# Lens Design I. Lecture 12: Correction I Herbert Gross. Summer term

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1 Les Desig I Leture : Corretio I Herbert Gross Summer term 05

3 3 Cotets. Symmetry priiple. Field flatteig 3. Chromatial orretio

4 4 riiple of Symmetry erfet symmetrial system: magifiatio m = - Stop i etre of symmetry Symmetrial otributios of wave aberratios are doubled (spherial) Asymmetrial otributios of wave aberratio vaishes W(-x) = -W(x) Easy orretio of: oma, distortio, hromatial hage of magifiatio frot part rear part 3

5 5 Symmetrial Systems Ideal symmetrial systems: Vaishig oma, distortio, lateral olor aberratio Remaiig residual aberratios:. spherial aberratio. astigmatism 3. field urvature 4. axial hromatial aberratio 5. skew spherial aberratio skew spherial aberratio

6 6 Symmetry riiple Appliatio of symmetry priiple: photographi leses Espeially field domiat aberratios a be orreted Also approximate fulfillmet of symmetry oditio helps Triplet sigifiatly: quasi symmetry Realizatio of quasisymmetri setups i early all photographi systems Double Gauss (6 elemets) Biogo Double Gauss (7 elemets) Ref : H. Zügge

7 7 Coma Corretio: Symmetry riiple erfet oma orretio i the ase of symmetry But magifiatio m = - ot useful i most pratial ases Image height: y = 9 mm Symmetry priiple upil setio: meridioal sagittal Trasverse Aberratio: y' 0.5 mm y' 0.5 mm (a) (b) From : H. Zügge

8 Offer-System Coetri system of Offer: relatio d d r r objet M image r r d d Due to symmetry: erfet orretio of field aberratios i third order 0. astigmatism 0-0. urvature distortio M M M sum

9 Dyso-System Catadioptri system with m = - aordig Dyso Advatage : flat field Appliatio: lithography ad projetio Relatio: r L r M Residual aberratio : astigmatism y T S r L r M objet image mirror z

10 0 Coma Corretio: Stop ositio ad Aspheres Combied effet, aspherial ase prevet orretio lao-ovex elemet exhibits spherial aberratio Sagittal oma y' 0.5 mm Spherial aberratio orreted with aspheri surfae aspheri Sagittal oma y' 0.5 mm aspheri aspheri Ref : H. Zügge

11 etzval Theorem for Field Curvature etzval theorem for field urvature:. formulatio for surfaes. formulatio for thi leses (i air) Importat: o depedee o bedig R ptz R ptz m ' k f j j k ' k ' r j k k k Natural behavior: image urved towards system objet plae roblem: olletig systems with f > 0: If oly positive leses: R ptz always egative R optial system real image shell ideal image plae

12 etzval Theorem for Field Curvature Goal: vaishig etzval urvature ad positive total refrative power for multi-ompoet systems R f ptz f j h h j f j j j Solutio: Geeral priiple for orretio of urvature of image field:. ositive leses with: - high refrative idex - large margial ray heights - gives large otributio to power ad low weightig i etzval sum. Negative leses with: - low refrative idex - samll margial ray heights - gives small egative otributio to power ad high weightig i etzval sum

13 3 Flatteig Meisus Leses ossible leses / les groups for orretig field urvature Iterestig adidates: thik mesisus shaped leses r k ' k ' r Rptz k k k k f d r r r d. Hoeghs mesius: idetial radii - etzval sum zero - remaiig positive refrative power F' ( ) r d. Coetri meisus, - etzval sum egative - weak egative foal legth - refrative power for thikess d: r R ptz r d ( ) d r r d ( ) d F' r ( r d) 3. Thik meisus without refrative power Relatio betwee radii r r d R ptz r ( ) d r d ( ) 0

14 4 Corretig etzval Curvature Group of meisus leses d ollimated r r Effet of distae ad refrative idies /R pet [/mm] 0 - K5 / d=5 mm 0 - K5 / d=5 mm SF66 / d=5 mm r [mm]

15 5 Corretig etzval Curvature Triplet group with r r r 3 d/ ollimated Effet of distae ad refrative idies 0 - /R pet [/mm] SF66 / FK3 / SF BK r [mm]

16 Field Curvature 6 Corretio of etzval field urvature i lithographi les for flat wafer R j F j j ositive leses: Gree h j large Negative leses : Blue h j small F j h h j F j Corretio priiple: ertai umber of bulges

17 7 Flatteig Field Les Effet of a field les for flatteig the image surfae. Without field les. With field les urved image surfae image plae image shell flat image field les

18 Ahromate : Basi Formulas Idea:. Two thi leses lose together with differet materials. Total power F F F 3. Ahromati orretio oditio F F 0 Idividual power values F F F F roperties:. Oe positive ad oe egative les eessary. Two differet sequees of plus (row) / mius (flit) 3. Large -differee relaxes the bedigs 4. Ahromati orretio idipedet from bedig 5. Bedig orrets spherial aberratio at the margi 6. Aplaati oma orretio for speial glass hoies 7. Further optimizatio of materials redues the spherial zoal aberratio

19 Ahromate: Corretio Cemeted ahromate: 6 degrees of freedom: 3 radii, idies, ratio / Corretio of spherial aberratio: divergig emeted surfae with positive spherial otributio for eg > pos Choie of glass: possible goals. aplaati oma orretio. miimizatio of spherohromatism 3. miimizatio of seodary spetrum s' rim ase with solutios Bedig has o impat o hromatial orretio: is used to orret spherial aberratio at the edge Three solutio regios for bedig. o spherial orretio. two equivalet solutios 3. oe aplaati solutio, very stable ase without solutio, oly sperial miimum R ase with oe solutio ad oma orretio

20 Ahomati solutios i the Glass Diagram row positive les flit egative les Ahromat

21 Ahromate Ahromate Logitudial aberratio Trasverse aberratio Spot diagram y' 486 m 587 m 656 m = 486 m axis r p = 587 m = 656 m siu' m 587 m 656 m s' [mm]

22 Relative artial Dispersio Log row ad short flit as speial realizatios of large Log row Short flit Crow Flit Ref.:H. Zuegge

23 3 Axial Colour : Apohromate Choie of at least oe speial glass gf Corretio of seodary spetrum: aomalous partial dispersio 0,6 0,60 N-FS6 () At least oe glass should deviate sigifiatly form the ormal glass lie 0,58 0,56 ()+() T N-KZFS (3) 656m 588m 0,54 () 90 N-FK m -0.mm z -0.mm 436m 0 mm z

24 Foal power oditio Ahromati oditio Seodary spetrum Curvatures of leses arameter E The 3 materials are ot allowed to be o the ormal lie The triagle of the 3 poits should be large: small j give relaxed desig 3 F F F F F F F F F F r r 3,, a a b a a E f 3,, b b a a b E f 3,, b a a E f b a a b b a a E Apohromate 4

25 Buried Surfae 5 Cemeted surfae with perfet refrative idex math No impat o moohromati aberratios Oly ifluee o hromatial aberratios Espeially 3-fold emeted ompoets are advatages Ca serve as a startig setup for hromatial orretio with fulfilled moohromati orretio Speial glass ombiatios with early perfet parameters Nr Glas d d d d SK F SK LF SSK F SK BaF d d d 3

26 6 riiples of Glass Seletio i Optimizatio Desig Rules for glass seletio Differet desig goals:. Color orretio: idex large dispersio differee desired positive les field flatteig etzval urvature. Field flatteig: large idex differee + + desired egative les olor orretio + - availability of glasses - - dispersio Ref : H. Zügge

27 Ahromati Hybrid Les Les with diffrative strutured surfae: hybrid les Refrative les: dispersio with Abbe umber = refrative les blue gree red Diffrative les: equivalet Abbe umber d d F Combiatio of refrative ad diffrative surfaes: ahromati orretio for ompesated dispersio C diffrative les R D red gree blue Usually remais a residual high seodary spetrum hybrid les blue gree red Broadbad olor orretio is possible but ompliated

28 Diffrative Optis: Siglet Solutios Combiatio of DOE ad aspherial arrier all. order d y' 50 mm y p y p diffrative surfae, phase aspherial d y' 50 mm -0.5 mm y p 0 s' y p refrative surfae, aspherial a d y' 50 mm y p -0.5 mm 0 y p s' diffrative surfae, arrier aspherial d,a y' 50 mm -0.5 mm y p 0 s' y p -0.5 mm 0 s'

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