Imaging and Aberration Theory

Transcription

1 Imagig ad Aberratio Theory Leture 9: Chromatia aberratio 0-- Herbert Gro Witer term 0

2 Preimiary time hedue 9.0. Paraxia imagig paraxia opti, fudameta aw of geometria imagig, ompoud ytem 6.0. Pupi, ourier opti, Hamitoia oordiate pupi defiitio, bai ourier reatiohip, phae pae, aaogy opti ad mehai, Hamitoia oordiate Eikoa ermat Priipe, tatioary phae, Eikoa, reatio ray-wave, geometria approximatio, ihomogeeou media Aberratio expaio ige urfae, geera Tayor expaio, repreetatio, variou order, top hift formua Repreetatio of aberratio differet type of repreetatio, fied of appiatio, imitatio ad pitfa, meauremet of aberratio Spheria aberratio pheomeoogy, ph-free urfae, kew pheria, orretio of ph, apheria urfae, higher order Ditortio ad oma pheomeoogy, reatio to ie oditio, apaati ytem, effet of top poitio, variou topi, orretio optio Atigmatim ad urvature pheomeoogy, Coddigto equatio, Petzva aw, orretio optio 9.. Chromatia aberratio Diperio, axia hromatia aberratio, travere hromatia aberratio, pherohromatim, eodary petrum 0.0. urther readig o aberratio eitivity i 3rd order, truture of a ytem, uperpoitio ad idued aberratio, aayi of optia ytem, e otributio, Sie oditio, iopaatim, ie oditio, Herhe oditio, iopaatim, reatio to oma ad hift ivariae, pupi aberratio, reatio to ourier opti ad phae pae 8.0. Wave aberratio defiitio, variou expaio form, propagatio of wave aberratio, reatio to PS ad OT 5.0. Zerike poyomia peia expaio for iruar ymmetry, probem, auatio, optima baaig, ifuee of ormaizatio, reauatio for offet, eiptiity, meauremet Mieaeou Adi theorem, teeetri ae, afoa ae, aberratio baaig, Deao diagram, Sheimpfug imagig, ree ee, tatitia aberratio Vetoria aberratio Itrodutio, peia ae, atua reearh, aamorphoti, partia ymmetri

3 3 Streh Ratio ad PS-Peak Height for Aberratio Differee betwee Streh ad I peak, if the profie i trutured 0.8 defouig atigmatim [] [] pheria aberratio 9 oma Streh peak [] []

4 4 Cotet. Materia diperio. Partia diperio 3. Aomaou partia diperio 4. Axia hromatia error 5. Ahromati 6. Apohromate 7. Spherohromatim 8. Chromatia variatio of Magifiatio 9. Seide theory of hromatia aberratio 0. Exampe

5 Diperio ad Abbe umber Deriptio of diperio: Abbe umber Viua rage of waveegth: typiay d,,c or e,,c ued e e C C refrative idex Typia rage of gae e = S fit Two fudameta type of ga: Crow gae: ma, arge, diperio ow it gae arge, ma, diperio high BK7 row

6 Curvature of the radii of a e oa power at the eter waveegth e for a thi e Differee i foa power for outer waveegth, C with the Abbe umber oa egth at the eter waveegth Differee of the foa egth for outer waveegth Ahromatizatio oditio for two thi ee oe 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

7 Ga Diagram Uua repreetatio of gae: diagram of refrative idex v diperio () Left to right: Ireaig diperio dereaig Abbe umber

8 Diperio Materia with differet diperio vaue: - Differet ope ad urvature of the diperio urve - Stroger hage of idex over waveegth for arge diperio - Iverio of idex equee at the boudarie of the petrum poibe refrative idex SK8A

9 Atomi mode for the refrative idex: oiator approah of atomi fied iteratio Semeier diperio formua: orrepodig futio Speia ae of ouped reoae: exampe quartz, degeerated oiator Atomi Mode of Diperio i r i f m Ne i og [mm] viibe (UV) (UV) 3 (IR) 4 (IR) vi () C B A 4 0 o C B B A

10 Diperio formua Shott formua empiria Semeier Baed o oiator mode Bauh-Lomb empiria Herzberger Baed o oiator mode 4 6 a a a a a a o ( ) A B C 4 D E ( ) A B C ( o) a a3 ) ao a ( o o mit 0.68 mm o o 8 Hartma Baed o oiator mode ( ) a o a a 3 a4 a 5

11 Reative partia diperio Reative partia diperio : Chage of diperio ope with Differet urvature of diperio urve Defiitio of oa ope for eeted waveegth reative to eodary oor P C i - g g - - e - C C - C - t () Speia -eetio for harateriti rage of the viibe petrum.49 = 656 / 04 m far IR = 656 / 85 m ear IR = 486 / 546 m bue 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 oor : 480 m C : 644 m : 486 m C : 656 m. eodary oor. eodary oor : 85 m IR edge t : 04 m IR edge

12 Partia Diperio ad Norma Lie The reative partia diperio hage approximatey iear with the diperio for gae P b, a, d, P 0.6 Neary a gae are oated o the orma ie i a P--diagram P g The ope of the orma ie deped o the eetio of waveegth 0.55 Gae apart from the orma ie how aomaou partia diperio P 0.5 P C P a d b P thee materia are importat for hromatia orretio of higher order

13 3 Partia Diperio Aorma partia diperio ad orma ie P g, N-K5 N-PK5 orma ie 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

14 Aomaou Partia Diperio There are ome peia gae with a arge deviatio from the orma ie Of peia iteret: og row ad hort fit P g, ie of orma diperio S N-S57 KZSN4 K5 K5 PSK53A ZKN7 LAK8 LASN30 P g, heavy fit with harater of og row fit og row og row hort fit hort fit row orma ie

15 Aomaou Partia Diperio Norma gae: Partia diperio hage iear with Abbe umber Defiitio of P deped o eeted waveegth Norma ie defied by ad K7 P P P P P C, t C,, e g, i, g d d d d d Deviatio from iear behavior: aomaou partia diperio P P a d b P P g d The vaue of P deped o the waveegth eetio Typia P oidered at the red ad the bue ed of the viibe petrum orma ie P g rea urve Large deviatio vaue P are eeary for apohromati hromatia orretio d

16 Aomaou Partia Diperio Arrow i the ga map: idiatio of the deviatio from the orma ie P h Vertia ompoet: at the red horizota: at the bue ed of the petrum P a d b P orma ie Ga d P h arrow of deviatio P tc d ga oatio P h bue ide red ide d

17 7 Axia Chromatia Aberratio Axia hromatia aberratio: Higher refrative idex i the bue reut i a horter iteretio egth for a ige e The oored image are defoued aog the axi Defiitio of the error: hage i image oatio / iteretio egth Corretio eed evera gae with differet diperio Sige e: orma diperio bue iteretio egth i horter tha red P Notatio: white. CHL = hromatia ogitudia. AXCL = axia hromati CHL C e bue C gree red

18 8 Axia Chromatia Aberratio Logitudia hromatia aberratio for a ige e Bet image pae hage with waveegth bet image pae = 648 m = 546 m = 480 m defou z Ref : H. Zügge

19 9 Seodary Spetrum P Simpe ahromatizatio / firt order orretio: - two gae with differet diperio - equa iteretio egth for outer waveegth (bue, red C) white C eodary petrum Reidua deviatio for midde waveegth (gree e): eodary petrum ( ) P, C P SSP C f ( ), C 644 C e ahromate bue red gree 546 e iget reidua error ahromate e C

20 Ahromate: Bai ormua Idea:. Two thi ee oe together with differet materia. Tota power 3. Ahromati orretio oditio 0 Idividua power vaue Propertie:. Oe poitive ad oe egative e eeary. Two differet equee of pu (row) / miu (fit) 3. Large -differee reaxe the bedig 4. Ahromati orretio idipedet from bedig 5. Bedig orret pheria aberratio at the margi 6. Apaati oma orretio for peia ga hoie 7. urther optimizatio of materia redue the pheria zoa aberratio

21 Ahromate Compeatio of axia oour by appropriate ga hoie (a) (b) Chromatia variatio of the pheria aberratio: pherohromatim (Gauia aberratio) Therefore perfet axia oor orretio (o axi) are ofte ot feaabe BK7 =.568 = 64.7 = BK7 = = = = = = r p r p 486 m 588 m 656 m z z -00 Ref : H. Zügge

22 Ahromate Ahromate Logitudia 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]

23 Ahomati outio i the Ga Diagram row poitive e fit egative e Ahromat

24 or oe give fit a ie idiate the uefu row gae ad vie vera Perfet apaati ie of orrepodig gae Coditio: Optimizatio of Ahromati Gae fixed fit ga ie of miima pheria aberratio fixed row ga ie of miima pheria aberratio r

25 Ahromate Reidua aberratio of a ahromate Ceary ee:. Ditortio. Chromatia magifiatio 3. Atigmatim

26 Surfae ad Le otributio of Axia Coor Coiderig the Abbe ivariat Derivative after the waveegth Summig over a urfae of a ytem with the margia ray height ratio ad the propagatio of the ratio Surfae ummatio for axia hromatia 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

27 Geera Ahromatizatio Cotributio of a thi e to the axia hromatia aberratio Axia hromatia aberratio of a ytem of thi ee Coditio of ahromatizatio of a ytem of ee Speia ae of ee oe together Coditio of apohromati (poyhromati) orretio with the partia reative diperio CHL e f K N CHL 0 0 P 0

28 Diayt approah: Ahromatizatio with two ee at fiite ditae Saig parameter k: With fiite margia ray height oa egth oditio Ahromatizatio oa egth of the ee 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 ) ( Diayt-Ahromat

29 Diayt Ahromat Uage of oy oe ga materia with ahromati orretio: diayt ahromate No rea imagig poibe Parameter: Setup kf f a f b k f ( k ) k e a k t k f e b image pae y a y b t f a

30 Axia Coor Corretio with Shupma Le Speia ayout of diayte approah aordig to Shupma Mirror guaratee rea imagig f = -00 mm mirror f = 300 mm rea image

31 oa power oditio Ahromati oditio Seodary petrum Curvature of ee Parameter E The 3 materia are ot aowed to by o the orma ie The triage of the 3 poit houd be arge: ma give reaxed 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

32 3 Axia Coour : Apohromate Choie of at eat oe peia ga P g Corretio of eodary petrum: aomaou partia diperio 0,6 0,60 N-S6 () At eat oe ga houd deviate igifiaty form the orma ga ie 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

33 33 Axia Coour: Ahromate ad Apohromate Effet of differet materia Axia hromatia aberratio hage with waveegth Differet eve of orretio:.no orretio: e, oe zero roig poit.ahromati orretio: - oiidee of outer oor - remaiig error for eter waveegth - two zero roig poit 3. Apohromati orretio: - oiidee of at eat three oor - ma reidua aberratio - at eat 3 zero roig poit - peia hoie of ga type with aomaou partia dipertio eeery apohromate iget C reidua error apohromate e reidua error ahromate ahromate e

34 34 Reidua Chromatia Aberratio Differet tate of hromatia orretio Ireaig umber of zero or oiidet oor Redued reidua aberratio

35 Spherohromatim Spherohromatim: variatio of pheria aberratio with waveegth, Aterative otatio: Gauia hromatia error Idividua urve of pheria aberratio with oor Covetioa ahromate: - oiidig image oatio for red (C ) ad bue ( ) o axi (paraxia) - differee ad eodary petrum for gree (e) - but differet iteretio egth for fiite aperture ray r p Better baaig with haf pherohromatim o axi 480 m 644 m aperture m 480 m 546 m 644 m i R U 0 e 0. mm 0. mm h tot

36 Spherohromatim Spheria aberratio of a e i 3rd order: Waveegth depedee of idue pherohromatim Typia petra variatio of thi aberratio with waveegth A 3 X f 3 3 ( ) M M z + a) ige e z +.5 b) orreted

37 New Ahromate Covetioa ahromate: trog bedig of image he, typia Speia eetio of gae:. ahromatizatio. Petzva fatteig Reidua fied urvature: Combied oditio R ptz R ptz.3 f But uuay o pheria orretio poibe 0 0 f f R P eeted row ga Petzva he mea image he perfet image pae ie of outio for fit ga y

38 Priipe of Ga Seetio i Optimizatio Deig rue for ga eetio Differet deig goa:. Coor orretio: idex arge diperio differee deired poitive e fied fatteig Petzva urvature. ied fatteig: arge idex differee + + deired egative e oor orretio + - avaiabiity of gae - - diperio Ref : H. Zügge

39 Burried Surfae Neary equa refrative idie Differee i Abbe umber ot arger tha 30.9 Ga Ga KZN N-PK KZN PSK N-LL Utra 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

40 Burried Surfae Cemeted ompoet with pae outer urfae or eter waveegth oy pae parae pate, ot ee i oimated ight Curved emeeted urfae: - diperio for outer petra weaveegth - oor orretio without diturbig the mai waveegth Exampe gree udefeted a) iget b) orreted iget orreted z

41 Latera Coor Aberratio Diperio of the hief ray deviatio i the e Effet reembe the diperio of a prim i the upper part of the e I the image pae, the differee i the oored ray age aue hage i the ray height The atera oor aberratio orrepod to a hage of magifiatio with the waveegth diperio prim effet y y CHV hief ray z top image pae

42 4 Chromati Variatio of Magifiatio Latera hromatia aberratio: Higher refrative idex i the bue reut i a troger ray bedig of the hief ray for a ige e The oored image have differet ize, the magifiatio i waveegth depedet Defiitio of the error: hage i image height/magifiatio Corretio eed evera gae with differet diperio The aberratio trogy deped o the top poitio y y CHV CHV y y y y y e C C top red y CHV bue referee image pae

43 Surfae ad Le otributio of Latera Coor If the imagig of the etrae to the exit pupi uffer from axia hromatia aberratio, thi deiver a error of the exit pupi oatio ad ao of the hief ray age: heomatia atera aberratio Travere hromatia aberratio of a e ytem Surfae otributio oeffiiet of atera oor Correpodig e ummatio formua 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

44 Chromati Variatio of Magifiatio Repreetatio of CHV:. Spot diagram. Magifiatio m() 3. Travere aberratio: offet of hief ray referee hromatia magifiatio differee pot diagram Y fied height CHV 0.08 travere aberratio urve y axi fied tagetia y fied agita x y y p y p x p

45 45 Chromati Variatio of Magifiatio Impreio of CHV i rea image Typia oored frige bue/red at edge viibe Coor equee deped o ig of CHV origia without atera hromati aberratio 0.5 % atera hromati aberratio % atera hromati aberratio

46 Chromatia Differee i Magifiatio Coor rig are hardy ee due to oored image Latera hift of oored pf poitio Ref: J. Katebah

47 Axia Chromatia Aberratio Speia effet ear bak-white edge boarder mageta bue boarder Ref: J. Katebah

48 48 Latera Coor Corretio: Priipe of Symmetry Perfet ymmetria ytem: magifiatio m = - Stop i etre of ymmetry Symmetria otributio of wave aberratio are doubed (pheria) Aymmetria otributio of wave aberratio vaihe W(-x) = -W(x) Eay orretio of: oma, ditortio, hromatia hage of magifiatio frot part rear part 3

49 Chromatia Cofoa Seor Spetra eitive eor with ofoa pihoe white ight oure Coor oded image Obetive e with arge axia hromatia aberratio gratig pihoe meaurig rage ofoae pihoe fouig obetive hromatia obetive detetor E m 546 m 656 m z [mm]

50 Chromatia Cofoa Seor Hyperhromati obetive e Goa:. arge CHL: arge rage of meauremet. orreted pherohromatim: high auray z = 644 m = 546 m = 480 m

51 Summary Diperio i deribed by the Abbe umber or higher order effet the partia diperio P i oidered Norma ie: uuay P hage iear with Aomaou partia diperio i eeary for apohromati orretio Axia hromati aberratio our due to the margia ray iteretio egth: image oatio Ahromatizatio eed row ad fit ga Geera urfae ad e otributio aaogou to moohromati aberratio of 3rd order Corretio by diayt: ue of ditae Chromatia variatio of the pheria aberratio: pherohromatim Buried urfae: deouped orretio of oor Chromatia variatio of magifiatio: atera hromatia aberratio Waveegth depedet path of the hief ray aue petra hage of image ize Coor rigig at bak-white edge Corretio of atera oor by ymmetry ad top poitio Hyperhromate a peia ytem type