Section 8. Paraxial Raytracing

Transcription

1 Secio 8 Paraxial aracig 8- OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp YNU arace efracio (or reflecio) occrs a a ierface bewee wo opical spaces. The rasfer disace ' allows he ra heigh ' o be deermied a a plae wihi a opical space (icldig viral segmes). efracio or eflecio: Trasfer: This pe of rarace is called a YNU rarace. All ras propagae from objec space o image space. 8- OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp A reverse rarace allows he ra properies o be deermied i he opical space psream of a ow ra segme. A ra ca he be wored bac o is origis i objec space. efracio or eflecio (reverse): Trasfer (reverse):

2 Paraxial arace Eqaios - Ssem Paraxial refracio eqaio: efracio a a opical ssem effecivel occrs a he pricipal plaes of he ssem. The ra emerges from he rear pricipal plae a he same heigh, b wih a differe agle. Trasfer: P P f E 8-3 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp The rasfer disace allows he ra heigh o be deermied a a plae wihi a opical space (icldig viral segmes). Paraxial refracio occrs a he verex plae of a srface. The srface sag is igored. or a ssem represeed b a power ad a pair of pricipal plaes, paraxial refracio occrs a he pricipal plaes. Paraxial arace Sigle Srface Paraxial refracio occrs a he verex plae of he srface. The srface sag is igored. The image locaio is fod b solvig for a ra heigh of ero. h V = h 8-4 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp h / / m h / / A rarace spacig is he disace from he crre srface o he ex srface.

3 Paraxial arace Sigle ompoe (i air) The pricipal plaes are he locaios of effecive refracio. h P P = h 8-5 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp h m h These relaioships also appl o a hi les i air. Geeral arace Eqaios Trasfer: efrac: j j j j j j j j j j 3 j j j j j j j j j j efracio occrs a each srface. The amo of ra deviaio depeds o he srface power ad he ra heigh. Trasfer occrs bewee srfaces. The ra heigh chage depeds o he ra agle ad he spacig bewee srfaces. The image locaio is fod b solvig for a ra heigh of ero i image space. 8-6 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp h h

4 Paraxial arace Series of Srfaces h 3 3 Trasfer: efrac: 3 j j j j j j j j j j + h 8-7 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp 3 3 Image Locaio ad Magificaio: h m h Paraxial arace Series of ompoes (i air) h P P P P 3 3 The geeral rarace eqaios hold (i air): j j jj P P 3 j j j j j 4 h j 8-8 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Each eleme or compoe refracs he ra, ad he pricipal plaes are he locaios of effecive refracio. Trasfer occrs bewee he rear pricipal plae of oe compoe ad he fro pricipal plae of he ex. Image locaio ad magificaio: h m h 3

5 arace Example Two Separaed Thi Leses i Air Two 5 focal legh leses are separaed b 5. A high objec is 4 o he lef of he firs les. h 4 5? h? 8-9 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp. (Arbirar) h m h h arace Example (oied) Two Separaed Thi Leses i Air A secod ra ca be raced o deermie he image sie. h h? OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp h..(arbirar) h 3 4.9

6 arace Example (oied) Two Separaed Thi Leses i Air If he arbirar iiial agle of he secod ra is chose o be ero, he locaio of he rear focal poi of he ssem ca also be deermied. h BD. - h? 8- OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp h h BD (rasfer o = ): BD 3 BD ardial Pois from a arace ear Pois The Gassia properies of a opical ssem ca be deermied sig a paraxial rarace wih pariclar ras. ear cardial pois: Trace a ra parallel o he axis i objec space. This ra ms go hrogh he rear focal poi of he ssem. The h srface is he fial srface i he ssem. Ssem: V P d V BD f 8- OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp f E f BD V dvp d BD f As rasfers: : BD P : d

7 arace Example (oied) Two Separaed Thi Leses i Air A ra from a axial objec a ifii ca be sed o deermie he rear cardial pois. 5 P d V f BD OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp BD 3 BD f f d VP or d BD f BD f ardial Pois from a arace ro Pois Trace a ra from he ssem fro focal poi ha emerges parallel o he axis i image space. The reverse rarace eqaios are sed o wor from image space bac o objec space. Ssem: f E D f V P d f V 8-4 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp D V d VP d D f D D P: d As rasfers: :

8 Example Thic Les i Air =./ = -./ = =.5 = 5 = - rom Gassia opics (for compariso): =./ =.5/ =.467/ f E = 68.6 f 68.6 f 68.6 = = 3 = V P P V d d 8-5 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp d =.7 d' = PP 3.9 There are several differe spreadshee forms ha ca be sed o faciliae he rarace. arace Example orward a - / Objec Srface Space Srface Space Srface Space 3 Image Srface 8-6 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

9 arace Example orward a irs, race a ra parallel o he axis i objec space o deermie he rear focal poi ad rear pricipal plae. ' - / Objec Srface Space Srface Space Srface Space 3 a parallel o axis * + * = = *.9333 =? * = Image Srface 8-7 Solve o obai = a ' OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp arbiraril chose o eqal arace Example rom he Trace of he orward a V V / fe 68.6 f OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp BD V f d BD f 4.54

10 arace Example ro Properies Now, race a ra from he fro focal poi ha emerges parallel o he axis i image space o deermie he fro focal poi ad fro pricipal plae. - / Objec Srface Space Srface Space Srface Space 3?. V Image Srface 8-9 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp a b c a parallel o axis avb.ba c 6.667cb.5 c c.5 b.9667 a.467 V arace Example everse a Use he reverse rarace eqaios. - / Objec Srface Space Srface Space Srface Space 3? * = * = +. Image Srface 8- a parallel o axis OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Solve for :

11 arace Example rom he Trace of he everse a V V / fe f OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp D V V f d D f.7 PP d d arace Example or a iie Objec h OV s OV - / * arbirar h.5 Objec Srface Space Srface Space Srface Space 3 svi m.5..*. * ? Image Srface Solve Image Locaio Image Sie Gassia chec: d.7 d fe 68.6 sd.7.8. m svi d98.3 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

12 YNU arace orm Srface / 8-3 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp arace Example YNU arace orm Srface /?/..5?/ /?. - / /?/ 6.667?/ /? rvares, powers ad ra heighs are associaed wih opical srfaces. Thicesses, idices ad agles are associaed wih opical spaces. 8-4 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

13 emeed Doble Srface ?. - / V V BD.85 ' f. E f. d BD f 7.5 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp 8-6 Mirror Ssem assegrai Telescope 8 5 P V V 3 WD d BD.5. f P ( 3 ) d./.4/ D f 8 Gassia edcio: (.)(.4)( )./ fe f 5 f 5 The fro focal poi ad boh pricipal plaes are well i fro of he ssem.. 8 d d 6. BD f d D f d WD BD OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

14 Mirror Ssem assegrai Telescope arace Srface /? ?/. - / /? ?/ BD V../ f f 5 E d BD f 4 WD BD V D V../ f 5 f 5 d D f 6 E OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Paraxial arace Thi Les i Air The pricipal plaes of a hi les are boh locaed i he plae of he les. 8-8 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Power: f efracio: Trasfer:

15 a Deviaio Thi Les i Air The paraxial ra deviaio irodced b a hi les is idepede of he objec-image cojgaes. emember ha paraxial agles are acall ra slopes. I depeds ol o he ra heigh a he les ad he les power or focal legh: 8-9 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Thi Les YU arace Srface f OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

16 Thi Les Telephoo Les f./ 5 f /.333/ f f 3 E f 3 f 3 P < f f f d f BD << f BD 8-3 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp 5 d d BD f d 5 D f d 5 Thi Les Telephoo Les - arace Srface f /? 5?/ BD V / f f 3 E d BD f 5 V OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp D V / f 3 f 3 d D f E

17 arace oes I a paraxial rarace, is he direced disace from he crre srface o he ex srface. As a resl, real objecs will sall have a posiive disace o he firs srface, as opposed o he pical egaive Gassia objec disace. Srfaces are raraced i opical order, o phsical order. All plaes of ieres i a opical space ms be aaled before rasferrig o a reflecive or refracive srface ad eerig he ex opical space. Wihi a opical space, rasfers move bac or forh alog he ra i ha space wiho chagig he ra agle. eal ad viral segmes of he space ca be accessed OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp YNU arace orm Srface / 8-34 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp

18 Thi Les YU arace orm Srface f OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Viral Objecs ad araces osider a opical ssem or projecor formig a real image. The ra heighs ad agles a he image are eas o deermie. A secod les is ow placed bewee he firs les ad is image. The origial image o loger exiss, b i ow serves as a viral objec for he secod les. A fial ssem image is formed b he secod les worig wih he firs les OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Oce agai, deermiig he ra heighs ad agles i he ssem image space is sraighforward. Trasfer from he firs les o he secod les ad refrac.

19 Viral Objecs ad araces A coo siaio is o be give he sie ad locaio of he viral objec for a les or ssem wiho a iformaio abo he opical ssem sed o prodce i (he firs les o he previos slide). as ms be creaed correspodig o his iermediae image (he viral objec). These ras exis i he opical space correspodig o he viral objec, which is he objec space of he opical ssem. Oce he iermediae space ras are defied, hese ras are rasferred b bac o he er verex of he opical ssem. The ra heighs ad agles are ow ow a he firs verex of he opical ssem, ad he are i he ssem objec space. These cosrced ras ca he be propagaed hrogh he ssem o he ssem image space. Pic wo ras, oe hrogh he op of he viral objec, he oher hrogh he axial objec poi. The agles are arbirar. osrced as i Objec Space h 8-37 Viral Objec OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp Viral Objecs ad araces Whe rasferrig bac o he fro verex, hese ras defiig he viral objec are o refraced b he opical ssem. These ras are alread i objec space. The egaive hicess rasfers o he lef alog he viral segmes of he ras. egardless of he phsical order, ras are raced i opical order: from objec space o image space. The hicesses are he direced disaces as defied b he sig coveios. osrced as i Objec Space h Viral Objec 8-38 OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp The rasfer disace is he direced disace from he viral objec o he fro verex of he ssem. This rasfer disace is i objec space ad is associaed wih he idex of refracio of objec space. The powers ad idices of he elemes ms o be sed i rasferrig bac o he fro verex of he ssem. If a ssem represeed js b is power ad pricipal plaes is o be aaled, he rasfer disace is he disace from he viral objec o he fro pricipal plae of he ssem P.

20 Viral Objec Example A high viral objec is locaed 4 o he righ of he firs srface of he followig focal legh covex-plao hic les: = 5.7 = Ifii = =.57 =.934/ = Deermie he image locaio ad sie. Srface Obj Image.934-4? / * * * Arbirar Lach ras from he axial objec locaio ad from he op of he objec a arbirar agles. Trasfer hese ra heighs o he firs srface of he les ( = -4 ). There is o refracio associaed wih his rasfer as hese are objec-space ras. Solve for he image locaio ad he image heigh: The image is locaed.98 o he righ of he rear srface of he les. The image heigh is This is a viral objec prodcig a real image. OPTI-5 Opical Desig ad Isrmeaio I oprigh 7 Joh E. Greiveamp