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1、幾何光學講義 p.96p99幾何光學講義 p.100WAVEWAVE ABERATIONABERATION FUNCTIONFUNCTION SECTIONSSECTIONSWAVEWAVE ABERATIONABERATION FUNCTION:FUNCTION:202222222 11110101322222 22222031()()()()xyWWxyW xW yWxyW Hy xyWH yWHxyW Hy MERIDIONALMERIDIONAL SECTIONASECTIONAL:L: (x=0)(x=0)2 11223432 04013122222031132 1131120222
2、22034 131040WW()()()()yyW yWyWHyWHWH yWH yyWWHyWWWH yWH yWy 20TRANSVERSETRANSVERSE SECTIONSECTION: : (y=0)(y=0)2242 2011040220224 1120220040()()()xxWW xW xWxWH xWxWWHxWx 幾何光學講義 p.101RAYRAY FANSFANS MERIDIONALMERIDIONAL FANFAN: : (x=0)(x=0)2232 20110401312222203113223 11131202222201310402432()(2()(3)
3、(4)yy cy cRW yWWyWHyWWH yWHnRWWHWWWHyWH yWyn TRANSVERSETRANSVERSE FANFAN: : (y=0)(y=0)32 201104013123 112022004032 1113131132 11311131243()(2)(4)()()xx cx cxy ccRW xWWxWHxnRWW xWHxWxnRWWHxWHnRyWWHWH xn 幾何光學講義 p.102ZONALZONAL DIAGRAMSDIAGRAMS23 11200402202 131323 111313112004022022 222131242sin3sin2
4、2242()coscos2 xx cyy cRWWWWHdnWHdRWWHWHWWWnWHdWHd 幾何光學講義 p.103SPHERICALSPHERICAL ABRRATIONABRRATION24 200403 200403 200403 200402sin4sin(24)sin(24)cosWWWwWdWdx WWdwWWdy ZONAL IMAGE IS CIRCLE CENTERED ON CHIEF RAY WITH RADIUS223 200402(24)nxy cRWWn ATAT PARAXIALPARAXIAL FOCUSFOCUS 3 0402(2)n cRWnDIAM
5、ETER OF IMAGE IS 0408cRWnDISTANCEDISTANCE FROMFROM PARAXIALPARAXIAL TOTO MARGINALMARGINAL FOCUSFOCUS220040224ccRRzWWnn幾何光學講義 p.104 （）（）CAUSTIC (EXTERNAL)d(r)/d=(2R/nrc ) (W20+6W040 2)=0 W20= -6W040 2PARAMETRICPARAMETRIC EQUATIONEQUATION DISTANCEDISTANCE FROMFROM PARAXIALPARAXIAL FOCUSFOCUSzc= -(12 R
6、2/nrc )W040 2RADIUSRADIUS OFOF CASTICCASTICrc=8 (R/nrc)W040 3CAUSTIC (AXIAL)gA= -4(R2/nrc2) W040 2 (LONEITUDINAL SPHERICAL ABERRATION)rA=0FOR ANY RAY PASSING THROUEG PUPIL AT PADIUS ，THE ABOVE EQUATIONS LOCATE THE CENTERS OF PRINCIAL CURVATURE OF THE WAVEFRONT AT THE LOCATION OF THE RAY IN THE PUPIL
7、.幾何光學講義 p.105MINIMUM CIRCLECAUSTICCAUSTIC INTERSECTINTERSECT MAREINALMAREINAL RAYRAY CONECONErc= r(1) 8 (R/nrc)W040 3=2(R/nrc)(W20+2W040 ) ，W20= -6 W040 2=4(R/nrc)W040 (-32 +1)23 = -32 +1(+1)2 (2-1)=0= -1=1/2 DIAMETER OF MINIMUM CIRCLE IS 2(R/nrc) W040DISTANCE FROM PARAXIAL FOCUS TO MINIMUM CIRCLE I
8、Sz= -3(R2/nrc2) W040幾何光學講義 p.106p.110FIGURES幾何光學講義 p.111COMACOMAW=W20 2 +W131 H 3 cos x = -(R/nrc)2W20 sin +W131 H 2 sin= -(R/nrc)2W20 + 2W131 H 2 cossin y = -(R/nrc)2W20 cos +W131 H 2 (2+cos2)= -(R/nrc) W131 H 2 +2W20 + 2W131 H 2 coscosZONAL IMAGE IS LIMAGON OF PASCAL WITH ORIGIN AT x = 0 ， y = -(R
9、/nrc) W131 H 2 FOR W20 =0 ，THIS DEGENERATES TO (DOUBLE) CIRCLE， CENTER AT x = 0 ， y = -2(R/nrc) W131 H 2 RADIUS r = (R/nrc) W131 H 2ZONAL IMAGE IS CARDIOID WHEN W20 = + W131 H = - W131 H 幾何光學講義 p.112幾何光學講義 p.113ASTIEMATIBMASTIEMATIBMW=W20 2 +W222 H2 2 cos2 + W220 H2 2 x = -(R/nrc)2W20 sin +2W220 H2
10、sin x = sin= -(2R/nrc)W20 + W220 H2 sin y = -(R/nrc)2W20 cos +2(W220 + W222) H2 cos = -(2R/nrc) W20 +(W220 + W222 )H2 cos y = cosZCNAL IMAGE IS EUIPSE CENTERED ON CHIEF RAYx2 /(2R/nrc)W20 +W220 H2 2 + y2 /(2R/nrc)W20 +(W220+W222 )H22=1SAGITTALSAGITTAL FOCUSFOCUS W20 = - W220 H2 y = -(2R/nrc) W222 H2 cos x = 0TANGENTIALTANGENTIAL FOCUSFOCUS W20 = -W222 H2 x = -(2R/nrc) W220 H2 sin y = 0MEPIALMEPIAL FOCUSFOCUS W20 = - (W220 + 1/2W222) H2 x = (R/nrc) W222 H2 sin y = -(R/nrc) W222 H2 cos
