Sources of straylight in the post-focus imaging instrumentation of the Swedish 1-m Solar Telescope

6.9 MB·English

by  M. G. Löfdahl

Astronomy&Astrophysicsmanuscriptno.17980 ©ESO2012
January16,2012
Sources of straylight in the post-focus imaging instrumentation of
the Swedish 1-m Solar Telescope
M.G.Lo¨fdahl1,2 andG.B.Scharmer1,2
1 InstituteforSolarPhysics,RoyalSwedishAcademyofSciences,AlbanovaUniversityCenter,10691Stockholm,Sweden
2 StockholmObservatory,Dept.ofAstronomy,StockholmUniversity,AlbanovaUniversityCenter,10691Stockholm,Sweden
ReceivedAugust30,2011;acceptedSeptember30,2011
ABSTRACT
2 Context.Recentlymeasuredstraylightpointspreadfunctions(PSFs)inHinode/SOTmakegranulationcontrastinobserveddataand
1 syntheticmagnetohydrodynamic(MHD)dataconsistent.Datafromearthboundtelescopesalsoneedaccuratecorrectionforstraylight
0 andfixedopticalaberrations.
2 Aims.Weaimtodevelopamethodformeasuringstraylightinthepost-focusimagingopticsoftheSwedish1-mSolarTelescope
(SST).
n
Methods.Weremovedanyinfluencefromatmosphericturbulenceandscatteringbyusinganartificialtarget.Wemeasuredintegrated
a straylightfromthreedifferentsourcesinthesamedata:ghostimagescausedbyreflectionsinthenear-detectoroptics,PSFscorre-
J
spondingtowavefrontaberrationsintheopticsbyusingphasediversity,andextendedscatteringPSFwingsofunknownoriginby
3 fittingtoanumberofdifferentkernels.Weperformedtheanalysisseparatelyintheredbeamandthebluebeam.
1 Results. Wavefront aberrations, which possibly originate in the bimorph mirror of the adaptive optics, are responsible for a
wavelength-dependent straylight of 20–30% of the intensity in the form of PSFs with 90% of the energy contained within a ra-
] diusof0(cid:48).(cid:48)6.Thereareghostimagesthatcontributeatthemostafewpercentofstraylight.Thefractionofothersourcesofscattered
M
lightfromthepost-focusinstrumentationoftheSSTisonly∼10−3oftherecordedintensity.Thiscontributionhaswidewingswitha
I FWHM∼16(cid:48)(cid:48)intheblueand∼34(cid:48)(cid:48)inthered.
. Conclusions.Thepresentmethodseemstoworkwellforseparatelyestimatingwavefrontaberrationsandthescatteringkernelshape
h
andfraction.Ghostimagescanbeexpectedtoremainatthesamelevelforsolarobservations.Thehigh-orderwavefrontaberrations
p
possiblycausedbytheAObimorphmirrordominatethemeasuredstraylightbutarelikelytochangewhenimagingtheSun.Wecan
-
o therefore make no firm statements about the origin of straylight in SST data, but strongly suspect wavefront aberrations to be the
r dominantsource.
t
s Keywords.Instrumentation:miscellaneous-Methods:observational-Techniques:imageprocessing-Techniques:photometric-
a
Telescopes
[

2
v
1. Introduction terr fromawide-fieldwavefrontsensor.However,thecontrast
3 0
correctiontheyfoundisnotsufficienttoreachthecontrastsex-
6
Formanyyears,therehasbeenadiscrepancybetweenthecon- pectedfromMHDsimulationsandHinodeobservations.
6
2 trastinobservedsolarimagesandthecorrespondingimagespro- In this paper we continue the search for the missing con-
. ducedbymagnetohydrodynamic(MHD)simulations.Itwasnot trastbyexaminingthepost-focusopticsoftheSST.Byinserting
0
clear whether compensation for straylight in the observations targets in the Schupmann focus, which is located close to the
1
or missing physics in the simulations were at fault. This has exit of the vacuum system, we removed all effects upstream of
1
now been resolved by measurements of the point spread func- thatpoint(atmosphereandtelescope)andconsideredonlyerror
1
: tion(PSF)intheSolarOpticalTelescope(SOT)ontheHinode sourcesontheopticaltable.WeestimatedthewavefrontPSFby
v spacecraft (Wedemeyer-Bo¨hm 2008)and comparisonwith arti- usingphasediversity(PD; Gonsalves&Chidlaw1979;Paxman
i
X ficial data (Wedemeyer-Bo¨hm & Rouppe van der Voort 2009). etal.1992;Lo¨fdahl&Scharmer1994)andfittedtheremaining
Scharmeretal.(2010,seetheirintroductionforafullaccountof straylight to a scattering PSF. In particular, we were interested
r
a theproblem)recentlyinitiatedaprojecttomeasurethestraylight intheintegratedfractionofscatteredlightintheimagedataand
sourcesoftheSwedish1-meterSolarTelescope(SST; Scharmer thewidthofthescatteringkernel.
etal.2003a)toalsocorrectSSTimagesforthemissingcontrast.
Scharmer et al. (2010) found that a significant part of the
2. Imagingmodel
contrastreductioncanbeexplainedbyhigh-ordermodesinthe
pupil wavefront phase that are not corrected by the Adaptive Wemodeltheimageformationas
Optics(AO; Scharmeretal.2003b)orimagerestorationswith
multi-frame blind deconvolution (MFBD; Lo¨fdahl 2002) tech- g= f ∗s ∗s +d+n (1)
φ K
niquesbecauseofthefinitenumberofmodesusedinthosetech-
niques. The authors also implemented a method for correcting wheregisaflat-fieldedanddark-correcteddataframe, f isthe
the contrast by means of the known statistics of atmospheric object, s is the point-spread function (PSF) of wavefront er-
φ
turbulence and simultaneous measurements of Fried’s parame- rorsφ, s isascatteringPSFwithextendedwings,drepresents
K
1
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
Table1:Scatteringkernels
Kernelname Definition FWHM
√
Gauss K (r;σ)∝exp(−r2/(2σ2)) W =σ·2 2ln2
G G
Lorentz K (r;γ)∝(1+r2/γ2)−1 W =γ·2
L L √
Moffat K (r;α,β)∝(1+r2/α2)−β W =α·2 21/β−1
M M
(cid:113)
Voigt K (r;σ,γ)∝K (r;σ)∗K (r;γ) W ≈0.5346W + 0.2166W2+W2
V G L V L L G
Notes.Allkernelsarefunctionsoftheradialcoordinater=(x2+y2)1/2.TheyarenormalizedintheFourierdomainbydivisionwiththevaluein
theorigin.K isfromMoffat(1969).TheapproximateexpressionforW isgivenbyOlivero&Longbothum(1977)andisclaimedtobeaccurate
M V
towithinafew‰.
x y
Hole Telescope
(mm) (mm) (µm)
(cid:31) CT
A −2 0 1000 Target PD
B 0 −2 250 DM DC
C 2 0 120
WB
D 0 0 60
EF √02 √22 2300 TM RL 0.2nmutter Bluebeam 395.4nm
3 h
6 S Re
Fig.1:Straylighttargetdrawing.Positions(x,y)inmm,diame- d
ters( )inµmwithtolerancesof1–2µm. bea
m
L
a resi(cid:31)dual dark level that was not subtracted properly in flat- WFASO Cs DualFPI
fielding, and n is additive Gaussian white noise. These quanti-
tiesareallfunctionsofthespatialcoordinates(x,y),suppressed
whenpossibleforcompactnotation.Thesymbol∗denotescon- Not
volution. WB used
ThescatteringPSF,s ,ismodeledas
K
s =cδ+(1−c)·K (2)
K
where δ is the Dirac delta function, K is a convolution kernel Fig.2:Setupschematics.Lightfromthetelescopeentersthrough
equaltooneofK ,K ,K ,orK asgiveninTable1.Because the target from upper left. TM = tip-tilt mirror; DM = de-
M L G V
itispartofthescatteringPSF,wewillrefertoK asascattering formable mirror; RL = reimaging lens; DC = dichrocic beam-
kernel.Boththeδfunctionandthekernelsarenormalizedinthe splitter;CT=correlationtracker;WFS=wavefrontsensor;LCs
Fourierdomainbydivisionwiththevalueintheorigin.Owing = Liquid Crystals; FPI = Fabry–Pe´rot interferometer. Only the
tothisnormalization,(1−c)expressestheintegratedfractionof cameras that produced images for this investigation are labeled
thistypeofstraylight. (WB, PD). The figure is not to scale and the following inten-
tionalerrorsareintroducedtosavespace:theangletothebeam
reflected off the DC is drawn too wide and the transmitted and
3. Data
reflectedbeamsfromthefirstredbeamsplitterareswitched.
The data used in this experiment were collected with the SST
(Scharmer et al. 2003a) on 29 May 2010 between 17:10 and
18:40UT. telescopepupilisre-imagedbyafieldlenslocatedjustinfront
TheprimaryopticalsystemoftheSSTisasingletlenswitha of the Schupmann focus. The pupil diameter is 34 mm at this
focallengthof20.3mat460nmanda98-cmaperture.Amirror location.Thereisa35mmdiameterpupilstopattheDM.This
attheprimaryfocusreflectsthelighttoaSchupmanncorrector, defines the pupil for pinhole images. The reimaging lens then
which forms an achromatic focus next to the primary focus. In makesaF/46beamparalleltotheopticaltable.Thelightisthen
thisfocalplaneweplacedanartificialtargettoisolatetheopti- splitbythe500nmdichroicbeamsplitterintoabluebeamand
cal aberrations and scattering downstream from this point. The a red beam. Both beams have several cameras behind different
target,manufacturedbyMolenaarOptics,isa25µmthickmetal filters. Table 2 summarizes the cameras and setup parameters
foil with six holes of different sizes, see Fig. 1. The manufac- usedforthisexperiment.
turingtolerancesareverysmall,butcloseinspectionoftheim- Inthebluebeamonecamerawasnominallya“focus”cam-
agesrevealedsmallirregularitiesattheedgesofthelargerholes, era and the other a defocused “diversity” camera of a PD pair.
probablycausedbydustparticles.Usingamotorstage,wewere These two cameras and their beamsplitter were mounted on a
also able insert a pinhole array used mainly for alignment pur- common holder and could be moved together along the optical
poses. axis. This made it possible to generate additional focus diver-
The setup following the Schupmann focus is illustrated in sitieswithoutchangingtherelativediversitybetweenthewide-
Fig.2.Thebeamexpands(viathetip-tiltmirror)toapupilplane band(WB)andPDcameras.Theholderanditscamerasarecov-
atthelocationofthebimorphdeformablemirror(DM).Here,the ered by a box that blocks light from directions other than the
2
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
Table2:Setupinthetwobeams.
Item Bluebeam Redbeam
Wavelength(nm) 395.4 630.2
No.ofcameras 4 3
No.ofcamerasused 2 1
Cameras MegaPlusIIes4020 SarnoffCAM1M100
FOV(pixels) 2048×2048 1024×1024
Imagescale(arcsec/pix) 0.034 0.059
Exposuretime(ms) 10 17
Fig.3: Straylight target images, WB0 in both beams, displayed
beam.TherelativerotationofthefieldintheWBandPDcam- with the same log scale. Left: blue beam; right: red beam.
eraswasmeasuredbycomparingthegridpatternsofthepinhole CompareFig.1.
arrayimages.Therotationalmisalignmentissmallerthan0◦.1.
Intheredbeamweusedasinglecamerathatwasalsocov-
4. Straylightmeasurements
ered bya box toblock external straylight. Here,we could only
adddiversitiesbymovingthecamera. 4.1. Ghostimages
The AO was running in closed loop on the central pinhole
Figure 3 shows a variety of weak duplicates of the pinhole im-
(D) of the straylight target while the artificial target data were
ages, commonly referred to as ghost images. The most signif-
collected, so aberrations are assumed to be stable during the
data collection.1 The telescope pointing was moving near disk icant ghost images are shifted by only a few arcseconds and
appear to be at different focus positions. These contributions
center to average out the granulation structure as well as pos-
mustcomefromreflectionsinthebeamsplittersandotheroptics
sible.Manyexposureswerecollectedateverypositionwithall
withinafewcmfromthedetectorfocus,andshouldthereforebe
cameras, 3500 exposures in the blue and 10000 in the red, for
present during ordinary observations of the Sun as well. There
the target data as well as for dark frames and flat fields. The
are many weaker contributions that appear to be mirror images
highnumberofframeswasnecessarybecauseweneededahigh
intheblueandrepetitionsinthedifferenttapsoftheredCCD,
signal-to-noise ratio (SNR) to measure the very faint straylight
probablyoriginatinginthecameraelectronics.2
far away from the pinholes. The target data were corrected for
The ghost images are not included in the image formation
biasandgainvariations.Thecorrectedimageg iscalculatedas
i
modelofEq.(1),butwecanmeasurethemhereandthenmask
them in later processing. The strongest more or less in-focus
gi =(hi−d)/(f −d), (3) ghosts are <∼ 1% in both the blue and red (measured on hole
A).
whereh istheobserveddataframe,distheaveragedarkframe,
i
and f istheaverageflatfieldimage.Tominimizetheinfluence 4.2. Wavefrontaberrations
fromsolarfeaturesintheaveragedflat-fieldimages,theindivid-
ualframeswerecollectedwhilethetelescopewascircledovera WeestimatedthewavefronterrorPSF, sφ,throughPDwiththe
quietareaneardiskcenterandtheDMproducedrandomwave- MOMFBDC++codeofvanNoortetal.(2005).Weprocesseda
fronts. subfieldcenteredonthe20µmstraylightholeF.Inthebluewe
The images collected in different focus positions were not used256×256pixelsandinthered128×128pixels,thedifferent
sizesarenecessarybecauseofthedifferenceinimagescale.The
recorded simultaneously and we took steps to ensure that tiny
toprowofFig.4showsthecentralpartofthissubfield.Wecan
imagemovementsdidnotviolatetheassumptionthatwemade
seedirectlythatthechosenfocuspositionswerenotideal.PD0
in PD processing, i.e. that there is a common object in all im-
isverysimilartoWB−andPD+toWB0intheblue,soinstead
ages after summation. In a first pass, the data frames g were
i ofsixdifferentdiversitychannels,wehaveinrealityonlyfour.
co-addedintheiroriginalform.Inasecondpass,eachexposure
The focus is somewhere between WB0 and WB+ in the red; it
was aligned to the summed WB image at nominal focus (WB0
is probably preferable3 to have one channel close to the focal
image)fromthefirstpass(separatelyinblueandred)withsub-
plane,toconstraintheobjectestimation.
pixel precision through centroiding (center of mass) on one of
Careful pre-processing is easier with point-like targets than
theholes,andanewsumwasformed.Byusingthesameimage
withextendedscenes,whichfacilitatesinversions.Inparticular,
as an alignment target, both the individual images in each sum
andalsothesumsatdifferentfocuspositionswerewellaligned. it is possible to fine-tune the intensity bias (dark level) correc-
tion,andthenmakesurethetotalenergyisthesameinallfocus
Intheremainderofthispaperwewillrefertothesesummed
positions.Suchrefineddark-levelcorrectionwasperformedfor
imagessimplyastheimages,correspondingtoginEq.(1).The
thepurposeofPDprocessing.First,allimagesinaPDsetwere
WB0imagesareshowninFig.3.
normalizedwithrespecttotheaverageintensityintheinnerpart
ofthe1mmtargethole(A).Weassumedthistobethebestavail-
1 Becausethetargetwasrepeatedlyremovedfromthebeam(when ablemeasureoftheintensitylevel,insensitivetotheblurringof
collectingflatfields)andinserted(whencollectingtargetdata),themir-
ror was alternately heated by the sunlight and allowed to cool again. 2 The Sarnoff CAM1M100 CCD is organized in 2 by 8 taps (sub-
Because these thermal variations cause changes in the mirror’s shape fields),thatarereadoutinparallel.
andstress,sotheleveltowhichtheassumptionisvalidisdifficultto 3 Wearenotawareofanystudiesaboutoptimaldistributionofsev-
predict. eralfocusdiversities.
3
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
(a)BlueWB− (b)BlueWB0 (c)BlueWB+ (d)BluePD− (e)BluePD0 (f)BluePD+ (g)RedWB− (h)RedWB0 (i)RedWB+
Fig.4: PD results, the central parts of target hole F images in log scale. Top row: observed image; center row: recreated images
M = 231;bottomrow:recreatedimages M = 36.TheFOVshownis2(cid:48).(cid:48)2×2(cid:48).(cid:48)2intheblueand1(cid:48).(cid:48)9×1(cid:48).(cid:48)9inthered.Beam,camera
anddiversityasnotedinsubcaptionsa)–i).
the edge of the hole. The WB0 images, which were collected Table3:Focusdiversities.
in nominal focus, we then subtracted a dark level measured as
the peak (as defined by a Gaussian fit) of the histogram of im- Blue Red
Diversity
ageintensitywithinthePDprocessingsubfield.Thiscorrectsfor WB− WB+ PD0 WB− WB+
someofthestraylightfromholeA.Forthedatafromotherfocus
positions,wesubtractedadarklevelcorrespondingtothediffer- Nominal(mm) −4.0 +4.0 +7.0 −7.0 +7.0
Estimated(mm) −3.8 +3.7 +4.8 −6.2 +5.4
enceinmedianintensityovertheentireframe(definingthedark
level). Finally, the images were normalized to the same mean Notes.Diversitiesareexpressedinmmshiftalongtheopticalaxis,rel-
value, making the total energy the same in all focus positions. ativetoWB0ineachbeam.ThePD±diversitiesinthebluearesimply
The dark corrections, d, in this refinement step were on the or- thesumsoftheWB±andPD0diversities.
der∼10−4oftheintensityinholeAintheblueandalmost∼10−3
inthered. Table4:RMSandStrehlratioofthewavefrontphase.
In the PD processing the wavefronts were expanded in at-
mosphericKarhunen–Loe`ve(KL)functions,expressedaslinear
Measured Infocus
combinationsofZernikepolynomials(Roddier1990).TheseKL Beam M
σ σ σ
functions are ordered as the dominating Zernike polynomial in (wλoabvses) (wλoabvses) Rλobs (w50a0ves) R500
the notation of Noll (1976), and not by monotonically decreas-
Blue 36 0.059 0.059 0.87 0.047 0.92
ing atmosphericvariance. Althoughwe were notmeasuring at-
Blue 231 0.105 0.103 0.66 0.082 0.77
mospheric wavefronts, we chose to use KL functions because
Red 36 0.100 0.052 0.90 0.065 0.85
bimorphmirrorsnaturallyproduceKLmodes.Weassumedthat
Red 231 0.121 0.070 0.82 0.088 0.74
the alignment of the PD channels described in Sect. 3 is suf-
ficient for PD processing, and accordingly did not include tilt Notes. σ is the RMS of the PD-estimated wavefront in waves at
coefficientsinthefit.Wedefined M astheindexofthehighest- theobservλoabtsionswavelengths,givenfortheentireestimatedwavefront
ordermodeused,i.e.,weusedKLmodes4–M. phase,aswellasaftersubtractingthebest-fitZernikefocuscomponent.
InadditiontotheKLparametrizationoftheunknownwave- StrehlratiocalculatedasRλ = exp{−(2πσλ)2}.Subscript500denotes
λ=500nm.
front,wealsoestimatedthe(Zernike)focusdiversitieswithre-
spect to the WB0 images, starting from the nominal values.
Because the WB and PD cameras sit on a common mount and
setup,sothiscamerawasinfactdefocusedbylessthan7mm.
arethereforemovedtogether,asingleadditionalfocusshifthad
TheseestimatesconfirmthatthediversitysettingofthePDcam-
to be determined when the three images from the PD camera
wereadded.Thediversitiesestimatedwithdifferent M varyby erawasnotverydifferentfromthestepsizeofthe(−,0,+)po-
sitions.
no more than a few tenths of a mm and we used the values es-
timated with M = 210 for both M used here. The nominal and Along with the observed images, g, in Fig. 4 we also show
estimateddiversitiesareshowninTable3. therecreatedimages,gˆ = fˆ∗sˆφ,basedonthePDestimates fˆand
Themagnitudesoftheestimateddiversitiesarealllowerthan φˆ,fordifferent M.Aninspectionoftheseimagesclearlyshows
their nominal values. This could be caused by a mismatch in thatthePSFsmustbesatisfactorilyestimated,particularlyinthe
the image formation model. We used the diameter of the ordi- blueM =231case.
narytelescopepupil,re-imagedonthebimorphmirror.Inreal- Theestimatedwavefrontphaseswithoutfocusareshownin
ity,thereisdiffractioninthepinhole,makingthere-imagedpupil Fig. 5. The M = 231 estimates in the blue and red show simi-
slightly fuzzy. The 7 mm defocus of the PD camera is particu- larities,althoughtheredwavefrontsarelesswellresolvedthan
larly underestimated. This may be because of a mistake in the the blue wavefronts because of the smaller subfields used and
4
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
11..00
yy
gg
rr
ee
nn 00..99
ee
d d Blue s
ee 0
osos 00..88 BRleude ss0
clcl φ
(a)Blue36 (b)Blue231 (c)Red36 (d)Red231 EnEn 00..77 Red sφ
Fig.5:Estimatedwavefronts,φˆ,infocus.Beamand M asnoted 00..00 00..22 00..44 00..66 00..88 11..00 11..22
rr // 11’’’’
in subcaptions a)–d). The scaling is between the same min and
maxforthetwowavefrontsfromthesamebeam.
Fig.6:Enclosedenergyforthediffraction-limitedPSFs, s ,and
0
fortheestimatedwavefrontaberrationPSFs,s .Thedottedlines
φ
possiblybecauseofthesmallernumberofimageswithdifferent illustratetheradiifor90%enclosedenergy.
diversities.Theybothhavetwobrightringsandadarkgradient
at perimeter. Both rings have brighter bumps at approximately
the same positions. Particularly in the blue wavefront, the pat-
ternresemblesthatoftheelectrodesonthebimorphmirror.The
M =36wavefrontestimatesaremuchlessresolved.Somesim-
ilarities to the 231-estimates can be seen along the outer bright
ring.However,withthesmaller M,theKLfunctionsapparently
cannot represent the inner ring pattern visible in the M = 231
wavefrontestimates.
The RMS values of the estimated wavefronts are listed in
Table4.TheWBcamerainthe“0”positionwasoutoffocusby
approximately0.1radintheblueand0.5radinthered.Tomake
the RMS comparable between beams, we also show the RMS
after subtracting the best-fit focus contribution as well as cal-
Fig.7:Maskedstraylighttargetimages,displayedwiththesame
culatedforacommonwavelength,500nm.Thismakesthe231-
logscaleasinFig.3.Left:bluebeam;right:redbeam.
estimatesinredandblueagree,σ =0.085±0.003waves.The
500
36and231-estimatesdonotagreeineitherbeam.Wearemore
confidentintheblue231-resultsbecause1)theresultsagreebe-
FortheWB0imagesusedforfittingthestraylightmodel,the
tween blue and red, 2) the details in the wavefront are the so-
second-passsumswerecorrectedforapatternofstripesrunning
lutionconvergedtowhen M isincreasedinincrementsfrom36
intheydirection.Thiscorrectionwasmadebysubtractingfrom
to231,and3)thesolutiongiveestimatedPSFsthatrecreatethe
allrowsasmoothedversionofthemeanofrows1–10.Theav-
observeddatawell,seeparticularlythelarge-diversityimagesin
erageofthiscorrectionwas∼10−4intheblueandalmost∼10−3
Fig.4.TheStrehlratioforthissolution(seeTable4)is0.66in
in thered, representinga correctionof thedark levelsimilar to
theblue.Takingthetwo231solutionsinredandbluetogether
we obtain a Strehl ratio4 of 75±2% at 500 nm after removing the levels corrected in the previous section. (Fig. 3 shows the
images after this step.) For this step the images were also nor-
thefocuserror.
malizedwithrespecttotheaverageintensityintheinnerpartof
Instrumental contributions to the wavefronts can in princi-
the1mmhole(A).
ple be estimated and corrected in solar data with the normal
A binary representation of hole A was generated by thresh-
MOMFBD image restoration, except that we usually use 36
olding the WB0 image at 50% of the maximum intensity and
modes,farlessthan231.Theinstrumentalhigh-ordermodesare
removing contributions from the other holes. Artificial images
notincludedinther measurementsofthewide-fieldwavefront
0
werethenmadebyconvolvingthisbinaryimagewiththeappro-
sensorsotheyarealsonotdealtwithinthehigh-ordercompen-
priatePSFs.
sationofScharmeretal.(2010).Theyarethereforeanindepen-
dentcontributiontotheloweredcontrastinoursolarimages. Figure 8 shows an azimuthal average (taking the mask into
InFig.6weshowtheenclosedPSFenergyasafunctionof account)ofholeA,zoomedinontheholeperimeter.(Thezoom
theradialcoordinate.Theenclosedenergiesfor s and s reach makesadiscrepancyinimagescaleofabout1%apparent.)We
90%atr = 0(cid:48).(cid:48)17and0(cid:48).(cid:48)62,respectively,intheblu0eandaφt0(cid:48).(cid:48)27 showtheartificialholeconvolvedwiththreedifferentPSFsand
and0(cid:48).(cid:48)55inthered. theobservedhole.TheartificialimagemadewithPDestimated
s match the observed data very well in the blue. Comparing
φ
withthediffractionlimitedimage,itisobviousthatweneedto
4.3. Extendedwings model the wavefront PSF to isolate other sources of straylight.
The match is fairly good also in the red but the near wings are
WeattemptedtofitascatteringPSFwithextendedwingstothe
overestimated. The two PD estimated PSFs (M = 36 and M =
WB0 images shown in Fig. 3. We preferred to use the 1 mm
231,resp.)givealmostindistinguishableresultsforthispurpose.
holeA,becauseittransmitsmorelightthantheotherholesand
ThestraylightwewilltrytomodelwiththescatteringPSF,s ,is
thereforehasbetterSNRinthefarwings.Toremovethepollu- K
thecomponentthatshowsupatr >∼5(cid:48).(cid:48)8intheblueandr >∼6(cid:48).(cid:48)2
tionfromtheotherholesandfromtheghostimages,wedefined
inthered.
binarymaskstobeusedwhenfitting,seeFig.7.
We now fitted Eqs. (1) and (2) to the data, using the M =
4 TheStrehlratioistheobservedpeakofthePSFdividedbythepeak 231 estimates of sφ as fixed contributions from the wavefronts.
ofthetheoreticalPSFforaperfectimagingsystem. WeusedtheLevenberg–Marquardtalgorithmasimplementedin
5
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
11..000000 11..000000
Observed image Observed image
Artificial image, PD M=36 Artificial image, PD M=36
Artificial image, PD M=231 Artificial image, PD M=231
Artificial image, diffr. lim. Artificial image, diffr. lim.
00..110000 00..110000
00..001100 00..001100
BLUE RED
00..000011 00..000011
44..55 55..00 55..55 66..00 66..55 77..00 44..55 55..00 55..55 66..00 66..55 77..00
rr // 11’’’’ rr // 11’’’’
Fig.8: Observed and artificial images, binary 1 mm hole convolved with s and s as measured with two different M. Left: blue
0 φ
beam;right:redbeam.
theMPFITpackageforIDL(More´ 1978;Markwardt2009).In respondsto36%ofthetotalintensity!Becauseofthelogscale,
practicewefittedwithtwoparametersc andc substitutedfor thisresiduallooksmuchlowerinthebluebutthecorresponding
1 2
cand(1−c)inEq.(2)toallowfornormalizationdifferencesin errorintheblueisinfact15%.Thismaysoundalarmingbutit
real and artificial data. We then report c = c /(c +c ) as the appearsthisisneededtocancelfittingerrorswithintheholeand
1 1 2
resultofthefit. attheholeperimeter.Thereareseveralpossiblereasonsforthe
The results of the fits are shown in Fig. 9 and in Table 5. badfitsatsmallradii.Therearesmallimperfectionsintheshape
With any of the kernels we get c > 0.99 in both beams, which oftheholethatcouldcausediffraction.The50%thresholddoes
appearstobeaveryrobustresultbytheagreementbetweenthe notnecessarilyproduceabinaryrepresentationoftheholewitha
differentfits.Intheblueweget0.2–0.4%scatteredlightandin correctsize.Thethicknessofthemetalfoilmaycausereflections
thered0.1–0.4%. intheinteriorwallsofthehole.Thereareremainingvariations
The d parameter is returned with low values, on the order inintensityofunknownoriginwithinthehole.Paricularlyinthe
of 10−6. This indicates that the subtraction of the average top red,thePDestimated s doesnotfitthecoreofthePSF.Owing
φ
rows worked well as a dark correction refinement. Note that in to the truncation of the wavefront expansion, the estimated s
φ
the red, outside the signal-dominated radii, there is just noise, may also under-represent the near wings of the PSFs. Thermal
seeminglyaroundzero.Inthebluethereseemstobearemaining relaxationmaycausevariationsinthe s errorsaroundthehole
φ
uncorrected dark level that is not modeled by the d fit parame- perimeter during the data collection. Despite the limited accu-
ter. This could be caused by a geometrical asymmetry, e.g., by racyatsmallradii,theresidualsfortheextendedwingsatlarger
insufficientmaskingof theotherholesoradark-level gradient. radiiarelowandwebelievethekernelfitscanbetrustedbecause
Itdoesnotseemtoruinthefits. the2Dfittingisdominatedbythelargerareaswheretheradiiare
Wehavelessconfidenceinthedetailsoftheredfitsthanin large.
the blue fits because the artificial image based on sˆ overesti-
φ
matesthecoreofthePSF,seetherightpanelofFig.8.However,
5. Discussion
it is apparent from Fig. 9 that there is less straylight in the red
thanintheblue.Comparisonoftheobservedreddata(blackin Thewavefrontaberrationsarequitesignificant,correspondingto
theredplots)withtheobservedbluedata(gray)revealsafactor aStrehlratioof∼75%.Thestructureoftheestimatedwavefronts
of∼3difference.Thiswouldfavorthelowerestimateof0.1%in (M =231)withtheir6-and12-foldsymmetriessuggeststhatthe
theredandmaketheLorentzkernelfitlessbelievable. bimorph mirror of the SST AO is responsible. Wavefront aber-
InthebluethefitwithaGaussiankernelseemstofailatlarge rations originating in the instrumentation will be at least partly
radii.ItalsohasthelargestFWHM,∼20(cid:48)(cid:48).TheLorentzianker- correctedforbyourstandardMOMFBDimagerestoration.Part
nelfollowsthesignaldominatedcurvebetterthantheotherker- of the wavefront aberrations came from modes of higher order
nelsbuttheVoigtandMoffatkernelsgivesimilarresults.These thanwenormallyincludeinthisprocessinganditisunclearhow
allhaveFWHM13(cid:48)(cid:48)–16(cid:48)(cid:48).IntheredtheLorentziankerneldif- much of this would be corrected for. With the point-like object
fersfromtheotherkernelsbygivingalargerFWHM.Whilethe usedhere,themagnitudeoftheestimatedwavefrontstronglyde-
Moffat kernel β is estimated with a very high value, which is pendsonthenumberofincludedmodes,M.However,asshown
compensated for by an α that is also very large, and the Voigt byScharmeretal.(2010),whentheobjectissolargranulation,
kernelisalmostdegeneratedtoaGaussian,thelatterthreeker- theMFBD/PD-typeproblemislessconstrainedandanestimated
nelsagreeonaFWHMof34(cid:48)(cid:48).WeconcludethattheVoigtand low-orderwavefronttendstoalsorepresenttheblurringcaused
Moffat kernels, by virtue of their two fit parameters, are better bythehigher-ordermodesthatarenotincluded.
able to represent the true shape of the extended wings. Using The aberrations give straylight that is mostly contained in
theirresults,weestimatetheFWHMto16(cid:48)(cid:48) intheblueand34(cid:48)(cid:48) the first diffraction rings of s , 90% of the energy is within a
φ
inthered. radius of 0(cid:48).(cid:48)6 (see Fig. 6). The origin of this surprisingly high
Therearenoticeableresidualsat10(cid:48)(cid:48)±afewarcsecinthefits level of wavefront errors is unknown. One possible source is
shown in Fig. 9. Particularly in the red, where this feature cor- the mounting of the 1 mm thick deformable mirror, which is
6
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
110000 110000
Blue, M=36 Observed image Blue, M=231 Observed image
Artificial image Artificial image
1100--11 Lorentz 1100--11 Lorentz
Moffat Moffat
Gauss Gauss
Voigt Voigt
1100--22 1100--22
1100--33 1100--33
1100--44 1100--44
1100--55 1100--55
00 1100 2200 3300 4400 5500 6600 00 1100 2200 3300 4400 5500 6600
rr // 11’’’’ rr // 11’’’’
110000 110000
Red, M=36 Observed image Red, M=231 Observed image
Artificial image Artificial image
1100--11 Lorentz 1100--11 Lorentz
Moffat Moffat
Gauss Gauss
Voigt Voigt
1100--22 1100--22
1100--33 1100--33
1100--44 1100--44
1100--55 1100--55
00 1100 2200 3300 4400 5500 6600 00 1100 2200 3300 4400 5500 6600
rr // 11’’’’ rr // 11’’’’
Fig.9:Fitresults,angularaveragesofthemaskedimages,centeredonthe1mmholeA.Beamand M asnotedintheplotlegends.
Black:observedimage;gray(intheredplots):blueobservedimage;brown:binaryimageconvolvedwith s estimatedwith M =
φ
231;Othercolors:binaryimageconvolvedwiths aswellass fittedwithkernelsaslisted.
φ K
Table5:Scatteringkernelfitresults
Blue Red
M Kernel
c Kernelparameters FWHM χ2 c Kernelparameters FWHM χ2
36 Gauss 99.8 σ= 8.31 19(cid:48).(cid:48)6 0.0143 99.9 σ= 13.74 32(cid:48).(cid:48)4 0.0595
36 Lorentz 99.6 γ= 6.61 13(cid:48).(cid:48)2 0.0142 99.7 γ= 17.78 35(cid:48).(cid:48)6 0.0595
36 Moffat 99.7 α= 9.03 β=1.36 14(cid:48).(cid:48)7 0.0142 99.9 α=416.03 β=458.67 32(cid:48).(cid:48)4 0.0595
36 Voigt 99.7 σ= 3.98 γ=4.23 14(cid:48).(cid:48)7 0.0141 99.9 σ= 13.64 γ=0.0008 32(cid:48).(cid:48)1 0.0595
231 Gauss 99.8 σ= 8.77 20(cid:48).(cid:48)6 0.0148 99.9 σ= 14.61 34(cid:48).(cid:48)4 0.0593
231 Lorentz 99.6 γ= 7.38 14(cid:48).(cid:48)8 0.0147 99.6 γ= 19.83 39(cid:48).(cid:48)7 0.0593
231 Moffat 99.7 α=11.04 β=1.56 16(cid:48).(cid:48)5 0.0147 99.9 α=524.28 β=644.53 34(cid:48).(cid:48)4 0.0593
231 Voigt 99.7 σ= 4.59 γ=4.26 16(cid:48).(cid:48)1 0.0147 99.9 σ= 14.39 γ=0.0008 33(cid:48).(cid:48)9 0.0593
Notes. M isthemaxKLindexusedinPD.Theparametersα,γ,andσareinunitsofarcsec,whileβisdimensionless.Thecparameteristhe
percentageoftheintensitythatisnotcontainedwithinthefarwings.
clamped between two O-rings with the tension adjusted manu- straylightandwouldhavetobestrongerbyafactor2thanthose
allyby12screws.Anotherpossibilityishigh-orderaberrations measuredheretofullyexplainthecontrastintheobservedgran-
inducedbyalargefocuserrorimposedonthemirror. ulationdata.
Scharmer et al. (2011, see the supporting online material) Our best estimate of the scattering PSF, s , is that it gen-
K
compared umbra intensity and granulation contrast in 630 nm erates only 0.3% straylight in the blue (∼397 nm) and 0.1% in
SST data to data from SOT/Hinode and inferred a 50% stray- the red (∼630 nm). In our best fits, the FWHM of the scatter-
lightlevelwithasmallFWHMoflessthan2(cid:48)(cid:48),consistentwith ingkernel K is∼16(cid:48)(cid:48) intheblueand∼34(cid:48)(cid:48) inthered,usingthe
this straylight originating from aberrations. However, the aber- VoigtandMoffatkernels.TheGaussandLorentzkernelfitsgive
rationsmeasuredherecanonlyaccountforabout1/3ofthe50% similarresults.
7
Lo¨fdahl&Scharmer:Sourcesofstraylightinthepost-focusimaginginstrumentationoftheSwedish1-mSolarTelescope
Itiscommontotruncatethewingsofthescatteringkernels ofLaPalmabytheInstituteforSolarPhysicsoftheRoyalSwedishAcademy
atsomeradiusbutourfitsworkwellwithouttruncation,possibly of Sciences in the Spanish Observatorio del Roque de los Muchachos of the
because we are including the dark level d in the fit. We cannot InstitutodeAstrof´ısicadeCanarias.
exclude that some pollution from the holes B–F influenced the
Note added in proof In October 2011 we were upgrading the
s fits.Abetterstraylighttargetshouldhaveonlythe1mmhole
K wavefrontsensoroftheSSTAOsystem.Wefoundthatswitch-
andthesmallesthole.
ing off the mirror voltages results in a change in the science
Aftertheordinarydark-currentcalibrations,whichconsistof
focus by approximately 9 cm along the optical axis. Due to
a subtraction of an average dark frame, the dark level was ma-
limitedelectroderesolution,deformablemirrorscannotproduce
nipulatedinvariousways.ForPDprocessing,weestimatedand
evenlow-ordermodesperfectly.Whensuchalargefocushasto
subtracted∼10−4oftheintensityinholeAfromthesubfieldcon-
be compensated for, there are therefore unavoidable high-order
tainingholeF,measuredbasicallyasthemodalvaluewithinthe
wavefront errors. We have simulated our setup and calculated
PD processing subfield. Before the straylight kernel fitting, we the wavefront phase corresponding to the difference between a
alsosubtractedontheorderof∼10−4basedonthetop10rowsof
9cmdefocusandtheapproximatefocusproducedbythemirror
pixels.Becausethekernelfittinginvolvedadarklevel,d,which
in order to compensate for it. The resulting RMS wavefront is
wasestimatedto∼10−6,wecanbereasonablysurethatthestan-
0.14wavesat500nmandthecorrespondingStrehlratiois0.48.
dard dark-correction is correct to the 10−4 level. However, this ThisisevenworsethantheeffectsreportedinTable4byafactor
is insignificant in comparison with the ghost images, the most
1.6inRMSwavefront.
significant of which could be measured to ∼1% of the hole A
Wenoteagainthatthesemeasurements(andsimulations)are
intensity. Consequently, we have to allow for an additive com-
notdirectlycomparabletosolarobservations.Nevertheless,this
ponentatthe∼10−2level,whichisnotmodeledbythescattering effect may well contribute by a significant amount to the loss
kernels.
ofcontrastinSSTdata.TheSSTopticalsetupwillbemodified
to take this into account when we install our new 85-electrode
6. Conclusions deformable mirror during the summer or fall of 2012. Before
that,wewillalsotrytocompensatefortheeffectbyintroducing
We have proposed a procedure for measuring the amount of
acorrespondingfocuschangeintheSchupmannsystem.
straylight in the SST post-focus instrumentation and applied it
to one wavelength in the blue beam and one wavelength in the
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thedatacollection.TheSwedish1-mSolarTelescopeisoperatedontheisland
8