New methods for masked-aperture and speckle interferometry

9 Pages·0.09 MB·English

by  Timothy R. Bedding

ToappearinPASP(May1999issue)
New methods formasked-aperture and speckle interferometry
TimothyR.Bedding
SchoolofPhysics,UniversityofSydney2006,Australia
E-mail: [email protected]
ABSTRACT
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1 Diffraction-limited images can be obtained with a large optical telescope using

n interferometry. Onesuchmethodforobjectsofsufficientbrightnessisnon-redundantmasking
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(NRM), in whichobservationsaremadethroughapupilmaskthatcontainsanarrayofsmall
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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,
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2 the mask canbe removedentirely, with the cylindricallenseffectivelycreating a continuous
2 series of one-dimensional interferograms. This modified form of speckle interferometry,
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which IcallMODS (Multiplexed One-DimensionalSpeckle), is intermediatebetweenNRM
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9 and conventionalfull-aperture speckle. An existing speckle camera can easily be converted
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to MODS observations by inserting a cylindrical lens. The feasibility of both MODS and
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ExtendedNRM are demonstratedusing observationswith MAPPIT at the Anglo-Australian
p
- Telescope.
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Subjectheadings: Instrumentation: interferometers–Techniques: interferometric
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r 1. Introduction
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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
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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
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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.
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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
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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
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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
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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
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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.
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–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.