Week6 •  “Midterm”scheduledMarch24
•  Lab2deadlinewillbe…
–  NoteskybrightnessGoogledoc
•  Lab3isoutthere.
–  RRLyraeGoogleDocswateringholeexists
•  Lab3observingcoordinaFonwillhappenduringeveningsessions
thisweekaswellasiniFalintroducFontoPythonreducFontools.
–  StellarphotometryandFme-seriesperiodfindinginparFcular
•  Reminder:Commentyourcodeusing“markdown”
–  TurnincalculaFonsasa“markup”commented.ipynb
–  Filename“lastname_something.ipynb”
•  Reminder:Nameyourlabswriteupsomethinguseful
–  Lastname_lab02.pdf(alsogoodifyousubmitpdf)
Week6 •  Topicsthisweek
–
–
–
–
–
–
FabricaFnglargetelescopeopFcs
LargetelescopeopFcalconfiguraFons
Astronomicalcatalogsandephemerides
AstronomicaldigitalimagerepresentaFon
Stellarphotometry
CounFngstaFsFcs
VernierScales
•  The6”doghousetelescopehasaprecision“Vernier”scaleonthe
DeclinaFonwheel.
•  Usethe“0”tofindthecoarsevalue.FindwheretheFckmarksline
uptoestablishthe“fine”value.
–  Tenthsatright
–  Arcminutesbelow
Consideranexperimenttomeasureπ
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  Note that about 1 in 100 times
a legitimate measurement lies
2.5 sigma from the mean.
•  32% of measurements are
more than 1 sigma away.
•  Outliers are a natural
consequence of measurement
•  Single measurements can be
dangerous.
3.1400
3.1410
3.1420
3.1430
Consideranexperimenttomeasureπ
•  Suppose you conduct 1000’s of
trials and make a histogram of the
number of times each measured
value occurred.
•  The uncertainty in the final
mean measured value –
estimated by the precision to
which you have determined the
peak of the distribution - is
quite small and much smaller
than the standard deviation by:
σ _ mean = σ _ distribution / Nsamples
•  Many imprecise measurements
can produce a precise result.
3.1400
3.1410
3.1420
3.1430
TelescopeMirrorPrecision
•
•
•
Mirrorscanonlydeviatefromthedesiredshape(usuallyaparabola)byafracFonofthe
shortestoperaFngwavelength.
Bluelighthasawavelengthof400nm,so50nmprecisionorbe[erisdesirable.
–  Acrossan8meterdiameterthisraFoisaboutonepartin108.
–  ExpandedtothesizeoftheU.S.thepeaksandvalleyswouldbeaboutgrapefruitsized.
Themirrorsupportstructuremustholdthispreciseshapeasthetelescopepointsaround
thesky.
Mirror Lab “Stressed
Lap” Polishing
MirrorGrinding
•  Glassisanamorphous(non-crystalline)solid.Itchips
(coarsegrinding)andflows(polishing)responsivelyand
enablesreachingsub-wavelengthprecision,evenbyhand.
•  Only spherical surface of
identical radius fit
together with no gap.
Casting a Mirror
Melting glass time lapse
Giant Magellan mirror fabrication
CassegrainTelescopesandCompoundOpFcs
•  ACassegraintelescopeisatwo-opFcsystem.
–  Theprimaryformsarealimage.
–  Thesecondary,whichhasanegaFvefocallength,relaysthisrealimageto
anotherrealimageinthefocalplanebehindtheprimarymirror.
–  InaCassegrainconfiguraFonthenegaFvesecondaryinterruptsthe
convergingbeamfromtheprimarybeforetherealimageforms,butthe
imageisthereforcalculaFon'ssakenonetheless
CompoundOpFcs
•  VirtuallyallopFcalsystemscontaintwoormoreelements.
•  Mostsystemscanbereducedtoanequivalentsinglethinlens.
•  Thefinalfocus(andfocalraFos)ofthatimaginarythinlensresults
frompropagaFngimagesthroughthesystemoneobject/image
pair/lensataFme.
TheThinLensEquaFon
•  Foralensofagivenfocallengththedistanceatwhichanimageis
formeddependsontheobject'sdistance.
•  Inastronomyd0,theobject’sdistance,istypicallyinfinitesothe
imageisonefocallengthawayfromthelens.
•  IncompoundopFcseachimagebecomesthe“object”forthenext
element.
•  ForthethinlensequaFoninthisformobjectdistancesareposiFvetothelehofthelens,
imagedistancesareposiFvetotheright.
•  ObjectandimagedistancescanbenegaFve.
CassegrainTelescopesasCompoundOpFcs
•  ACassegraintelescopeisatwo-opFcsystem.
–  Theprimaryformsarealimage.
–  Thesecondary,whichhasanegaFvefocallength,relaysthisrealimageto
anotherrealimageinthefocalplane.
–  InaCassegrainconfiguraFonthesecondaryinterruptstheconvergingbeam
fromtheprimarybeforetherealimageforms,buttheimageistherefor
calculaFon'ssakenonetheless.
In a “classical” Cassegrain the primary is parabolic requiring a hyperbolic
secondary to form optimal images.
CassegrainTelescopesasCompoundOpFcs
•  ACassegraintelescopeisatwo-opFcsystem.
–  Theprimaryformsarealimage.
–  Thesecondary,whichhasanegaFvefocallength,relaysthisrealimageto
anotherrealimageinthefocalplane.
–  InaCassegrainconfiguraFonthesecondaryinterruptstheconvergingbeam
fromtheprimarybeforetherealimageforms,buttheimageistherefor
calculaFon'ssakenonetheless.
A “Ritchey-Chretien” telescope has both a hyperbolic primary and secondary.
This combination results in better off axis performance.
Schmidt-CassegrainTelescopes
•  ThisconfiguraFonusesaspherical(!)primarymirror.
–  LightentersthrougharefracFve(butweak)“correctorplate”that
compensatesforthesphericalaberraFon(makestheprimarylooklikea
parabola).
–  No“spider”sincethecorrectorplatesupportsthesecondary.
Curvature grossly exaggerated
SphericalAberraFon
•  An“on-axis”aberraFonthatarisesfromdifferentradialzones
(rings)onaopFcproducingafocusatdifferentdistances.
–  Spheresaretheposterchildforthiseffect,thusthename.
–  ByitsgeometricaldefiniFon,aparabolaisfreeofsphericalaberraFon(but
guiltyofothers).
GregorianTelescopes
•  IntheGregorianconfiguraFontheconcavesecondarymirrorlies
beyondtheprimefocusoftheprimary.Arealimageisformedin
spaceaheadofthesecondary.
SerrurierTrusses
•  ACassegraintelescopeconsistsofanextremelymassiveprimary
mirrorandalightweightsecondarymirrorthatmustbeheldrelaFve
tooneanotherwithaprecisionoftensofmicronsasthetelescope
pointsaroundthesky.
•  Telescopemountssagundertheweightoftheirmirrorsandsupport
elements.Engineerthesagtocancelout!
BalanceandCounterweights
l
Since motor (and human) drives tend to be of
modest capacity, telescopes are exquisitely
balanced on their axes.
-
-
-
l
most (unclamped) telescopes can be swung on both
axes with a finger.
movable counterweights adjust the balance.
every instrument change requires re-balance.
An out of balance telescope is a hazard (a
potentially fatal one).
-
Never disconnect an instrument from a telescope
without considering the consequences of lost
balance, especially the action of lever arms.
BalanceandCounterweights
l
Since motor (and human) drives tend to be of
modest capacity, telescopes are exquisitely
balanced on their axes.
-
-
-
l
most (unclamped) telescopes can be swung on both
axes with a finger.
movable counterweights adjust the balance.
every instrument change requires re-balance.
An out of balance telescope is a hazard (a
potentially fatal one).
-
Never disconnect an instrument from a telescope
without considering the consequences of lost
balance, especially the action of lever arms.
GearMeshandPreloads
•  Outofnecessity,gearteethdon’tmesh
perfectly
–  Iftheydidthenthegearswouldgetstuckor
wearexcessively.
•  Atelescopedrivewillpushthetelescope
alongonthetrailingsideofthegearteeth(or
willletthetelescoperidealongonthe
leadingside)
–  Whichoneofthesedependsonbalance.
•  Aperfectlybalancedtelescopewill“float”
betweengearteeth.
–  Sincethisslopecanbeanarcminuteofangle,
perfectbalanceisactually“bad”.
•  A“preload”isaweightorweakmotordrive
intendedtode-balancethetelescopeslightly
toforceittorideononegeartoothsideor
theother.
–  Eachaxis(RAorDec,AltorAz)needsapreload
TelescopesWithoutBalanceIssues
•  Butwithotherrelatedproblems.Angularmomentumis
conserved....
KeplerandRadiaFonPressure
SomemoreLabFeedback
•  Makereportedmeasurementsreproducible
–  Detailsofmethods
–  Sourcesofuncertainty
–  SpeculaFonaboutunexpectedoutcomes
•  MeFculousstaFsFcs
–  AppropriatepropagaFonofuncertainFes
–  Correctnumberofsignificantfigures
–  AppropriateuseofstandarddeviaFonvs.standarddeviaFonofthemean
(sqrt(N)scaling)
SomemoreLabFeedback
•  Makereportedmeasurementsreproducible
–  Detailsofmethods
–  Sourcesofuncertainty
–  SpeculaFonaboutunexpectedoutcomes
•  MeFculousstaFsFcs
–  AppropriatepropagaFonofuncertainFes
–  Correctnumberofsignificantfigures
–  AppropriateuseofstandarddeviaFonvs.standarddeviaFonofthemean
(sqrt(N)scaling)
•  AprofoundperspecFve….
–  “NoFngandreporFngreadingsofdials–Oxfordphilosophy’spictureof
experiment–isnothing.AnotherkindofobservaFoniswhatcounts:the
uncannyabilitytopickoutwhatisodd,wrong,instrucFveordistortedinthe
anFcsofone’sequipment”--IanHacking
RRLyraeScheduling
•  Reminderslide….
StarCatalogs
•  Youdon’thavetoobserve
withatelescopeanymore!
Othershavedoneitforyou…
–  Everystarvisibletotheunaided
eyewascatalogedlongago.
–  Today’sskysurveyshave
createdextensivelistsofthe
posiFonsandmagitudesof
billionsofstarsacrossthe
electromagneFcspectrum.
–  Thefirststepinresearchinga
parFculartargetisfindingout
whatisalready(likely
extensively)known.
Not a “picture” !!
Simbad,VizieR,Aladin
•  EnteranidenFfier(name)orcoordinatesandget
instantaccesstoexisFngmeasurementsofthesource,
referencestopapersaboutthesource,skyimages,and
more…
simbad
IRSA
CatalogAdjustments:ProperMoFon
•  AllstarshaverandomvelociFesrelaFvetous.Someareclose/fast
enoughtohavesignificantannual“propermoFon”
–  Barnard'sStar(17h57m+04d41m)istherecordholderat10.3”peryear.
–  Catalogsget“stale”overFmewithoutprecisepropermoFonmeasurements.
CatalogAdjustments:StellarParallax
•  TheposiFonsofnearerstarsshihmorethanthoseofmoredistant
starsduetotheannualmoFonoftheEarth.
–  Thelargestparallaxis0.75”-1.5”annualmoFon,soitisasmalleffect.Most
stellarparallaxesareunobservable(<0.001”)
Stellar Parallax
q
The positions of nearer stars shift more than those of more distant stars due to
the annual motion of the Earth.
PlanetaryEphemerides
•  SolarSystemobjectscanmovesubstanFallyfasterthanthehighest
propermoFonstars.
–  Updatedcoordinatesmayberequiredhour-to-hourorevenminute-tominute(orsecond-to-secondfornear-Earthasteroids).
–  TheJPLHorizonssystemprovidesoneofthemostcomprehensiveandflexible
ephemeriscalculators.
–  AlternaFvely,XEphemprovidesgoodcoordinatesandhastheopFonof
loadingobjectfileswiththeorbitalelementsofSolarSystemobjects.
Atmospheric Transmission vs. Wavelength
text
l
AtmosphericTransmissionvs.Wavelength
Spitzer Infrared
•  SoluFon1–leavetheatmospherebehind
Hubble – Ultraviolet, Visible, Infrared
Compton Gamma-ray
Observatory
AtmosphericTransmission
•  MolecularabsorpFon,waterinparFcular,contributessubstanFal
atmosphericopacityintheinfrared.
MaunaKea–14,000feet
AtmosphericTransmissionintheSubmillimeter
•  TheAtacamaLargeMillimeterArray(ALMA)issitedat17,000feet
alFtudeinoneofthedriestdesertsonEarth.
AtmosphericTransmission
•  Sincewaterpredominatelyresidesinthetroposphere,youjusthave
togetintothestratospheretoseeintospace.
AtmosphericTransmission
•  Sincewaterpredominatelyresidesinthetroposphere,youjusthave
togetintothestratospheretoseeintospace.
SOFIA flies at
40,000 feet. High
altitude balloons
can take massive
payloads to
120,000 feet.
Atmospheric
Extinction
Calibrating stellar
photometry requires
correction for loss of light
passing through the
atmosphere.
l
Extinction Correction in Practice
In each filter measure the star at a variety of airmasses (Δx
below is (airmass – 1)) and determine the extinction in units of
magnitudes per airmass for each observing band.
l
Alternatively, have a calibrated star in your field of view (easy in
the era of sky surveys.
l
Time
Variability of Extinction
SystemaFcs,I
• ExFncFon
–  Rayleighsca[ering
(opFcal;proporFonal
tostaFcpressureand
airmass)
–  Ozone(opFcal)
–  Water(IR)
–  Volcanicaerosols
•  Canvaryby0.1-1%
•  Episodicproblem
•  IRimpactuncertain
SCTF1/29/2014
NabroerupFon,13June2011
(Bourassa,etal.(2012))
!
46
!
Filter Bandpasses
Calibrating observations precisely is dependent upon having
precisely defined bandpasses.
l
Infrared Bandpasses
Atmospheric absorption provides natural boundaries for defining
infrared filter bandpasses.
l
Stellar Photometry with Filters
Differences between magnitudes (which are ratios when you
think about it) measured in different filters are diagnostic of
temperature of blackbodies (stars).
l
V R
I
Stellar Photometry with Filters
These color differences become more diagnostic (for example of
luminosity class) when you account for stellar spectral features
and how they change with stellar surface gravity.
l
The Ideal Imaging Device
TheIdealImagingDevice
•  Reportscounts/eventsincells
•  Detectsonlyphotonevents–nonoise
–  Norandomcounts
–  Noleakageof“fake”signal
•  Doesnot“miss”incidentphotons
–  Perfect“quantumefficiency”
–  100%“fillfactor
•  Doesnotsaturate
–  Infinite“well”capacity
•  UniformsensiFvityfrompixeltopixel
–  Perfect“flatfield”
Real-worldImagingDevices
•  Reportscounts/eventsincells
–  MeasureselectronicsignalproporFonalto
counts.
•  Detectsonlyphotonevents–nonoise
–  Norandomcounts
–  ElectronicmeasurementissuscepFbleto
noise–fakecounts…
–  Noleakageof“fake”signal
•  “Darkcurrent”createscountsnot
originaFngfromphotons.
•  Doesnot“miss”incidentphotons
–  Perfect“quantumefficiency”
–  100%“fillfactor
–  Nope…butclose
•  Doesnotsaturate
–  Infinite“well”capacity
–  Maximumcountcapacityinanycell.Ifthe
sourceistoobrightthemeasurementfails.
•  UniformsensiFvitypixeltopixel
–  Nope…butcloseagain
FITSFormat:BehindtheCurtain
•  Imagestorageand“representaFon”aretwodifferentthings.
•  Aseriesofnumbersrepresentsatwodimensionalimageifyouhave
theformatandother“metadata”available.
•  FITSfilesconsistofametadatatext“header”followedbydata
values.
–  Theheaderconsistsofanintegralnumberof2880characterblocks.
•  Eachblockcontainsaseriesof80character“keyword”parameters
•  Thelastkeywordofthelastblockis“END”paddedoutbyblanks
•  Thefirstbytes(howmanyandwhatsortdependontheheader
informaFon)ofthenextblockisthefirstpixeloftheimage.