431 0141 ACTAPHOTONICASINICA Vol.43No.1 December014 犱狅犻 :10.3788/gzxb014431.100 ZemaxR 01A56Z.J + ( 8, 1003) :. EFW #'6EI % ;; <, W #'_,N O _ B Zemax 9,-',Q O = > ; T W # = > ' ^ % ; ;J*W #=>' S66E, 3 W #=>6EI=>^ % ;'V* E. E? ' ; T? 'W # E.J K P :W # '6EN E'?? ' ; W #QO Zernike6, ^ % QO ; V,?.!: O_? /,-; _;Zemax 9, -;W # E;1 0 ; ' %; _ ;_ ; % "#$%&:R778 ' :A ' &:1004 413(014)1 100 5 犚犲狊犲犪狉犮犺狅犳狋犺犲犆狉狔狊狋犪犾犻狀犲犔犲狀狊犕狅犱犲犾犻狀犎狌犿犪狀犈狔犲犗狆狋犻犮犪犾犛狔狊狋犲犿犅犪狊犲犱狅狀犣犲犿犪狓犐狀狋犲狉犳犪犮犲犜犲犮犺狀狅犾狅犵狔 KONG Mei mei ( 犛犮犺狅狅犾狅犳犗狆狋狅 犈犾犲犮狋狉狅狀犻犮犈狀犵犻狀犲犲狉犻狀犵, 犖犪狀犼犻狀犵犝狀犻狏犲狉狊犻狋狔狅犳犘狅狊狋狊犪狀犱犜犲犾犲犮狅犿犿狌狀犻犮犪狋犻狅狀狊, 犖犪狀犼犻狀犵 1003, 犆犺犻狀犪 ) 犃犫狊狋狉犪犮狋 :Lenssurfacetypeandrefractiveindexdistributionofthecrystalinelensmodelineyeoptical modelwasresearched.basedonthelensopticalpproperties,theefectofdiferentlenscombinedmodels onthehumaneye modeltoreproducethe measuredeyeaberrations wasanalyzedcomparatively with Zemaxinterfacetechnology.Thelenscombined modelsincludeddiferentsurfacetypesanddiferent gradient indexdistributionsbydiferentcontinuousformulas.thelensmodelwiththeminuamreproduce precisionwasalsopresented.theresultsshowthattheaberrationsoftheeyemodelwithcomplexlens sufaceisclosetomeasuredeyeaberrations,thelensmodelwiththeminuamreproduceprecisionincluds Zernikesurfaceandgradient indexdistributionbypiecewisefunctionformulas. 犓犲狔狑狅狉犱狊 :Medicalopticsandbiotechnology;Visualoptics;Zemaxinterfacetechnology;Crystalinelens model;imagequality;lightrefraction;opticaldesign;opticalproperties;refractiveindex 犗犆犐犛犆狅犱犲狊 :0.740;330.4060,330.4595,330.731,330.736 0 () 5A6 B A G, ) @ * ^ 7 6 Z.. ^[1]. 5,Z. 5 6 5 A = 9? @, 6 8[ B D, [A8 6, b9,56az. B GHA9 M, ) A8+M? [], W,`? A3, : AI % M, 8+ 8+A; L,DZ.? *BC @ A >, @ ;56A, 5 A 8 D [3 5]. Z.[ 56, 5 6. A ` [6]. [7][8]@ [ 5 : (No.613006) +" (Nos.BK0143,BK01175) +", (Nos. 13KJB51005,11KJD14000) 8 (Nos.NY09011 NY1110)#$ : (1983-),,[,, ()* ;6.Email:kongmm@njupt.edu.cn :014 05 14; :014 07 03 100 1 犺狋狆 : 狑狑狑. 狆犺狅狋狅狀. 犪犮. 犮狀
6Z., A D 6 J ; P A ; [9] Z. A \ A?7, J P MN F. Z.AJ J 6 675AB 8`.Z.J L 68 1, 5 Z. 1,N 5 Z. A [10 11] ;1 A,. Z.A G H 0 1 A,5 6 Z.A @ @, 56P 3,U 5 6 Z. J A H ) M. [1], A J A @ @ @ F X B. Zemax, L VC K 3 A @ @,.Q A Z. J U J 6 5 A ; B56J QP 0#A (<(Root MeanSquare,RMS)"#*, Z.J A @ @ F X B @ W, ] " # AZ.J M. 1 @L Z. A.,@ L (Conic) (Biconic) Zernike *C O ( F. Zemax 5, *C A 狕 A ( @ (1)~ (3)K O, 5 Zernike A K ; ],KU (1)A. ) 狉 ().A, N Zernike%,. 犮狉狕 = 1+ 槡 1- ( 1+ 犽犮 ) 狉 犮狓狓 + 犮狔狔狕 = 1+ 1- ( 1+ 犽狓 ) 犮狓狓 槡 - ( 1+ 犽狔 ) 犮狔狔 (1) () 犮狉狕 = 1+ 槡 1- ( 1+ 犽犮 ) 狉 + 8 犖 α 犻犻狉 + ( 犃犻犣犻 ρ, φ ) ( 3) 犻 =1 犻 =1 (1)5, 犮 *Z. A, AL, 狉 * ), 狉 = 狓 + 狔, 犽 * ( 犽 <-1T O ; 犽 = -1T OD9 ;-1< 犽 <0 T O ; 犽 =0 T O ; 犽 >0 T O ); ()5, A *, * 狕, A U 狓狅狕, U 狔狅狕, 犮狓 犮狔 @ O ^U A A, 犮狓 =1/ 犚狓, 犮狔 =1/ 犚狔, 犚狓 犚狔 @ * A, 犽狓 犽狔 @ O ^ U A A ; (3)5, 犣犻, A ` A Zernike%,.U A., 36, Zernike%,, 犖 =36,< Z. A,U X B M J 6 5, Zernike%, A 犃犻 A P *, D 狉 A,. @ $ 56b9 A Z.A@ c@ A [13] :Z. % @ A 9 > 9?,) 5 U. * #,DZ.A GHB., 5,D B @ c [14].? L Z R < O Z. A c @ @ ` [15]. *! A Z. @ @ K `,@ L Liou & Brennan [15] A.V.Goncharov & C. Dainty [16] Blaker [17] A * D A J 6, ] A Z.@ @ AR @ * 烄 1.368+0.049057 狕 - 0.01547 狕 0< 狕 1.59-0.001978 狉狀 ( 狉, 狕 )= 烅 1.407+0.0 狕 - 0.006605 狕 -0.001978 狉 1.59< 狕 4. 0 烆 (4) 狀 ( 狉, 狕 )=1.36-0.001490 狉 -0.0000106 狉 4 + 0.049467 狕 -0.015958 狕 +0.0001715 狕 3 + 4 0.000141 狕 (5) 狀 ( 狉, 狕 )=1.387+0.014 狕 -0.00384 狕 -0.001 狉 (6) 5, 狕 O Z. A 5?, 狉 * Z. A ). Liou & BrennanU A 5 6 J 5, Z.@* @,@ @ Z. @ Ac @ (, (4).? 狕 $%*1.59< 狕 4.0 T, F B A + :L 狕 -1.59 (4) 狕, @ A ; @ A Z, Q, P. (4)A (,+ 1.368+0.049057 狕 -0.01547 狕 -0.001978 狉 0< 狕 1.59 狀 ( 狉, 狕 ) = { 1.407+0.0( 狕 -1.59)-0.006605( 狕 -1.59) -0.001978 狉 1.59< 狕 4. 0 (7) (7) (5) (6) L Z.J A 5T, VC K 3, $ L Zemax; VC A R 0 1,U L Zemax A 5 6 J 5, @ D * @ @ R A VC,,< O Z.A*C @ @ `.I (5)AK3 4 1, 5, index Z. A @, 犖 0 犖 6 @ (5)5YB,] A.* >,U 56P A 56 J 5, D (7) (5) (6) OAZ.AJ 6@ *J 1(Model1) J (Model)J 3(Model3). 100
: ZemaxR 01A56Z.J case6: 犖 0=FD >param[]; 犖 1=FD >param[3]; 犖 =FD >param[4]; 犖 3=FD >param[5]; 犖 4=FD >param[6]; 犖 5=FD >param[7]; 犖 6=FD >param[8]; 狓 =UD > 狓 ; 狔 =UD > 狔 ; 狕 =UD > 狕 ; 狋 =FD >thic; 狉 = 狓 狓 + 狔 狔 ; index= 犖狅 + 犖 1 狉 + 犖 狉 狉 + 犖 3 狕 + 犖 4 狕 狕 + 犖 5 狕 狕 狕 + 犖 6 狕 狕 狕 狕 ; if(index<1.0)index=1.0; UD >index=index; UD >dndx=.0 犖 1 狓 +4.0 犖 狉 狓 ; UD >dndy=.0 犖 1 狔 +4.0 犖 狉 狔 ; UD >dndz= 犖 3+ 犖 4 狕 +3 犖 5 狕 狕 +4 犖 6 狕 狕 狕 ; break; 1 8 Zemax % ( (5)) VC Fig.1 Thelensrefractiveindexdistribution (Eq.(5)) withvccompiler(excerpts)usedinzemax 3 \ 3.1 6 * b$ 56 A" # P 3 BA67,@ ;. G 8 6 < = > ] 6 5 5 ] 8 ] ( + " 5 ] )A6 5, B 56 @A" 3,,?6@ 3.] KLMN Baush& Lomb( )RS ZeissRS, RS\, 3 U P ] " L 5 D A 1, A 5 6 3. U8 5 < 3 K A 6, 6 [ 0.8 +0.75~ -1.75DS Jena,Germany), N Orbscan Ⅱ B. " 6 @ W L Zywave0 # M (Baush & Lomb, USA) ; ^? 7 Z.?6 Pentacam 6 @ W M (Oculus,Wetzlar, Germany),IOL Master \ 9 M (CarlZeiss, Jena,Germany) N6 L A/B O L M(BVI, France). 3. \ 56 J T, P 560#*. A 4, Q P 5 6 0 # *, XB Z.A,EJ.XBA *: Z. * FXB,XB?, *, Z.A@ @ * FXB. 5 6 0 # A M N Shack Hartmann0# : [18], 5 6 U ^.? * B ^ <, T Shack Hartmann0# M 5 A W ; 5 6 A ] D, A A U 5 6.A0#, U56 J 5,J A 56A? 0,; U B ) A.K,* > J,U56A [, B ;P 5 6 0 # A ] [, U X B 5, B I ] [ U A 8 A 0#(RMS) *XBA, X B T 8 A0# RMS * 5 6 J Q P 0 #A,E^ ][, XA 0# P 56 0 #, T A * K A 56J. 5, AXB, 4 A b,d0#,k B 0# RMS A A. 4 ; $L A @ 5 6 Z. F J,X B 4. B (Conic)X B A Q P 0 # ARMS" # (Biconic)X B <0.75D 6 A B A 6 50, 5 18 5,'95, 19~45C, (6.64±5.)C. P A D: ^ A ^A5?,I 7 Z. 5? UA6@ 6, N56A0#;6.A5? 6 ^ 6@. Y A F3,, TKLA]MN@ *:56 ^ 560# D ^[`4 0#@W " A CRS Master Twinline (Carl Zeiss, X % 3X? RMSO Fig. Thereproduceprecision(RMSeror)comparisonof eyemodelswiththelensofdiferentsurfacetypes 100 3
A 8, Zernike A X B * 5 A,* J A RMS U0.μm, > A X B, Z. A H G H 56J A0 # ; P 5 6 A 0 # H R,? U 5 6 A J 5 Zernike < J Z.. 43* TXBZ.A @ A QP 0#A RMS"#.,J Q P 0 # ARMS 8 A,E 3 ^ %X 3X? RMSO Fig.3 Thereproduceprecision (RMSerror)comparisonof surface eyemodelswiththelensofdiferentsurfacetypes anddiferentgradient indexdistributions @) L 犣犲狉狀犻犽犲 #; Zernike J 3 A E #; KD*,J 1AXBE A,U c@ @ 5,Liou & BrennanA J 6 L A (7)AE.?,UJ 65 L (7)<J Z.Ac@ @. @W,QP 0# RMS"# A5 6J 5Z. J A. 1~3. 5,Z.A O @ * L Zernike ( 犣 1 犣 15* Zernike ), L B A, Z.Ac@ @ L (7)A ` ( 狀 00 狀 10@ *@ K 5] A ). 犜犪犫犾犲 犜犺犲犾犲狀狊犪狀狋犲狉犻狅狉狊狌狉犳犪犮犲犣狀狉狀犻犽犲犮狅犲犳犻犮犻犲狀狋狊 1 犚犕犛 " @ Q: 犜犪犫犾犲 1 犜犺犲狊狋狉狌犮狋狌狉犪犾狆犪狉犪犿犲狋犲狉狊狅犳犾犲狀狊犿狅犱犲犾狑犻狋犺狋犺犲犿犻狀犻犿狌犿犚犕犛犲狉狉狅狉 Surface Radius/ Conic Central Type mm coeficient thickness/mm Anterior Anteriorpart 1.66 Zernike 15.01-5.00 surface Posteriorpart.33 Posterior conic -9.81-5.00 16.0 犣 1 犣 犣 3 犣 4 犣 5 犣 6 犣 7 犣 8 犣 9 犣 10 犣 11 犣 1 犣 13 犣 14 犣 15 0 0 0-8.066-1.139 1.679-1.743-1.06 5.473-1.886 -.687-3.01 1.11 -.765-1.096 10-3 10-3 10-10 -3 10-3 10-4 10-3 10-3 10-5 10-4 10-4 10-5 3 @ $ 犜犪犫犾犲 3 犜犺犲犮狅犲犳犻犮犻犲狀狋狊狅犳犾犲狀狊狉犲犳狉犪犮狋犻狏犲犻狀犱犲狓犱犻狊狋狉犻犫狌狋犻狅狀 狀 00 狀 01 狀 0 狀 10 Anteriorpart 1.3680.0495-0.01568-0.00053 Posteriorpart1.407 0-0.007181-0.00053 5 ; $L ZemaxA R 0 1 U 5 6 J 5 @ @ ` A Z. J, Z. A, Z.AJ F B A @W, O, Z. Zernike @ Liou & Brennan J 6 L A c @ @ ` T,J 6;P A,*56J A L 0 A Z. J.D P A " # J @ W A 6 7, U 3 ] B < F A, J @ WA. = [ N _ F ' I F _ (^& F ) F 'D,? 100 4 5 6 '. QR' [1].6 [M].! :5: \,1996. [] LIU Yong ji,fang Zhi liang,wang Zhao qi.astudyon eye'sopticalcharacters withanatomicalyaccurateshel lens [J]. 犃犮狋犪犗狆狋犻犮犪犛犻狀犻犮犪,005,5(1):136 140.,(,,. D Z.A56J A >[J].,005,5(1):136 140. [3] KORETZJF,COOK C A,KAUFMAN P L.Agingofthe humanlens:changesinlensshapeuponaccommodationand withaccommodativeloss[j]. 犑狅狌狉狀犪犾狅犳狋犺犲犗狆狋犻犮犪犾犛狅犮犻犲狋狔狅犳犃犿犲狉犻犮犪犃,00,19(1):144 151. [4] DUBBELMAN M,VANDER HEIJDEGL,WEEBER H A, 犲狋犪犾. Changes in the internal structure of the human crystalinelens with age and accommodation [J]. 犞犻狊犻狅狀犚犲狊犲犪狉犮犺,003,43:363 375. [5] DUBBELMAN M,VANDER HEIJDEGL,WEEBER H A. Changein shape oftheaging human crystalinelens with accommodation[j]. 犞犻狊犻狅狀犚犲狊犲犪狉犮犺,005,45:117 13. [6] SMITH G.Theopticalpropertiesofthecrystalinelensand theirsignificance[j]. 犆犾犻狀犻犮犪犾牔犈狓狆犲狉犻犿犲狀狋犪犾犗狆狋狅犿犲狋狉狔, 003,86(1):3 18. [7] ZHANG Li Yan.Finiteelementanalysisofhumancrystaline lensaccommodationanddeterminationofelastic modulusof rabbitlens[d].taiyuan:taiyuan UniversityofTechnology, 01. 9.56Z., " A D 6 J N 6 Z. J [D]. : : 8,01.
: ZemaxR 01A56Z.J [8] SONGFan,ZHAO Xi yu,du Rui qi, 犲狋犪犾.Accommodation theories and mechanical properties of human lens [J]. 犕犲犮犺犪狀犻犮狊犪狀犱犈狀犵犻狀犲犲狉犻狀犵,01,34(1):1 9.,,K A,,.56Z., [[J].[ ;P,01,34(1):1 9. [9] MICHAELR,BRON AJ.Theageinglensandcataract:a modelofnormaland pathologicalageing[j]. 犘犺犻犾狅狊狅狆犺犻犮犪犾犜狉犪狀狊犪犮狋犻狅狀狊狅犳狋犺犲犚狅狔犪犾犛狅犮犻犲狋狔犅,01,366(1568):178 19. [10] RAO Feng, WANG Zhao qi, WANG Yan, 犲狋犪犾. Constructionofeye modelandintraocularlensdesignafter cornealrefractivesurgery[j]. 犃犮狋犪犘犺狅狋狅狀犻犮犪犛犻狀犻犮犪,009, 38(7):1805 1810. 0,, U,,. ^ 1 6 J A M 5 Z. [J].,009,38(7):1805 1810. [11] ZHAO Xing,ZHANG Mei hui, FANG Zhi liang. Title analysisofthesphericalaberrationcorrection withconical anteriorchamberphakicintraocularlens[j]. 犃犮狋犪犘犺狅狋狅狀犻犮犪犛犻狀犻犮犪,011,40(6):865 871.,,(,. 7 DZ.65 Z.A # @W[J].,011,40(6):865 871. [1] KONG Mei mei, GAO Zhi shan,li Xin hua, 犲狋犪犾. A genericeye model by reverse building based on Chinese population[j]. 犗狆狋犻犮狊犈狓狆狉犲狊,009,17 (16):1383 1397. [13] ZHAO Qiu ling,wang Zhao qi,zhang Chun shu.the actionsofaspheric surfaces and gradient index on optical imageoftheeye[j]. 犃犮狋犪犘犺狅狋狅狀犻犮犪犛犻狀犻犮犪,00,31(11): 1409 141. 9,,#. c@ U6? 5A L[J].,00,31(11):1409 141. [14] L Fan.Eyebaloptics[J]. 犆犺犻狀犲狊犲犑狅狌狉狀犪犾狅犳犗狆狋狅犿犲狋狉狔牔犗狆犺狋犺犪犾犿狅犾狅犵狔,001,3(1):53 55. F.6 (B[)[J].6 H,,001,3(1):53 55. [15] LIOU H L,BRENNAN N A.Anatomicalyaccurate,finite modeleyeforopticalmodeling[j]. 犑狅狌狉狀犪犾狅犳狋犺犲犗狆狋犻犮犪犾犛狅犮犻犲狋狔狅犳犃犿犲狉犻犮犪犃,1997,14(8):1684 1695. [16] BLAKERJW.Towardandadaptivemodelofthehumaneye [J]. 犑狅狌狉狀犪犾狅犳狋犺犲犗狆狋犻犮犪犾犛狅犮犻犲狋狔狅犳犃犿犲狉犻犮犪,1980,70 ():0 4. [17] GONCHAROV A V,DAINTY C.Wide fieldschematiceye modelswithgradient indexlens[j]. 犑狅狌狉狀犪犾狅犳狋犺犲犗狆狋犻犮犪犾犛狅犮犻犲狋狔狅犳犃犿犲狉犻犮犪犃,007,4(8):157 174. [18] NIRMAIER T,PUDASAINIG,BILLEJ.Veryfastwave frontmeasurementsatthehumaneyewithacustom CMOS basedhartmann Shacksensor[J]. 犗狆狋犻犮狊犈狓狆狉犲狊狊,003,11 (1):704 716. 100 5