How to Optimize NonSequential Optical Systems.docx
《How to Optimize NonSequential Optical Systems.docx》由会员分享,可在线阅读,更多相关《How to Optimize NonSequential Optical Systems.docx(22页珍藏版)》请在冰豆网上搜索。
HowtoOptimizeNonSequentialOpticalSystems
HowtoOptimizeNon-SequentialOpticalSystems
Thisarticlegivesarecommendedapproachtotheoptimizationofnon-sequentialopticalsystems. TherecommendedmethodsaretousePixelInterpolation,aggregatedetectordata(momentofilluminationdata)andtheorthogonaldescentoptimizer.Asanexample,afree-formmirrorisoptimizedtomaximizethebrightnessofanLEDfrom23Cdto>250Cdinjustafewminutesofoptimization.
AuthoredBy:
AkashArora
Introduction
Optimizationistheprocessbywhichadesignisimprovedbychangingthevaluesofasetofparameters(calledvariables)suchthatthevalueofameritfunctionisreduced,orideally,driventozero.Theprocessrequiresdefinitionofperformancecriteriaviathemeritfunctionandeffectivevariablestoachievethisgoal.Thisarticleprovidesarecommendedapproachfortheoptimizationspecificallyofnon-sequentialopticalsystems.Therecommendedapproachis:
∙UsePixelInterpolationonalldetectorsthatareusedinthemeritfunction,toavoidquantizationeffectsduetopixelateddetectors.
∙Useaggregatedatafromthesedetectors,suchasRMSspotsize,RMSangularwidth,angularcentroid,centroid locationetcratherthanthedatacontainedinspecificpixels.This'MomentofIllumination'dataismuchsmoothertooptimizethananyspecificpixel'sdata.
∙UsetheOrthogonalDescentoptimizeratthestartoftheoptimizationprocess,andthenrefinetheresultwiththedampedleastsquaresand/orHammeroptimizers.OthogonalDescentisusuallymuchfasterthanthedampedleastsquaresoptimizer,butmayyieldslightlylessoptimalsolutions.UseOrthogonalDescentfirst.
Asanexample,afree-formmirrorisoptimizedtomaximizethebrightnessofanLEDfrom23Cdto>250Cdinjustafewminutesofoptimization.
DampedLeastSquaresvsOrthogonalDescent
TherearetwolocaloptimizationalgorithmsinZemax:
dampedleastsquares(DLS)andorthogonaldescent(OD).DampedLeastSquares(DLS)usesnumericallycomputedderivativestodetermineadirectioninsolutionspacewhichproducesadesignwithalowermeritfunction.Thisgradientmethodhasbeendevelopedspecificallyforopticalsystemdesignandisrecommendedforallimagingandclassicalopticaloptimizationproblems.Intheoptimizationofpurenon-sequentialsystemshowever,DLSislesssuccessfulbecausedetectionisperformedonpixelateddetectors;themeritfunctionisinherentlydiscontinuousandthiscancausethegradientmethodtofail.
BelowisascanofthemeritfunctionofaNSsystemasafunctionofjustonevariable.
Itcanbeseenthatforlongregionsofmeritfunctionspace,thereisnochangeinthemeritfunctionatall,andwhenchangedoescomeitissuddenanddiscontinuous.Thismakesoptimizationbygradientsearchtechniquesdifficult.
OrthogonalDescent(OD)optimizationusesanorthonormalizationofthevariablesanddiscretesamplingofsolutionspacetoreducethemeritfunction.TheODalgorithmdoesnotcomputenumericalderivativesofthemeritfunction.Forsystemswithinherentlynoisymeritfunctions,suchasnon-sequentialsystems,ODwillusuallyoutperformDLSoptimization.Itisveryusefulinoptimizationproblemslikeilluminationmaximization,brightnessenhancement,anduniformityoptimization.
PixelInterpolationandNSDD
Inadditiontothespecificalgorithmused,ZemaxcontainsseveralfeaturesthatsignificantlyimprovetheoptimizationofNSsystems.
Asmentionedpreviously,NSsolutionspacetendsbediscontinuousduetothepixelatednatureofdetectors.Iftheenergyinagivenrayisassignedtoonlyonepixel,thereisnoquantitativedifferencewhenasystemchangecausestheraytoshiftanywherewithinthatpixel.Asaresult,optimizationisdifficult,withdiscontinuousderivativesinthemeritfunctionoccurringwhenaraycrossestheboundaryintoanewpixel.
Thiscanbeillustratedbyscanningasinglerayacrossadetector.Theuniversalplotbelowshowshowtheirradiancecentroidonadetectorchangeswithraylocation.
Onewaytosolvethisproblemistousepixelinterpolation.Insteadof100%ofaray’senergybeingassignedtothesinglepixelstruck,afractionoftheenergyisapportionedtoadjacentpixelsbaseduponthelocationoftherayinterceptinsidethepixel.Asaresult,thereisanoticeablechangeinthemeritfunctionasasystemchangecausesaraytomoveacrossapixel.
PixelinterpolationcanbeenabledintheObjectproperties>Typetab.
Ifwescanarayacrossadetectorwithpixelinterpolationenabled,thechangeinirradiancecentroid,andmostothercriteria,iscontinuous,andDLScanbeeasilyused.
TheirradiancecentroidreportedinthemeritfunctioniscomputedusingtheNSDDoptimizationoperand.NSDDstandsfornon-sequentialdetectordata,andisthemostusefuloperandforreportingincoherentdetectordata.NSDCistheequivalentforcoherentcalculations.ThesyntaxfortheNSDDoperandisasfollows:
NSDD Surf Det# Pix# Data
Surfdefinesthenon-sequentialgroupsurface(1inpureNSC),Det#definesthedesireddetectorfromwhichtoreportdata(itcanalsobeusedtoclearoneoralldetectors),Pix#definesthespecificpixelorcomputedvaluetoreturnandDatadefineswhethertoreturnflux,irradianceorintensitydata.Theseargumentsallowoptimizationofanumberofcriteria:
minimumspotsize(minRMSspatialwidth),maximumenergy(totalflux),spatialuniformity(standarddeviationofallpixels),collimation(minimumRMSangularwidth),andmore.ForadetaileddescriptionofNSDDcapabilities,seetheOptimizationchapterintheZemaxuser’sguide.
SystemSetup
Light-emittingdiodes(LEDs)areimportantlightsourcesinawiderangeofapplications.Inareaslikeautomotiveilluminationanddisplaylighting,itisoftenrequiredtoimproveonthebrightnessofanLEDbyaddingauxiliaryopticstomodifytheluminousintensityofsuchasource.
WewillstartwiththemeasureddatafromarealLEDsource.SeethisarticleformoredetailsonhowtheLEDismodeled:
fornow,allweneedtoknowisthata“sourceradial”isusedtoinputthemeasuredpowerasafunctionofangle.Thesourcewasmeasuredtohaveatotaloutputpowerof27Lumens,andisreasonablymonochromaticwithapeakwavelengthof627nm.SeethearticleHowtoCreateaSimpleNon-SequentialSystemifyouarenotfamiliarwithhowtoenterthisdata.ThesourceusesSobolsamplingforbestsignal/noisewithfewestrays.
UnderGeneral...Unitswesetthesystemunitsasfollows:
TheluminousfluxoftheLEDismeasuredinunitsofLumenssowechoosethatunitforthissimulation.Illuminanceisthereforemeasuredintermsoflm/m2,orLux.Luminousintensity("brightness")ismeasuredinlumens/steradianorCandela(Cd).Luminanceismeasuredinlm/m2/sr,orCd/m2,whichissometimesreferredtoasanit.
Thestartingsystemissetupasfollows:
TheLEDsourcefiresraysontoaflatmirrorwhichthenilluminatesadetectorsurface.Thisfilecanbedownloadedfromthelinkattheendofthisarticle.Thedetectorseesthefollowingspatialandangulardistributions:
ItcanbeseenthatthemirrorisslightlyoverfilledbytheLED,andsothespatialandangulardistributionsareslightlyasymmetric.Thisisdonedeliberately,justtoaddalittlemorecomplexitytothedesign.
Lookingattheluminousintensityplot,itcanbeseenthatpeakbrightnessofabout41Cdoccursatpolaranglesofaround27degrees.Rayswhichareapproximatelynormaltothedetectorsurfacehavealuminousintensityofonly22Cd(howthisnumberisobtainedisdiscussedonthenextpage).Suchaprofileisnotgoodforaheadlampilluminationsystem,orprojectorilluminationsystem.Itisgenerallydesiredtohaveashighbrightnessforlow-angleraysaspossible,sothesourcecanbeprojectedoveradistance.
Wewillnowoptimizetheshapeofthemirrortogivethehighestbrightnessonaxis.Todothis,wemustperformthefollowingsteps:
•Defineameritfunctionthatdescribeswhatwewanttoachieve
•Definehowthemirrorsurfacecanchange
•Runanoptimization
TheMeritFunction
Ameritfunctiondefinesthe'quality'ofanopticaldesign,intermsofhowwellthedesignmeetsitsspecifiedoperatingcharacteristics.Inthiscase,wewanttogetthehighestbrightness(luminousintensity)atzerodegreesangle.ThisiseasilyachievedwiththeNSDDandNSTRoperands.
Inthisdesign,thedetectorisobjectnumber3,andwewanttoobtaintheluminousintensityatzerodegrees.Thedetectorviewershowsthis:
Thisshowstheangularrangeoftheraysthatareincidentonthedetectorfromtherange-90°to+90°inbothxandy.Norayslandwithanglesbeyondabout35°becausetheLEDdoesnotemitbeyondthisangle.Peakintensityoccursataround27degrees.Weareinterestedinthepowerlandingatanglesclosetozero.Therearetwocriteriathatwilltargetsuchadistribution:
RMSangularwidthandluminousintensitycentroid.TheRMSwidthtargetsraystobecollimated(i.e.thesameangleofincidence),andthecentroidtargetsthisangleofincidencetobezero.Thefollowingmeritfunctionretrievestheluminousintensityseenatthisangle:
ThefirstNSDDoperandreadsoutdetectorobject0,whichdoesnotexist;noobject0canexist.Thisisaspecialusageoftheoperand:
Zemaxinsteadclearsalldetectors.Alternately,detectorsmaybeclearedonanindividualbasisbydefininganegativenumber(i.e.Det#=-3clearsonlydetector3).Thisisusefulinasystemwithmultipledetectorsdefined.
Then,theNSTRoperandtellsZemaxtotracerays.