Lecturer: Ivan Kassamakov, Docent Assistant: Kalle Hanhijärvi. Course webpage:

Transcription

1 Lecturer: Iva Kaamakov, Docet Atat: Kalle Hahjärv Coure webpage:

2 Peroal formato Iva Kaamakov e-mal: offce: PHYSICUM - PHY C 38 (9:00-9:00) Kalle Hahjärv e-mal: kalle.hahjärv@helk.f offce: PHYSICUM - PHY C 37

3 Geometrcal Optc The urface of a object that ether elf-lumou or exterally llumated behave a f t coted of a very large umber of radatg pot ource; Each of thee pot emt phercal wave - ray emaate radally the drecto of eergy flow; I th cae, the ray dverge from a gve pot ource S, wherea f the phercal wave were collapg to a pot, the ray would be covergg. Image: If a coe of ray from a pot object S arrve at the certa pot P, P called the mage of S. A pot ource S ed out phercal wave. A coe of ray eter a optcal ytem that vert the wavefrot, caug them to coverge o pot P. I cro ecto ray dverge from S, ad a porto of them coverge to P. If othg top the lght at P, t cotue o.

4 Perfect Imagg L = L = L = L =... opt opt opt opt L t opt S Optcal Sytem L L t opt 2 2 opt 3 t3 P Object Space L t opt 4 4 Image Space Perfect Image! For all ray emaatg from S to coverge P they all have to be tatoary OPL,.e. they hould have the ame OPL meag they are ochroou 4

5 Optc Termology ad Aumpto Focu or focal pot pot from whch a porto of wave dverge or o whch they coverge. Optcal Ax cetral ax through optcal elemet. Prcple of Reverblty f ource ad mage are terchaged, the route the lght follow uchaged. A object ( object pace) related to a mage ( mage pace) a cojugate pot (.e. the object would be equally well maged at ether pot). Real mage a lumou mage of the object would appear f a cree wa placed at the focu mage pace. Vrtual mage o lumou mage of the object would appear f a cree wa placed at the focu.

6 Defto S Object Space Optcal Sytem P Image Space S ad P are cojugate pot I the deal optcal ytem there a cojugate pot mage pace for each pot object pace I the real optcal ytem there a umber of factor prevetg perfect magg: Scatterg correctable prcple Aberrato correctable prcple Dffracto correctable oly uattaable lmt of λ 0 Attaable degree of perfecto o catterg or aberrato dffracto-lmted-mage If all the dmeo the ytem are much larger tha wavelegth, the the lmt of λ 0 we are the doma of Geometrcal Optc 6

7 Dffracto-lmted mage We could ot focu a beam to a pot ad o obta ftely good patal reoluto. ~0 The mallet poble focal pot about the wavelegth, λ. Same for the bet patal reoluto of a mage. Th fudametally due to the wave ature of lght, whch ha ot bee cluded geometrcal optc. >λ d λ f D

8 Ray Optc ax We'll defe lght ray a drecto pace, correpodg, roughly, to k-vector of lght wave. We wo t worry about the phae. Each optcal ytem wll have a ax, ad all lght ray wll be aumed to propagate at mall agle to t. Th called the Paraxal Approxmato.

9 Geometrcal optc (ray optc) the mplet vero of optc. Geometrcal Optc treat the cotrolled mapulato of wavefrot (or ray) by mea of the terpotog of reflectg ad/or refractg bode, eglectg ay dffracto effect. Ray optc Geometrcal optc: Whe λ 0, dffracto effect ca be eglected, ad lght propagate rectlearly homogeeou meda. Phycal optc: Whe λ ~ D, the wave ature of lght mut be take to accout.

10 Lee Le: A refractg devce that caue each dvergg wavelet from a object to coverge or dverge ad to form the mage of the object. Aphercal le ca form perfect mage but hard to maufacture. Sphercal le caot form perfect mage but eay to make. Aphercal urface How to determe the hape of the urface of a le: The optcal path legth (OPL) from the ource to the output wavefrot hould be a cotat. Example: collmatg a pot ource OPL = FA + ( FA + t / t AD ) AD = = cotat cotat F y A(x,y) t D d x The urface a hyperbola (hyperbolod) whe t / > ad a ellpe (ellpod ) whe t / <. 0

11 Hyperbolodal & ellpodal urface x a y b 2 2 = 2 2 F P F 2 P = 2a F P + F 2 P = 2a x a y b = 2 2 Hyperbolodal ad ellpodal refractg urface form a perfectly parallel beam

12 Apherc Lee Two apherc urface make up a apherc le S P The frt qualty gla apherc to be maufactured great quatte (te of mllo) wa a le for the Kodak dk camera (982) 2

13 Apherc Lee Apherc Codeer Lee

14 Defto: Focal pot of a curved terface f 4

15 Bac Lee Covergg (covex) le, the cetral ecto thcker tha the rm. Lght parallel to the prcpal ax focued to a real focal pot. Dvergg (cocave) le, cetral ecto ther tha the rm. Lght dverge from a vrtual focal pot. Whe a parallel budle of ray pae through a covergg le, the pot to whch t coverge (or whe pag through a dvergg le, the pot from whch t dverge) a focal pot of the le.

16 Bac Lee

17 Type of lee Le omeclature Whch type of le to ue (ad how to oret t) deped o the aberrato ad applcato.

18 Refracto at phercal terface θ r S θ O O θ V h R A 2 θ t I C P Sg coveto: o, f o + left of V, f x o x R + rght of V + left of F o + rght of F + curved toward left y o, y + above ax. Lght travel left to rght optcal ax 2. V = vertex = org meaure all dtace from here 3. R = radu of phercal terface, potve to the rght of V, egatve to the left 4. S O = object dtace - potve for real object (.e. oe to the left of V), egatve for vrtual 5. S = mage dtace - potve for real mage (to rght of V), egatve for vrtual mage 6. y o, y - heght potve up, egatve dow

19 V C S θ O P θ θ t From tragle SAC ad CPA 2 A ϕ h R O I Refracto at phercal terface = + = + = = + = = + o o o o o t t o o t o o l l R l l l R l R l R l R l R l R ) ( ) ( ) ( ) ( θ θ θ θ ϕ π θ ϕ θ π θ r 0 l l Gaua (paraxal, frt-order) optc: Whe ϕ mall, coϕ, ϕ ϕ, l o o, l. R o 2 2 = + Paraxal magg: t 2 θ θ = Ivoke Sell Law

20 Specal Cae Flat terface R + = R 2 2 O = 2 O I O 2 θ O θ Jut a Sell Law I O 20

21 Specal Cae -Focug Object at Ifty O + = R 2 2 O 2 = R= f 2 2 F 2 Back Focu f I f back focal legth 2

22 Specal Cae -Collmato Image at Ifty + = R 2 2 O O = R= fo f 2 2 Frot Focu F f O f O Frot focal legth 22

23 Specal Cae (a) f a pot maged at fty ( = ) the object focal legth (f o = o ) gve by F = R o f o 2 (b) f o =, the mage focu F the axal pot where the ray coverge. The mage focal legth f (= ) gve by 2 f = 2 R We could alo have a vrtual mage whe the ray dverge from the terface ad a vrtual object whe the ray coverge toward t. f o f F Note < 0, R < 0 F C V C V o F o Note o < 0, R < 0

24 Lateral (Travere) Magfcato Let u trace the ray 2 h O O θ V F 2 I h θ 2 O I t Ray goe through Vertex 2 d Ray parallel to ax ad goe through back focu Sell Law θ= 2θ2 Lateral Magfcato m h h = = O 2 O Iverted Image 24

25 Cartea perfect refractg urface Reflectve or refractve urface that ca form perfect mage are called Cartea Surface P(x,y) 2 2 > y O x Reé Decarte I o Surface ƒ(x,y) 25

26 Paraxal ray approxmato We would lke a gle urface to provde magg for all o, Th wll be true f we place certa retrcto o the budle of ray collected by the optcal ytem Make the PARAXIAL RAY APPROXIMATION Aume y << o, (.e. all agle are mall) x << o, (of coure). Ray early parallel to the optcal ax 2. All agle ϕ ad h are mall => coϕ, ϕ ϕ 3. Sell law o θ o = θ

27 Defto of Paraxal Optc Cyldrcal ymmetry every ray pae through the optcal ax No kewed ray θ 3 3 θ θ θ = θ +... θ θ θ ta θ = θ θ θ θ co θ = θ Le tha perfect mage phercal aberrato 27

28 Paraxal Ray We wat to mplfy the ed reult of lght ray phyc We aume the followg equato that lght ray make mall agle wth the optc ax 5deg (.262 rad) deg: (.75 rad) deg: (.873 rad) optc ax deg: (30.5 mrad) 30.5 E-3 30 deg: (.524 rad).5 45 deg: (.785 rad).707

29 Paraxal Optc Cartea Surface Make Perfect Image.but dffcult to make r 2 4 z ( )... c r = Ar + Br + Oly eve power of r 0 V R ( ) z R + r = R z Cloe to the ax ay Cartea urface ca be approxmated by a phere z r R R r R R r r r r 2 R 8 R 2 R 8 R ( ) = = For mall r Sphercal urface approxmate the Cartea oe farly well f R = / 2A Le tha perfect mage phercal aberrato 29

30 Maufacturg Lee Cao EF Le Plat - Le Machg Proce2

31 Th Lee Le: A le cot of a pece of gla or platc, groud o that each of t two refractg urface a egmet of ether a phere or a plae Le type: Smple le : Oe elemet le Compoud le : May elemet le th or thck-that, whether or ot t thcke effectvely eglgble We wll oly coder th lee where the thcke of the le mall compared to the object ad mage dtace. Lee are commoly ued to form mage by refracto optcal trumet

32 R Coveto R R > 0 R 2 < 0 R 2 R R < 0 R 2 R 2 >0 R > 0 whe le lad o rght R < 0 whe le lad o left

33 Th lee Treat a two phercal terface Aume that the le thcke t eglgble t urface 2 d urface S P' P (R, m, l ) (R 2, l, m ) m m S P C 2 C L R R 2 o

34 Th le: Frt urface t urface m L S P' (R, m, l ) P S V R S o, R > 0 o + = m L L o R < 0 ce to the left of V, vrtual mage m

35 Th le: Secod urface 2 d urface P' P m m (R 2, l, m ) P R 2 P d L 2 35

36 36 Th le: ecod terface 2 2 R t L m m o L = + + o o = Secod terface Frt terface Object dtace d + o = d - o Th le d 0, o object dtace = - o 2 2 R m L m o L = + R m L L o m = +

37 R R m L m L m o m = + Frt terface Secod terface R m L L o m = R m L m o L = + Th Le Equato

38 38 If the le th eough, t 0. Aume m =, we have the th le equato (le maker formula): = + 2 ) ( R R l o f o o = = lm lm = 2 ) ( R R f l f o = + Gaua le formula: Th Le Equato

39 Potve ad Negatve Lee = ( ) + f R R 2 ymmetrc lee cacel ome aberrato Double covex f>0 R >0 R 2 >0 F F 2 f f Potve le creae f of ytem ymmetrc lee cacel ome aberrato Double cocave f<0 R <0 R 2 <0 F 2 F f f Negatve le 39

40 Potve ad Negatve Lee = ( ) + f R R 2 Plao-covex f>0 R >0 R 2 = focu or magfy lght produce real or vrtual mage F F 2 f f Potve le Plao-cocave f<0 R <0 R 2 = lght expader produce real or vrtual mage F 2 F f f Negatve le 40

41 Potve ad Negatve Lee = ( ) + f R R 2 Potve Mecu R >0 R 2 <0 f>0 R 2 >R ued to chage f or lght collecto ytem F F 2 f f Potve le Negatve Mecu f<0 R >0 R 2 <0 R 2 <R F 2 F f f Negatve le 4

42 Cyldrcal lee A "phercal le" focue both travere drecto. A "cyldrcal le" focue oly oe travere drecto.

43 Focug Lght the Real World Lght ca ot be focued through a aperture maller tha a dffractolmted pot pot radu =. 22 f λ D for a tadard 630 m, th ~ 3 µm

44 Focug Lght the Real World θ m f θ m = ource ze f I cae we wat to collmate: lmtato wll alway be at leat θ m creag f may be requred to reduce pot ze at the expee of loog lght

45 Maufacturg Lee how t made 8 ep4- optcal lee tage 2