How to Optimize NonSequential Optical Systems.docx

How to Optimize NonSequential Optical Systems.docx

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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.