Imaging and Aberration Theory

Size: px

Start display at page:

Download "Imaging and Aberration Theory"

Wesley Cummings
5 years ago
Views:

1 Imagig a Aberratio Theor Lecture : Paraxial imagig --9 Herbert Gro Witer term

2 Overview Time: ria,. 3.3 Locatio: Abbeaum, HS, röbeltieg Web page o IAP homepage uer learig/material provie lie a exercie Zemax ile Cotet Semiar: Exercie a olutio o give problem time: Weea, SR 3, Max Wie Platz tartig ate: --4 Shit o ome ate coul be poible

3 3 Literature [] H. Buchahl, A Itrouctio to Hamiltoia Optic, Dover, 7 [] A. E. Cora, Applie Optic a Optical Deig, Part oe a two, Dover, 85 [3] H. Buchahl, Optical Aberratio Coeiciet, Dover 968 [4] Y. Matui / K. Nariai, uametal o practical aberratio theor, Worl Scietiic, 993 [5] A. Walther, The ra a wave theor o lee, Cambrige Uiverit Pre, 995 [6] V. Lakhmiaraaa / A. Ghatak / K. Thagaraa, Lagragia optic, Kluwer [7] M. Berek, Grulage er praktiche Optik, e Gruter, 97 [8] W. T. Welor, Aberratio o optical tem, Aam 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 ata, Aam Hilger, 97 [] A. Romao, Geometric optic, Birkhäuer, [3] G. Sluarev, Aberratio a optical eig theor, Aam Hilger, 984 [4] D. Malacara / Z. Malacara, Habook o optical eig, Marcel Dekker, 4 [5] A. Cox, A tem o optical eig, The ocal Pre, 967 [6] V. Mahaa, Optical imagig a aberratio I, Ra geometrical optic, SPIE Pre, 998 [7] V. Mahaa, Optical imagig a aberratio II, Wavew iractio optic, SPIE Pre,

4 Prelimiar time cheule 4

5 5 Cotet t Lecture. Carial elemet. Le propertie 3. Imagig, magiicatio 4. Aocal tem a telecetricit 5. Matrix calculu

6 Carial 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 beig pricipal plae P u BL ocal plae oal plae P u N N u Noal poit: Ra through N goe through N a preerve the irectio

7 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 raiu o urace curvature O thicke SS rerative iex BL P P BL a a

8 Mai propertie o a le Mai otatio a propertie o a le: - raii o curvature r, r curvature c ig: r > : ceter o curvature i locate o the right ie - thicke alog the axi - iameter D - iex o reractio o le material ocal legth (paraxial) Optical power Back ocal legth iterectio legth, meaure rom the vertex poit c r c r, ta u H ta u

9 Le hape Dieret hape o iglet lee:. bi-, mmetric. plae covex / cocave, oe urace plae 3. Meicu, both urace raii with the ame ig Covex: beig outie Cocave: hollow urace Pricipal plae P, P : outie or meicu hape 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

10 Le beig u hit o pricipal plae Ra path at a le o cotat ocal legth a ieret beig The ra agle iie the le chage The ra iciece 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

11 Magiicatio Parameter Magiicatio parameter M: eie ra path through the le M<- M U U U U 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>+

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

13 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 r r ormula or urace a le imagig

14 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

15 Deiitio o iel o View a Aperture Imagig o axi: circular / rotatioal mmetr Ol pherical aberratio a chromatical aberratio iite iel ize, obect poit o-axi: - chie ra a reerece p p - kew ra buel: coma a itortio - Vigettig, coe o ra bule ot circular mmetric - to itiguih: tagetial a 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

16 Obect or iel at iiit Image i iiit: - collimate exit ra bule - realize i biocular image image at iiit Obect i iiit - iput ra bule collimate - realize i telecope - aperture eie b iameter ot b agle le act a aperture top iel le top ee le obect at iiit collimate etrace bule image i ocal plae

17 7 Telecetricit Special top poitio:. top i back ocal plae: obect ie telecetricit. top i rot ocal plae: image ie telecetricit 3. top i itermeiate ocal plae: both-ie telecetricit Telecetricit:. pupil i iiit. chie ra parallel to the optical axi obect obect ie chie ra parallel to the optical axi telecetric top image

18 8 Telecetricit Double telecetric tem: top i itermeiate ocu Realizatio i lithographic proectio tem obect le telecetric le top image

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

20 Agle Magiicatio Aocal tem with obect/image i iiit Deiitio with iel agle w agular amgiicatio ta w ta w h h w w Relatio with iite-itace magiicatio

21 Axial Magiicatio Axial magiicatio Approximatio or mall z a = z z ta ta u u z z z

22 Paraxial approximatio Paraxial approximatio: i i Small agle o ra at ever urace Small iciece agle allow or a liearizatio o the law o reractio All optical imagig coitio become liear (Gauia optic), calculatio with ABCD matrix calculu i poible No aberratio occur i optical tem There are o trucatio eect ue to travere iite ize compoet Serve a a reerece or ieal tem coitio I the uamet or ma tem propertie (ocal legth, pricipal plae, magiicatio,...) The ag o optical urace (ierece i z betwee vertex plae a real urace iterectio poit) ca be eglecte i x All wave are plae o pherical (parabolic) R E( x) E e The phae actor o pherical wave i quaratic

23 Paraxial approximatio Law o reractio i I i I Talor expaio 3 5 x x i x x... 3! 5! Liear ormulatio o the law o reractio i i Error o the paraxial approximatio i- I) / I =.9 =.7 =.5 i i I I i i arci i

24 Sigle Surace Sigle urace betwee two meia Raiu r, reractive iice, Imagig coitio, 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

25 Paraxial Approximatio Law o reractio i I i I Expaioi o the ie-uctio: i x x 3 x 3! 5 x... 5! Liearize approximatio o the law o reractio: I ----> i i i Relative error o the approximatio i i I I i i arci i- I) / I =.9 =.7 = i

26 Liear Collieatio Geeral ratioal traormatio Liear expreio Decribe liear colliear traorm x,,z ---> x,,z Aalog i the image pace Ierte i ol imeio ocal legth Pricipal plae 3,, z x,,,,3 z c b x a 3,, z x,,,3, z c b x a 3 3, z c a z c z c z o o 3 3, a c c c c a 3 3 3, a c c c a c z c a z P P

27 Liear Collieatio Special choice o origi o cooriate tem: Newto imagig equatio iite agle: ta(u) mut be take: Magiicatio: m ta u ta u O ocal legth: ta u ta u h u P h P N N u Ivariat: ta u ta u z z O a a

28 Image Cotructio o a Le b imple Ra Poitive le Real image or > Negative le virtual image

29 Imagig b a Le Rage o imagig Locatio o the image or a igle le tem < image virtual magiie image image Obekt Chage o obect loactio = Image coul be:. real / virtual. elarge/reuce 3. i iite/iiite itace image at iiit > > image real magiie obect obect image = image real : obect image obect > image image real reuce

30 Graphical Image Cotructio ater Litig Graphical image cotructio accorig to Litig b 3 pecial ra: 3. irt parallel through axi, through ocal poit i image pace. irt through ocal poit, the parallel to optical axi P P 3. Through oal poit, leave the le with the ame agle Proceure work or poitive a egative lee or egative lee the / equece i revere 3 P P

31 Geeral Graphical Ra Cotructio irt ra parallel to arbitrar ra through ocal poit, become parallel to optical axi Arbitrar ra: - cotat height i pricipal plae S S - meet the irt ra i the back ocal plae, eire ra i S Q arbitrar ra S S geuchter Augagtrahl Q parallel ra through P P

32 Traer Legth / Total Track L Ditace obect-image: (traer legth) Two olutio or a give L with ieret magiicatio m L L L L m m 6 5 m L mi = 4 m max = L / - No real imagig or L < magiie 4-imagig reuce L /

33 Newto ormula Imagig equatio accorig to Newto: itace z, z meaure relative to the ocal poit z z ocal poit P P ocal poit image obect -z - z - pricipal plae

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

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

36 Matrix Calculu Paraxial ratrace traer Matrix ormulatio Paraxial ratrace reractio Ierte Matrix ormulatio U U i i i U U U U i i U U U U U U

37 Liear Collieatio Matrix ormalim or iite agle ta u A C B D ta u

38 Matrix ormulatio o Paraxial Optic Liear relatio o ra traport x x Simple cae: ree pace propagatio ra u u x x B z Geeral cae: paraxial egmet with matrix ABCD-matrix : x x 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 cooriate x a 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 cougate 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 etm ADBC

40 Stem iverio Traitio over itace 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, epth A B C D AD BC C D C 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

Imaging and Aberration Theory

Imaging and Aberration Theory Imagig a Aberratio Theor Lecture : Paraxial imagig --9 Herbert Gro Witer term www.iap.ui-ea.e Overview Time: ria,. 3.3 Locatio: Abbeaum, HS, röbeltieg Web page o IAP homepage uer learig/material provie