binary optical and zemax.docx

binary optical and zemax.docx

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binaryopticalandzemax

ZEMAXUsers'KnowledgeBase -

HowtoDesignDiffractiveOpticsUsingtheBinary2surface

Nam-HyongKim

By Nam-HyongKim

Publishedon 26September2005

Thisarticleexplains:

∙HowdiffractivesurfacesaremodeledinZEMAX

∙Howtousethe Binary2surfacetomodeladiffractiveopticalelement

ThisarticleillustratestheuseofBinary2surfaceusingasamplefile.Thesamplefilecanbedownloadedfromthelastpageofthearticle.

TheBinary2Surface

ZEMAXDevelopmentCorporationthanksMr.RobertE.FischerofOptics1forthepermissiontousethegraphicsfromhisbookOpticalSystemDesign,andalsoforprovidingustheoriginalgraphicfiles.

Manysurfaces inZEMAXcanhavediffractivepowerinadditiontorefractivepower.Diffractivepowerisindependentoftheindexandthesurfacesag and changesthe phaseoftherays. FormoreinformationonhowdiffractivesurfacesaremodeledinZEMAX,pleaserefertothearticle"HowDiffractiveSurfacesareModeledinZEMAX."

Thediffractivepower inaBinary2surfaceintroducescontinuousphase changeacrossthe surface accordingto thefollowingformula:

 wherethecoefficientsAiareinunitsofradians.

Sincethephase change iscontinuousacrossthesurface, aBinary2surfacerepresentsanidealbinarydiffractiveopticalelement,inwhichthesizeofthebinary（discrete）stepsareinfinitesimallysmalloratleast verysmallcomparedtothewavelength.

Generally,thephysicalDOEmodeledbytheBinary2surfacewillhavediffractivezoneswith varyingperiodasafunctionofradialdistancefromthevertex,asshowninthefollowingdiagram. ZEMAXcancalculatethe radialcoordinates ofeachdiffractionzone,wherethephasediffersexactlyby2πfromadjacentzones.

Figure13.5fromOpticalSystemDesign

Theamountofphaseinwaves addedbyaBinary2surfaceataparticularradialcoordinateisindependentofwavelength.Thewavelength-dependentopticalpathlength（OPL）isgivenby

OPL=（Phase*wavelength）/（2π）

ThefollowinglayoutshowsthechromaticeffectduetoaBinary2surface.

AchromatizationusingBinary2:

A

TheBinary2surfaceisoftenusedforachromatization.ConsiderasimplesingletlensinwhichthelongerwavelengthfocusesatalargerZdistancefromthelensthantheshortwavelength. ArotationallysymmetricDOEsuchasBinary2surfacecanbeusedtominimizethelongitudinalcolor.

Figure13.13ofOpticalSystemDesign

Let'sgothroughtheprocessofdesigningtheBinary2opticsintheabovefigure.Ifyouarenotfamiliarwithany ofthestepsintheexercise,pleaserefertothearticleDesigningaSingletinZEMAX.

WewilldesignaDOEusingtheBinary2surfacewithdiffractionorderm=1tocorrectlongitudinalcolor.Thecompleteddesigncanbedownloadedfromthelastpageofthisarticle.

Setthesystemlengthunitstomm（System>General>Units）

SetthesystemapertureasEntrancePupilDiameterof30mm（System>General>Aperture）

SetthewavelengthtoF,dandC.（System>Wavelengths）;select"F,d,C"fromthedrop-downmenuintheWavelengthDatawindow.

SetonefieldwithvaluesX=0andY=0（System>Fields）

SetsurfacesintheLDEwithfollowingparameters.

The3Dlayoutshowsthesinglet.

AchromatizationusingBinary2:

B

OptimizethesystemforbestfocususingtheRMSSpotRadiusdefaultmeritfunction.

Afteroptimizationthevariableintheeditor,thethicknessofsurface#2, willbecloseto51.608mm.

ThelongitudinalaberrationplotunderUnalysis>Miscellaneous>LongitudinalColorshowssignificantamountoflongitudinalcolorabberation.

WewillnowaddsomediffractivepowertotheBinary2surface.

OpentheExtraDataEditorandsetthefollowingparametervaluesand setthecoefficientsofr^2andr^4asvariables..

Re-optimizethesystem.

Notice thatthelongitudinalcolorisnowmuchsmallerthanbefore.

AchromatizationusingBinary2:

C

NowthatwehavethecoefficientsfortheBinary2surfaceandknowthephaseprofile,weneedtocalculatetheradialcoordinatesofeach2*m*πdiffractionzonestobeusedforthefabrication.Thephase ateachdiffractionzoneswilldifferexactlyby+2*πor-2*πradian fromtheadjacentzonesasshowninfigure13.3（a）.

Runthemacro“Phases.zpl”andspecifysurface#2whenprompted.

Theresultshowsthatthereare246zoneswiththelastzonebeingat14.94mmfromthevertexofthesurface.

Thediagrambelowillustratesseveraldifferentpossibilitiesfor theDOEsurfaceprofile.

Figure13.9fromOpticalSystemDesign

SummaryandReferences

ThisarticlehasdemonstratedthebasicuseofBinary2surface.Insummary:

∙ZEMAXcancalculatethe2mπdiffractivezonecoordinatesfortheBinary2surface 

∙Achromatizationusingthebinary2surfacehasbeendemonstrated usinganexample.

References

1.OpticalSystemDesignbyRobertEFischer/BiljanaTadic-Galeb

2.ZEMAXusermanual