Synopsisof
CylindersinVs
Anoptomechanicalmethodology
DouglasS.Goodman
Proc.ofSPIEVol.3132,OptomechanicalDesignandPrecisionInstruments,
Ed.AEHatheway(Oct1997)CopyrightSPIE
by
LucasWoodard
UniversityofArizona
CollegeofOpticalSciences
October31,2011
Abstractfromthearticle
Themountingofrotationallysymmetricopticalelementsincylinders,whicharethenlocatedina
V‐shapedtrough,isoftenaconvenientoptomechanicalapproach.Thisisanearidealgeometry,
sincelensalignmentnormaltotheaxisistypicallymostcritical,axialpositionislessso,and
azimuthisirrelevant.Themechanicalconstraintscorrespondtotheopticalrequirements,sothe
arrangementisassimpleaspossibleandnosimpler.Locationiskinematicorsemi‐kinematic,and
hencerepeatable,allowingforquick,accurateswappingbetweensetups,withcriticaladjustments
madeonce.Axialpositioncanbewithoutinfluencinglateralpositionandtilt.Likewise,rotation
alonecanbedone.Selfcheckingalignmentmethodscanbeused.Theapproachiscompatiblewith
othermeansofmounting.Practicalconsiderationsofthissurprisinglyflexibleapproachare
discussed,includingvariouswaystomakeVs;methodsoftestingVs;errorsincylindricityandthe
testingofcylinders;methodsofcenteringopticsincylinders;thesystematicestablishmentof
mastersandworkingfixtures;themeasurementandcontrolofaxialseparations;clamping;lens
systems.
Introduction
Inhispaper,theauthorintroducesthereadertotheterminologyandconsiderationsforthedesign,
manufacturing,andmetrologyofcylindersandVs.Alsodiscussedarewaystoutilizecylindersand
Vsinpractice.Thebodyofthepaperiscomprisedofanintroductorysectionandthreemain
sections:TheV,TheCylinder,andTheCylinderandVTogether,eachwithpertinentsubsections.
FollowingthebodyofthepaperisanAppendixofVirtueswhichsummarizestheusefulfeaturesof
cylindersinVs.Theformatofthissynopsiswillbetolisteachsectiontitleandprovidekey
elementsaboutitscontents.
Introductorysection
TheauthorintroducesthesubjectbybroadlydiscussinghowtheuseofcylindersinVscameinto
practiceinhisexperienceandthemotivationfortheiruseinboththefieldandthelaboratory.
Thebasicideafortheiruseisthatrotationallysymmetricopticshavefourcriticaldegreesof
freedom,decenterinxandyandtiltaboutxandy,allofwhichareconstrainedinacylinder‐in‐V
system.Movementalong,androtationabout,thecenterlineaxisisunconstrainedbutmay
constrainedifneeded.
Hedefinestheterms“cylinder”and“V”tobeanyshapesthatbehavelikeastandardcylinderanda
planarV‐shapedtrough.Thekeyparametersarestraightnessandtangentialcontacttocertain
roundshapes.
TheV
Inthissection,hediscussestheterminologyandgeometryofVs,aswellasdifferentwaysto
manufactureandmeasureVs.Somekeyelementsofthissectionare:
 ThedistancefromthevertexofaVtoitscenterlineis(d/2)/sin(θ/2),wheredisthe
diameterofthecylinderandθisthevertexangleoftheV.
 Planar90°Vsareusuallytheeasiesttomakeandarethemostconvenientinthelaboratory,
andtheycanbeusedwithsquareobjectsaswell.
 Planar60°Vsproducesymmetricalforcesonacylinderclampedonthebisectorofthe
vertexangle.Theycanalsobeusedwithhexagonalobjects.
 TheangleoftheVisnotcriticalforopticalelementsaccuratelycenteredincylinders.
 MonolithicVscanbemadestifferandmorestablethanfabricatedVs.
 Thematerials,coatings,andfinishofVsandmatingcylindersshouldbeconsidered
together.
 Communicatewiththemechanicaldesignerandtheshopaboutwhatiscriticalandwhatis
notcriticalaboutthedesignandmanufactureoftheV.
TheCylinder
Inthissection,asinthesectiononVs,hediscussestheterminologyandgeometryofcylinders,as
wellasdifferentwaystomanufactureandmeasurethem.Somekeyelementsofthissectionare:
 Themostusefulformsformountingopticalelementsarethesimplecylinder,thebarbell,
andthebone.Anillustrationoftheseformsisshownbelow:
2 Typesofcylinders
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Forstability,aruleofthumbisthatthediameterofthecylindershouldbenogreaterthan
thelength.
Deviationsfromanidealcylinderneedonlytobeevaluatedforitseffectontheoptical
element.
“Roundnumber”diametersarepreferredformaterialpurchase,gaging,andtooling.
AswithVs,communicatewiththemechanicaldesignerandtheshopaboutwhatiscritical
andwhatisnotcriticalaboutthedesignandmanufactureofthecylinder.
Inpricingcylinders,findoutthecostof“extra”accuracy.Mechanicalaccuracybeyondwhat
isneededopticallymaybeasurprisinglyinexpensiveluxurythatloosenstolerances
elsewhere.
TheCylinderandVTogether
Inthissection,theauthordiscussesanumberoftopics:
 TherepeatabilityandinterchangeabilityaspectsofcylindersandVs.
 Techniquesforcenteringandcentrationverificationofopticalelements.
 Videomethodsforalignment.
 Methodsforlateralandaxialpositioningofcylinders
 Mountingopticalelementsincylinders.
 Incorporationofstops,baffles,andtubes.
 Clampingconsiderationsandmethods.
 Rotationorconstraintaboutthecenterlineaxis.
 Incorporationofnon‐centeredelements,suchasfilters.
 Lightsources.
 Non‐cylindersinVs.
Somekeyelementsofthissectionare:
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Thecylinder‐in‐Vsystemprovidesrepeatableandinterchangeablelocationbecausethereis
lineorpointcontact,evenwithimperfectcomponents.
Forhigh‐accuracyaxialspacing,theendsofthecylindershouldbemachinedintoatoroidal
shapetoproduceasinglecontactsurface.
TheV,andnottheclamp,shoulddeterminethelocationofacylinder,sotheclampneednot
bestiff,andaspringorflexurecanbeused.
Theclampingforceshouldnominallybesymmetricallyapplied,alongthebisectorofthe
vertexangle.
AppendixofVirtues
Thefulltextofthefinalsectionoftheauthor’spaperisincludedherebecauseofitssummarizing
format,andbecauseitreiteratesoraddstothekeyelementsinthesynopsis.
KINEMATICASPECTS
 Thelocationiskinematicorsemi‐kinematic.
 Thecontactisonlinesorpoints.
 Locationisrepeatable,evenwithimperfectobjects.
 Thereisenoughconstraint,butnooverconstraint.
 Thereisrepeatablerearrangementandquick,accurateswappingbetweensetups.
 Thereisanunderstandable"flowofaccuracy"frommasterstoworkingfixturestoproduct.
 Mechanicalerrorsarerepeatable,measurable,understandable,andcorrectable.
 CylindersandVswithdifferentlevelsofaccuracycanbeusedinanycombination.
 Thesamebasicmethodologycanbeusedwithanyleveloraccuracyandwithvarious
materials.
 Cylinderscanbeclampedwithouttheirmoving
 Axialpositioncanbekinematicallydetermined.
 Angularpositioncanbekinematicallydetermined.
SYMMETRY
 Themechanicalcylinderhasthesamesymmetryasrotationallysymmetricoptical
elements.
 Thereisasmuchsymmetryaspossible‐rotationalandbilateral.
 Someerrorsandchangesinconditionsmaintainbilateralsymmetry.
 Cylinderscanbereversedend‐to‐endandalignmentmaintained.
MOTIONandLACKTHEREOF
 Thetworemainingdegreesoffreedomareuseful.
 Thesedegreesoffreedomcanbeexercisedindependently.
 Rotationofelementsabouttheaxisisstraightforward.
 Rotationwithoutothermotionsispossible.
 Fine,repeatableangularpositioningcanbedone.
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Axialtranslationisstraightforward.
Axialmotionwithoutothermotionsispossible.
Fine,repeatableaxialpositioningcanbedone.
Thetworemainingdegreesoffreedomcanbeexercisedindependently.
TESTINGandCENTERING
 Thegeometryisself‐checking.
 Centrationistestedbyrotation.
 Cylinderroundnessistestedbyrotation.
 CenteringcanbedoneinaVoroutofit.
 Vstraightnessistestedbytranslation(aswithanautocollimator).
 Therearemanywaystocheckstraightnessandroundness.
 Bilaterallysymmetricelementscanbesetusing180°rotation.
 Opticalandmechanicalalignmenttechniquescanbecombinedinavarietyofways.
 Cylindricalgagesandstraightedgesformeasurementarecommonplace.
MANUFACTURING
 OnlyasmallamountofmaterialisworkedinproducingthecriticalpartsofVsand
cylinders.
 TheangleofVnotcritical.
 PlanarVsareformedbytwoportionsofplanarsurfaceswhoserelativepositionsarenot
critical.
 SomemachinetoolerrorscanbecanceledbyreorientingtheVbetweencuts.
 Standardmachininggivesgoodenoughaccuraciesformanyopticalapplications.
 Vscanbemadebymanydifferentmachiningmethods.
 Vsaresuitableforcastingsandextrusions.
 Vscanbefabricatedinmanyways,e.g.tworods,rodandflat,twoflats.
 RigiddisplacementsofthecomponentsofafabricatedVdonotaffectitsstraightness.
MISCELLANEOUS
 Forelementsusedintermittently,criticaldegreesoffreedomareadjustedonce.
 Opticalelementsmountedincylinderscanbeusedelsewhere.
 Acylinder‐in‐Vunitcanbeusedwithotherapparatus.
 Thesamebasicapproachcanbeusedinthelaboratoryandinthefield.
 OthershapescanbeusedinaV,e.g.squaresina90°degreeV.
 TheVstructureisageneral‐purposebasetowhichotherapparatuscanbeattached.
 Thereisageneralinsensitivitytooveralltemperaturechange.
 Theentirestructureisrobust.
 Therearemanywaystodoanything,e.g.rotation,translation,rotation180°,etc.
 Thegeometryisassimpleaspossible,butnosimpler.
Conclusion
5 Thecylinder‐in‐Vconfigurationisaninvaluableengineeringtoolforbothproofofconceptsand
failureanalysis.Complex,foldedopticalsystemscanoftenbereducedtoin‐lineformsusingthese
methodstoprovidegreaterconfidenceinevaluatingopticalperformanceindependentofthe
mechanicalstructure.
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