消色差复合透镜之模拟与分析

消色差複合透鏡之模擬與分析,林正峰，林世堃，杜彥錫,Modeling and analysis of the hybrid achromatic lens,Department of Electrical Engineering Southern Taiwan University of Technology Tainan,CONTENTS,Introduction of the hybrid lensProfile of the diffractive surfaceHybrid lens and aberrationsThickness comparison and ray fan plotFabrication errorsSimulation of diffraction efficiencyPSF and MTF of the hybrid lensSummary,Introduction of the hybrid lens,Advantages： Correct the chromatic aberration and other aberrations Reduce weight, volume, and cost,+,=,Refractive lens,Diffractive lens,Hybrid lens,nd-vd,d-line(587nm)、C-line(656nm) and F-line(486nm),Phase shift function,由於,如果將修改成modulo 2的相位結構，我們便可得到blazed-type Fresnel 透鏡的相位函數,m為第幾個zone的意思，rm為第m個zone的內半徑。,f :焦距 r: 半徑,Profile of the diffractive surface,繞射面的表面輪廓(profile)T(r)可表示為：,Topt為繞射面的最大深度，即 ， 為設計波長,Design procedures of the hybrid lens,Define Purpose、Environment and Fabrication technology,Find achromatic coefficient(A) and spherical aberration coefficient(G),Use the commercial optical system design software to optimize,Produce diffractive profile,Simulate the SPDT,Simulate diffraction efficiencies of diffractive surfaces by different types of diamond turning tools and different tools radii.,Compare and analyze,Hybrid lens and aberrations,h,y,f,Marginal ray,Chief ray,B=1 convex to left and plane to right,y: radius(aperture/2) ref:optical power C:conjugate parameter n: refractive index B:bending parameter,Spherical aberration of refractive surface:,Hybrid lens and aberration,Using the equation below, we can find spherical aberration coefficient (G):,By the commercial optical system design softwareOSLO, we can optimize the coefficients A and G.,Assume the object is at infinity, i.e., C=-1. In addition, the refractive index for the diffractive surface is infinite, so we can find the relationship:,Design cases,EFL : 99.76mm, aperture/2 : 25mm, F/#:2 Principal wavelength: 0.589mm, other wavelengths: 0.486mm and 0.656mm, view angle: 3o,EFL : 100mm, aperture/2 : 64mm, F/#:3.3 Principal wavelength: 0.589mm, other wavelengths: 0.486mm and 0.656mm, view angle: 25.17o,case1,case2,Thickness comparison,Doublet,Eyepiece,Ray fan plot of the doublet,縱軸實際光束與參考光束(chief ray )在像面上的位移。 橫軸為歸一化(normalize)後的入孔(entrance pupil)座標 左圖為子午光束擷取曲線(meridional ray intercept curve)，右圖為徑向光束擷取曲線(sagittal ray intercept curve) 上中下圖分別為全視場 、0.7視場及0視場,Ray fan plot of the eyepiece,Fabrication errors (round tool ),To model effects of fabrication errors, we assume the hybrid lens is fabricated by single-point diamond turning technique.,The x is fabrication error in x direction ，d is fabrication error of depth.,Diffractive surface,The diffractive surface obtained by using a 50mm round tool,Fabrication error ( half-radiused tool ),Diffractive surface obtained by using a 1mm half-radiused tool,Diffraction efficiency (case 1-BK7),Doublet, (Round tool),Doublet, (half-radiused tool),PSF&MTF (hybrid lens),設計編號：A1,A1：Doublet, BK7,全R刀 籃色：理想 綠色：2m紅色： 12m淡籃色：32m 粉紅色：47m,A2： Doublet, BK7,半R刀 籃色：理想 綠色：2m紅色：50m淡籃色：0.5mm 粉紅色：1mm,PSF,PSF,MTF,MTF,MTF (different wavelengths),d-line(587nm) C-line(656nm) F-line(486nm),Ideal (No fabrication errors),Round tool- (47um),PSF,PSF,MTF,MTF,Summary,Comparing with conventional achromats, the hybrid lens not only can correct chromatic aberration and spherical aberration, but also can reduce weight and volume. Diffraction efficiency of the diffractive surface will decrease due to fabrication errors, which depend on types of tools used and tool radii.PSF and MTF will deteriorate when tool size increases. Under wavelengths other than the design wavelength, diffraction efficiency of the diffractive surface will decrease.,Reference,1 D.A.Buralli, G.M.Morris,” Design of a wide filed diffractive landscape lens” Appl. Opt Vol 8(18), pp3950-3959 ,(1989)2 W. T. Welfford ,“Aberration of optical system” Hilger,Bristol,1986,pp226-2393 W. A. Kleinhans, “Aberration of curred zone plates and Fresnel lens” Appl. Opt Vol 16(6) ,PP.1701-1704 (1977)4 L.N.Hazra,C. A.Delisle, “Higher order kinoform lenses :diffraction efficiency and aberrational properties” Optical Engineering, Vol 36(5), pp1500-1507(1997)5 C.G.Blough, “A new approach to chromatic aberrations unilizing ahybrid surface” OSA Diffractive Optics PP272-274(1998)6 T. Stone, N.George, “Hybrid diffractive-refractive lenses and achromats” ,Appl. Opt Vol 27(14) ,PP. 2960-2971 (1988)7 M. J. Riedl ,“Diamond-turned diffractive optical elements for the infrared”,SPIE Vol 2540 pp257-269 (1995)8 趙麗萍,“折衍混合單透鏡代替雙腔合望遠鏡的設計研究”,光學學報Vol.18 (2), pp223-227,(1998)9 G.J.Swanson,”Binary optics technology:the theory and design of multi-level diffravtive optical elements,”U.S Department of Commerce. National Technical information Service ,Aug(1989)10 J.W.Goodman,” fourier optics “,(1996) 11 M.Yamagata,Y. Tanaka,T.Sasano ,”Efficiency Simulation for Diamond-Turned Diffractive Lenses”,Jpn.J.Appl.Phys,Vol.37,pp3695-3700,(1998)12 J.A.Cox, B.Fritz, T.Werner,” Process error limitations on optics performance “, SPIE vol.1551,(1991)13 D.A.Buralli,G.M.Morris,J.R.Roger, “Optical performance of holographic kinoforms”, applied optics,vol .28,no.5,(1989),阿貝數與折射率,無色光學玻璃： 按色散分二類，色散小是冕類(K)，色散大是火石類(F)冕類: 氟冕(FK)、輕冕(QK)、磷冕(PK)、重磷冕(ZPK)、冕(K)、重冕(ZK)、鋇冕(BaK)、鑭冕(LaK)、鈦冕(TiK)、特冕(TK) 火石類: 輕火石(QF)、火石(F)、重火石(ZF)、鋇火石(BaF)、重鋇火石(ZBaF)、鑭火石(LaF)、重鑭火石(ZLaF)、鈦火石(TiF)、冕火石(KF)、特種火石(TF),Phase shit function,A(P)以及f(P)分別是此電磁波在P點的振幅及相位，而v是此電磁波的頻率。,電場u(P,t)亦可以複數表示，即,其中 U(P)=A(P)exp-jf(P) 為u(P,t) 的相位(phase)或複數振幅(complex amplitude)。,wavefront aberration,Welford提出的波前像差 (wavefront aberration),為歸一化後的瞳孔座標(normalized radius coordinate)h 是經過歸一化(normalized)的光入射高度 為 的瞳孔極座標之相角(polar pupil coordinate),SISV分別表示球差(spherical aberration)、慧差(coma)、像散(astigmatism)、場曲(curvature of field )及畸變(distortion),焦距的運算,光學塑膠特性,資料來源：光學KOGAKU (Japanese Journ