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ToappearinPASP(May1999issue) New methods formasked-aperture and speckle interferometry TimothyR.Bedding SchoolofPhysics,UniversityofSydney2006,Australia E-mail: [email protected] ABSTRACT 9 9 9 1 Diffraction-limited images can be obtained with a large optical telescope using n interferometry. Onesuchmethodforobjectsofsufficientbrightnessisnon-redundantmasking a (NRM), in whichobservationsaremadethroughapupilmaskthatcontainsanarrayofsmall J 8 holes. However, NRM only uses a small fraction of the available light. Here I describe a 1 method for Extended NRM in which a cylindrical lens allows interferograms from many 1 one-dimensionalarraystoberecordedside-by-sideonatwo-dimensionaldetector. v Forfainterobjects,theholesintheaperturemaskshouldbereplacedbyslits. Inthiscase, 5 2 the mask canbe removedentirely, with the cylindricallenseffectivelycreating a continuous 2 series of one-dimensional interferograms. This modified form of speckle interferometry, 1 which IcallMODS (Multiplexed One-DimensionalSpeckle), is intermediatebetweenNRM 0 9 and conventionalfull-aperture speckle. An existing speckle camera can easily be converted 9 to MODS observations by inserting a cylindrical lens. The feasibility of both MODS and / h ExtendedNRM are demonstratedusing observationswith MAPPIT at the Anglo-Australian p - Telescope. o r t s a Subjectheadings: Instrumentation: interferometers–Techniques: interferometric : v i X r 1. Introduction a Thereare two approachesto achievinghighangularresolutionwith a large ground-basedtelescope. Bothinvolvecompensatingfordistortionsinthewavefrontofthelightthatresultfromitspassagethrough the atmosphere. The first approach is to make these corrections in real time using an adaptive optics system,whichemploysadeformablemirrorwhoseshapeiscontrolledbyalargenumberofactuators(see Beckers1993forareview). However,althoughadaptiveopticsshowsgreatpromiseforinfraredimaging, its application to visible wavelengths poses formidable problems because of the very large number of actuatorsrequired. Thepassiveapproachtohigh-resolutionimagingreliesoninterferometryandinvolvesrecordingmany short-exposureimages, eachofwhich ‘freezes’the atmosphericturbulence. Theseimagesare processed –2– off-linebycalculatingthepowerspectrumandbispectrum,whichyieldthevisibilitiesandclosurephasesof theobject. Thistechniqueisknownasspeckleimaging(Labeyrie1978;Weigelt1991;Negrete-Regagnon 1996)andcanbeusedtoreconstructadiffraction-limited image. A variationonthis passiveapproachis non-redundantmasking(NRM), in whichthe short-exposure images are taken through a pupil mask that contains a small number of holes, arranged so that all the baselinevectorsaredistinct(Haniffetal.1987;Nakajimaetal.1989). Maskingthetelescopepupilinthis way,althoughonlyfeasibleforbrightobjects,hasseveraladvantages(Haniff1994;seealsoBeddingetal. 1993). Theseinclude: (i)animprovementinsignal-to-noiseratiosfortheindividualvisibility andclosure phase measurements; (ii) attainment of the maximum possible angular resolution by giving full weight to the longest baselines; and (iii) a resistance to variations in atmospheric conditions and a consequent improvement in the accuracy of visibility calibration. The spatial-frequency plane is coarsely sampled relativetoobservationswithafully-filledaperture,buteachmeasurementismoreaccurate. NRM has been successfullyused to image close binaries and to measure angulardiameters of cool stars (Haniff et al. 1987; Nakajima et al. 1989; Bedding et al. 1994; Haniff et al. 1995; Bedding et al. 1997). Mostimportantly, ithasrevealedthepresenceofhotspotsandotherasymmetriesonthesurfaceof redsupergiantsandMiravariables(Buscheretal.1990;Wilsonetal.1992;Haniffetal.1992;Tuthilletal. 1997;Beddingetal.1997). 2. ExtendedNRM TwodisadvantagesofNRMstemfromits useofonlya smallfraction ofthe telescopepupil: (i) the instantaneouscoverageof spatial frequencies is sparse; and (ii) most of the available light is discarded. The first point can be mitigated by combining observations made with different masks and/or with the masksrotatedtoseveraldifferentpositionanglesonthesky. Thesecondismoreseriousandispresumably responsibleforareluctancein thewidercommunityto makeuseofaperturemasks. Interestingly,similar considerationshavenotpreventedtheuseofdetectorswithlowdutycycles,suchasintensifiedCCDsthat are only capable of recording a few frames per second (Weigelt et al. 1996; Klu¨ckers et al. 1997). In contrast,NRMexperimentshavebeenabletotakeadvantageoffastone-dimensionaldetectorswith100% dutycycle,intheformofCCDswithon-chipbinning(Buscheretal.1990). Inanycase,itwouldclearlybedesirabletodeviseaschemewhichmakesuseofthewholepupilwhile maintainingtheadvantagesofNRM. Kulkarni(1988)discussesmethodsforso-calledExtendedNRM,in whichthepupilisdividedintomanyslicesthataretreatedseparately. Oneversionrequiresaninstrument withaseriesofmasks,eachtransmittingafractionofthelighttoadetectorandreflectingtheremainderto subsequentmasks. Analternativemethodis to imagethepupilonto abundleofopticalfibres,which are againdividedamongseveraldetectors. A much simpler approach, mentioned briefly by Buscher (1988a), is to use a cylindrical lens. A method for this is shown schematically in Figure 1. The mask, which contains several parallel linear arraysofholes,is placedina collimatedbeam. Theopticsin theinterferencedirection(top view)forma –3– conventionalimage-planeinterferometer, with the cameralensproducinganimageofthestarcrossedby interferencefringes. In the orthogonaldirection (side view), the cylindricallensproducesa pupil image, which ensures that the beams from the different hole arrays are spatially separated in the focal plane. Forsimplicity, Figure 1 showsa mask with three identical four-hole arrays. In practice, more than three arrays would be used and they could all be different. Also required, but not shown in the diagram, are a narrow-band filter and a two-dimensional detector. A microscope objective may also be necessary to ensuresufficientmagnification. Notethatthearrangementproposedhereisverysimilartothewavelength-dispersedsystemdeveloped byBeddingetal. (1994), butwith thedispersingprismbeingreplacedbyanarrow-bandfilterandwith a mask having severalparallel arrays of holes. The seconddimension of the detectoris now used, not for wavelengthinformation,butforrecordingmanysimultaneoussetsoffringes. 2.1. TestobservationsofExtendedNRM Atestofthisconceptwasmadeatthecoude´focusofthe3.9-metreAnglo-AustralianTelescope(AAT) usingtheMAPPITfacility, whichwasdevelopedforinterferometry andNRM(Beddingetal.1994). The componentsofMAPPITare mountedontwo opticalrails attachedto thetelescopefoundation,providing greatfreedomto experimentwith different opticalconfigurations. Thetests were madeon 1995January 14 duringperiodsof intermittent cloudwhich hadinterrupted the scheduledobservingprogram. Despite thecloud,theseeingwasquitegood(∼1′′). Thedetectorwasa1024×1024ThomsonCCDwith 19µm pixels, although only a subset of the CCD was read out. The wavelength region was selected using an interferencefilterwithcentralwavelengthof650nmandatransmissionbandwidthof40nm. Figure2showsanobservationofabrightstarmadewith this system. Theimage(centre)isa single 2-secondexposureand contains225×205pixels. The horizontalscale is 0.016′′ per pixel, so the image ′′ widthis3.5 onthesky. Intheverticaldirection,whichcorrespondstoanimageofthemaskedpupil,one rowontheCCDprojectsto0.9cmontheprimarymirror. Thediagramontheleftshowstheapproximate positionofthemaskwithrespecttotheAATpupil. Ascanbeseen,themaskholesaresquareandcomein twosizes—thesehaveprojecteddiametersof5and8cm,respectively. The right panel of Figure 2 shows the result of calculating the power spectrum of each row of the image. Zero spatial frequency is at the left, and each baseline sampled by the mask produces a spot. Despitetherelativelylongexposure(2s), whichwassubstantiallylongerthantheatmosphericcoherence time,powerisdetectedonmostbaselinesinthissingleexposure. Inpractice,onewouldusealargenumber ofshorterexposures. ThispreliminarytestdemonstratesthefeasibilityofExtendedNRM. Themaskwasnotdesignedfor this application, and two of the holes actually fall outside the AAT pupil. An optimized system would usea mask with manymore arrays, perhapshavingdifferentnumbers ofholeswith variousdistributions and sizes. Extracting the object visibilities and closure phases, followed by model fitting or image reconstruction,wouldproceedasforconventionalNRM. –4– TheimprovementoverconventionalNRMcomesfromtheabilitytomakeobservationssimultaneously with many parallel mask array. It should be possible to fit up to 20–30 different arrays on the pupil, which would reduce by this factor the total observing time required to acquire a given amount of data. However,this gainmaybealmostcompletelyoffsetby theneedto usea two-dimensionaldetector,since onewouldbeforcedtoalowerdutycyclethanispossiblewith afullybinnedCCD,asarecurrentlyused forconventionalNRM(Buscheretal.1990). ApracticalsystembasedonExtendedNRMshouldprobably waitforatwo-dimensionaldetectorwithhighdutycycle. 3. Multiplexedone-dimensionalspeckle(MODS) Anobviouswaytoextendaperturemaskingtofainterobjectsistoreplacethearrayofsmallholesby athinslit. Indeed,aslitwassuggestedbyAime&Roddier(1977)asagoodcompromisebetweenstandard speckle techniquesand Michelson interferometry. Buscher& Haniff (1993) confirmed this by showing thatthebestsignal-to-noiseforindividualvisibility andclosurephasemeasurementsatlowlightlevelsis achievedwith a pupil having a high degree of redundancyand a small surface area. This is becausethe signalon a givenbaseline(or closure-phasetriangle) increaseswith the redundancy,while photon noise increaseswith the total area of the pupil(we are assumingthat photon noisedominates anycontribution from detector read noise). A slit, having high redundancyper unit area, is ideal. It largely retains two of the advantagesof NRM mentioned in the Introduction (improved signal-to-noise and full resolution), althoughtheaccuracyofvisibilitycalibrationinthepresenceofvariableseeingisnotmuchbetterthanfor conventionalfull-aperturespeckle. The method describedin Section 2. can easily be applied to a mask with slits. The cylindricallens ensuresthateachslitisimagedseparatelyonthedetector. Furthermore,wecanimagineaddingmoreand more slits untiltheybecomeso closetogetherthattheyfillthe wholepupil. At this pointwecanremove themaskentirely. Suchanarrangementeffectivelyhasmanyadjacentpseudo-slits,andIwillrefertoitas MultiplexedOne-DimensionalSpeckle(MODS). 3.1. TestobservationsofMODS Observationsusing the MODS technique were made using the setup describedabove, but with the mask removed. Figure 3 presents observationsof a bright star. The diagram on the left shows the AAT pupil,includingtheobstructionfromthesecondarymirrorandthevanesthatsupportit. Theimage(centre) is a single 0.2-secondexposureand contains225×400pixels. The horizontal and verticalscalesare the sameasin Figure 2. Specklepatternsandtheshadowsofthe vanesareclearly visible,asare finefringes duetointerferenceacrossthecentralobstruction. Asbefore,wecanprocesseachrowofthedetectorindependently. Therow-by-rowpowerspectrumis shownintherightpanelofFigure3andshowspowerouttothediffraction limit. Thecentralobstruction –5– ofthe AAT is more than onethird ofthe telescopediameter, sothe centralpartofthe row-by-row power spectrumcontainsagapinthecoverageofspatialfrequencies. Observations were also made of the double star γ Cen (HR 4819), which has equal components ′′ separatedby1.2 (Hirshfeld&Sinnott1982). Thepositionangleoftheobservationwaschosensothatthe separationvectorofthetwostarswasalmostperpendiculartotheaxisofthecylindricallens. Inthisway, ′′ theprojectedseparationofthebinaryalongtheinterferometerdirectionwasonly0.15 . Theleftpanelof Figure 4showstherow-by-row powerspectrumofa single0.2-secondexposure. The verticalstripes are theclearsignatureofadoublestar. The right panel of Figure 4 shows the row-by-row power spectrum of the same data, but here the original image was binned eight rows at a time before transforming. Each row, instead of projecting to 0.9cmontheprimarymirror, nowprojectsto7cm. Thus,bybinningseveralrowstogether,wehavebeen abletoincreasethe“slit”widthinpost-processinganddecreasethenoisefromphotonstatistics,ascanbe seen in the figure. In practice, the optimum binning factor would depend on the atmospheric coherence length(r )atthetimeofobservationandcouldbedeterminedduringdatareduction. Infact,asshownby 0 Buscher(1988b),theoptimumaperturesizeformeasuringvisibilitiesisnotthesameasforclosurephases. WithMODSdataonewouldbeabletoaccommodatethisbyvaryingthebinningfactorinpost-processing. The analysis of MODS data, as with conventional speckle and NRM techniques, proceeds by estimatingthepowerspectrumandclosurephasesoftheobject. Thefirststepistocalculatetherow-by-row powerspectrum,asdescribedabove. Calibrationforatmosphericandinstrumentaleffectswouldbedone usingsimilarobservationsofanunresolvedreferencestar. Theresultwouldbeaseriesofmeasurementsof theobjectpowerspectrumatmanydifferentspatialfrequencies. Estimatesoftheclosurephasewouldbe obtainedinasimilarwaybycalculatingtherow-by-rowbispectrum. Together,thesevisibility amplitudes and closure phases would be used either to fit a model or to produce and image by deconvolution. Theseprocessesare nowstandardin opticalinterferometry — the advantageof the MODS systemis the multiplexingofdatacollection. 4. Discussionandconclusions The observations reported here have shown the feasibility of using a cylindrical lens for Extended NRM and for MODS. In these test observations, the detector scale was not optimal in that the vertical directionwasoversampled. Inprinciple,onlyoneortwo pixelsarerequiredacrosseachr -sizedstripon 0 thepupil. Oversamplingincreasesthecontributionfromreadoutnoiseand,unlikethecaseofphotonnoise, thiscannotbereducedbyrebinninginpost-processing. Thebestsolutionwouldbetouseamorepowerful cylindricallens, which wouldreducethe heightofthe pupilimage. Alternatively, the effectivepixelsize ontheCCDcouldbeincreasedbyon-chipbinning. For MODS observations, no aperture mask is used and so there is no need to form an intermediate pupilimage. Thus,anexistingspecklecameracouldbemodifiedtoperformMODSmerelybyinsertinga cylindricallensinfrontofthetelescopefocus. Thelensshouldbepositionedsoastoimagethetelescope –6– pupilontothefocalplane. Itisnothardtoshowthattheheightofthere-imagedtelescopepupilwouldbe equalthefocallengthofthecylindricallensdividedbythefocalratioofthetelescopebeam. Forexample, at the f/36 coude´ focus of the AAT, a cylindrical lens with f = 100mm would produce a pupil image 2.8mmhigh. Withsuchamodifiedspecklecamera,measurementsatdifferentpositionanglescouldbeobtainedby rotatingthecylindricallens. Unlessthedetectorwerealsorotated,thiswouldrequirethedetectedimageto bede-rotatedbeforeonecouldperformtherow-by-rowanalysisdescribedabove,butsuchrebinningshould notpresentseriousproblems. Reconstructingatwo-dimensionalimagefromthisseriesofone-dimensional measurementsisastandardprocedure,asdescribedforexamplebyBuscher&Haniff(1993). SinceMODS uses the full pupil, the number of detected photons is the same as for conventionalspeckle (neglecting any slight reflective losses from the extra lens). The advantageis a higher signal-to-noise on individual visibility and closure phase measurements, at the expenseof requiring observations at severaldifferent positionangles. How would the performance of a speckle camera be enhanced by this modification? The same numberofphotonswouldbecollected,sooneshouldnotexpectalargechangeinthelimiting magnitude. Nor would MODS bring anyimprovedresistanceto variations in the seeing. However,there would be a gain in angularresolution. This arises becausea one-dimensionalpupil givesmore weightto the longer baselines. IthasbeendemonstratedthatNRMcanresolvebinariesstarswiththeAATdowntoseparations of 15mas (Robertson et al. 1999), whereas full-aperture speckle has only given useful results with 4-m classtelescopesforseparationsaboveabout25mas. Inaddition,observationsusingMODSwouldspread thestarlight moreuniformly overthe detector,makingdetectornon-linearitiesmuchlessimportant. This isespeciallyusefulfordetectorsthatemployanimageintensifier,whicharecommoninspecklecameras, and is seen by Buscher& Haniff (1993) as the most important advantageof pupil apodizationat optical wavelengths. The main feature of MODS is that it confines the high-resolution information to one dimension, therebyincreasingthecontrastofthespecklepatternandimprovingtheSNRofthe visibility andclosure phasemeasurements. AsdiscussedbyBuscher&Haniff(1993),thisallowsmeasurementofclosurephases in regions of the bispectrumthat would otherwise be useless. The key advantageof MODS is therefore an ability to image similar objects to speckle with higher fidelity and dynamic range. Image quality is frequentlyanimportantissuein extractingsciencefromspeckleimages,sothereisclearlyapotentialfor theMODStechniquetomakeanimportantcontribution. The observationscould not have been made without the help of Gordon Robertson, Ralph Marson and John Barton. I also thank Gordon Robertson and Ralph Marson for comments on this paper. The developmentofMAPPITwassupportedbyagrantundertheCSIROCollaborativePrograminInformation Technology, and by funds from the University of Sydney Research Grants Scheme and the Australian ResearchCouncil. –7– References Aime,C.,&Roddier,F.,1977,Opt.Commun.,21,435 Beckers,J.M.,1993,ARA&A,31,13 Bedding, T. R., von der Lu¨he, O., Zijlstra, A. A., Eckart, A., & Tacconi-Garman, L. E., 1993, ESO Messenger,74,2 Bedding,T.R.,Robertson,J.G.,&Marson,R.G.,1994,A&A,290,340 Bedding,T.R.,Zijlstra, A.A.,vonderLu¨he,O.,Robertson,J.G.,Marson,R.G.,Barton,J.R.,&Carter, B.S.,1997,MNRAS,286,957 Buscher, D. F., 1988a. In: Merkle, F. (ed.), High-Resolution Imaging by Interferometry, p. 613, ESO: Garching Buscher,D.F.,1988b,MNRAS,235,1203 Buscher,D.F.,&Haniff,C.A.,1993,J.Opt.Soc.Am.A,10,1882 Buscher,D.F.,Haniff,C.A.,Baldwin,J.E.,&Warner,P.J.,1990,MNRAS,245,7P Haniff, C.A., 1994.In:Robertson,J.G., &Tango,W.J.(eds.),IAU Symposium158: VeryHigh Angular ResolutionImaging,p.317,Dordrecht: Kluwer Haniff,C.A.,Mackay,C.D.,Titterington,D.J.,Sivia,D.,Baldwin,J.E.,&Warner,P.J.,1987,Nat,328, 694 Haniff, C. A., Ghez,A. M., Gorham, P. W., Kulkarni, S. R., Matthews, K., &Neugebauer,G., 1992, AJ, 103,1662 Haniff,C.A.,Scholz,M.,&Tuthill,P.G.,1995,MNRAS,276,640 Hirshfeld,A.,&Sinnott,R.W.(eds.),1982,SkyCatalogue2000.0,CambridgeUniversityPress Klu¨ckers,V.A.,Edmunds,M.G.,Morris,R.H.,&Wooder,N.,1997,MNRAS,284,711 Kulkarni, S. R., 1988. In: Merkle, F. (ed.), High-Resolution Imaging by Interferometry, p. 595, ESO: Garching Labeyrie,A.,1978,ARA&A,16,77 Nakajima, T., Kulkarni, S.R., Gorham, P. W., Ghez, A. M., Neugebauer,G., Oke, J. B., Prince, T. A., & Readhead,A.C.S.,1989,AJ,97,1510 Negrete-Regagnon,P.,1996,J.Opt.Soc.Am.A,13,1557 Robertson,J.G.,Bedding,T.R.,Aerts,C.,Waelkens,C.,Marson,R.G.,&Barton,J.R.,1999,MNRAS, 302,245 Tuthill,P.G.,Haniff,C.A.,&Baldwin,J.E.,1997,MNRAS,285,529 Weigelt,G.,1991.In:Wolf,E.(ed.),ProgressinOptics,p.295,Vol.XXIX,North-Holland: Amsterdam Weigelt,G.,Balega,Y.,Hofmann,K.-H.,&Scholz,M.,1996,A&A,316,L21 Wilson,R.W.,Baldwin,J.E.,Buscher,D.F.,&Warner,P.J.,1992,MNRAS,257,369 –8– focal collimator pupil camera plane lens mask lens cylindrical lens TOP VIEW image plane telescope pupil focus plane SIDE VIEW pupil plane Fig. 1.—ExtendedNRMusingmultipleholearraysandacylindricallens. Fig. 2.—ExtendedNRMobservationofthestarCanopus. Left: theapproximateorientationofthemaskand AATpupil(notethattheoutertwoholesinthebottomarrayarenotilluminated). Centre: asingle2-second exposure. Right: the row-by-row power spectrum, with spots corresponding to the spatial frequencies sampledbythemask. –9– Fig. 3.—MODS observationof the star β Cen. Left: the approximatepupilorientation. Centre: a single 0.2-secondexposure. Right: therow-by-rowpowerspectrumaveragedovertensuchexposures. Fig. 4.— MODS observation a double star (γ Cen). Left: the row-by-row power spectrum of a single 0.2-secondexposure. Right: thesame,excepttheimagewasbinnedeightrowsatatimebeforecalculating thepowerspectrum.