Imaging and Aberration Theory

Transcription

1 Imagig ad Aberratio Theory Leture 9: Chromatial aberratio Herbert Gro Witer term 04

2 Prelimiary time hedule Paraxial imagig paraxial opti, fudametal law of geometrial imagig, ompoud ytem Pupil, ourier opti, pupil defiitio, bai ourier relatiohip, phae pae, aalogy opti ad 06.. Hamiltoia oordiate mehai, Hamiltoia oordiate Eikoal ermat priiple, tatioary phae, Eikoal, relatio ray-wave, geometrial approximatio, ihomogeeou media Aberratio expaio igle urfae, geeral Taylor expaio, repreetatio, variou order, top hift formula Repreetatio of aberratio differet type of repreetatio, field of appliatio, limitatio ad pitfall, meauremet of aberratio Spherial aberratio pheomeology, ph-free urfae, kew pherial, orretio of ph, apherial urfae, higher order 7.. Ditortio ad oma pheomeology, relatio to ie oditio, aplaati ytem, effet of top poitio, variou topi, orretio optio Atigmatim ad urvature pheomeology, Coddigto equatio, Petzval law, orretio optio Chromatial aberratio Diperio, axial hromatial aberratio, travere hromatial aberratio, pherohromatim, eodary poetrum 0 Sie oditio, aplaatim ad Sie oditio, ioplaatim, relatio to oma ad hift ivariae, pupil 5.0. ioplaatim aberratio, Herhel oditio, relatio to ourier opti.0. Wave aberratio defiitio, variou expaio form, propagatio of wave aberratio 9.0. Zerike polyomial PS ad trafer futio 4.0. Additioal topi peial expaio for irular ymmetry, problem, alulatio, optimal balaig, ifluee of ormalizatio, meauremet ideal pf, pf with aberratio, Strehl ratio, trafer futio, reolutio ad otrat Vetorial aberratio, geeralized urfae otributio, Aldi theorem, itrii ad idued aberratio, revertability

3 3 Cotet. Material diperio. Partial diperio 3. Aomalou partial diperio 4. Axial hromatial error 5. Ahromati 6. Apohromate 7. Spherohromatim 8. Chromatial variatio of magifiatio 9. Example

4 4 Diperio ad Abbe umber Deriptio of diperio: Abbe umber Viual rage of wavelegth: typially d,,c or e,,c ued e e C C refrative idex Typial rage of glae e = S flit Two fudametal type of gla: Crow glae: mall, large, diperio low lit glae: large, mall, diperio high BK7 row

5 Curvature of the radii of a le oal power at the eter wavelegth e for a thi le Differee i foal power for outer wavelegth, C with the Abbe umber oal legth at the eter wavelegth Differee of the foal legth for outer wavelegth Ahromatizatio oditio for two thi lee loe together Abbe Number ad Ahromatizatio, r r e e e ) ( ) )( ( e e e e C C C ) ( ) ( f e e e ) ( e e e C C C C f f f f ) ( ) )( ( C e e 0 f f 5

6 6 Gla Diagram Uual repreetatio of glae: diagram of refrative idex v diperio () Left to right: Ireaig diperio dereaig Abbe umber

7 7 Diperio Material with differet diperio value: - Differet lope ad urvature of the diperio urve - Stroger hage of idex over wavelegth for large diperio - Iverio of idex equee at the boudarie of the petrum poible refrative idex flit mall lope large.65 row large lope mall.65 SK8A.6 VIS

8 Atomi model for the refrative idex: oillator approah of atomi field iteratio Sellmeier diperio formula: orrepodig futio Speial ae of oupled reoae: example quartz, degeerated oillator Atomi Model of Diperio i r i f m Ne i log [mm] viible (UV) (UV) 3 (IR) 4 (IR) vi () C B A 4 0 o C B B A 8

9 9 Diperio formula Shott formula empirial Sellmeier Baed o oillator model 4 6 a a a a a a o ( ) A B C Bauh-Lomb empirial Herzberger Baed o oillator model 4 D E ( ) A B C ( o) a a3 ) ao a ( o o mit 0.68 mm o o Hartma Baed o oillator model ( ) a o a a 3 a4 a 5

10 0 Relative partial diperio Relative partial diperio : Chage of diperio lope with Differet urvature of diperio urve Defiitio of loal lope for eleted wavelegth relative to eodary olor P C i - g g - - e - C C - C - t () Speial -eletio for harateriti rage of the viible petrum.49 = 656 / 04 m far IR = 656 / 85 m ear IR = 486 / 546 m blue edge of VIS = 435 / 486 m ear UV = 365 / 435 m far UV.48 i : 365 m UV edge g : 435 m UV edge e : 546 m d : 588 m mai olor : 480 m C : 644 m : 486 m C : 656 m. eodary olor. eodary olor : 85 m IR edge t : 04 m IR edge

11 Partial Diperio ad Normal Lie The relative partial diperio hage approximately liear with the diperio for glae P b, a, d, P 0.6 Nearly all glae are loated o the ormal lie i a P--diagram P g The lope of the ormal lie deped o the eletio of wavelegth 0.55 Glae apart from the ormal lie how aomalou partial diperio P 0.5 P C P a d b P thee material are importat for hromatial orretio of higher order

12 Partial Diperio Aormal partial diperio ad ormal lie P g, N-K5 N-PK5 ormal lie GG375G34 N-BA5 N-BA3 N-BA5 K5G0 N-BAK4 N-BA0 N-SK N-SK8 N-LA3 SK0G0 N-BAL5 N-LL6 BAKG N-SSK8 SK4G3 N-BAL4 N-SK5 SSK5G06 N-SK4 N-SSK5 N-K5 SK5 N-BAK N-K9 K7 N-SK N-PK5 N-SK5 N-PSK53 N-PSK57 N-PSK58 BK7G5 N-PSK3 N-K5 N-BK0 BK7G8 N-BK7 N-LAK7 N-LAK N-ZK7 N-SK6 N-PSK3 N-SK4 SK5G06 N-LL N-LA N-BA4 BAS5 5 N-BAK N-LAK4 S5 N-LA7 N-S64 N-S8 N-S5 N-S9 N-LAS40 N-L5 N-BAS N- G N-LAK33 N-LAK N-LAK9 N-LAK LAKL N-SK0 N-S N-S0 N-S5 S0 N-LAK8 S S5 N-LAS45 N-LAS36 LAN7 N-KZS N-BAS64 L5G5 L5 KZSN5 N-LAS43 N-LAS3 N-LA LL N-LAS4 N-LA33 N-KZS KZSN4 KZS4G0 N-LAS30 N-LAS44 N-KZS4 N-LA N-LA3 LAK9G5 K0 N-LAK34 N-KZS N-S4 N-S6 S4 N-S57 N-LA35 N-LA8 N-LA34 N-LAK0 N-SSK LAKN3 S66 SL57 S57 S S N-S56 S6G05 S6 S56A S4 N-LAS35 S8G07 N-LAS46 LASN9 S5G0

13 3 Aomalou Partial Diperio There are ome peial glae with a large deviatio from the ormal lie Of peial iteret: log row ad hort flit P g, lie of ormal diperio S N-S57 KZSN4 K5 K5 PSK53A ZKN7 LAK8 LASN30 P g, heavy flit with harater of log row flit log row log row hort flit hort flit row ormal lie

14 4 Aomalou Partial Diperio Normal glae: Partial diperio hage liear with Abbe umber Defiitio of P deped o eleted wavelegth Normal lie defied by ad K7 P P P P P C, t C,, e g, i, g d d d d d Deviatio from liear behavior: aomalou partial diperio P P a d b P P g d The value of P deped o the wavelegth eletio Typial P oidered at the red ad the blue ed of the viible petrum ormal lie P g real urve Large deviatio value P are eeary for apohromati hromatial orretio d

15 5 Aomalou Partial Diperio Arrow i the gla map: idiatio of the deviatio from the ormal lie P h Vertial ompoet: at the red horizotal: at the blue ed of the petrum P a d b P ormal lie Gla d P h arrow of deviatio P tc d gla loatio P h blue ide red ide d

16 6 Chromatial Aberratio Axial hromatial aberratio: - diperio of margial ray - differet image loatio Travere hromatial aberratio: - diperio of hief ray - differet image ize obet ideal image ideal image margial ray hief ray margial ray axial hromatial aberratio ExP ExP hief ray travere hromatial aberratio

17 7 Overview o Chromatial Aberratio. Third order hromatial aberratio: - axial hromatial aberratio error of the margial ray by diperio - travere hromatial aberratio error of the hief ray by diperio. Higher order hromatial aberratio: - eodary petrum reidual axial error, if oly eleted wavelegth are oiidig - pherohromatim hromatial variatio of the pherial aberratio, oberved i a ahromate - hromatial variatio of all moohromati aberratio e.g. atigmatim, oma, pupil loatio,...

18 8 Chromatial Aberratio Variou ae of hromatial aberratio orretio a) axial ad lateral olor orreted b) axial olor orreted MR CR C C C C ) lateral olor orreted d) o olor orreted C C C C

19 9 Axial Chromatial Aberratio Axial hromatial aberratio: Higher refrative idex i the blue reult i a horter iteretio legth for a igle le The olored image are defoued alog the axi Defiitio of the error: hage i image loatio / iteretio legth Corretio eed everal glae with differet diperio Sigle le: ormal diperio blue iteretio legth i horter tha red P Notatio: white. CHL = hromatial logitudial. AXCL = axial hromati CHL C e blue C gree red

20 0 Axial Chromatial Aberratio Logitudial hromatial aberratio for a igle le Bet image plae hage with wavelegth bet image plae = 648 m = 546 m = 480 m defou z Ref : H. Zügge

21 Seodary Spetrum P Simple ahromatizatio / firt order orretio: - two glae with differet diperio - equal iteretio legth for outer wavelegth (blue, red C) white C eodary petrum Reidual deviatio for middle wavelegth (gree e): eodary petrum ( ) P, C P SSP C f ( ), C 644 C e ahromate blue red gree 546 e iglet reidual error ahromate e C

22 Ahromate: Bai ormula Idea:. Two thi lee loe together with differet material. Total power 3. Ahromati orretio oditio 0 Idividual power value Propertie:. Oe poitive ad oe egative le eeary. Two differet equee of plu (row) / miu (flit) 3. Large -differee relaxe the bedig 4. Ahromati orretio idipedet from bedig 5. Bedig orret pherial aberratio at the margi 6. Aplaati oma orretio for peial gla hoie 7. urther optimizatio of material redue the pherial zoal aberratio

23 3 Ahromate Compeatio of axial olour by appropriate gla hoie (a) (b) Chromatial variatio of the pherial aberratio: pherohromatim (Gauia aberratio) Therefore perfet axial olor orretio (o axi) are ofte ot feaable BK7 =.568 = 64.7 = BK7 = = = = = = r p r p 486 m 588 m 656 m z z -00 Ref : H. Zügge

24 4 Ahromate Ahromate Logitudial aberratio Travere aberratio Spot diagram y 486 m 587 m 656 m = 486 m axi r p = 587 m = 656 m iu m 587 m 656 m [mm]

25 Ahromate: Corretio Cemeted ahromate: 6 degree of freedom: 3 radii, idie, ratio / MR aplaati ae Corretio of pherial aberratio: divergig emeted urfae with poitive pherial otributio for eg > po Choie of gla: poible goal. aplaati oma orretio. miimizatio of pherohromatim 3. miimizatio of eodary petrum Bedig ha o impat o hromatial orretio: i ued to orret pherial aberratio at the edge Three olutio regio for bedig. o pherial orretio. two equivalet olutio 3. oe aplaati olutio, very table ae without olutio, oly pherial miimum R ae with olutio ae with oe olutio ad oma orretio

26 6 Ahromati Solutio i the Gla Diagram large -differee give relaxed bedig row poitive le flit egative le Ahromat

27 or oe give flit a lie idiate the uefull row glae ad vie vera Perfet aplaati lie of orrepodig glae (orreted for oma) Coditio: Optimizatio of Ahromati Glae fixed flit gla lie of miimal pherial aberratio fixed row gla lie of miimal pherial aberratio r 7

28 8 Ahromate Crow gla loatio for aplaati ahromate M flit gla row gla loatio.8 aplaati row lie flit available glae

29 9 Ahromate Reidual aberratio of a ahromate Clearly ee:. Ditortio. Chromatial magifiatio 3. Atigmatim

30 Surfae ad Le otributio of Axial Color Coiderig the Abbe ivariat Derivative after the wavelegth Summig over all urfae of a ytem with the margial ray height ratio ad the propagatio of the ratio Surfae ummatio for axial hromatial aberratio with the urfae otributio oeffiiet h h d d r d d d d r d d r r Q Q N N N CHL r r N CHL N N N N N N CHL K Q CHL Q K 30

31 3 Geeral Ahromatizatio Cotributio of a thi le to the axial hromatial aberratio Axial hromatial aberratio of a ytem of thi lee K CHL le CHL N f Coditio of ahromatizatio of a ytem of lee 0 Speial ae of lee loe together 0 Coditio of apohromati (polyhromati) orretio with the partial relative diperio P 0

32 Dialyt approah: Ahromatizatio with two lee at fiite ditae Salig parameter k: With fiite margial ray height oal legth oditio Ahromatizatio oal legth of the lee Le ditae a f t k a f b k f f 0 b b b a a a f y f y k f f a b a b a b k k f f f k k d a b ) ( Dialyt-Ahromat 3

33 33 Dialyt Ahromat Uage of oly oe gla material with ahromati orretio: dialyt ahromate No real imagig poible Parameter: Setup kf f a f b k f ( k ) k le a k t k f le b image plae y a y b t f a

34 34 Axial Color Corretio with Shupma Le Speial layout of dialyte approah aordig to Shupma Mirror guaratee real imagig f = -00 mm mirror f = 300 mm real image

35 35 Axial Colour : Apohromate Choie of at leat oe peial gla P g Corretio of eodary petrum: aomalou partial diperio 0,6 0,60 N-S6 () At leat oe gla hould deviate igifiatly form the ormal gla lie 0,58 0,56 ()+() T N-KZS (3) 656m 588m 0,54 () 90 N-K m -0.mm z -0.mm 436m 0 mm z

36 oal power oditio Ahromati oditio Seodary petrum Curvature of lee Parameter E The 3 material are ot allowed to be o the ormal lie The triagle of the 3 poit hould be large: mall give relaxed deig P P P r r 3,, a a b a a P P E f 3,, b b a a b P P E f 3,, b a a P P E f b a a b b a a P P P P P P E Apohromate 36

37 37 Relative Partial Diperio Preferred gla eletio for apohromate N-S N-S6 N-S57 N-S66 P-S68 P-S67 N-K5A N-PK5A N-PK5 N-KZS N-KZS4 N-LA33 N-LAS4 N-LA37 N-LA N-LA35 N-LAK0 N-KZS

38 38 Axial Colour: Ahromate ad Apohromate Effet of differet material Axial hromatial aberratio hage with wavelegth Differet level of orretio:.no orretio: le, oe zero roig poit.ahromati orretio: - oiidee of outer olor - remaiig error for eter wavelegth - two zero roig poit 3. Apohromati orretio: - oiidee of at leat three olor - mall reidual aberratio - at leat 3 zero roig poit - peial hoie of gla type with aomalou partial dipertio eeery apohromate iglet C reidual error apohromate e reidual error ahromate ahromate le

39 39 Spherohromatim Spherohromatim: variatio of pherial aberratio with wavelegth, Alterative otatio: Gauia hromatial error Idividual urve of pherial aberratio with olor Covetioal ahromate: - oiidig image loatio for red (C ) ad blue ( ) o axi (paraxial) - differee ad eodary petrum for gree (e) - but differet iteretio legth for fiite aperture ray r p Better balaig with half pherohromatim o axi 480 m 644 m aperture m 480 m 546 m 644 m i R U 0 e 0. mm 0. mm hl tot

40 40 Spherohromatim Spherial aberratio of a le i 3rd order: Wavelegth depedee of idue pherohromatim A 3 X f 3 3 ( ) M M Typial petral variatio of thi aberratio with wavelegth z + a) igle le z +.5 b) orreted

41 4 New Ahromate Covetioal ahromate: trog bedig of image hell, typial R ptz.3 f Petzval hell mea image hell y Speial eletio of glae:. ahromatizatio. Petzval flatteig Reidual field urvature: Combied oditio R ptz But uually o pherial orretio poible 0 0 f f R P eleted row gla perfet image plae lie of olutio for flit gla

42 4 Priiple of Gla Seletio i Optimizatio Deig rule for gla eletio Differet deig goal:. Color orretio: idex large diperio differee deired poitive le field flatteig Petzval urvature. ield flatteig: large idex differee + + deired egative le olor orretio + - availability of glae - - diperio Ref : H. Zügge

43 43 Burried Surfae Nearly equal refrative idie Differee i Abbe umber ot larger tha 30.9 Gla Gla KZN N-PK KZN PSK N-LL Ultra KZSN L N-PSK SK SK N-SSK SK PSK SSK SSK4A LAKL N-PSK N-SK SK SK N-SK N-S4 N-LAK SL4 N-LAK SL56 LAN S LA

44 44 Burried Surfae Cemeted ompoet with plae outer urfae or eter wavelegth oly plae parallel plate, ot ee i ollimated light Curved emeeted urfae: - diperio for outer petral weavelegth - olor orretio without diturbig the mai wavelegth Example gree udefleted a) iglet b) olor orreted iglet orreted z

45 45 Lateral Color Aberratio Diperio of the hief ray deviatio i the le Effet reemble the diperio of a prim i the upper part of the le I the image plae, the differee i the olored ray agle aue hage i the ray height The lateral olor aberratio orrepod to a hage of magifiatio with the wavelegth diperio prim effet y y CHV hief ray z top image plae

46 46 Chromati Variatio of Magifiatio Lateral hromatial aberratio: Higher refrative idex i the blue reult i a troger ray bedig of the hief ray for a igle le The olored image have differet ize, the magifiatio i wavelegth depedet Defiitio of the error: hage i image height/magifiatio Corretio eed everal glae with differet diperio The aberratio trogly deped o the top poitio y y CHV CHV y y y y y e C C top red y CHV blue referee image plae

47 Surfae ad Le otributio of Lateral Color If the imagig of the etrae to the exit pupil uffer from axial hromatial aberratio, thi deliver a error of the exit pupil loatio ad alo of the hief ray agle: heomatial lateral aberratio Travere hromatial aberratio of a le ytem Surfae otributio oeffiiet of lateral olor Correpodig le ummatio formula p p p p CHV Q H y y H CHV CHV p p p p CHV Q y y p p p CHV y y 47

48 48 Chromati Variatio of Magifiatio Repreetatio of CHV:. Spot diagram. Magifiatio m() 3. Travere aberratio: offet of hief ray referee hromatial magifiatio differee pot diagram Y field height CHV 0.08 travere aberratio urve y axi field tagetial y field agital x y y p y p x p

49 49 Chromati Variatio of Magifiatio Impreio of CHV i real image Typial olored frige blue/red at edge viible Color equee deped o ig of CHV origial without lateral hromati aberratio 0.5 % lateral hromati aberratio % lateral hromati aberratio

50 50 Chromatial Differee i Magifiatio Color rig are hardly ee due to olored image Lateral hift of olored pf poitio Ref: J. Kaltebah

51 5 Axial Chromatial Aberratio Speial effet ear blak-white edge boarder mageta blue boarder Ref: J. Kaltebah

52 5 Lateral Color Corretio: Priiple of Symmetry Perfet ymmetrial ytem: magifiatio m = - Stop i etre of ymmetry Symmetrial otributio of wave aberratio are doubled (pherial) Aymmetrial otributio of wave aberratio vaihe W(-x) = -W(x) Eay orretio of: oma, ditortio, hromatial hage of magifiatio frot part rear part 3