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1、摘要題名:波前像差曲面擬合方法研究碩士姓名:張晶導(dǎo)師姓名:舒華忠學(xué)校名稱:東南大學(xué)近年來,波前像差的理論和檢測技術(shù)在眼科的應(yīng)用使得屈光領(lǐng)域的研究有了新的突破。I臨床實驗結(jié)果表明,與常規(guī)的眼科手術(shù)相比,準(zhǔn)確的波前像差引導(dǎo)的眼科手術(shù)可以使眼科手術(shù)患者術(shù)后的視覺質(zhì)量有進一步的改善。本文依據(jù)由角膜高度數(shù)據(jù)值計算眼睛波前像差的方法,采用正交徑向多項式擬合角膜高度曲面和波前像差曲面,從而得到精確的波前像差數(shù)據(jù)。在已有的應(yīng)用中,傳統(tǒng)的Zemike多項式被廣泛應(yīng)用在曲面擬合領(lǐng)域。D.R.Iskander通過實驗證實,另一類徑向多項式——傳統(tǒng)的Pseudo—Ze
2、rnike(BW)多項式相對于Zemike多項式表現(xiàn)出更加健壯的擬合性質(zhì)。本文試圖尋找其它的正交多項式,并期待它們的擬合性能比傳統(tǒng)的Zemike多項式和傳統(tǒng)的Pseudo.Zemike(BW)多項式更優(yōu)。在此基礎(chǔ)上,本文分別提出了應(yīng)用連續(xù)的擴展的Zemike多項式和擴展的Pseudo.Zemike多項式來進行角膜高度曲面和波前像差曲面的擬合。角膜高度面實驗數(shù)據(jù)分別采用兩個模擬正常人眼角膜的曲面(球面和橢球面)和用Keratron型角膜地形圖儀測量得到的真實角膜面;波前像差面實驗數(shù)據(jù)則采用波前像差傳感器測量得到的數(shù)據(jù)。實驗結(jié)果表明,擴展的Zemi
3、ke多項式和擴展的Pseudo.Zemike多項式在小尺寸的角膜曲面和波前像差曲面上具備更加穩(wěn)定的擬合性能。為了避免連續(xù)多項式在離散化后帶來的誤差和正交化過程,本文又結(jié)合離散Tchebichef多項式和離散Krawtchouk多項式,提出了離散徑向Tchebichef多項式和離散徑向Krawtchouk多項式,并且將其應(yīng)用到角膜高度曲面擬合和波前像差曲面擬合中。實驗數(shù)據(jù)依舊采用上述的各個曲面,實驗結(jié)果表明離散徑向Tchebiehef多項式和離散Krawtchouk多項式在角膜高度曲面和波前像差曲面擬合方面的性能優(yōu)于其它連續(xù)徑向多項式。關(guān)鍵詞:波
4、前像差擬合、角膜面擬合、擴展的Zemike多項式、擴展的Pseudo.Zemike多項式、Tchebichef多項式、Krawtchouk多項式AbstractTHESISTITLE:MethodstudyforthemodelingofwavefrontaberrationsurfaceMASTERNAME:ZHANGJingSUPERVISORNAME:SHUHua-zhongSCHOOLNAME:SoutheastUniversityInrecentyears,theapplicationofwavefrontaberrationtheo
5、ryanditstestingtechnologyinOphthalmologyhavemadesomenewbreakthroughsinthefieldofrefractive.Clinicalexperimentalresultsshowthatcomparedwithconventionaleyessurgery,thesurgery1cadsbyaccuratewavefrontaberrationcouldimprovethepost-surgeryvisualqualitysignificantly.Basedontheproce
6、duretoobtainthecomealaberrationsfromthecornealelevationdata,radialorthogonalpolynomialsaleusedtofitthecomealelevationsurfacesandcomealwavefrontaberrationsurfaces,SOthattheaccuratewavefrontdatacouldbegot.Sofar,traditionalZemikepolynomialshavebeenwidelyusedinthesurfacefittingf
7、ield.Anothersetofpolynomials—廿aditionalPseudo-Zemike餌W)polynomialsshowsmorerobustfiaingcapabilitythantheZemikePolynomials.Intllisthesis.newmethodsformodelingcornealelevationsurfaceandwavefrontaberrationstlrfacewithcontinuousGeneralizedZemikePolynomialsandcontinuousGeneralize
8、dPseudo—ZemikePolynomialsareproposed.Theexperimentaldataforthecomealelevati