescope at 500 nmone can resolve structures as small as 1,arc-second. With a 10,m telescope the angularresolution is 10 milliarcseconds (mas), ex-actly 100 times better. If one wants to ob-tain even higher angular resolution, one hasto build an even larger optical device, yetcurrent telescope technology is preventinglarger single aperture sizes.

In an optical interferometer, the angu-lar resolution is given by λ/B, with B thedistance between two telescopes, also calledthe baseline.

The principle of an optical interfero-meter can be best illustrated by Young’spinhole experiment, which is displayed inFig. 1. A light source at infinity produces aflat wavefront which is passing through twoholes which are separated by a distance B.On the screen behind these two holes, aninterference pattern proportional to 1+coscan be observed, with a period length ofλ/B. This interference pattern is also calleda fringe. The fringes disappear if the opticalpath difference (OPD – here: αB) is largerthan the coherence length. The envelopeof the fringe pattern is determined by theFourier transform of the spectrum of thesource modified by the optical filters used.With a light source under an inclination an-gle the fringe pattern shifts. The spacing ofthe fringes is solely determined by the spac-ing of the pinholes. If the source is resolved,the contrast of the fringes is diminishing, asseveral, respectively slightly shifted, fringe

Fig. 1. Young’s pinhole experiment.

patterns are adding up, smearing out themaxima and minima.

An interferometer is similar to mask-ing a large telescope with just two pinholes.Changing the distance and the orientationbetween the two pinholes, one can slowlyretrieve every single spatial frequency thata full aperture naturally gives in one in-stance. When observing with the full un-masked aperture, one gets an interferogramwhich has fringes between all subapertures.We call this also an image.

Fig. 2 shows the implementation of theVLT Interferometer. Instead of having justa screen with two holes, the light is fol-lowing a complicated optical path. Themain difference between the screen and areal setup is that the distance between thebeams as they hit the telescopes and whenthey arrive within the beam combinationdevice, is not the same anymore. The con-trast of the fringes is determined by the res-olution of the interferometer, i.e. the dis-tance between the single apertures. Thefringe spacing is solely determined by thedistance of the beams in the laboratory.

The incoherent imaging equation de-scribes the transfer function of an opticalsystem as the autocorrelation of the pupilfunction. The transfer function is locatedin the Fourier space, or as interferometristslike to call it, the uv-plane, after the widelyadapted names for its coordinates. In aninterferometer with telescopes fixed to theground the projected baselines change withthe rotation of the earth. The baseline vec-

196 Markus Scholler: Optical interferometry — A brief introduction

Fig. 2. The optical layout of the VLTI withtwo telescopes. The light is transported via aCoude train to the Coude focus and from therevia relay optics into a tunnel which houses thedelay lines. Finally, the light is sent into the in-terferometric laboratory where it is combinedin an interferometric instrument.

Fig. 3. The left image shows the VLTI with itsfour 8 m Unit Telescopes and the six baselinesspanned by them. The right image shows theuv-coverage determined by this layout for anobject located at zenith.

tors follow trajectories which are ellipseswhose location is determined by the dec-lination of the source and the latitude ofthe position of the interferometer. Theseellipses become circles for objects with adeclination of ±90◦ and degenerate to linesfor objects with a declination of 0◦. Fig. 3shows the layout of the VLTI and a snap-shot of the uv-plane for an object at zenith.

An interferometer measures visibilities.A visibility is a complex entity, the Fouriertransform of the object intensity distribu-tion, measured at the spatial frequency de-termined by the entrance pupil of the inter-ferometer. The modulus of the visibility isdetermined by the contrast of the fringes,the phase of the visibility by the position

of the fringe. The contrast of a fringe is af-fected by the atmosphere and the interfero-meter itself. It has to be calibrated by anunresolved source, which has a visibility of1. The fringe position is influenced mainlyby the atmospheric turbulence, namely bythe piston term. This effect can not be di-rectly measured or calibrated. Phase in-formation, which is the key to interfer-ometric imaging, can be retrieved eitherthrough closure phases or through phasereferencing. Closure phases are the sumof three simultaneously measured phaseson three baselines which span a triangle.Closure phases are not influenced by atmo-spheric turbulence. Referenced phases aredetermined between a science object and anearby unresolved source. They are usuallyretrieved with a dual feed system.

For a deeper understanding of the imag-ing process by means of Fourier optics, thereader is referred to Goodman (1968).

3. Ingredients of an interferometer

For an interferometer to work, the followingcomponents are sufficient: two telescopes, abeam combiner and the optical trains to tiethem together. Most interferometers havetelescopes which are fixed to the ground,and thus need delay lines to compensate forthe OPD between the arms of the interfero-meter, while the source moves across thesky.

3.1. Telescopes

The main task of the interferometric tele-scopes as in any single aperture opera-tion is to collect photons. A rigid designis needed to avoid any introduction of opti-cal path difference due to vibrations, as forall components of the interferometer. As agolden rule, all telescopes of an interfero-meter should be of the same type, with thesame orientation of mirrors and the samecoatings on all conjugating optical surfacesto control differential polarization.

Markus Scholler: Optical interferometry — A brief introduction 197

Fig. 4. Two delay lines of the VLTI.

3.2. Delay Lines

The delay lines have to compensate theOPD for all baselines in an interferometer.To do this, they have to cancel the OPD atany given time, i.e. follow the sidereal delaywhile the object moves across the sky.

The optics of delay lines are typically ei-ther a roof mirror or a cat’s eye. Delay linescan be moved in various ways, with linearmotors, voice coils or piezos. Typically theyconsist of a composition of these compo-nents, e.g. a linear motor for the coarse anda piezo for the fine positioning. This mixof devices makes it possible to achieve thepositioning requirements of the delay lineswith an accuracy of tenths of nanometersover a stroke length of tenths of meters.

Fig. 4 shows the implementation of theVLTI delay lines.

3.3. Beam combination

A beam combiner brings the beams fromthe telescopes close enough together sothey can interfere. If the beam combinationscheme requires the coding of the fringes intime, a device to modulate the OPD be-tween the beams is required. Further, sometype of detector to record data is needed.

There are two different ways to combinebeams in a beam combiner: in a multiaxialbeam combiner the beams are placed adja-cent to each other and form a fringe patternin space. In a coaxial beam combiner, thebeams are added on top of each other, for

1 2 3

spatialinterferogram

Beamsplitter

Detector

1 2

1+2

PSF

Pupil Plane

Fig. 5. Fringe combination schemes: multiax-ial (left) and coaxial (right). An OPD modu-lating device has to be used in one of the armsof the coaxial beam combiner to form fringes.

example with a beam splitter. The fringesare produced in time by modulating theOPD between the two beams. Fig. 5 illus-trates the two combination schemes and inFig. 6 one can see the data resulting fromthe beam combination.

The actual implementation of a beamcombiner is usually done in bulk optics.Another type of beam combiner is madeout of single mode fibers, which are notonly combining the light within the fibers,but also serve as spatial filters (Coude duForesto et al. 1993). Lately, progress inthe production of integrated optics has al-lowed to build beam combiners of the sizeof a coin (Malbet et al. 1999; Berger et al.2001).

3.4. Further components

Since the light of two (or more) telescopeshas to be combined, it is necessary to bringtheir light onto the same spot in an imageplane. Tip-tilt sensors for each telescopeare employed to ensure the image stabil-ity needed. If the telescopes are larger thanthe diameter of the atmospheric turbulencecells (the Fried Parameter r0), then thetelescopes have to be equipped with adap-tive optics to ensure the maximum flux be-ing available for beam combination. A spa-tial filter ideally removes residual inhomo-geneities of the individual wavefronts (andthus makes them similar), at the cost of re-ducing the amount of light which is avail-

198 Markus Scholler: Optical interferometry — A brief introduction

Fig. 6. The fringes resulting from multiaxialand coaxial beam combination: on the top asimulation of fringes similar to the ones whichwill be produced by the AMBER instrumenton VLTI is presented. The bottom panel dis-plays fringes observed by the VINCI instru-ment on VLTI.

able for beam combination. Finally, a fringetracker stabilizes the fringes, which are oth-erwise moved backwards and forwards inOPD by the atmospheric piston.

4. Observing with opticalinterferometers

Optical interferometers have two limita-tions which have to be taken into accountwhen looking for the science cases they cantackle: a limited field of view and a rela-tively poor limiting magnitude.

The field of view is limited to a fewarcseconds due to the transfer optics thatbring the light from the telescopes to thebeam combination device. A larger field ofview would require larger optical elements.Furthermore, beam combination devices of-

ten use spatial filters, which are adaptedto the Airy disk of a diffraction limitedtelescope. High resolution information canthen only be retrieved within this field,which is e.g. 55 mas for an 8m telescopeat 2.2 µm. Information is sampled only onB/D resolution elements, which e.g. cor-responds to 130m/8 m≈ 16 elements forthe VLTI 8 m telescopes or 220m/1.8 m≈112 elements for the 1.8m telescopes. Waysto overcome these field of view limitationsare mosaicing and homothetic mapping,which both have not been successfully im-plemented on optical interferometers yet.

The limiting magnitude is determinedby the atmosphere moving the fringesback and forth due to the piston term.Interferometers have to beat this motion,limiting the integration time to the at-mospheric coherence time τ0. Apart frombuilding an interferometer at an excep-tional site with a large τ0, one can over-come this limitation by using large tele-scopes with adaptive optics to collect morephotons and use off-axis fringe trackers indual feed systems. A limiting magnitude inthe K band of about 20 is within reach ofthe existing large interferometers.

The most simple interferometric obser-vations are of rotationally symmetric ob-jects, like diameter measurements of stars.Fig. 7 shows such observations for α CenAand B. Each obtained (squared) visibilityvalue is plotted against the baseline length(or the spatial frequency) and a model fitis made to the data, here a uniform diskdiameter. It is possible to find asymme-tries from visibilities without phase infor-mation, but there is always a 180◦ am-biguity. With interferometers which allowto obtain more information, more complexmodels can be fitted. Especially phase in-formation allows to distinguish between dif-ferent models and finally permits imaging.Yet, although there are optical interferom-eters which are regularly measuring closurephases, not a single model independent im-age has been retrieved so far.

The classical field of optical interferom-etry is the determination of fundamental

Markus Scholler: Optical interferometry — A brief introduction 199

Fig. 7. Visibility values and the resulting uni-form disk fits for the three stars α CenA(lower solid curve), α Cen B (upper solidcurve) and θ Cen (dashed curve – the calibra-tor used). The derived uniform disk diame-ters are 8.338±0.018mas and 5.905±0.045 masfor α CenA and α CenB, respectively (seeKervella et al. 2003).

stellar quantities, like the diameter, limbdarkening profiles or asymmetries. Surfacestructures on stars should become acces-sible in the future with longer baselines.Another field are binarity studies, espe-cially in star forming regions. Other top-ics of interest are stellar environments likestellar debris disks, circumstellar disks andjets of pre-main sequence stars, or massoutflows of evolved stars. Finally, the twobig challenges for optical interferometry arethe detection of extrasolar planets (see e.g.Glindemann et al. (2000) for an overview ofavailable techniques) and the observationsof active galactic nuclei, the first extra-galactic sources for optical interferometry.Since optical interferometry is improvingangular resolution by more than one mag-nitude over what is available with singletelescopes, the history of astronomy tells usthat we can expect to find a wide varietyof new phenomena.

Acknowledgements. I would like to thank thewhole interferometric community for fruitful

discussions over the years, especially the peo-ple in the VLTI group at ESO. Pierre Kervellakindly provided the figure on α Cen.

References

Berger, J.P., P. Haguenauer, P. Kern, et al.A&A, 376:L31, 2001.

Colavita, M.M. and P.L. Wizinovich SPIE4838, 625, 2003.

Coude du Foresto, V., G. Maze, andS. Ridgway. ASP Conf. Ser. 37:285, 1993.

Glindemann, A., F. Delplancke, P. Kervella,et al. In: Planetary Systems in theUniverse, IAU Symp. 202, 2000,Ed. A.J. Penny, P. Artymowicz, A.-M. Lagrange, S.S. Russell, 2000

Glindemann, A., J. Argomedo, R. Amestica,et al. In: The Very Large TelescopeInterferometer: Challenges for the Future,Ed. P.J.V. Garcia, A. Glindemann, Th.Henning, F. Malbet , in print, 2003.

Goodman, J.W. Introduction to FourierOptics, McGraw-Hill, 1968

Haniff, C.A., J.E. Baldwin, A.G. Basden, et al.SPIE 4838, 19, 2003.

Kervella, P., Thevenin, F., Segransan, D., etal. A&A accepted

Lane, B.F., M. Konacki, and R.R. ThompsonSPIE 4838, 62, 2003.

Malbet, F., P. Kern, I. Schanen-Duport, et al.A&AS, 138:135, 1999.

Mourard, D., L. Abe, A. Domiciano, et al.SPIE 4838, 9, 2003.

Mozurkewich, D., J.A. Benson, andD.J. Hutter SPIE 4838, 53, 2003.

Nishikawa, J. SPIE 4838, 101, 2003.Quirrenbach, A. Annual Review of Astronomy

and Astrophysics, 39:353–401, 2001.Scholler, M. In: The Very Large Telescope

Interferometer: Challenges for the Future,Ed. P.J.V. Garcia, A. Glindemann, Th.Henning, F. Malbet , in print, 2003.

Shao, M. and M.M. Colavita. Annual Reviewof Astronomy and Astrophysics, 30:457–498, 1992.

Tango, W.J. SPIE 4838, 28, 2003.ten Brummelaar, T.A., H.A. McAlister,

S.T. Ridgway, et al. SPIE 4838, 69, 2003.Traub, W.A., A. Ahearn, N.P. Carleton, et al.

SPIE 4838, 45, 2003.