AY122A-AdaptiveOpticsLab

PurposeInthislab,afteranintroductiontoturbulenceandadaptiveopticsforastronomy,youwillget to experiment first hand the three main components of an adaptive optics system,namely thedeformablemirrorand thewavefrontsensor,and thereal-timecomputerandcontrol software. This lab makes use of the Thorlabs Adaptive Optics (AO) kit. EachThorlabs AO Kit is a complete adaptive optics imaging solution, including a deformablemirror, wavefront sensor, control software, and optomechanics for assembly. Theseprecision wavefront control devices are useful for beam shaping, microscopy, lasercommunications,andretinalimagingaswellaseducationaldemonstrations.

BackgroundAdaptive optics (AO) is a rapidly growing multidisciplinary field encompassing physics,chemistry, electronics, and computer science.AO systemsareused to correct (shape) thewavefrontofabeamoflight.Historically,thesesystemshavetheirrootsintheinternationalastronomy and US defense communities. Astronomers realized that if they couldcompensate for theaberrations causedbyatmospheric turbulence, theywouldbeable togenerate high resolution astronomical images; with sharper images comes an additionalgain incontrast,which isalsoadvantageous forastronomerssince itmeans that theycandetectfainterobjectsthatwouldotherwisegounnoticed.Whileastronomersweretryingtoovercome the blurring effects of atmospheric turbulence, defense contractors wereinterested in ensuring that photons from their high-power lasers would be correctlypointed so as to destroy strategic targets. More recently, due to advancements in thesophisticationandsimplicityofAOcomponents,researchershaveutilizedthesesystemstomake breakthroughs in the areas of femtosecond pulse shaping, microscopy, lasercommunication, vision correction, and retinal imaging. Although dramatically differentfields,alloftheseareasbenefitfromanAOsystemduetoundesirabletime-varyingeffects.Typically, an AO system is comprised from three components: (1) a wavefront sensor,whichmeasures these wavefront deviations, (2) a deformable mirror, which can changeshape in order to modify a highly distorted optical wavefront, and (3) real-time controlsoftware, which uses the information collected by the wavefront sensor to calculate theappropriate shape that thedeformablemirror should assume in order to compensate forthedistortedwavefront.Together,thesethreecomponentsoperateinaclosed-loopfashion.By this,wemean thatanychanges causedby theAOsystemcanalsobedetectedby thatsystem.Inprinciple,thisclosed-loopsystemisfundamentallysimple;itmeasuresthephaseas a functionof theposition of the opticalwavefront under consideration, determines itsaberration, computes a correction, reshapes the deformable mirror, observes theconsequence of that correction, and then repeats this process over and over again asnecessaryifthephaseaberrationvarieswithtime.Viathisprocedure,theAOsystemisableto improveoptical resolutionofan imagebyremovingaberrations fromthewavefrontofthelightbeingimaged.

EquipmentTheThorlabsAOKitIncludes:

o ContinuousSurfaceDeformableMirrorfromBostonMicromachines(BMC)o Shack-HartmannWavefrontSensoro LaserDiodeModule(635nm)o AllImagingOpticsandAssociatedMountingHardwareo FullyFunctionalStand-AloneControlSoftwareforWindows

Shack-HartmanWavefrontsensorTheroleofthewavefrontsensorinanadaptiveopticssystemistomeasurethewavefrontdeviations from a referencewavefront.There are three basic configurations ofwavefrontsensors available: Shack-Hartmann wavefront sensors, shearing interferometers, andcurvaturesensors.Eachhasitsownadvantagesintermsofnoise,accuracy,sensitivity,andeaseofinterfacingitwiththecontrolsoftwareanddeformablemirror.Ofthese,theShack-Hartmannwavefrontsensorhasbeenthemostwidelyused.

Figure 1: When a planarwavefront is incident on the Shack-Hartmannwavefront sensor'smicrolensarray,thelightimagedontheCCDsensorwilldisplayaregularlyspacedgridofspots.If,however,thewavefront is aberrated, individual spotswill be displaced from the optical axis of each lenslet; if thedisplacementislargeenough,theimagespotmayevenappeartobemissing.Thisinformationisusedtocalculatetheshapeofthewavefrontthatwasincidentonthemicrolensarray.

AShack-Hartmannwavefrontsensorusesalensletarraytodivideanincomingbeamintoabunchofsmallerbeams,eachofwhichisimagedontoaCCDcamera,whichisplacedatthefocal planeof the lenslet array. If a uniformplanewave is incident on a Shack-Hartmannwavefrontsensor(refertoFigure1),afocusedspotisformedalongtheopticalaxisofeachlenslet,yieldingaregularlyspacedgridofspots in the focalplane.However, ifadistortedwavefront (i.e., anynon-flatwavefront) isused, the focal spotswillbedisplaced from theopticalaxisofeachlenslet.Theamountofshiftofeachspot’scentroidisproportionaltothelocalslope(i.e.,tilt)ofthewavefrontatthelocationofthatlenslet.Thewavefrontphasecanthenbereconstructed(withinaconstant)fromthespotdisplacementinformationobtained(seeFigure2).

Figure2:TwoShack-Hartmannwavefront sensor screen capturesare shown: the spot field (left-handframe)andthecalculatedwavefrontbasedonthatspotfieldinformation(right-handframe).

The four parameters that greatly affect the performance of a given Shack-Hartmannwavefront sensor are the number of lenslets (or lenslet diameter,which typically rangesfrom~100–600μm),dynamicrange,measurementsensitivity,andthefocallengthofthelensletarray(typicalvaluesrangefromafewmillimeterstoabout30mm).Thenumberoflenslets restricts the maximum number of Zernike coefficients that a reconstructionalgorithm can reliably calculate; studies have found that the maximum number ofcoefficientsthatcanbeusedtorepresenttheoriginalwavefrontisapproximatelythesameasthenumberoflenslets.Whenselectingthenumberoflensletsneeded,onemusttakeintoaccounttheamountofdistortions/heistryingtomodel(i.e.,howmanyZernikecoefficientsare needed to effectively represent the true wave aberration). When it comes tomeasurementsensitivityθminanddynamicrangeθmax,thesearecompetingspecifications(seeFigure3totheright).Theformerdeterminestheminimumphasethatcanbedetectedwhilethelatterdeterminesthemaximumphasethatcanbemeasured.AShack-Hartmannsensor’smeasurementaccuracy(i.e.,theminimumwavefrontslopethatcanbemeasuredreliably)dependsonitsabilitytopreciselymeasurethedisplacementofafocusedspotwithrespecttoareferenceposition,whichislocatedalongtheopticalaxisofthelenslet.Aconventionalalgorithmwillfailtodeterminethecorrectcentroidofaspotifitpartiallyoverlapsanotherspotorifthefocalspotofalensletfallsoutsideoftheareaofthesensorassignedtodetectit(i.e.,spotcrossover).Specialalgorithmscanbeimplementedtoovercometheseproblems,buttheylimitthedynamicrangeofthesensor(i.e.,themaximumwavefront slope that can be measured reliably). The dynamic range of a system can beincreasedbyusingalensletwitheitheralargerdiameterorashorterfocallength.However,thelensletdiameteristiedtotheneedednumberofZernikecoefficients;therefore,theonlyotherwaytoincreasethedynamicrangeistoshortenthefocallengthofthelenslet,butthisinturn,decreasesthemeasurementsensitivity.Ideally,choosethelongestfocallengthlensthatmeetsboththedynamicrangeandmeasurementsensitivityrequirements.

Figure3:Dynamic rangeandmeasurement sensitivityare competingpropertiesofaShack-Hartmannwavefrontsensor.Here,f,Δy,anddrepresentthefocallengthofthelenslet,thespotdisplacement,andthelensletdiameter,respectively.Theequationsprovidedforthemeasurementsensitivityθminandthedynamic rangeθmaxareobtainedusing the small angleapproximation.θminis theminimumwavefrontslope that can be measured by the wavefront sensor. The minimum detectable spot displacementΔymindepends on the pixel size of the photodetector, the accuracy of the centroid algorithm, and thesignal tonoise ratioof the sensor. θmaxis themaximumwavefront slope that canbemeasuredby thewavefrontsensorandcorrespondstoaspotdisplacementofΔymax,whichisequaltohalfofthelensletdiameter.Therefore,increasingthesensitivitywilldecreasethedynamicrangeandviceversa.

15HzCCDSensorOurThorlabsAOkitisequippedwithaWFS150-5C1.3Megapixelwavefrontsensorhasawavefrontsensitivityofuptoλ/50RMSthankstothehighspatialresolutionoftheCCDsensor(4.65µmpixelpitch).Thissensoroperatesataframerateof15Hz,andisincludedwiththeAOK1AdaptiveOpticsKits(seeFigure4).

• CCD-BasedorHigh-SpeedCMOS-BasedWavefrontSensorsAvailable• WavelengthRange:300-1100nm• Real-TimeWavefrontandIntensityDistributionMeasurements• NearlyDiffraction-LimitedSpotSize• ForCWandPulsedLightSources• FlexibleDataExportOptions(TextorExcel)• LiveDataReadoutviaTCP/IP

Figure4:ThorlabsAOkitWFS15HzCCD,λ/50Sensitivity.Model

WFS150-5C.

Deformablemirror(DM)Thedeformablemirror(DM)changesshapeinresponsetopositioncommandsinordertocompensate for the aberrations measured by the Shack-Hartmann wavefrontsensor.Ideally,itwillassumeasurfaceshapethatisconjugatetotheaberrationprofile(seeFigure 5). In many cases, the surface profile is controlled by an underlying array ofactuatorsthatmoveinandoutinresponsetoanappliedvoltage.Deformablemirrorscomein several different varieties, but the two most popular categories are segmented andcontinuous(seeFigure6).Segmentedmirrorsarecomprisedfromindividualflatsegmentsthat caneithermoveupanddown(ifeachsegment is controlledby justoneactuator)orhave tip, tilt, and pistonmotion (if each segment is controlled by three actuators).Thesemirrorsaretypicallyusedinholographyandforspatiallightmodulators.Advantagesofthisconfiguration include the ability to manufacture the segments to tight tolerances, theelimination of coupling between adjacent segments of the DM since each actsindependently,andthenumberofdegreesoffreedompersegment.However,onthedownside,theregularlyspacedgapsbetweenthesegmentsactlikeadiffractionpattern,therebyintroducingdiffractivemodesintothebeam.Inaddition,segmentedmirrorsrequiremoreactuatorsthancontinuousmirrorstocompensateforagivenincomingdistortedwavefront.Toaddress theopticalproblemswithsegmentedDMs, continuous faceplateDMs(suchasthose included in our AO Kits) were fabricated. They offer a higher fill factor (i.e., thepercentage of the mirror that is actually reflective) than their segmentedcounterparts.However, their drawback is that the actuators are mechanically coupled.Therefore,whenoneactuatormoves,thereissomefiniteresponsealongtheentiresurfaceof the mirror. The 2D shape of the surface caused by displacing one actuator is calledtheinfluencefunctionforthatactuator.Typically,adjacentactuatorsofacontinuousDMaredisplaced by 10-20% of the actuation height; this percentage is known as theactuatorcoupling.NotethatsegmentedDMsexhibitzerocouplingbutthatisn’tnecessarilydesirable.

Figure5:TheaberrationcompensationcapabilitiesofaflatandMEMSdeformablemirrorarecompared.(a)Ifanunabberatedwavefrontisincidentonaflatmirrorsurface,thereflectedwavefrontwillremainunabberated. (b) A flat mirror is not able to compensate for any deformations in the wavefront;therefore, an incoming highly aberrated wavefront will retain its aberrations upon reflection. (c) AMEMS deformablemirror is able tomodify its surface profile to compensate for aberrations; theDMassumestheappropriateconjugateshapetomodifythehighlyaberratedincidentwavefrontsothatitisunaberrateduponreflection.

TherangeofwavefrontsthatcanbecorrectedbyaparticularDMislimitedbytheactuatorstroke and resolution, the number and distribution of actuators, and the model used todeterminetheappropriatecontrolsignalsfortheDM;thefirsttwoarephysicallimitationsof theDM itself,whereas the lastone is a limitationof the control software.Theactuatorstroke isanother termfor thedynamicrange(i.e., themaximumdisplacement)of theDMactuators and is typicallymeasured inmicrons. Inadequate actuator stroke leads to poorperformanceandcanpreventtheconvergenceofthecontrolloop.Thenumberofactuatorsdetermines the number of degrees of freedom that the mirror can correct for. Althoughmany different actuator arrays have been proposed, including square, triangular, andhexagonal,mostDMsarebuiltwithsquareactuatorarrays,whichareeasytopositiononaCartesiancoordinatesystemandmapeasilytothesquaredetectorarraysonthewavefrontsensors.Tofitthesquarearrayonacircularaperture,thecorneractuatorsaresometimesremoved(e.g., thedeformablemirror includedwith theAOK1-UM01orAOK1-UP01hasa12 x 12 actuator configuration but only 140 actuators since the corner ones are notused).Althoughmoreactuatorscanbeplacedwithinagivenareausingsomeoftheotherconfigurations,theadditionalfabricationcomplexityusuallydoesnotwarrantthatchoice.

Figure6: CrosssectionalschematicsofthemaincomponentsofBMC'scontinuous(left)andsegmented(right)MEMSdeformablemirrors.

Figure7(leftframe)showsascreenshotofacrossformedonthe12x12actuatorarrayoftheDMincludedwiththeadaptiveopticskit.Tocreatethisscreenshot,thevoltagesappliedto the middle two rows and middle two columns of actuators were set to cause fulldeflectionofthemirrormembrane.InadditiontothesoftwarescreenshotdepictingtheDMsurface, quasi-dark field illumination was used to obtain a photograph of the actual DMsurfacewhenprogrammedtothesesettings(seeFigure7,rightframe).

Figure 7: A cross-like pattern is created on the DM surface by applying the voltages necessary formaximumdeflectionofthe44actuatorsthatcomprisethemiddletworowsandmiddletwocolumnsofthearray.The frameon the left showsa screen shotof theAOkit softwaredepicting theDMsurface,whereas the frameon the right,whichwasobtained throughquasi-dark field illumination, shows theactual DM surface when programmed to these settings. Note that the white light source used forilluminationisvisibleinthelowerright-handcornerofthephotograph.

To facilitate installation and setup, each package includes the deformablemirror, driver,and control software. Thesemirrors are capable of changing shape in order to correct ahighlydistortedincidentwavefront.Micro-electro-mechanical(MEMS)deformablemirrorsare currently the most widely used technology in wavefront shaping applications giventheirversatility,maturityoftechnology,andthehighresolutionwavefrontcorrectionthattheyafford.These versatile DMs, which are fabricated using polysilicon surface micromachiningfabricationmethods,offersophisticatedaberrationcompensation ineasy-to-usepackages.Themirrorconsistsofamembranethatisdeformedby140electrostaticactuators(i.e.,a12x12actuatorarraywithfourinactivecorneractuators),eachofwhichcanbeindividuallycontrolled.Theseactuatorsprovide3.5μmstrokeoveracompactarea.Unlikepiezoelectricdeformable mirrors, the electrostatic actuation used with BMC's mirrors ensuresdeformationwithouthysteresis.BostonMEMSmulti-DMfeatures(Figure8):• Multi-DM:12x12ActuatorArray(140Active)• 3.5μmMaximumActuatorDisplacement• ZeroHysteresis• Sub-NanometerRepeatability(AverageStepSize<1nm)• LowInter-ActuatorCouplingof~13%ResultsinHighSpatialResolution• Gold-Coated• ProtectiveWindowwith6°WedgeandBroadbandAntireflectionCoatingfor400-1100

nm• Setofdriverselectronics.

Figure8:BMCMEMSMulti-DMwithitsdriverselectronics.

TheRTC&ControlSoftwareIn an adaptive optics setup, the control software is the vital link between thewavefrontsensor and the deformable mirror.It converts the wavefront sensor’s electrical signals,whichareproportionaltotheslopeofthewavefront,intocompensatingvoltagecommandsthataresenttoeachactuatoroftheDM.Theclosed-loopbandwidthoftheadaptiveopticssystemisdirectlyrelated to thespeedandaccuracywithwhich thiscomputation isdone,but in general, these calculationsmust occur on a shorter time scale than the aberrationfluctuations.Inessence,thecontrolsoftwareusesthespotfielddeviationstoreconstructsthephaseofthebeam(inthiscase,usingZernikepolynomials)andthensendsconjugatecommandstotheDM.Aleast-squaresfittingroutineisappliedtothecalculatedwavefrontphaseinordertodeterminetheeffectiveZernikepolynomialdataoutputtedfortheenduser.Althoughnotthe only form possible, Zernike polynomials provide a unique and convenient way todescribethephaseofabeam.Thesepolynomials formanorthogonalbasissetoveraunitcirclewith different terms representing the amount of focus, tilt, astigmatism, comma, etcetera; the polynomials are normalized so that the maximum of each term (except thepiston term) is +1, the minimum is –1, and the average over the surface is alwayszero.Furthermore, no two aberrations ever add up to a third, thereby leaving no doubtaboutthetypeofaberrationthatispresent.

LabactivitiesYourmaingoalforthislabistogetfamiliarwiththe3mainelementsofanAOsystem:thewavefrontsensor,thedeformableandtherealtimecontrolsystem.IMPORTANT NOTE: the hardware youwill be using is very sensitive to cleanliness andelectrostaticdischarges.Washyourhandspriortothelab,andwearanESDwriststrapatalltimeswhentouchingtheDManditselectronics.

PartI:alignmentandregistrationThe AO kit has been assembled and tested prior to the lab. It is in fully functioning order.Unfortunately,anearthquakeofmagnitude6(notquitethebigone!)thismorninghasbrokenthe alignment of the wavefront sensor and final CMOS camera. Your mission, should youchoosetoacceptit,istorealignthesystemandregistertheSHWFStotheDM.Foreachstepinthealignmentandcalibration,describethestateofthesystem,youractions(hardwareandsoftware),andtheresultofyouractions.

Figure9:SchematicshowingthemajorcomponentsincludedwiththeAdaptiveOpticsKits.L,M,DM,BS,andBDrefertolens,mirror,deformablemirror,beamsplitter,respectively.

If you are not familiar with Thorlabs' 30 mm cage assemblies, they consist of cage-compatiblecomponentsthatareinterconnectedwithØ6mmcagerods.Thisdesignensuresthattheopticalcomponentshousedinsidethecagesystemhaveacommonopticalaxis.

The first two preassembled cage sections of the AOK1-UM01 consist of a lens L1, irisdiaphragm,fouridentical75mmfocallengthlenses(L2-L5).Light is exiting the fiber-fed star simulator and collimated by L1. It then hits an irisdiaphragmwhichdefinestheentrancepupilofthesystem.TwoLA1608-B75mmfocallengthlensesareusedtoimagethesystempupilontotheDM.ByhavingthesystempupilattheDMsurface,therangeofactuationneededtocorrectforanyaberrationsisminimized.TheDMreflects thebeam througha shallowangleof~30° into thesecondpreassembledcage section. This section contains twomore 75mm focal length lenses, which are onceagainhousedusingaCP02CagePlate.TheselensesareusedtoplacetheDMinaplanethatisconjugatewiththeShack-Hartmannlensletarray,therebyenablingtheAOkitsoftwaretooptimizethepositionoftheDMactuators.Afterexitingthethirdcagesubassembly,a92:8pelliclebeamsplitter(BS)isusedtodirectasmallportionofthelighttothelastmajorcomponentoftheAOkit,theWFS150-5CShack-HartmannWavefront Sensor. Theportionof light transmittedby thebeamsplitter canbelaunchedintoanapplication,hereacoronagraph(subjectofanotherlabsession),andmoreimportantlyfortodayareimagingCMOScamera.

PartII:calibrationandclosedloopoperationBuild the interaction matrix (IM) between the BMC MEMS Multi-DM and SH WFS, andsuccessfullyclosetheloop.Step1:calibratespotintensities.Step2: measure interaction matrix between DM and SH-WFS by moving each actuatorsequentiallyandrecordingthespotmotionontheWFS.Step3: verify calibration (control matrix, invert of interaction matrix is displayed) andautomaticpupilillumination.Step4:closetheloop,andmonitorsystemstability.Step5:perturbthewavefrontinthesamplelocationbyinsertinglenses,plasticsheets,etc…andnotethesystem’sreaction.Foreachstepinthealignmentandcalibration,describethestateofthesystem,youractions(hardwareandsoftware),andtheresultofyouractions.

LabreportinstructionsTreatthislabreportasanyhomeworkassignment.Youareencouragedtotakenotesduringthelab.Thereportshouldcontainthefollowingelements.

1. Introduction:purposeoftheexperimentandexplainhowitwillbeaddressedwiththeequipment.

2. Summaryofequipment:Describewhatequipmentwassetup,andwhy.Sketchthelayout.Provideenoughdetailtoallowothertorepeatyourexperiment,ortofigureoutwhatwentwrongifsomethinggoesawry.Don’tjusttranscribethelabhandout,but accurately describe the equipment used. Record during the lab session (takepicturesifneeded/relevant).

3. Measurements: Describe what measurements were made. Indicate uncertaintyestimateswhenever possible, andmake sure they’re reasonable. Checkmeasuredvaluesagainstexpectations.Describeanyproblems(e.g.,equipmentproblems)anddiscusswhatstepsweretakenasaresult.Recordduringthelabsession.

4. Dataanalysis:Discusshowyouconvertedyourrawmeasurementsintomeaningfulresults,ifapplicable.Showrelevantequationsandcalculation.Showtablesandplotswhen appropriate, using axis labels and explanatory captions. Answer anyembeddedquestions in the lab instructions.Discusssourcesoferror,andquantifymeasurement errors in your end results, paying attention to significant figures.Clearlystateyourconclusions.

5. Interpretationanddiscussion:Whatdoyourresultsmean?Discussanyunexpectedresultsandtrytoexplainthem.Whatmightyoudodifferentlynext time,andhowcouldthelabbeimproved?Includeabriefdiscussionofwhatyoulearned.Thiscanbedoneathomeafterthelab.

6. Summaryandconclusion:This should referback to the introductorymaterial andsummarizeyourresultsrelativetoyourexpectations.

Additionalproblemset:seeing,coherencetimeandisoplanaticangleOnOct22, 2015between20:00HSTand22:00HSTonMaunaKea, theDIMMandMASSseeingmonitorsbothconsistentlymeasuredaburstofbadseeing,peakingatroughly≃1”.0(seefigure10).Calculatethefollowingquantities:

1. TheFriedparameterr0correspondingtothe≃1”.0seeingmeasurement.2. DerivethecorrespondingFriedparameterandequivalentseeingangleatthesciencewave

lengthintheKband.3. Referring to the figure 11 below, and assuming a wind speed of 10 m/s for the

dominant turbulent layer, compute the coherence time at both the DIMM/MASSwavelengthandsciencewavelength.

4. Whatwastheisoplanaticangleattheworstofthisbadseeingburst.Bonusquestion:describewhytheDIMMandMASSprovidedifferentseeingmeasurements,and explainwhatmight have happened during the burst of bad seeing (hint: look at thefigure11).

Figure10:DIMM/MASSmonitorforMaunaKeaonOct22,2015.

Figure11:MASSCN2turbulenceprofileaboveMaunaKeaonOct22,2015.