Lens Design II. Lecture 3: Aspheres Herbert Gross. Winter term

Transcription

1 Lens Design II Lectue 3: Asphees Hebet Goss Winte tem 18

2 Pelimina Schedule Lens Design II Abeations and optimiation Repetition 4.1. Stuctual modifications Zeo opeands, lens splitting, lens addition, lens emoval, mateial selection Asphees Coection with asphees, Fobes appoach, optimal location of asphees, seveal asphees Feefoms Feefom sufaces, geneal aspects, suface desciption, qualit assessment, initial sstems Field flattening Astigmatism and field cuvatue, thick meniscus, plus-minus pais, field lenses Chomatical coection I Achomatiation, axial vesus tansvesal, glass selection ules, buied sufaces Chomatical coection II Seconda spectum, apochomatic coection, aplanatic achomates, spheochomatism Special coection topics I Smmet, wide field sstems, stop position, vignetting Special coection topics II Telecenticit, monocentic sstems, anamophotic lenses, Scheimpflug sstems Highe ode abeations High NA sstems, boken achomates, induced abeations Futhe topics Sensitivit, scan sstems, eepieces Mio sstems special aspects, double passes, catadioptic sstems Zoom sstems Mechanical compensation, optical compensation Diffactive elements Colo coection, a equivalent model, stalight, thid ode abeations, manufactuing

3 3 Contents 1. Asphees. Conic sections 3. Fobes asphees 4. Sstem impovement b asphees 5. Asphees in Zemax

4 4 Aspheical Coection Coection of spheical abeation b an asphee a) spheical lens efaction too stong b) aspheical lens asphee educes powe Ref: A. Hekomme

5 5 Conic Sections Explicite suface equation, esolved to Paametes: cuvatue c = 1 / R conic paamete Influence of on the suface shape c c Paamete Suface shape = - 1 paaboloid < - 1 hpeboloid = sphee > oblate ellipsoid (disc) > > - 1 polate ellipsoid (ciga ) Relations with axis lengths a,b of conic sections a b 1 c b a b 1 c 1 a c 1 1

6 6 Aspheical Shape of Conic Sections Conic aspheical suface Vaiation of the conical paamete c c

7 x x c x c x R R R R x x Conic section Special case spheical Cone Tooidal suface with adii R x and R in the two section planes Genealied onic section without cicula smmet Roof suface c x c c x c x x x tan 7 Aspheical Suface Tpes

8 Polnomial Aspheical Suface Standad otational-smmetic desciption 8 Basic fom of a conic section supeimposed b a Talo expansion of c () c M m a... adial distance to optical axis x m m4 () c a m cuvatue conic constant aapheical coefficients Ref: K. Uhlendof

9 Polnomial Aspheical Suface Othe desciptions x s s c s c s C s b s b B k A C B A M m N n n m ij M m m m h a h a h k h ) ( ) ( t g t f h Supeconic (Genolds ) Implicit -polnomial asphee (Lene/Sasian ) Tuncated paametic Talo (Lene/Sasian ) 9 Ref: K. Uhlendof 9

10 1 Simple Asphee Paabolic Mio Equation Radius of cuvatue in vetex: R s Pefect imaging on axis fo object at infinit Stong coma abeation fo finite field angles Applications: 1. Astonomical telescopes. Collecto in illumination sstems R s axis w = field w = field w = 4

11 11 Paabolic Mio Equation c : cuvatue 1/R s : eccenticit ( = -1 ) c 1 1 (1 ) c C F a R sag vetex cicle sagittal cicle of cuvatue tangential cicle of cuvatue R tan vetex cicle R s paabolic mio F x R adii of cuvatue : tan Rs 1 R s paabolic mio R tan Rs 1 R s R s f 3

12 1 Ellipsoid Mio Equation c: cuvatue 1/R : Eccenticit e c 1 1 (1 ) c b oblate vetex adius Rso F polate vetex adius R sp a F' ellipsoid

13 13 Simple Asphee Elliptical Mio Equation Radius of cuvatue in vetex, cuvatue c eccenticit Two diffeent shapes: oblate / polate Pefect imaging on axis fo finite object and image loaction Diffeent magnifications depending on used pat of the mio Applications: Illumination sstems s c 1 1 (1 ) c s' F F'

14 14 Asphee: Pefect Imaging on Axis Pefect stigmatic imaging on axis: elliptical font suface elliptical concentic

15 15 Asphee: Pefect Imaging on Axis Pefect stigmatic imaging on axis: Hpeoloid ea suface s n 1 s n 1 s n 1 n 1 1 n s F Stong decease of pefomance fo finite field sie : dominant coma Altenative: ellipsoidal suface on font suface and concentic ea suface 1 5 D spot m] 1 w in

16 Gacing Incidence-Xa Telescope Xa telescopewolte tpe I Nested shells with gacing incidence Incease of numeical apetue b seveal shells paaboloids hpeboloids Wolte tpe I towads paaboloid focus point as detecto nested clindical shells

17 Gacing Incidence-Xa Telescope Woltetp 1. Paaboloid. Hpeboloid

18 18 Asphees - Geomet Refeence: deviation fom sphee Deviation along axis Bette conditions: nomal deviation s () deviation height tangente () deviation along axis height sphee pependicula deviation s aspheical shape spheical suface aspheical contou

19 19 Aspheical Expansion Ode Impovement b highe odes Geneation of high gadients () 1 6. ode 5 D ms [m] ode 8. ode 1. ode 1. ode ode k max

20 Asphees: Coection of Highe Ode Coection at discete sampling Lage deviations between sampling points Lage oscillations fo highe odes Bette desciption: slope, defines a bending esidual spheical tansvese abeations pefect coecting suface Coected points with ' = coected points esidual angle deviation points with maximal angle eo paaxial ange ' = c d A /d eal asphee with oscillations A

21 Polnomial Aspheical Suface Fobes Asphees - Q con 1 New othogonaliation and nomaliation using Jacobi-polnomials Q m c () / max amqm / c m M 4 max equies nomaliation adius max (1:1 convesion to standad asphees possible) Mean squae slope M m a m / m 5 () 4 Q () 4 Q 1 () 4 Q () 4 Q 3 () 4 Q 4 () 4 Q 5 () Ref: K. Uhlendof

22 Polnomial Aspheical Suface Fobes Asphees - Q bfs Limit gadients b special choice of the scala poduct () 1 max max M c a mb m 1 1 c 1 c m max (1:1 convesion to standad asphees () not possible) Mean squae slope 1/ h max M m a m Ref: K. Uhlendof u(u-1)b (u) u(u-1)b 1 (u) u(u-1)b (u) u(u-1)b 3 (u) u(u-1)b 4 (u) u(u-1)b 5 (u) u = (/ max )

23 3 Fobes Asphees Stong asphee Q con sag along -axis slope othogonal tue polnom tpe Q 1 in Zemax Mild asphee Q bfs diffeence to best fit sphee sag along local suface nomal not slope othogonal not a polnomial due to pojection tpe Q in Zemax c () / max amqm / c m M 4 max () 1 max max M c a mb m 1 1 c 1 c m max diect toleancing of coefficients () no diect elation of coefficients to slope () 4 Q () 4 Q 1() 4 Q () 4 Q 3() 4 Q 4() 4 Q 5() u(u-1)b (u) u(u-1)b 1(u) u(u-1)b (u) u(u-1)b 3(u) u(u-1)b 4(u) u(u-1)b 5(u) u = (/ max)

24 4 Selection of Asphee Tpes Coection of Reto focus tpe camea lens F# =.8, d=1, w = 94 Consideabl bette esukt and faste optimiation b the use of Q asphees a) standad asphee b) Qbfs asphee Ref: C. Menke

25 5 Impact of Asphee Asphee fa fom pupil: - a bundels of field points sepaated - field dependend coection - also impact on distotion suface Asphee nea pupil: - all a bundels equall affected - poblem field angles: coma suface 15

26 6 Aspheical Single Lens Coection on axis and field point Field coection: two asphees spheical axis field, tangential field, sagittal 5 m 5 m 5 m a one aspheical 5 m 5 m 5 m a a double aspheical 5 m 5 m 5 m

27 7 Reducing the Numbe of Lenses with Asphees Example photogaphic oom lens Equivalent pefomance 9 lenses educed to 6 lenses Oveall length educed a) all spheical 9 lenses Vaio Sonna / f = 8-56 b) with 3 asphees 6 lenses length educed aspheical sufaces Ref: H. Zügge

28 8 Reducing the Numbe of Lenses with Asphees Example photogaphic oom lens Equivalent pefomance 9 lenses educed to 6 lenses Oveall length educed Photogaphic lens f = 53 mm, F# = 6.5 a) all spheical, 9 lenses axis field x x 436 nm 588 nm 656 nm p x p p x p b) 3 asphees, 6 lenses, shote, bette pefomance axis field x x A 1 A 3 A p x p p x p Ref: H. Zügge

29 9 Reducing the Numbe of Lenses with Asphees Binocula Lenses 1.5x Neal equivalent pefomance Distotion, Field cuvatue and pupil abeation slightl impoved 1 lens emoved Bette ee elief distance a) Binocula 1.5x, all spheical field cuvatue in dpt distotion in % tan sag b) Binocula 1.5x, 1 aspheical suface tan sag

30 3 Lithogaphic Pojection: Impovement b Asphees Consideable eduction of length and diamete b aspheical sufaces Pefomance equivalent a) NA =.8 spheical 31 lenses lenses emovable b) NA =.8, 8 aspheical sufaces -9% -13% 9 lenses Ref: W. Ulich

31 31 Best Position of Asphees Location depending on coection taget: spheical : pupil plane coma and astigmatism: field plane No effect on Petval cuvatue aspheical effect.4.3. spheical coma astigmatism distotion d/p'

32 3 Aspheical Sensitivit 3 spheical abeation Example: Lithogaphic lens Sensitivities fo aspheical coection coma suface index astigmatism suface index distotion suface index.1.5 S1 S4 S5 S1 S16 stop S3 S suface index

33 33 Aspheiation of a Camea Lens Selection of one aspheical suface in a photogaphic lens S S 5 S 9 S 11 S spheical abeation coma suface index spheical sstem: 197 nm suface : 196 nm suface 5: 185 nm suface 9: 187 nm suface 11: 78 nm suface 14: 178 nm astigmatism suface index distotion suface index suface index

34 Hand Phone Objective lenses Examples US L = 4. mm, F'=.8, f = 3.67 mm, w=x34 US L = 6. mm, F'=.8, f = 4. mm, w=x31 EP L = 5.37 mm, F'=.88, f = 3.3 mm, w=x33.9 Olmpus L = 7.5 mm, F'=.8, f = 4.57 mm, w=x33 Ref: T. Steinich

35 35 Realiation Aspects fo Asphees Stong asphee : Tuning points ''= Deviation fom sphee asphee pofile () deivative '() 3 pofile deviation () deivative '(). deivative ''()

36 36 Suface popeties and settings Setting of suface popeties

37 Impotant Suface Tpes Standad Even asphee Paaxial Paaxial XY Coodinate beak Diffaction gating Gadient 1 Tooidal Zenike Finge sag Extended polnomial Black Box Lens ABCD spheical and conic sections classical asphee ideal lens ideal toic lens change of coodinate sstem line gating gadient medium clindical lens suface as supeposition of Zenike functions genealied asphee hidden sstem, fom vendos paaxial segment