Paraxial ray tracing

Transcription

1 Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig EE 566 OE Ssem Desig Paraxial ra racig Derivaio o reracio & raser eqaios φ, φ φ Paraxial ages Sbsie io i-les eqaio Reracio eqaio Traser eqaio Rober cleo Heig o ra a srace. & se [m] φ Power o srace [iopers] Paraxial ra agle icie o srace [raias] Paraxial ra agle exiig srace [raias] Toal isace bewee srace a [m] 7

2 Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig EE 566 OE Ssem Desig Paraxial ra racig Oe meo o rea iere iices Dealig wi iere iices o reracio: siθ siθ ) ) Sell s Law Paraxial approximaio Rece agle variable Gassia i les eqaio Rece isace variables We ca ow wrie eqaios ivolvig agle a isace b igorig cages i iex. Weever we eal wi problems wi several ierece iices, we simpl mae e above sbsiios. Rober cleo 73

3 Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig EE 566 OE Ssem Desig - racig A ablar meo obj 8 mm eepiece mm ee? Tbe leg 6 3 Qesio o be aswere: wa is e ro worig isace o a x, 8mm objecive we se wi a 6 mm be, as sow?. Fill i wa o ow. Fill i wa o o ow sig paraxial reracio a raser eqaios. Srace Ssem Axial ra φ / /8 8.4 g 84 e 68 -/ c -/ b 3 / - a a ose arbiraril b Reracio: ( ) c Traser: ( ) Reracio: ( ) Rober cleo e Traser: Reracio: g Traser: O Sea.3 ( )

4 Desig o ieal imagig ssems wi geomerical opics Sigle a compo les ssems EE 566 OE Ssem Desig Te elescope epleria Sow i e aocal geomer ( ). Relaxe ee ocses a ~m, s elescope are sall o aocal. Aalsis simpler, owever. Aocal: ssem as o power: ra o OA - oes o iersec OA i image space α β θ α β Deiiio o aglar magiicaio Via similar riagles Tis is bo impora a ameal. Rober cleo 75

5 Desig o ieal imagig ssems wi geomerical opics Sigle a compo les ssems EE 566 OE Ssem Desig Te elescope Galilea - ore compac, prig image. Same aocal coiio: - α β θ β α ( ) oe a ormla is ieical o epleria. Tis is e avaage o e sig coveio. Rober cleo 76

6 Desig o ieal imagig ssems wi geomerical opics Sigle a compo les ssems EE 566 OE Ssem Desig icroscope obj eepiece Focal ssem. Form image a iii or simplici o aalsis. be leg Saar be leg is 6 mm. Visal magiicaio o isrme is proc o liear magiicaio o objecive a visal magiicaio o eepiece: vmicroscope obj veepiece l be obj D p eepiece oe eq.s are approximae l be >> obj, D p >> eepice obj 4 6 obj [mm] Tpical A Rober cleo 77

7 Desig o ieal imagig ssems wi geomerical opics Sigle a compo les ssems EE 566 OE Ssem Desig Overea projecor Rober cleo 78

8 79 EE 566 OE Ssem Desig Rober cleo ABD marices arix ormlaio o paraxial ra-racig Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig T R φ Traser eqaio Reracio eqaio TR R T R Ssem marix R T T ojgae marix φ φ φ - φ

9 Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig EE 566 OE Ssem Desig R Properies o, A B AD B Deermia D T Wrie o e marix eqaio or : I plaes a are cojgaes, ial ra eig oes o epe o iiial ra agle: ojgae coiio I plae is e objec space ocal plae, e slope a e exi plae epes ol o e objec eig: Rober cleo Objec a ro ocal plae I plae is e image space ocal plae, e image-space ra eig epes ol o e erace agle: I e ssem is aocal, e irecio o e image-space ra epes ol o e irecio o e objec-space ra: Image a rear ocal plae Aocal coiio 8

10 8 EE 566 OE Ssem Desig Rober cleo Use o marices, Fi image plae give objec D A D A D B A D B A ) ( T T gives e image locaio D B A ojgae coiio Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig φ φ φ - ( ) φ φ E.g. sigle les

11 Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig EE 566 OE Ssem Desig Form o A EFL, irs ic-les cocep A I e is e magiicaio Deermia F Φ Eecive ocal leg & ssem power Φ Φ TR T φ φ E.g. sigle les φ ( φ ) φ Rober cleo 8

12 83 EE 566 OE Ssem Desig Rober cleo Opical ivaria A objec/image plae (special case) Desig o ieal imagig ssems wi geomerical opics Paraxial ra-racig φ Paraxial Sell s Law Sbsie io Triagles I a cascae ssem... H A coserve qai