基于相位差法的波前检测技术

3311Vol.33,No.11200611Opto-ElectronicEngineeringNov,20061003501X(2006)110114061,21(1.6102092.100039)O439AWavefrontsensingusingphasediversitymethodLIQiang1,2SHENMang-zuo1(1.TheStateKeyLabofOpticalTechnologiesforMicrofabrication,theInstituteofOpticsandElectronics,theChineseAcademyofSciences,Chengdu610209,China;2.GraduateSchooloftheChineseAcademyofSciences,Beijing100039,China)AbstractAsawavefrontsensingtechnique,phasediversitycanestimatethepupilphaseandobjectfrompairsofsimultaneouslyrecordedfocusedanddefocusedimages.ComparedwithHartmanwavefrontsensorandShearinterferometer,theopticalbeamtrainofphasediversityissimpler.Inaddition,phasediversitycanbeusedwithextendedsourcesandissuitedtoslowerapplication.Theaberrationinducedbyatmosphericturbulenceandtheimage-formingsystemhavebeensimulatedbycomputer,andtheunknownwavefrontandobjecthavebeenestimatedbyusinglimitedmemoryBroyden-Fletcher-Goldfarb-Shanno(BFGS)method.Simulationresultsshowphase-diversitymethodcanaccuratelyretrievethewavefrontanddefocusingofonewavelengthisoptimal.KeywordsWavefrontsensing;Phaseretrieval;Imagerestoration;Phasediversity(Hartmannwavefrontsensor)(Shearinterferometer)20060530200608018631978)[e-mail]200611115(Curvaturesensor)(Phaseretrieval)[1,2](Phasediversity)Gonsalves[3,4]GS()[5~10][11,12]1CCD1CCD2CCD∆zCCD),(),(),(),,(),(),(2211yxhyxoyxiyxhyxoyxitttt∗=∗=(1)o(xy)h1t(xy)h2t(xy)t()2i122i11}e{,}e{θφφ+−−==ttpFhpFhtt(2)F-1{}pφttZernike[13]∑=Njjjttza),(ηξφ(3)zj(ξη)jajttja={ajt}Nξηθ)(π222ηξλθ+∆=w(4)∆w=∆z/8(F#)2λF#=f/DfD∆w(1)(2)CCDo(xy)(1)o(xy)(h[φ]=h[φ+2nπ])(Phaseretrieval)()Fig.1Telescopicopticalsystemandimage-collectionprocedureofphasediversitymethodObjectAtmosphericturbulenceBeamsplitterChannel1CCDDefocusdistanceChannel2CCDTelescope3311116(1)oa[6][14]212120221),(oihoaoJTtktktkγ+⎟⎠⎞⎜⎝⎛−∗=∑∑==(5)||…||Frobenius2/1112⎟⎟⎠⎞⎜⎜⎝⎛=∑∑==xyNiNjijaANxNyCCDxy(5)oaγ0Parseval(5)212120221),(OIOHaOJTtktktkγ+⎟⎠⎞⎜⎝⎛−=∑∑==(6)OHtkItkohtkItk(6)∑∑∑∑====+=TtktkTtktktkHIHO1212121*γ(7)*”(7)(6)[14]⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛+−=∑∑∑∑∑∑======21212121*212121)(TtktkTtktktkTtktkHHIIaJγ(8)(8)J(a)o(xy)a[15](L-BFGS)[16]2ZernikeKolmogoroff[17]1)ZernikeNC2)SVDC=VSVT(C,V)3)SBA=VB(A=[a1a2…aN])4)aj=aj×(D/r0)5/65)(3)NollZernike[13]55Zernike2Fig.2FlowchartofphasediversityalgorithmImagei1Imagei2Setbreak-offconditionSetregularizingparameterpupilfunctionpanda0=0FouriertransformI1,I2ComputerPSFh1,h2OTFH1,H2ComputerobjectfunctionJasequation(8)CalloptimizationprogramL-BGFSEstimateaBreak-offconditionComputephaseasequation(3)andobjectasequation(7)NoYes200611117ZernikeZernikeZernikeD=1.00mf=20mλ=600nm3256×2564r0=0.1mRMS0.310λPV1.734λ(128×128)5(a)5(b)∆w1.0λ1.92mm(RMSE)[]pupil1120/),(),()(NjijiRMSExyNiNj∑∑==−=φφφ(9)φφ0Npupil2a0γ=10-5ZernikeNs=556J2007RMSE0.002λ2CCD28r00.1m0.2m0.3m∆w1.0λ0.75λ~1.50λ9r00.1m0.2m0.3mNsNsNNsNsN[2];NsNNsNPV(3Fig.3Simulatedobject4Fig.4Randomphasescreen500100150020406080100120140yx1.0φ(waves)-1.00.50-0.5512CCDFig.5SimulatedimagescollectedbyCCDonChannel1and21e+91e+81e+71e+6J6JFig.6CostfunctionvaringwithiterationnumberIteration0501001502003311118r0=0.1m)[18][1]RK.Tyson.Adaptiveopticsengineeringhandbook[M].NewYorkMarcelDekkerInc1999.[2].[M].1996.ZHOURen-zhong.AdaptiveOpticsTheory[M].BeijingBeijingInstituteofTechnologyPress1996.[3]R.A.GonsalvesRobertChildlaw.Wavefrontsensingbyphaseretrieval[J].SPIE19792073239.[4]R.A.Gonsalves.Phaseretrievalanddiversityinadaptiveoptics[J].OpticalEngineering198221(5)829832.[5]R.G.PaxmanJ.R.Fienup.Opticalmisalignmentsensingandimagereconstructionusingphasediversity[J].J.Opt.Soc.Am.A198959(6)914923.[6]R.G.PaxmanT.J.SchulzJ.R.Fienup.Jointestimationofobjectandaberrationsbyusingphasediversity[J].J.Opt.Soc.Am.A19929(7)10721085.[7]M.G.LöfdahlG.B.Scharmer.Wavefrontsensingandimagerestorationfromfocusedanddefocusedsolarimages[J].Astronomy&AstrophysicsSupplementSeries1994107243264.[8]R.L.KendrickRayBellA.L.Duncan.Closedloopwavefrontcorrectionusingphasediversity[J].SPIE19983356844853.[9]R.G.PaxmanJ.H.SeldinM.G.Löfdahletal.Evaluationofphase-diversitytechniquesforsolar-imagerestoration[J].TheAstrophysicalJournal199646610871099.[10]D.V.LeeC.RoggemannB.M.Welshetal.Evaluationofleast-squaresphase-diversitytechniqueforspacetelescope7φ-φ0Fig.7Residualerrorofwavefrontretrieval1501.0∆φ(waves)0.50-0.5-1.0500100020406080100120140yx0.0070.0060.0050.0040.0030.0020.001RMSE(waves)r0=0.3mr0=0.2mr0=0.1m8r0Fig.8RMSEversusdefocusinvariousr00132456Defocus∆w(waves)r0=0.3mr0=0.2mr0=0.1m0.300.200.100.000.40RMSE(waves)608020400Zernikenumber9r0Fig.9RMSEversusZernikemodenumberinvariousr0200611119wave-frontsensing[J].AppliedOptics199736(35)91869197.[11].-[J].200222(10)12361239.LIXin-yangJIANGWen-han.ZernikeModalWavefrontReconstructionErrorofHartmann-ShackWavefrontSensor[J].ACTAOPTICASINICA200222(10)12361239.[12].[J].200412(5)471479.LIUXiao-junGAOYong-sheng.Accuratephaserecoveryalgorithminlateralshearinginterferometry[J].OpticsandPrecisionEngineering200412(5)471479.[13]R.J.Noll.Zernikepolynomialsandatmosphericturbulence[J].J.Opt.Soc.Am.A197666(3)207211.[14]C.R.VogelTonyChanR.Plemmons.