Ground-based astrometry with wide field imagers. V. Application to near-infrared detectors: HAWK-I@VLT/ESO

3.6 MB·

by  M. Libralato

Astronomy&Astrophysicsmanuscriptno.ms c ESO2014
(cid:13)
January16,2014
Ground-based astrometry with wide field imagers
⋆
V. Application to near-infrared detectors: HAWK-I@VLT/ESO
M.Libralato1,2,3,⋆⋆,A.Bellini2,L.R.Bedin3,G.Piotto1,3,I.Platais4,M.Kissler-Patig5,6,A.P.Milone7
1 DipartimentodiFisicaeAstronomia,Universita`diPadova,Vicolodell’Osservatorio3,Padova,I-35122,Italy
e-mail:[email protected];[email protected]
2 SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD-21218,USA
e-mail:[email protected]
4 3 INAF-OsservatorioAstronomicodiPadova,Vicolodell’Osservatorio5,Padova,I-35122,Italy
1 e-mail:[email protected]
0 4 DepartmentofPhysicsandAstronomy,TheJohnsHopkinsUniversity,Baltimore,MD-21218,USA
2 e-mail:[email protected]
5 GeminiObservatory,N.AohokuPlace670,Hilo,Hawaii,96720,USA
n
e-mail:[email protected]
a 6 EuropeanSouthernObservatory,Karl-Schwarzschild-Str.2,Garchingb.Mu¨nchen,D-85748,Germany
J
7 ResearchSchoolofAstronomyandAstrophysics,TheAustralianNationalUniversity,CotterRoad,Weston,ACT,2611,Australia
4 e-mail:[email protected]
1
Received11June2013/Accepted18December2013

]
M
ABSTRACT
I
. High-precisionastrometryrequiresaccuratepoint-spreadfunctionmodelingandaccurategeometric-distortioncorrections.Thispaper
h
demonstratesthatitispossibletoachievebothrequirementswithdatacollectedatthehighacuitywide-fieldK-bandimager(HAWK-
p
I),awide-fieldimagerinstalledattheNasmythfocusofUT4/VLTESO8mtelescope.Ourfinalastrometricprecisionreaches 3mas
- ∼
percoordinateforawell-exposedstarinasingleimagewithasystematicerrorlessthan0.1mas.Weconstructedcalibratedastro-
o
photometriccatalogsandatlasesofsevenfields:theBaade’sWindow,NGC6656,NGC6121,NGC6822,NGC6388,NGC104,and
r
t theJamesWebbSpaceTelescopecalibrationfieldintheLargeMagellanicCloud.Wemakethesecatalogsandimageselectronically
s
availabletothecommunity.Furthermore,asademonstrationoftheefficacyofourapproach,wecombinedarchivalmaterialtaken
a
[ with the optical wide-field imager at the MPI/ESO 2.2m with HAWK-I observations. We showed that we are able to achieve an
excellentseparationbetweenclustermembersandfieldobjectsforNGC6656andNGC6121withatimebase-lineofabout8years.

1 UsingbothHSTandHAWK-Idata,wealsostudytheradialdistributionoftheSGBpopulationsinNGC6656andconcludethatthe
v radialtrendisflatwithinouruncertainty.WealsoprovidemembershipprobabilitiesformostofthestarsinNGC6656andNGC6121
4 catalogsandestimatemembershipforthepublishedvariablestarsinthesetwofields.
4
3 Keywords.Instrument:InfraredDetectors–Techniques:GeometricDistortionCorrection–Astrometry–Photometry–Globular
Cluster:NGC104,NGC6121,NGC6388,NGC6656–Galaxy:Bulge–NGC6822–LMC
3
.
1
0
1. Introduction the majoroperativewide-fieldimagerson 3m+ telescopes(we
4
1 [email protected]/ESOasreference).
Multiple fields within astronomy are driving the execution
:
v of larger and yet larger surveys of the sky. Over the last two In addition, two wide-field imagers mounted on 1m tele-
i decades, this scientific need has stimulated the construction scopes should be mentioned. The LaSilla-QUEST Variability
X
of instruments equipped with mosaics of large-format digi- surveyisaprojectthatusestheESO1.0-mSchmidtTelescopeat
r
a tal detectors for wide-field imaging at both the optical and theLaSillaObservatoryoftheEuropeanSouthernObservatory
near-infrared (NIR) wavelengths. The most recent generation inChilewiththenewlargeareaQUESTcamera.Itisamosaic
of these wide-field imagers now competes with the older of 112 600 2400 pixels CCDs covering a field of view of
×
technology of Schmidt telescope and photographic plates in about 4◦.6 3◦.6. The camera, commissioned in early 2009 has
×
termsofnumberofresolutionelementsonskybutdoessowith been built at the Yale and Indiana University.La Silla-QUEST
order-of-magnitudegreatersensitivityandefficiency. surveyisexpectedtocoverabout1000squaredegreespernight
Alistofsomewidely-usedwide-fieldimagerswasgivenby repeatedwitha2-daycadence(Hadjiyskaetal.2012).
Andersonet al. (2006,hereafterPaper I). Since then, however,
The Panoramic Survey Telescope and Rapid Response
many wide-field imagers have been upgraded or decommis-
System (Pan-STARRS) also is of great interest for the astro-
sioned,andadditionalnewwide-fieldimagershavebeguntheir
nomical community. The Pan-STARRS survey will cover the
operations.Inthetop-halfofTable1, weprovidea brieflistof
skyusingwide-fieldfacilitiesandprovideastrometricandpho-
tometric data for all observed objects. The first Pan-STARRS
⋆ Basedonobservationswiththe8mVLTESOtelescope. telescope,PS1, is locatedatthe summitof HaleakalaonMaui,
⋆⋆ VisitingPh.D.StudentatSTScIunderthe2013DDRFprogram. Hawaii and began full time science observations on May 13,
1
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Table 1. List of the major operative wide-field imagers on 3m + telescopes. The [email protected] MPI/ESO has been included as
reference.
Name Telescope Detectors PixelScale[ /pixel] FoV
′′
OPTICALREGIME
WFI 2.2mMPI/ESO 8 (2048 4096) 0.238 34 33
′ ′
× × ×
PrimeFocusCamera WilliamHerschelTelescope 2 (2048 4100) 0.24 16.2 16.2
′ ′
× × ×
LBC(blueandred) LBT 4 (2048 4608) 0.23 23 23
′ ′
× × ×
Suprime-Cam SubaruTelescope 10 (2048 4096) 0.202 34 27
′ ′
× × ×
MOSA KPNOMayall4m 8 (2048 4096) 0.26 36 36
′ ′
× × ×
LAICA CalarAlto3.5mTelescope 4 (4096 4096) 0.225 44.36 44.36
′ ′
× × ×
MegaCam CFHT 36 (2048 4612) 0.187 57.6 56.4
′ ′
× × ×
OmegaCam VST 32 (2048 4102) 0.21 60 60
′ ′
DECam CTIOBlanco4m 62 (2048 4×096)+1×2 (2048 2048) 0.27 132×132
′ ′
× × × × ×
NIRREGIME
GSAOI Gemini 4 (2048 2048) 0.02 1.42 1.42
′ ′
× × ×
HAWK-I VLT 4 (2048 2048) 0.106 7.5 7.5
′ ′
× × ×
ISPI CTIOBlanco4m 1 (2048 2048) 0.3 10.25 10.25
′ ′
× × ×
FourStar Magellan 4 (2048 2048) 0.159 10.8 10.8
′ ′
× × ×
WFCAM UKIRT 4 (2048 2048) 0.4 12.6 12.6
′ ′
× × ×
Omega2000 CalarAlto3.5mTelescope 4 (2048 2048) 0.45 15.4 15.4
′ ′
× × ×
WIRCAM CFHT 4 (2048 2048) 0.3 20.5 20.5
′ ′
× × ×
NEWFIRM CTIOBlanco4m 4 (2048 2048) 0.4 27.6 27.6
′ ′
× × ×
VIRCAM VISTA 16 (2048 2048) 0.339 35.4 35.4
′ ′
× × ×
2010 (Kaiser et al., 2010). With its 1.8m primary mirror, it The VVV is monitoringthe Bulge and the Disk of the Galaxy.
coversaFoVof 7squaredegrees. The survey will map 562 square degrees over 5 years (2010-
Amongwide∼-fieldimagersplannedforthefuture,theLSST1 2014) and give NIR photometry in Z, Y, J, H, and K bands.
S
(LargeSynopticSurveyTelescope)representsthe mostsignifi- ThefirstdatasetoftheVVVprojecthasalreadybeenreleased
cantstepforwardforwide-fieldimagersinmodernastrophysics. tothecommunity(Saitoetal.2012).Itcontains348individual
Itwillbea8.4mwide-fieldground-basedtelescopewithaFoV pointings of the Bulge and the Disk, taken in 2010 with 108
∼
of about9.6 square degrees. With its 189 4k 4kCCDs, it will stars observed in all filters. Typically, the declared astrometric
×
observe over 20000 square degrees of the southern sky in six precisionsvaryfrom 25masforastarwith K = 15,to 175
S
∼ ∼
optical bands. Construction operations should begin in 2014; masforastarwithK =18mag.
S
thesurveywillbetakenin2021. Ground-based telescopes are not alone in focusing their
While a greatnumberofpapershavepresentedphotometry attention on this kind of detector. The James Webb Space
obtained with these facilities over the last decade, their astro- Telescope (JWST) will be a 6.5-meter space telescope opti-
metric potentialhas remained largelyunexploited.Our team is mized for the infrared regime. It will orbit around the Earth’s
committedin pushingthe astrometriccapabilities of wide-field second Lagrange point (L2), and it will provide imaging and
imagers to their limits. Therefore, we have begun to publish spectroscopic data. The wide-field imager, NIRCam, will be
in this Journal a series of papers on Ground-based astrometry madeupbyashort-(0.6–2.3µm)andalong-wavelength(2.4
with wide field imagers. In Paper I, we developed and applied –5.0µm)channelwithaFoVof2.2 4.4each.
′ ′
our tools to data collected with the [email protected] MPI/ESO ×
In this paper, we explore the astrometric performance of
telescope. The techniquesused in Paper II (Yadav et al. 2008)
the HAWK-I@VLT facility and provide astrometric catalogs
and Paper III (Bellini et al. 2009) produced astro-photometric
(together with stacked images) of seven dense stellar fields
catalogsandpropermotionsoftheopenclusterM67andofthe
along with the tools required to correct any observed field for
globularclusterNGC5139,respectively.InPaperIV (Bellini&
geometricdistortion.We adopttheUCAC4catalog(Zacharias
Bedin2010),weappliedthetechniquetothewide-fieldcamera
et al. 2013) as a reference frame to determine the linear terms
onthebluefocusoftheLBC@LBT2 8.4m.
× ofthedistortionandtoputalltheobjectsinontheInternational
In this paper, we turn our attention to wide-field imagers
CelestialReferenceSystembutattheepochofourobservations.
equipped with NIR detectors. Indeed, the pioneering work of
2MASS has shown the great potential of these instruments The paper is organized as follows: In Sect 2, we briefly
(Skrutskie et al. 2006). The number and the quality of NIR describe the instrument. Section 3 presents the observations.
detectors has improved considerably since then. New genera- Section 4 describes the tools developed to extract the position
tions of 2k 2k arrays are now mounted at the foci of various and flux of the sources. In Sect. 5, we derive our geometric-
telescopes(×bottom-halfofTable1). distortion solution. In Sect. 6, we discuss the periodic feature
These wide-field imagers enable wide surveys, such as the of the residual highlighted during the geometric-distortion
VISTA variables in the Via Lactea (VVV, Minniti et al 2010). correction and give a possible explanation. Sections 7 and 8
describe how we removed the point-spread function (PSF)
1 http://www.lsst.org/lsst/. artifacts from the catalogs and the photometric calibration,
2
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Fig.2. Outline of the relative positions of pointings in our
adopteddither-patternstrategy.The25imagesareorganizedin
a5 5array,wherethecenterofthefieldfallsinthecentralposi-
×
tion13.Theotherpointingsaretakeninawaythatthegapsbe-
Fig.1.HAWK-Ilayout.Thelabelsgivethedimensionsinarcsec tweenthefourdetectorsnevercoverthesamepointofskymore
andarcmin(andinpixels)ofthefourdetectorsandofthegaps. than once. The 25 images were designed for astrometric pur-
Numbersinsquarebracketslabelthechipdenominationusedin posesallowingstarsinframe13tobeimagedinasmanydiffer-
thiswork(notethatthechoiceisdifferentfromthatofFig.9of entlocationsofthedetectorsaspossible.Thisenablesustoself-
Kissler-Patig etal. 2008).In eachchip,we indicatethe coordi- calibratethegeometricdistortion.Thezoom-ininthebluepanel
nate of the chip center. This is also the reference position that showsanexampleoftheadoptedditherbetweentwopointings.
we used while computing the polynomial correction described AsdescribedinTable2,the shiftstepcanchangefromfield to
in Sect. 5.1. The black cross in the middle showsthe center of field.
thefieldofviewinasingleexposurethatweusedinFig.2.
3. Observations
InTable2weprovideadetailedlistoftheobservations.
respectively.Section9showssomepossibleapplicationsofour
All of the HAWK-I images used here were collected
calibrations. Finally, we describe the catalogs that we release
during the instrument commissioning, when several fields
withthispaperinSect.10.
were observed with the aim of determining an average optical
geometric-distortion solution for HAWK-I and for monitoring
itsstabilityintheshort-andmid-term.
2. HAWK-I@VLT Tothisend,thefieldswereobservedwithanobservingstrat-
egythatwouldenableaself-calibrationofthedistortion.Briefly,
AnexhaustivedescriptionofHAWK-IisgiveninKissler-Patig
the strategy consists of observing a given patch of sky in as
etal.(2008).Here,weonlyprovideabriefsummary.
manydifferentpartsofthedetectorsaspossible.Eachobserving
TheHAWK-Ifocalplaneisequippedwithamosaicoffour block(OB)isorganizedinarunof25consecutiveimages.The
2048 2048pixelsRockwellHgCdTeMolecularBeam Epitaxy exposuretime for each imagewas the integrationtime (DIT in
×
HAWAII-2RGarrays.Thepixel-scale(Kissler-Patigetal.2008) s)timesthenumberofindividualintegrations(NDIT).Figure2
is about 106 mas pixel−1, resulting in a total FoV of about showstheoutlineoftheadopteddither-patternstrategy2.
7.′5 7.′5(withgapsof 15′′ betweenthedetectors).Asketched Importantby-productsofthiseffortareastrometricstandard
× ∼
outlineoftheHAWK-IFoVlayoutisshowninFig.1.Thedetec- fields(i.e., catalogs of distortion-freepositionsof stars), which
torsandthefilterwheelunitareconnectedtothesecondstageof inprinciplecouldbepointedbyHAWK-Ianytimeinthefuture
theClosedCycleCoolerandoperatedatatemperaturecloseto to efficiently assess whether the distortion has varied and by
75–80K.Theremainingpartsoftheinstrumentarecooledtoa howmuch.Furthermore,theseastrometricstandardfieldsmight
temperaturebelow140K.Theacquisitionsystemisbasedonthe serve to calibrate the geometric distortions of many other
IRACE system (InfraredArray Control Electronics) developed camerasonothertelescopes(includingthoseequippedwithAO,
atESO.HAWK-Ialsois designedtoworkwith a ground-layer MCAO,orthosespace-based).However,theutilityofourfields
adaptiveopticsmodule(GRAAL)aspartoftheAdaptiveOptics deteriorateovertimesinceapropermotionestimateforstarsin
Facility (Arsenault et al. 2006) for the VLT (scheduled to be
installedinthesecondhalfof2014).HAWK-Ibroadbandfilters 2 Notethatthisstrategyhadbeenmodifiedforsomefields.Wespec-
followtheMaunaKeaObservatoryspecification. ifythesechanges,whennecessary,inthefollowingsubsections.
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Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Table 2. List of the HAWK-I@VLT data set used for this work. N is the number of dithered images per observing block.
dither
“Step” is the dither spacing (shift in arcsec from one exposureto the nextone). The integrationtime (DIT) times the numberof
individualintegrations(NDIT)givestheexposuretime.σ(Radialresidual)givesanassessmentoftheastrometricaccuracyreached
(seeSect.5.5forthefulldescription).
Filter N Step ExposureTime Image-quality Airmass σ(Radialresidual)
dither
(arcsec) (NDIT DIT) (arcsec) (secz) (mas)
×
Commissioning1,August3-6,2007
Bulge—Baade’sWindow(#1)
J 25 95 (6 10s) 0.56-1.07 1.038-1.085 4.5
×
H 25 95 (6 10s) 0.40-0.76 1.081-1.149 4.3
×
K 25 95 (6 10s) 0.25-0.45 1.042-1.091 2.8
S ×
Bulge—Baade’sWindow(Rotatedby135 )(#2)
◦
K 25 95 (6 10s) 0.49-0.85 1.015-1.044 5.6
S ×
NGC6121(M4)
J 4 25 95 (6 10s) 0.36-1.04 1.010-1.540 6.5
× ×
K 5 140 (6 10s) 0.40-0.51 1.050-1.056 3.8
S ×
NGC6822
J 9 190 (12 10s) 0.61-0.83 1.028-1.049 5.3
×
K 9 190 (12 10s) 0.43-0.75 1.050-1.082 4.8
S ×
Commissioning2,October14-19,2007
NGC6656(M22)
K 25 47.5 (6 10s) 0.28-0.41 1.252-1.420 3.1
S ×
NGC6388
J 25 95 (6 10s) 0.64-0.94 1.287-1.428 9.7
×
K 25 95 (6 10s) 0.50-0.75 1.436-1.637 12.2
S ×
JWSTcalibrationfield(LMC)
J 25 95 (6 10s) 0.51-0.65 1.408-1.412 5.3
×
K 24 95 (6 10s) 0.45-0.60 1.411-1.429 4.8
S ×
Commissioning3,November28-30,2007
NGC104(47Tuc)
J 25 47.5 (6 10s) 0.51-0.82 1.475-1.479 7.1
×
K 23 47.5 (6 10s) 0.54-1.01 1.475-1.483 15.0
S ×
ourcatalogsisonlyprovidedforthosestarsthatareincommon the saturation threshold. Second, the large-scale semi-periodic
withUCAC4catalog.Inthispaper,wemaketheseastrometric andcorrelatedatmosphericnoise(withestimatedscalelengthat
standardfieldsavailabletothecommunity. 3-5)notedbyPlataisetal.(2002,2006)essentiallydisappears
′
∼
atexposuresexceeding30s.Thus,60swasagoodcompromise
of integration time. According to the formula developed by
3.1.TheBaade’sWindowastrometricfield Lindegren (1980) and Han (1989), a standard deviation due to
atmospheric noise on the order of 15 mas is expected over the
The first selected astrometric field is located in Baade’s
angularextentofHAWK-IFoV.Thiscertainlyisanupperlimit
Window. Our field is centered on coordinates (α,δ)
J2000.0 of the actual standard deviation because the seeing conditions
(18h03m10.s4, 29 5648.4). Most of this field has a smooth∼,
◦ ′ ′′ of our NIR observationswere 2-3 times better than those con-
−
uniform distribution of Galactic Bulge stars. Stars just below
sideredbytheaforementionedauthorsforvisualwavelengths.
saturation in a 60s K exposure are typically separated by a
S
few arcseconds, so that there are many of them in each field. The images were taken close to the zenith in an effort to
Ingeneral,however,theyaresufficientlyisolatedtoallowusto minimize differential refraction effects, which plague ground-
computeaccuratepositions. based images (and consequently affect the estimate of the
low-ordertermsofthedistortionsolution).
The choice of a cumulative integration time of 60s was
driven by two considerations. First, we wanted to have the TheBaade’sWindowfieldisthemainfieldweusetoderive
upper main sequence in a CMD of all chosen targets to be the geometric-distortion solution that is tested for stability
optimally exposed with low-luminosity RGB stars still below –or refined– with the other fields. In Sect. 5, we derive the
4
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Fig.3.(FromLefttoRight):TheFirstPanelisadepth-of-coveragemapof25K HAWK-I’simagescollectedinBaade’sWindow
S
duringtherunofAugust3-6,2007.Thegray-scalegoeslinearlyfrom1to25.Thegreenboxisthe7.5 7.5patchofskywithin
′ ′
×
which there are always at least five images. The Second Panel shows the resulting stack of the 25 images. The dark spot on the
top-rightisthesignatureleftbythe“shadow”oftheprobe,whichpick-upthestarusedforthesimultaneousActiveOpticcorrection
of the VLT/UT4’s primary mirror. On the bottom-left, there is the globular cluster NGC 6522. Note that neither the dark spot
nor NGC 6522are inside the regionenclosedby the greenbox. The Third Panel focuseson the green regionand showsthat the
distributionofstarsinthisfieldisremarkablyhomogeneous.TheFourthPanelisazoom-inofarepresentativesub-setofthefield
(indicatedbythe10 10 redboxinallpanels),whichisabletoshowabetterresolvedimage.
′′ ′′
×
geometric-distortion solution in this field for each of the three These data were impacted by an internal reflection of the
available filters, J, H and K , using 25 images dithered with a Moon in the optics, causing an abnormally-high sky value on
S
step of about 95 . In addition to this, we also collected 25 K the rightmost 300 pixels of the detector. In spite of this, the
′′ S
images of the same field but with the de-rotator at a position exquisite image quality of these data makes them among the
of135 clockwise.Weusedthisfieldtoperformacheckofthe bestinourdatabase.Weusedthisfieldtotestthesolutionofthe
◦
distortionwithdifferentangles(seeSect.5.8). geometricdistortion(seeSect.5.7fordetail).
In Fig. 3, we show a summary of one of these observing
runs in filter K from left to right: the overlap of the different
S 3.2.2. NGC6121(M4)
pointings, the stacked image, a zoom-in of the region actually
usedtocalibratethegeometricdistortion(theregionhighlighted ThethirdfieldiscenteredonglobularclusterNGC6121(M4),
in green), and a further zoom-in at a resolution able to reveal (α,δ) = (16h23m35.s22, 26 3132.7, Harris 1996, 2010
J2000.0 ◦ ′ ′′
−
individualpixels(regionindicatedinredintheotherpanels). edition).ItistheclosestglobularclustertotheSun,anditsrich
starfieldhasasmallangulardistancefromtheGalacticBulge.
The observingstrategy for the J-filter is similar to that de-
3.2.Thestar-clusterastrometricfields scribedbefore.EachOBisorganizedinarunof25consecutive
exposures and the the same block was repeated four times in
The tangential internal motions of Bulge stars is on average fourdifferentnights,shiftingthegridbyfewarcseceachtime.
100 km s 1, and assuming an average distance of 8 kpc, this
− ThisfieldwasalsoobservedintheK -filterbutwithadither
yields a proper motion dispersion of 3 mas yr−1 (see, for patterncompletelydifferentfromtheothSers.Thereareonlyfive
∼
example,Bedinetal.2003).Injustafewyears,propermotions
exposuresditheredwithstepsof100 ,whicharetakenwiththe
′′
this large can mask out systematic distortion trends that have
purposeofestimatingstars’color.
amplitudesbelowthe3-mas-yr 1 level(suchasthosediscussed
−
in Sect. 5.2). It is therefore important in some applications to
havemorestableastrometricfields. 3.2.3. NGC6388
For this reason, we also observed four globular clusters. NGC6388isaglobularclusterlocatedintheGalacticBulgeat
Starsgravitationallyboundinglobularclustershaveaninternal (α,δ) = (17h36m17s.23, 44o4407 .8)(Harris1996,2010
J2000.0 ′ ′′
velocity dispersion .20 km s−1 in their cores and are even edition).Someexposuresof t−hisfield showthe same darkspot
smallerin theiroutskirts.Althoughthesystemic motionofstar duetotheprobeasintheBaade’swindow(seeFig.3).
clustersisusuallydifferentto(andlargerthan)theGalacticfield
dispersion,theircommonrest-framemotionsaregenerallymore
than 10 times smaller than the internalmotions of Bulge stars, 3.2.4. NGC104(47Tuc)
so clusters members can be expected to serve as astrometric
The last globular cluster observed during the HAWK-I
standardswithmuchsmallerinternalpropermotions.
commissioning is NGC 104 (47Tuc), (α,δ) =
J2000.0
(00h22m05.s67, 72 0452.6) (Harris 1996, 2010 edition).
◦ ′ ′′
−
Twoofthe25pointingsoftheK -filterdatawerenotusable.
3.2.1. NGC6656(M22) S
The second field was centered on the globular cluster
3.3.TheExtra-Galacticastrometricfields
NGC 6656 (M 22). At a distance of about 3.2 kpc, M 22
(α,δ) = (18h36m23.s94, 23 5417.1, Harris 1996, 2010 Extra-galactic fields are more stable than Galactic fields, since
J2000.0 ◦ ′ ′′
−
edition)isoneoftheclosestglobularclusterstotheSun. their internal proper motions are negligible compared to fore-
5
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
groundstars, evenwitha10-yrtimebaseline.Thedownsideof to compute the sky value in a given location). After the sky
such extra-galacticfieldsis the need to increase the integration subtraction, we split each multi-extension FITS file in four
timetocompensateforthefaintnessofthetargets. differentFITSfiles,oneperchip.Thenextstepwastocompute
thePSFmodels.
HAWK-I’s PSF is always well sampled, even in the best-
3.3.1. NGC6822
seeing condition. To compute PSF models, we developed the
The first extra-galactic field is centered on the Local Group software img2psf HAWKI in which our PSF models are com-
dwarf irregular galaxy NGC 6822 at a distance of 500 kpc [email protected]
(Madoreetal.2009). ∼ package(PaperI).Theyarerepresentedbyanarrayof201 201
×
For this galaxy,we tookfewer pointings(9 in a 3 3array) gridpoints,whichsuper-samplePSFpixelsbyafactorof4with
butwith alongerintegrationtime.Adoptingthesame×numbers respect to the image pixels. The fraction of flux contained in
asinFig.2,weonlyusedditherslabeled1,3,5,11,13,15,21, the central pixel of a star is given by the central PSF pixel. A
23, and 25.The integrationtime was 120s with NDIT=12and bi-cubicsplineisusedtointerpolatethevalueofthePSFinbe-
DIT=10s. tweenthegridpoints.ThevalueofagivenpixelPi,jinthevicin-
ityofastaroftotalfluxz thatislocatedatposition(x ,y )is:
∗ ∗ ∗
3.3.2. AnastrometricfieldforJWSTinLMC P =z ψ(i x ,i y )+s ,
i,j
∗· − ∗ − ∗ ∗
In 2005, a field near the center of the Large Magellanic Cloud
whereψ(∆x,∆y)istheinstrumentalPSF,orspecifically,the
(LMC)wasselectedasreferencefieldtosolveforthegeometric
fractionoflight(perunitpixelarea)thatfallsonthedetectorat
distortionandto eventuallyhelp calibratethe relativepositions a point offset (∆x,∆y) = (i x , j y ) from the star’s center,
of JWST’s instruments in the focal plane. This field is in the and s is the local sky bac−kgr∗oun−d v∗alue. For each star, we
JWST continuous viewing zone and it can be observed when- have a∗n array of pixels that we can fit to solve for the triplet
ever necessary. In 2006, it was observed with the Advanced
of parameters: x , y , and z . The local sky s is calculated as
CameraforSurveys(ACS)WideFieldChannel(WFC)tocreate the 2.5σ-clipped∗me∗dian of∗the counts in the∗annulus between
areferencecataloginF606W.
16and20pixelsfromthelocationwherethestar’scenterfalls.
The JWST calibration field is centered at (α,δ) =
J2000.0 The previousequation can be inverted(with an estimate of the
(5h21m55.s87, 69o2947.05).Thedistortion-correctedstarcata-
′ ′′ positionandfluxforastar)tosolveforthePSF:
−
logweprovideinthispapercanbeusedasdistortion-freeframe
to compute the geometric distortion of the JWST’s detectors P s
i,j
whenthe time comes. We adoptedthe same observingstrategy ψ(∆x,∆y)= − ∗ .
z
asabovewith25imagesorganizedina5 5array.Unfortunately, ∗
oneofthepointingsintheK -filterdata×setwasnotusable. This equation uses each pixel in a star’s image to provide
S
an estimate of the 2-dimensional PSF at the location of that
pixel,(∆x,∆y).Bycombiningthearrayofsamplingfrommany
4. PSF-modeling,fluxesandpositioning stars,wecanconstructareliablePSFmodel.Asopposedtothe
pioneering work of Stetson and his DAOPHOT code (Stetson
Inourreductions,weusedthecustom-madesoftwaretools.Itis
1987) that combines an empiric and semi-analytic PSF model,
essentiallythesamesoftwareusedinthepreviouspapersofthis
wecreatedafully-empiricalPSFmodel,asdescribedinPaperI.
series.Westartedfromarawmulti-extensionFITSimage.Each
The software img2psf HAWKI iterates to improve both
multi-extensionFITSimagestoresallfourchipsina datacube.
the PSF model and stellar parameters. The starting point is
WekeptthisFITSformatuptothesky-subtractionphase.
givenbysimplecentroidpositionsandaperture-basedfluxes.A
First, we performed a standard flat-field correction3 on all
descriptionofthesoftwareisgivenindetailinPaperI.
the images. In the master flat fields, we built a bad-pixelmask
To model the PSFs in both the core and the wings, we use
by flagging all the outliers respect to the average counts. We
only stars with a high S/N (signal-to-noiseratio). This is done
used the bad-pixel-mask table to flag warm/cold/dead pixels
bycreatingalistofstarsthathaveafluxofatleast5000counts
in each exposure. Cosmic rays were corrected by taking the
above the local sky (i.e., S/N>60-70 in the central pixel) and
averagevalue of the surroundingpixels if they were notinside
also have no brighter neighbors within 15 pixels. We need at
a star’s region4; bad columns were replaced by the average
least50suchstarsforeachPSFmodel,sothatwecaniteratively
betweenthepreviousandfollowingcolumns.
reject stars that may be compromised by nearby neighbors,
Digital saturation in our images starts at 32768 counts.
cosmicrays,ordetectordefects(e.g.,bleedingcolumns).
To be safe, we adopted a saturation limit of 30000 counts
DeterminingbothagoodmodelforthePSFanddetermining
to minimize deviations from linearity close to the saturation
stellar positionsandfluxesrequiresan iterativesolution,so the
regime (accordingly to Kissler-Patig et al. 2008) and flat-field
softwareiteratesthisprocessseveraltimesuntilconvergenceis
effects. Each pixel for which the counts exceed the saturation
reachedwithbothgoodPSFmodelsandstellarparametersthat
limitwasflaggedandnotused.
fit well. The result is a 5 5 grid of PSF models for each chip,
Finally, we subtracted the sky from the images, computing ×
whicharebi-linearlyinterpolatedtoprovideamodelPSFatany
the median sky value in a 10 10 grid and then subtracting the
× pixelposition.
sky according to the table (bi-linear interpolation was used
WithanarrayofPSFmodels,weareabletomeasurestars’
positionsandfluxesforallthestarsintheimagebyusingasoft-
3 The correction was performed using a single master flat field for
ware analog to that described in Paper I. As an input, we need
eachofthethreefilters.Wedidnotuseaflatfieldtailoredtoeachepoch
becausesomeofthemwerenotcollected. togivethefaintestlevelabovetheskyforastartobefoundand
4 Cosmic rays close to the star’s center increase the apparent flux determinehowclosethisstarcanbetobrighterneighbors.The
and shift the center of the star, resulting in a large QFIT value (see programfinds and measuresall stars that fit these criteria. The
AppendixAfordetail). finalcatalogs(oneforeachchip)containpositions,instrumental
6
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
magnitudes, and another quantity called quality-of-PSF-fit 5.1.Polynomialcorrection(P)
(QFIT,whichrepresentsthefractionalerrorinthePSF-modelfit
We followedthe methodgivenin Anderson& King (2003)for
tothestar).Foreachpixelofastarwithinthefittingradius(2.5
the Wide-Field Planetary Camera 2 (WFPC2). This method
pixels),theQFITisdefinedasthesumoftheabsolutevalueof
thedifferencebetweenthepixelvaluesP (skysubtracted)and was subsequently used to derive the distortion correction for
i,j
the ACS High Resolution Channel (Anderson & King 2004)
whatthelocalPSFmodelpredictsatthatlocationψ(i x , j y ),
normalizedwithrespecttothesky-subtractedP : − ∗ − ∗ and for the Wide Field Camera 3 (WFC3) Ultraviolet-Visual
i,j
(UVIS) channel (Bellini & Bedin 2009; Bellini, Anderson &
Bedin 2011).The same strategy was also used by two of us to
(Pi,j sky) z ψ(i x , j y ) calibrate the blue prime-focus camera at the LBT (Paper IV).
QFIT= − −P ∗· sky− ∗ − ∗ , Wetreatedeachchipindependently,andwesolvedthe5th-order
Xi,j (cid:12)(cid:12) i,j− (cid:12)(cid:12) polynomial that provided the most correction. We chose pixel
(cid:12) (cid:12)
where(x ,y ) isthe(cid:12)(cid:12)(cid:12)star’s center.The QFITis closeto(cid:12)(cid:12)(cid:12) zerofor (1024,1024)ineachchipasareferencepositionandsolvedfor
well-mea∗sur∗ed stars and close to unity for ones that are badly- thedistortionwithrespecttoit.
measured(ornotstar-like).TypicallywefoundQFIT.0.05for Thepolynomialcorrectionisperformedasfollows:
well-measuredstarsinourimages.Saturatedstarsarealsomea-
suredinourpipeline.Forthese,starsweonlyfittedthePSFon – Ineachofthelistofunsaturatedstarsfoundineachchipof
the wingsof the stars usingunsaturatedpixels. In thisway, we each exposure(4 25 lists), we first selected stars with an
×
areabletomeasureafluxandapositionforsaturatedstars,even instrumentalmagnitudebrighterthan K 11and with a
S
≃ −
iftheyarelessaccurate(highQFIT)thanforunsaturatedstars. QFIT lower than 0.05, to ensure that the master list would
be free from poorly measured stars, which would harm the
distortionsolution.
5. Geometricdistortioncorrection
– We computedthe linear transformation(T ) between stars
j,k
ineachchipofeachexposureandthecurrentmasterframe.
In this section, we present a geometric-distortion solution for
– Eachstar inthemasterframewasconformallytransformed
the HAWK-Iin threebroadbandfilters(J, H, and K ) derived
S in the raw-coordinatesystem of each chip/image(T 1) and
using exposures of the Baade’s Window field. No astrometric j−,k
referencedataisavailablefortheBaade’sWindowfield,so we cross-identified with the closest source. Each such cross-
iterativelyconstructedourown. identificationgeneratesapairofpositionalresiduals(δx,δy),
Adopting the observing strategy described in Sect. 3, the whichcorrespondtothedifferencebetweentheobservedpo-
systematic errors in the measure of stars’ positions from one sitionandthetransformedreference-frameposition.
exposure to the other have a random amplitude and the stars’ – These positional residuals were distilled into a look-up ta-
averagedpositions providea better approximationof their true blemadeupof12 12elementsof170.7 170.7pixelseach.
× ×
positionsinthedistortion-freemasterframe. This setup proved to be the best compromise between the
To build the master frame, we cross-identified the star needofanadequatenumberofgridpointstomodelthepoly-
catalogs from each individual HAWK-I chip. Conformal nomialpartofthe distortionsolutionandan adequatesam-
transformations (four-parameter linear transformations, which plingof eachgridelement.We foundabout19000pairsof
include rigid shifts in the two coordinates, one rotation, and residuals in each chip with a median number of 135 pairs
one change of scale, so the shape is preserved) were used to per cell (the number varied between 30, which occurred in
bring the stars’ positions, as measured in each image, into a corner grid element, and 170, which was near the chips’
the reference system of the master frame. We considered only center).
well-measured, unsaturated objects with a stellar profile and – We performed a linear least-square fit of the average posi-
measuredinatleastthreedifferentimages. tionalresidual of each of the 144 cells to obtain the coeffi-
Our geometric-distortion solution for HAWK-I is made cients for the two fifth-orderpolynomialsin each chip (see
up of five parts: (1) a linear transformation to put the four PaperIVforadetaileddescription).
chipsintoaconvenientmasterframe(Hereafter,werefertothe – WeappliedthisPcorrectiontoallstars’positions.
transformation from chip k of the coordinate system of image – Finally, we iterated the entire process, deriving a new and
j to themaster system T .),(2)two fifth-orderpolynomialsto improvedcombinationof a master frame and distortionso-
j,k
deal with the general optical distortion (hereafter, the “P” cor- lution.Theresidualsimprovedwitheachiteration.
rection), (3) an analytic correction for a periodic feature along
thex-axis,asrelatedtothedetectorread-outamplifiers(the“S” The iterative process was halted when the polynomial coeffi-
correction),(4) a fine-tuningto correctsecond-ordereffects on cientsfromoneiterationtothenextdifferedbylessthan0.01%.
thex-residualsoftheScorrection(the“FS”correction),and(5) The final P correctionreduced the averagedistortion resid-
atableofresidualsthataccountsforbothchip-relatedanomalies uals (from the center of the detector to the corner) from 2.1
∼
andafine-structureintroducedbythefilter(the“TP”correction). pixels down to 0.2 pixel. By applying the P correction, the
The final correction is better than 0.027 pixel ( 2.8 mas) accuracyofourd∼istortionsolution(definedas68.27thpercentile
∼ ∼
in each coordinate. We provide the solution in two different of the σ(Radial residual), see Sect. 5.5 for detail) improves
forms:aFORTRANsubroutineandasetofFITSfilesforeach from 0.336to 0.043pixelpercoordinatefora well-exposed
∼ ∼
filter/chip/coordinate.Since focus, flexures, and generalcondi- star, which translates from 35.6 mas to 4.5 mas. In Fig. 4,
∼ ∼
tionsoftheopticsandtelescopeinstrumentationchangeduring we show the HAWK-I distortion map before and after our P
theobservations(withinthesame nightandevenbetweencon- correction. Although the aim of our work is not to analyze
secutiveexposures),wederiveanaveragedistortioncorrection. whatmakes the distortionhappen,the distortion patternbefore
Here, we describe our correction procedure for filter K . the correction appears to be primarily a radial distortion in
S
TheprocedureforfiltersJ andHisidentical,andtheresultsare the focal plane with some vignetting at the edges plus some
presentedintheSect.5.6. shift-rotation-shearinthedetectorpositioning.
7
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Fig.4. (Left): Residual trends for the four chips when we use uncorrected stars’ positions. The size of the residual vectors is
magnified by a factor of 500. For each chip, we also plot the single residual trends along X and Y axes. Units are expressed in
HAWK-Irawpixel.(Right):Residualsafterourpolynomialcorrectionisapplied.Thesizeoftheresidualvectorsisnowmagnified
byafactor5000.
5.2.Averageperiodic“step”correction(S) Tomodelthetrendinthe residuals,we useda square-wave
function (panel (5a) of Fig. 5). The amplitude of this function
Our P correction reveals a high-frequency, smaller-amplitude is defined as the 3σ-clipped median value of the residuals
effect, which is a periodic pattern in the x-positional residuals betweenpixels2.8–62.2and66.8–126.2.Tomodeltheaverage
asafunctionofthexpositionsinallHAWK-Ichips.Thiseffect periodicitybetween62.2 xraw 66.8pixels,wefittedthedata
is clearly shown in the distortion map after the P correction is pointswithastraightline≤using≤bylinearleastsquares.
applied(δxvs.XpanelsinFig.4).Forevery128columns,stars’
We corrected the stars’ positions by applying 75% of the
positionshavepositiveresiduals(about0.075HAWK-Ipixel)in
Scorrection(toencouragesmoothconvergence)andthe Pcor-
thefirst64pixelsandnegativeresiduals(about0.045HAWK-I
rection.Wecomputedanimprovedmasterframeandcalculated
pixel)inthesecond64pixels(seepanels(a)ofFig.5).Atfirst
new, generally smaller, residuals. New square-wave-function
glance,thisresidualpatternhastheappearanceofbeingcaused
amplitudeswere derived and added to the previouscorrections
byirregularitiesinthepixelgridofthedetectors.However,ade-
toimprovetheScorrection.Theprocedurewasiterateduntilthe
tailedanalysis(seeSect.6)leadsustoconcludethatitisinstead
observedaverageperiodicityresidualshadanamplitudesmaller
apatterncausedbya“periodiclag”inthereadoutprocess,which than10 4pixel.
−
isoffsetinoppositedirectionsinalternating64pixelsectionsof
Combiningthetwocorrections(S+P,appliedinthisorderto
thedetectoraddressedbyeachofthe32read-outamplifiers. therawcoordinates),weareabletoreducethe68.27thpercentile
Weadoptedaniterativeproceduretoempiricallycorrectfor oftheσ(Radialresidual)downto 4.0mas(0.038pixel).
this periodic pattern that shows up only along the x axis. We ∼
startedwiththemasterframemadebyusingcatalogscorrected
withourPcorrection.Wethentransformedthepositionofeach 5.3.Fine-tunedcorrectionoftheresidualperiodicity(FS)
star (i) from the master frame back into the raw coordinate
Inpanels(b)ofFig.5,weshowtheresidualtrendaftertheS+P
system of each chip (k) of each image (j). We determined the
correction is applied. Looking at panels (1–4b), it is obvious
quantity:
that the amplitude of the δx periodicity pattern is not constant
fromchiptochip.Inadditiontothis,thereisstillapolynomial
δx = xraw xP−1(T−j,k1), residualthatneedstoberemoved.Forthisreason,weapplieda
i i − i,j fine-tunedresidualcorrectionasfollows.
We first computed a master frame by applying the S+P
where xraw are the raw x-coordinates, and xP−1(Tj−,k1) are the correctionto the raw positions of each chip/exposure.We then
i i,j determined the residuals as the difference between the raw
x-coordinatesonthemasterframetransformedtotherawcoor-
dinatesystemandcorrectedwiththeinversePcorrection.Weas- x-coordinatescorrectedwiththeScorrectionandxP−1(T−j,k1).Next,
i,j
sumedthattheperiodictrendhadaconstantamplitudeacrossthe we divided each chip into 32 bins of 64 pixels each along the
detector.Panels(a)inFig5showδxvsxraw foreachchip(from xaxis,computedthe3σ-clippedaveragevalueoftheresiduals,
1to4)andδxvs.xrawmodulus128,inwhichwecollecttogether and subtractedthe 75%of it fromthe δx residualsin each bin.
alltheresiduals(panel5)beforeapplyingtheScorrection. Then,weiteratedtheprocedureuntilthedifferencebetweenthe
8
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
Fig.5. (Top): δx as a function of X in units of HAWK-I pixels before S correction. (Middle): As above but after S correction.
(Bottom):Same as above but after S and FS corrections. In the left panels (from 1 to 4), we took 32 bins of 64 pixels each and
computedthemedianofresidualsineachbin(redsquares).Intherightpanels(5),weshowtheperiodogramwithaperiodof128
columnscontainingallthepointsplottedintheleftpanels.Thereddashedlinesshow+0.05,0,and 0.05HAWK-Ipixel.
−
3σ-clippedaveragevalueoftheresidualsinallbinsofallchips This approach was able to provide accuracies (68.27th
fromone iterationto the nextone was smaller than 10 3 pixel. percentileofthe σ(Radialresidual))downto 0.035pixel( 3.7
−
∼
Inpanels(c-1)to(c-4)ofFig.5,weshowtheresidualtrendsfor mas)level.
allchipsafterourS+FS+Pcorrectionsareapplied.
9
Libralato,M.etal.:Ground-basedastrometrywithwidefieldimagers.V.
5.5.Accuracyofthegeometric-distortioncorrection
In Fig. 7, we show the final HAWK-I distortion map after we
applied our full distortion solution (S+FS+TP+P). To have a
reliable assessment of the errors in the distortion correction,
wecomputedther.m.s.ofthepositionresidualsofeachstar(i)
observedineachchip(k)oftheimage(j),whichhavebeendis-
tortion corrected and conformallytransformedinto the master-
frame reference system (xTj,k,yTj,k). The difference between
i,j,k i,j,k
thesepositionsandthedistortion-freepositions(Xmaster,Ymaster)
i i
directlyquantifieshowclosewearetoreachtheidealdistortion-
freesystem.Wedefinedtheσ(Radialresidual)as:
(xTj,k Xmaster)2+(yTj,k Ymaster)2
σ(Radialresidual) = i,j,k− i i,j,k− i .
Fig.6. (Left): Example of cell and grid-point locations on the i,j s 2
bottom-leftareaofchip[1].Dottedlinesmarkthe 170.7 170.7
pixels square elements inside which we computed the m×edian InFig.8,weshowthesizeoftheseσ(Radialresidual)versus
value of the distortion residual to use as grid point (empty cir- instrumental KS magnitude after each step of our solution. To
cles) in the look-up table. For a given star (marked with an test the accuracy of the geometric-distortion solution, we only
), we used the four surrounding closest grid point to perform used unsaturated stars with an instrumental magnitude K
S
∗the bi-linear interpolation(sketched with the arrows) and eval- 12.4(reddashedline)inthemasterlist,whichisobservedina≤t
−
uatetheresidualgeometricdistortioninthatlocationofthede- leastthreeimagesandwithaQFIT 0.05.Faintstarshavelarger
≤
tector. (Right): Bi-linear interpolation outline. Each grid point residuals due to an increasing contribution of random errors.
P ,...,P is weightedby the correspondingarea A ,...,A to The 3σ-clipped 68.27th-percentile value of these residuals is
1 4 1 4
associatethecorrectionin . shownontherightofeachpanel.The3σclippingruleexcludes
∗ outliers,whichcanbiasthepercentilevalue.Theseoutlierscan
have different explanations. For example, most of the outliers
for the Bulge field are close to the edge of the FoV, where the
distortionsolutionislessconstrained.InthecaseofNGC6656,
most of these outliers are close to the center of the cluster
(crowding effects) or are located in the region affected by the
5.4.Tableofresidualgeometric-distortioncorrection(TP)
internalreflectionoftheMoonintheoptics.Hereafter,werefer
inthetextwithσ tothe3σ-clipped68.27th-percentilevalue
The final step of our distortion-solution model consists of perc
oftheσ(Radialresidual).Thedistributionsofther.m.s.isvery
four look-up tables (one for each chip) to minimize all the
non-Gaussianandthe68.27th-percentileisanarbitrarychoiceto
remaining detectable systematic residuals that were left. We
representtheerrors.Althoughitisnotabsolutelycorrectmathe-
constrained the look-up tables using the same procedure that
matically,itgivesagoodindicationsofwhereanoutlierwilllie.
Bellini, Anderson& Bedin (2011)used to derivethe distortion
In the bottom panel, we plot the σ(Radial residual) ob-
correctionfortheWFC3/UVIScamera.
tained using more-general 6-parameter linear transformations
First, we corrected all stars’ positions by applying the S, to compute the master-frame average positions. These trans-
FS,andPcorrections(inthisorder).Wethenbuiltanewmaster formations also include other two terms that represent the
frameandcomputedtheresiduals,asdescribedinSect.5.1.We deviationfrom the orthogonalitybetween the two axes and the
subdividedagaineachchipinto12 12squareelements.Weused changeofrelativescale betweenthe two axes(the shapeis not
×
thestars’residualswithineachcelltocomputea3σ-clippedme- preserved anymore). When general linear transformations are
dianpositionalresidualsandassignedthesevaluestothecorre- applied, most of the residuals introduced by variations in the
spondinggridpoints(opencirclesinFig6).Whenacelladjoins telescope+opticssystemanddifferentialatmosphericrefraction
detectoredges,thegridpointisdisplacedtotheedgeofthecell, areremoved,andσ furtherreducesto0.027pixel( 2.8mas).
perc
asshown.Forthegridpointontheedges,thevalueofthemedian ∼
onlyatthefirstiterationiscomputedatthecenterandshiftedto
theedge.Then,weiterativelyfoundthevaluethatthegrid-point 5.6.Geometric-distortioncorrectionforJandHfilters
element on the edge should have to remove the systematic
Each HAWK-I filter constitutes a different optical element,
errors.Webuiltalook-uptablecorrectionforanygivenlocation
which could slightly change the optical path and introduce
ofthechip,usingabi-linearinterpolationamongthesurround-
changes in the distortion. To test the filter-dependency of our
ingfourgridpoints.Figure6showsanexampleofthegeometry
K -based distortion solution, we corrected the positions mea-
adoptedforthelook-uptableandofthebi-linearinterpolation. S
sured on each J- and H-filter images of Baade’s Window field
We correctedstars’positionsusingonly75%oftherecom- with our K -filter-derived distortion solution and studied the
s
mendedgrid-pointvalues,computedanimprovedmasterframe, residuals.We foundσ(Radialresidual)significantlylargerthan
andcalculatednew(generallysmaller)residuals.Wecalculated those obtained for the K -band images. We also tried to apply
s
new grid-point values and added them to the previous values. the K -filter distortionsolutionplusan ad-hoctable of residual
s
The procedure was iterated until the bi-linear interpolation (TPcorrection)foreachfilterwithoutsignificantimprovements.
offerednegligibleimprovementofthepositionalresidualsr.m.s. For these reasons, we decided to independently solve for the
fromoneiterationtothenext. distortionfortheJandH images.
10