Imaging and Aberration Theory

Transcription

1 Imagig ad Aberratio Theor Lecture : Paraxial imagig 3--7 Herbert Gro Witer term 3

2 Overview Time: Thurda, Locatio: Abbeaum, HS, röbeltieg Web page o IAP homepage uder learig/material provide lide, exercie, olutio, iormatio Semiar: Exercie ad olutio o give problem time: rida, Bepr.Raum Abbeaum tartig date: --5 Shit o ome date could be poible Writte examiatio, 9

3 3 Literature [] H. Buchdahl, A Itroductio to Hamiltoia Optic, Dover, 97 [] A. E. Corad, Applied Optic ad Optical Deig, Part oe ad two, Dover, 985 [3] H. Buchdahl, Optical Aberratio Coeiciet, Dover 968 [4] Y. Matui / K. Nariai, udametal o practical aberratio theor, World Scietiic, 993 [5] A. Walther, The ra ad wave theor o lee, Cambridge Uiverit Pre, 995 [6] V. Lakhmiaraaa / A. Ghatak / K. Thagaraa, Lagragia optic, Kluwer [7] M. Berek, Grudlage der praktiche Optik, de Gruter, 97 [8] W. T. Welord, Aberratio o optical tem, Adam Hilger, 986 [9] K. Lueburg, Mathematical theor o optic, Uiverit o Calioria Pre, 964 [] H. Römer, Theoretical optic, Wile VCH, 5 [] J. Palmer, Le aberratio data, Adam Hilger, 97 [] G. Sluarev, Aberratio ad optical deig theor, Adam Hilger, 984 [3] D. Malacara / Z. Malacara, Hadbook o optical deig, Marcel Dekker, 4 [4] A. Cox, A tem o optical deig, The ocal Pre, 967 [5] V. Mahaa, Optical imagig ad aberratio I, Ra geometrical optic, SPIE Pre, 998 [6] V. Mahaa, Optical imagig ad aberratio II, Wavew diractio optic, SPIE Pre, [7] J. Saia, Aberratio i optical imagig tem, Cambridge Uiverit Pre, 3

4 4 Prelimiar time chedule 7.. Paraxial imagig paraxial optic, udametal law o geometrical imagig, compoud tem 4.. Pupil, ourier optic, pupil deiitio, baic ourier relatiohip, phae pace, aalog optic ad Hamiltoia coordiate mechaic, Hamiltoia coordiate Eikoal ermat Priciple, tatioar phae, Eikoal, relatio ra-wave, geometrical approximatio, ihomogeeou media Aberratio expaio igle urace, geeral Talor expaio, repreetatio, variou order, top hit ormula Repreetatio o aberratio dieret tpe o repreetatio, ield o applicatio, limitatio ad pitall, meauremet o aberratio 6.. Spherical aberratio pheomeolog, ph-ree urace, kew pherical, correctio o ph, apherical urace, higher order Ditortio ad coma pheomeolog, relatio to ie coditio, aplaatic tem, eect o top poitio, variou topic, correctio optio Atigmatim ad curvature pheomeolog, Coddigto equatio, Petzval law, correctio optio 9.. Chromatical aberratio Diperio, axial chromatical aberratio, travere chromatical aberratio, pherochromatim, ecodar poectrum 9.. urther readig o aberratio eitivit i 3rd order, tructure o a tem, aali o optical tem, le cotributio, Sie coditio, ioplaatim, ie coditio, Herchel coditio, relatio to coma ad hit ivariace, pupil aberratio, relatio to ourier optic 9.. Wave aberratio deiitio, variou expaio orm, propagatio o wave aberratio, relatio to PS ad OT 6.. Zerike polomial pecial expaio or circular mmetr, problem, calculatio, optimal balacig, iluece o ormalizatio, recalculatio or oet, ellipticit, meauremet Micellaeou Itriic ad iduced aberratio, Aldi theorem, telecetric cae, aocal cae, aberratio balacig, Scheimplug imagig, reel lee, tatitical aberratio Vectorial aberratio Itroductio, pecial cae, actual reearch, aamorphotic, partial mmetric 5 6..

5 5 Cotet t Lecture. Cardial elemet. Le propertie 3. Imagig, magiicatio 4. Aocal tem ad telecetricit 5. Paraxial approximatio 6. Matrix calculu

6 Modellig o Optical Stem Pricipal purpoe o calculatio: Imagig model with level o reiemet Stem, data o the tructure (radii, ditace, idice,...) Aali imagig aberratio theorie Sthei le deig uctio, data o propertie, qualit perormace (pot diameter, MT, Strehl ratio,...) Paraxial model (ocal legth, magiicatio, aperture,..) liear approximatio Aaltical approximatio ad claiicatio (aberratio,..) Talor expaio Geometrical optic (travere aberratio, wave aberratio, ditortio,...) with diractio approximatio --> Wave optic (poit pread uctio, OT,...) Re: W. Richter

7 Sigle Surace Sigle urace betwee two media Radiu r, reractive idice, Imagig coditio, paraxial r Abbe ivariat alterative repreetatio o the imagig equatio Q r r obect arbitrar ra vertex S C image r ra through ceter o curvature C pricipal plae urace

8 Cardial elemet o a le ocal poit:. icomig parallel ra iterect the axi i. ra through i leave the le parallel to the axi Pricipal plae P: locatio o apparet ra bedig pricipal plae P u BL ocal plae odal plae P u N N u Nodal poit: Ra through N goe through N ad preerve the directio

9 Notatio o a le P pricipal poit S vertex o the urace ocal poit O iterectio poit o a ra with axi ocal legth P u S P P N N S u r radiu o urace curvature O d thicke SS rerative idex BL P P BL a d a

10 Mai propertie o a le Mai otatio ad propertie o a le: - radii o curvature r, r curvature c ig: r > : ceter o curvature i located o the right ide - thicke d alog the axi - diameter D - idex o reractio o le material ocal legth (paraxial) Optical power Back ocal legth iterectio legth, meaured rom the vertex poit c r c r, ta u P ta u

11 Le hape Dieret hape o iglet lee:. bi-, mmetric. plae covex / cocave, oe urace plae 3. Meicu, both urace radii with the ame ig Covex: bedig outide Cocave: hollow urace Pricipal plae P, P : outide or meicu haped lee P P P P P P P P P P P P bi-covex le plae-covex le poitive meicu le bi-cocave le plae-cocave le egative meicu le

12 Le bedig ud hit o pricipal plae Ra path at a le o cotat ocal legth ad dieret bedig The ra agle iide the le chage The ra icidece agle at the urace chage trogl The pricipal plae move or ivariat locatio o P, P the poitio o the le move P P X = -4 X = - X = X = + X = +4

13 Magiicatio Parameter Magiicatio parameter M: deie ra path through the le M<- M U U U U m m M=- Special cae:. M = : mmetrical 4-imagig etup. M = -: obect i rot ocal plae 3. M = +: obect i iiit M= The parameter M trogl iluece the aberratio M=+ M>+

14 Optical imagig Optical Image ormatio: All ra emergig rom oe obect poit meet i the perect image poit Regio ear axi: gauia imagig ideal, paraxial Image ield ize: Chie ra ield poit O chie ra pupil top Aperture/ize o light coe: margial ra deied b pupil top obect axi margial ra optical tem O O image O

15 Sigle urace imagig equatio Thi le i air ocal legth Thi le i air with oe plae urace, ocal legth Thi mmetrical bi-le Thick le i air ocal legth r r r r r r r d r r ormula or urace ad le imagig

16 Imagig equatio Imagig b a le i air: le maker ormula real obect real image 4 virtual obect real image Magiicatio m Real imagig: <, > Iterectio legth, meaured with repective to the pricipal plae P, P real obect virtual image - virtual obect virtual image - 4

17 Imagig b a Le Rage o imagig Locatio o the image or a igle le tem < image virtual magiied image image Obekt Chage o obect loactio = Image could be:. real / virtual. elarged/reduced 3. i iite/iiite ditace image at iiit > > image real magiied obect obect image = image real : obect image obect > image image real reduced

18 Newto ormula Imagig equatio accordig to Newto: ditace z, z meaured relative to the ocal poit z z ocal poit P P ocal poit image obect -z - z - pricipal plae

19 Two lee with ditace d ocal legth ditace o ier ocal poit e Sequece o thi lee cloe together Sequece o urace with relative ra height h, paraxial Magiicatio d e d k k k k k k k r h h k k k m Multi-Surace Stem

20 ocal legth e: tube legth Image locatio Two-Le Stem le le d e e d ) ( ) ( d d d

21 Magiicatio Lateral magiicatio or iite imagig Scalig o image ize m ta u ta u pricipal plae obect ocal poit ocal poit P P z z image

22 Agle Magiicatio Aocal tem with obect/image i iiit Deiitio with ield agle w agular magiicatio ta w ta w h h w w Relatio with iite-ditace magiicatio m

23 Axial Magiicatio Axial magiicatio Approximatio or mall z ad = z z m m ta ta u u mz z z

24 Deiitio o ield o View ad Aperture Imagig o axi: circular / rotatioal mmetr Ol pherical aberratio ad chromatical aberratio iite ield ize, obect poit o-axi: - chie ra a reerece p p - kew ra budel: coma ad ditortio - Vigettig, coe o ra budle ot circular mmetric - to ditiguih: tagetial ad agittal plae O obect plae margial/rim ra u w etrace pupil chie ra chie ra exit pupil R AP w u image plae O

25 The Special Iiit Cae Simple cae: - obect, image ad pupil are lig i a iite ditace - o-telecetric rela tem Special cae : - obect at iiit - obect ided aocal - example: camera le or ditat obect Special cae : - image at iiit - image ided aocal - example: eepiece Special cae 3: - etrace pupil at iiit - obect ide telecetric - example: camera le or metrolog Special cae 4: - exit pupil at iiit - image ided telecetric - example: old ahio lithographic le

26 The Special Iiit Cae Ver pecial: combiatio o above cae Example: - both ided telecetric: 4-tem, lithographic le - both ided aocal: aocal zoom - obect ided telecetric, image ided aocal: microcopic le Notice: telecetricit ad aocalit ca ot be combied o the ame ide o a tem

27 7 Telecetricit Special top poitio:. top i back ocal plae: obect ided telecetricit. top i rot ocal plae: image ided telecetricit 3. top i itermediate ocal plae: both-ided telecetricit Telecetricit:. pupil i iiit. chie ra parallel to the optical axi obect obect ide chie ra parallel to the optical axi telecetric top image

28 8 Telecetricit Double telecetric tem: top i itermediate ocu Realizatio i lithographic proectio tem obect le telecetric le top image

29 Paraxial Approximatio Paraxialit i give or mall agle relative to the optical axi or all ra Large umerical aperture agle u violate the paraxialit, pherical aberratio occur Large ield agle w violate the paraxialit, coma, atigmatim, ditortio, ield curvature occur

30 ield-aperture-diagram Claiicatio o tem with ield ad aperture ize Scheme i related to ize, correctio goal ad etedue o the tem w Biogo Triplet photographic lithograph Braat Ditago Aperture domiated: Dik lee, microcop, Collimator 4 Soar ield domiated: Proectio lee, camera lee, Photographic lee Spectral widthz a a correctio requiremet i mied i thi chart plit triplet proectio Gau proectio double Gau achromat Petzval proectio micro x.4 diode collimator micro 4x.6 dic lithograph 3 micro x.9 cotat etedue microcop collimator ocuig NA

31 3 Microcopic Obective Le Icidece agle or chie ad margial ra margial ra microcope obective le Aperture domiat tem Primar problem i to correct pherical aberratio chie ra icidece agle

32 3 Photographic le Icidece agle or chie ad margial ra Photographic le ield domiat tem Primar goal i to cotrol ad correct ield related aberratio: coma, atigmatim, ield curvature, lateral color chie ra 6 icidece agle margial ra

33 Paraxial approximatio Paraxial approximatio: Small agle o ra at ever urace Small icidece agle allow or a liearizatio o the law o reractio All optical imagig coditio become liear (Gauia optic), calculatio with ABCD matrix calculu i poible No aberratio occur i optical tem There are o trucatio eect due to travere iite ized compoet Serve a a reerece or ideal tem coditio I the udamet or ma tem propertie (ocal legth, pricipal plae, magiicatio,...) The ag o optical urace (dierece i z betwee vertex plae ad real urace iterectio poit) ca be eglected All wave are plae o pherical (parabolic) The phae actor o pherical wave i quadratic E( x) E i i e i x R

34 Paraxial approximatio Law o reractio or iite agle I, I i I i I Talor expaio i x x 3 x 3! 5 x... 5! Liear ormulatio o the law o reractio or mall agle i, i i i i- I) / I =.9 =.7 =.5 Relative directio error o the paraxial approximatio i i I I i i arci i

35 Liear Collieatio Geeral traorm obect - image pace Geeral ratioal traormatio with liear expreio Decribe liear colliear traorm x,,z ---> x,,z Iverio Aalog i the image pace Ierted i ol dimeio ocal legth rom coditio o = ad o = Pricipal plae 3,, z x,,,,3 d z c b x a 3,, z x,,,3, d z c b x a 3 3, d z c b d z c d z c z o o 3 3, a c c d d c c b 3 3 3, a c c d d c a c z c d a z P P ),, (, ),, (, ),, ( z x z z x z x x

36 Liear Collieatio iite agle: ta(u) mut be take: Magiicatio: ta u m ta u ocal legth: ta u ta u h O h Ivariat: u N N u ta u ta u P P O z z a a

37 Matrix Calculu Paraxial ratrace traer Matrix ormulatio Matrix ormalim or iite agle Paraxial ratrace reractio Ierted Matrix ormulatio U d U i i i U U U U i i U U U d U U U u D C B A u ta ta

38 Matrix ormulatio o Paraxial Optic Liear relatio o ra traport x x Simple cae: ree pace propagatio ra u Advatage o matrix calculu:. imple calculatio o compoet combiatio. Automatic correct ig o propertie 3. Ea to implemet x x u B x x z Geeral cae: paraxial egmet with matrix ABCD-matrix : x A u C B x x M D u u u ra x A B C D x u z

39 Matrix ormulatio o Paraxial Optic Liear traer o patio coordiate x ad agle u x AxBu u CxDu Matrix repreetatio x A u C B x M D u x u Lateral magiicatio or u= Agle magiicatio o cougated plae Reractive power or u= A x / x D u / u C u / x Compoitio o tem M M k M... M M k Determiat, ol 3 variable detm ADBC

40 Stem iverio Traitio over ditace L Thi le with ocal legth Dielectric plae iterace Aocal telecope A C B D M L M M M L M Matrix ormulatio o Paraxial Optic

41 Matrix ormulatio o Paraxial Optic Calculatio o iterectio legth Magiicatio:. lateral. agle 3. axial, depth A B C D AD BC C D C D d d AD BC AC AD BC C D Pricipal plae ocal poit a H a AD BC C A C D A a H C D a C

42 Decompoitio o ABCD-Matrix x ABCD-matrix o a tem i air: 3 arbitrar parameter Ever arbitrar ABCD-etup ca be decompoed ito a imple tem Decompoitio i 3 elemetar partitio i alwa poible Cae : C # oe le, traitio Stem data M A B L L C D L L A C C D C Iput x i Le Output x o L L

43 Decompoitio o ABCD-Matrix Cae : B # two lee, oe traitio M A B L C D Stem data: B A L B B D Iput Le Le Output L