计算机图形技术在光学教学中的应用(IJEME-V3-N1-12)

I.J.EducationandManagementEngineering,2013,1,66-71PublishedOnlineJanuary2013inMECS()DOI:10.5815/ijeme.2013.01.12Availableonlineat:Computergraphics;opticsteaching;imageprocessing©2013PublishedbyMECSPublisher.Selectionand/orpeerreviewunderresponsibilityoftheInternationalConferenceonE-BusinessSystemandEducationTechnology1.INTRODUCTIONInrecentdecades,applicationsofcomputertechnologyhavepushedforwardreformofphysicseducationandimprovedteachingefficiency.Usingcomputersimulationcanassiststudentstounderstandthephysicalconceptandtheprocessesofphysicalexperiments.Simulationresultsbydifferentsoftwarehavebeensuccessfullyappliedinallaspectsofphysicaleducation.[1-5].Agoodpictureisworthonethousandwords,[6]becauseofthemoreinformationcontainedintheimage.Amongthesetechnologies,demonstrationofstaticimagesorthecontinuouslychangedimages(video),showingthecomplexphysicalprocessandtheresult,isanimportantmeansofteachingandlearning.Inpractice,wecanachievebettereffectthroughthevisualstimulationofgraphicalimagesinteachingprocess.Opticsisanimportantpartoftheuniversityphysics,andrelatedtomorecomplexphysicalpatternsandprocesses,comparedtootherpartsofphysics[7].Therefore,puttingemphasisonphysicalconceptsandphysicalphenomenaismoresignificantinopticaleducation.Usingthevisualizationofclassicalopticalexperimentforaclassroomdemonstrationishighlystimulatingandencouragingforstudentsinanopticalcourse[8].Nowadays,MATLAB,Mathematicaandothersoftwarehavepowerfulgraphicalprocessfunction,whichprovideavarietyofsimulationmethod.Howtousecomputergraphicstechnologytopromotethestudentstounderstandthephysicalconceptsandtheexperimentalprocessisasignificantissue.Inthisarticle,wediscusstheapplicationofThisworkwassupportedbytheNaturalScienceFoundationofAnhuiProvince,China(GrantNo.090416238),ResearchFoundationofEducationDepartmentofAnhuiProvince,China(GrantNo.KJ2009A125),andNaturalScienceFoundationofFYNC(GrantNo.2010FSKJ06).*Correspondingauthor:E-mailaddress:[e-mail],[e-mail]erGraphicsTechnologyinOpticalTeaching67computergraphicstechnologyinopticalteaching.Wefocusonthethreeaspectsasfollows:usingpatterndisplaystheresultsofnumericalcomputation,usingthevisualizationshowstheprocessofsolvingmathematicalproblems,usingcolorimagesshowssimulationresults,andusingimageprocessingtechnologyenhancespictureofexperimentresults.2.UsingPatterndisplaysTheResultsofNumericalComputationandUsingTheVisualizationShowsTheProcessofSolvingMathematicalProblems.Thereismuchdifficultyinunderstandingofthemathematicalformulasinopticalcourse.Ifwefocusonsolvingmathematicalproblems,physicalconceptsshouldbediluted.Inordertosolvemathematicalproblemsinoptics,weuseMATLABsoftwaretohelpstudentssolvingmathematicalformula,whichfavorstheunderstandingofphysicalconcepts.Figure1.thesolutionofequationu=tan(u)Forexample,theexperimentofFraunhofersingleslitdiffraction,theminimumvalueofthesolutionisobtainedbyatranscendentalequationu=tan(u).Firstly,weusetracingpointmethodtodynamicallydescribedthecurvesofy=tan(u)withtheparameterurangefromu=-10to10(thebluecurvesinFig.1).Thenweusethenumericalcalculationmethodstartingfromu=-10to10todynamicallydrawthecurveofy=u.Ifthevalueofabs(tan(u)-u)lessthanthespecifiedvalueoftheerrorwhichisassumedpreviously,anasteriskisremarkedonthecurve.Bydynamicimageprocessing,theerrorsinhand-drawingwereovercomeandhighprecisionsolutionswereobtained.Fraunhoferdiffractionatacircularapertureisaneffectofgreatpracticalsignificanceinthestudyofopticalinstrumentation.AccordingtoHuygens-Fresnelprinciple,theexpressionfortheopticaldisturbanceatP,arisingfromanarbitraryapertureinthefar-fieldcase[7],is：02[(sin)]cossin0200RikrRtikPAEeeddRwhereRistheradiusofhole,A0istheamplitudeofthediffractionplane,θisangleofdiffraction.ρandφarethepolarradiusandthepolarangleofobservationpoints(P)respectively.Finally,(1)canbesimplifiedas:22232220111[1...]232!43!pmmIAmwhereIPislightintensityofpoint(P),misequaltoπRsinθ/λ.68TheApplicationofComputerGraphicsTechnologyinOpticalTeachingFigure2.TheFranuhoferdiffractionpatternofcircularapertureUnderstandingofthisformulaisdifficult,sothatwehavedrawnlightintensity(IP)byMATLAB.Fig.2showsone-dimensional,two-dimensionalandthree-dimensionalpatterns.LineAandBcorrespondtothemaximumdistributionandthelocation