Field Guide to. Geometrical Optics. John E. Greivenkamp. University of Arizona. SPIE Field Guides Volume FG01. John E. Greivenkamp, Series Editor

Transcription

1 Field Guide to Geometrical Optics Joh E. Greivekamp Uiversity of Arizoa SPIE Field Guides Volume FG01 Joh E. Greivekamp, Series Editor Belligham, Washigto USA

2 Library of Cogress Catalogig-i-Publicatio Data Greivekamp, Joh E. Field guide to geometrical optics / Joh E. Greivekamp p. cm.-- (SPIE field guides) Icludes bibliographical refereces ad idex. ISBN (softcover) 1. Geometrical optics. I. Title II. Series. QC381.G '. 32--dc22 Published by SPIE The Iteratioal Society for Optical Egieerig P.O. Box 10 Belligham, Washigto USA Phoe: Fax: spie@spie.org Web: Copyright 2004 The Society of Photo-Optical Istrumetatio Egieers All rights reserved. No part of this publicatio may be reproduced or distributed i ay form or by ay meas without writte permissio of the publisher. The cotet of this book reflects the work ad thought of the author. Every effort has bee made to publish reliable ad accurate iformatio herei, but the publisher is ot resposible for the validity of the iformatio or for ay outcomes resultig from reliace thereo. Prited i the Uited States of America.

3 Itroductio to the Series Welcome to the SPIE Field Guides! This volume is oe of the first i a ew series of publicatios writte directly for the practicig egieer or scietist. May textbooks ad professioal referece books cover optical priciples ad techiques i depth. The aim of the SPIE Field Guides is to distill this iformatio, providig readers with a hady desk or briefcase referece that provides basic, essetial iformatio about optical priciples, techiques, or pheomea, icludig defiitios ad descriptios, key equatios, illustratios, applicatio examples, desig cosideratios, ad additioal resources. A sigificat effort will be made to provide a cosistet otatio ad style betwee volumes i the series. Each SPIE Field Guide addresses a major field of optical sciece ad techology. The cocept of these Field Guides is a format-itesive presetatio based o figures ad equatios supplemeted by cocise explaatios. I most cases, this modular approach places a sigle topic o a page, ad provides full coverage of that topic o that page. Highlights, isights ad rules of thumb are displayed i sidebars to the mai text. The appedices at the ed of each Field Guide provide additioal iformatio such as related material outside the mai scope of the volume, key mathematical relatioships ad alterative methods. While complete i their coverage, the cocise presetatio may ot be appropriate for those ew to the field. The SPIE Field Guides are iteded to be livig documets. The modular page-based presetatio format allows them to be easily updated ad expaded. We are iterested i your suggestios for ew Field Guide topics as well as what material should be added to a idividual volume to make these Field Guides more useful to you. Please cotact us at fieldguides@spie.org. Joh E. Greivekamp, Series Editor Optical Scieces Ceter The Uiversity of Arizoa

4 Field Guide to Geometrical Optics The material i this Field Guide to Geometrical Optics derives from the treatmet of geometrical optics that has evolved as part of the academic programs at the Optical Scieces Ceter at the Uiversity of Arizoa. The developmet is both rigorous ad complete, ad it features a cosistet otatio ad sig covetio. This material is icluded i both our udergraduate ad graduate programs. This volume covers Gaussia imagery, paraxial optics, firstorder optical system desig, system examples, illumiatio, chromatic effects ad a itroductio to aberratios. The appedices provide supplemetal material o radiometry ad photometry, the huma eye, ad several other topics. Special ackowledgemet must be give to Rolad V. Shack ad Robert R. Shao. They first taught me this material several years ago, ad they have cotiued to teach me throughout my career as we have become colleagues ad frieds. I simply caot thak either of them eough. I thak Jim Palmer, Jim Schwiegerlig, Robert Fischer ad Jose Sasia for their help with certai topics i this Guide. I especially thak Greg Williby ad Da Smith for their thorough review of the draft mauscript, eve though it probably delayed the completio of their dissertatios. Fially, I recogize all of the studets who have sat through my lectures. Their desire to lear has fueled my ethusiasm for this material ad has caused me to deepe my uderstadig of it. This Field Guide is dedicated to my wife, Kay, ad my childre, Jake ad Katie. They keep my life i focus (ad mostly aberratio free). Joh E. Greivekamp Optical Scieces Ceter The Uiversity of Arizoa

5 Table of Cotets Glossary x Fudametals of Geometrical Optics 1 Sig Covetios 1 Basic Cocepts 2 Optical Path Legth 3 Refractio ad Reflectio 4 Optical Spaces 5 Gaussia Optics 6 Refractive ad Reflective Surfaces 7 Newtoia Equatios 8 Gaussia Equatios 9 Logitudial Magificatio 10 Nodal Poits 11 Object-Image Zoes 12 Gaussia Reductio 13 Thick ad Thi Leses 14 Vertex Distaces 15 Thi Les Imagig 16 Object-Image Cojugates 17 Afocal Systems 18 Paraxial Optics 19 Paraxial Raytrace 20 YNU Raytrace Worksheet 21 Cassegrai Objective Example 22 Stops ad Pupils 24 Margial ad Chief Rays 25 Pupil Locatios 26 Field of View 27 Lagrage Ivariat 28 Numerical Aperture ad F-Number 29 Ray Budles 30 Vigettig 31 More Vigettig 32 Telecetricity 33 Double Telecetricity 34 Depth of Focus ad Depth of Field 35 Hyperfocal Distace ad Scheimpflug Coditio 36 vii

6 Table of Cotets (cot.) Optical Systems 37 Parity ad Plae Mirrors 37 Systems of Plae Mirrors 38 Prism Systems 39 More Prism Systems 40 Image Rotatio ad Erectio Prisms 41 Plae Parallel Plates 42 Objectives 43 Zoom Leses 44 Magifiers 45 Kepleria Telescope 46 Galilea Telescope 47 Field Leses 48 Eyepieces 49 Relays 50 Microscopes 51 Microscope Termiology 52 Viewfiders 53 Sigle Les Reflex ad Triagulatio 54 Illumiatio Systems 55 Diffuse Illumiatio 56 Itegratig Spheres ad Bars 57 Projectio Codeser System 58 Source Mirrors 59 Overhead Projector 60 Schliere ad Dark Field Systems 61 Chromatic Effects 62 Dispersio 62 Optical Glass 63 Material Properties 64 Dispersig Prisms 65 Thi Prisms 66 Thi Prism Dispersio ad Achromatizatio 67 Chromatic Aberratio 68 Achromatic Doublet 69 viii

7 Table of Cotets (cot.) Moochromatic Aberratios 70 Moochromatic Aberratios 70 Rays ad Wavefrots 71 Spot Diagrams 72 Wavefrot Expasio 73 Tilt ad Defocus 74 Spherical Aberratio 75 Spherical Aberratio ad Defocus 76 Coma 77 Astigmatism 78 Field Curvature 79 Distortio 80 Combiatios of Aberratios 81 Coics ad Aspherics 82 Mirror-Based Telescopes 83 Appedices 84 Radiometry 84 Radiative Trasfer 85 Photometry 86 Sources 87 Airy Disk 88 Diffractio ad Aberratios 89 Eye 90 Retia ad Schematic Eyes 91 Ophthalmic Termiology 92 More Ophthalmic Termiology 93 Film ad Detector Formats 94 Photographic Systems 95 Scaers 96 Raibows ad Blue Skies 97 Matrix Methods 98 Commo Matrices 99 Trigoometric Idetities 100 Equatio Summary 101 Bibliography 107 Idex 111 ix

8 Glossary Uprimed variables ad symbols are i object space. Primed variables ad symbols are i image space. Frequetly used variables ad symbols: a Aperture radius A, A Object ad image areas B Image plae blur criterio BFD Back focal distace c Speed of light C Curvature CC Ceter of curvature d, d Frot ad rear pricipal plae shifts D Diopters D Diameter D Airy disk diameter DOF Depth of focus, geometrical E, E V Irradiace ad illumiace EFL Effective focal legth EP Etrace pupil ER Eye relief f, f E Focal legth or effective focal legth f F, f R Frot ad rear focal legths f/# F-umber f/# W Workig F-umber δf Logitudial chromatic aberratio F, F Frot ad rear focal poits FFD Frot focal distace FFOV Full field of view FOB Fractioal object FOV Field of view h, h Object ad image heights H Lagrage ivariat H Normalized field height H, H V Exposure HFOV Half field of view I Optical ivariat I, I V Itesity ad lumious itesity L Object-to-image distace L, L V Radiace ad lumiace x

9 L H Glossary (cot.) Hyperfocal distace L NEAR, L FAR Depth of field limits LA Logitudial aberratio m Trasverse or lateral magificatio m Logitudial magificatio m V Visual magificatio (microscope) M, M V Exitace ad lumious exitace MP Magifyig power (magifier or telescope) MTF Modulatio trasfer fuctio Idex of refractio N, N Frot ad rear odal poits NA Numerical aperture OPL Optical path legth OTL Optical tube legth P Partial dispersio ratio P, P Frot ad rear pricipal poits PSF Poit spread fuctio Q Eergy r P Pupil radius R Radius of curvature s Surface sag or a separatio s, s Object ad image vertex distaces S Seidel aberratio coefficiet SR Strehl ratio t Thickess T Temperature TA Trasverse aberratio TA CH Trasverse axial chromatic aberratio TIR Total iteral reflectio t uu, Exposure time Paraxial agles; margial ad chief rays U Real margial ray agle V Abbe umber V, V Surface vertices W Wavefrot error W IJK Wavefrot aberratio coefficiet WD Workig distace x, y Object coordiates x, y Image coordiates xi

10 Glossary (cot.) x P, x P Normalized pupil coordiates XP Exit pupil yy, Paraxial ray heights; margial ad chief rays z Optical axis z, z Object ad image distaces δz Image plae shift δz Depth of focus, diffractio z, z Object ad image separatios α Dihedral agle or prism agle δ Prism deviatio δ MIN Agle of miimum deviatio δφ Logitudial chromatic aberratio Prism dispersio ε Prism secodary dispersio ε X, ε Y Trasverse ray errors ε Z Logitudial ray error θ Agle of icidece, refractio or reflectio θ Azimuth pupil coordiate θ C Critical agle θ 1/2 Half field of view agle κ Coic costat λ Wavelegth ν Abbe umber ρ Reflectace ρ Normalized pupil radius τ Reduced thickess φ Optical power Φ, Φ V Radiat ad lumious power ω, ω Optical agles; margial ad chief rays Ω Solid agle Æ Lagrage ivariat xii

11 Fudametals of Geometrical Optics 1 Sig Covetios Throughout this Field Guide, a set of fully cosistet sig covetios is utilized. This allows the sigs of results ad variables to be easily related to the diagram or to the physical system. The axis of symmetry of a rotatioally symmetric optical system is the optical axis ad is the z-axis. All distaces are measured relative to a referece poit, lie, or plae i a Cartesia sese: directed distaces above or to the right are positive; below or to the left are egative. All agles are measured relative to a referece lie or plae i a Cartesia sese (usig the right-had rule): couterclockwise agles are positive; clockwise agles are egative. The radius of curvature of a surface is defied to be the directed distace from its vertex to its ceter of curvature. Light travels from left to right (from z to +z) i a medium with a positive idex of refractio. The sigs of all idices of refractio followig a reflectio are reversed. To aid i the use of these covetios, all directed distaces ad agles are idetified by arrows with the tail of the arrow at the referece poit, lie, or plae.

12 2 Geometrical Optics Basic Cocepts Geometrical optics is the study of light without diffractio or iterferece. Ay object is comprised of a collectio of idepedetly radiatig poit sources. First-order optics is the study of perfect optical systems, or optical systems without aberratios. Aalysis methods iclude Gaussia optics ad paraxial optics. Results of these aalyses iclude the imagig properties (image locatio ad magificatio) ad the radiometric properties of the system. Aberratios are the deviatios from perfectio of the optical system. These aberratios are iheret to the desig of the optical system, eve whe perfectly maufactured. Additioal aberratios ca result from maufacturig errors. Third-order optics (ad higher-order optics) icludes the effects of aberratios o the system performace. The image quality of the system is evaluated. The effects of diffractio are sometimes icluded i the aalysis. Idex of refractio : Speed of Light i Vacuum Speed of Light i Medium c = m/s c = -- v v = c -- Followig a reflectio, light propagates from right to left, ad its velocity ca be cosidered to be egative. Usig velocity istead of speed i the defiitio of, the idex of refractio is ow also egative. Wavelegth λ ad frequecy ν: v λ = i vacuum: ν -- λ = The waveumber w is the umber of wavelegths per cm. c ν -- w = 1 -- λ uits of cm 1

13 Fudametals of Geometrical Optics 3 Optical Path Legth Optical path legth OPL is proportioal to the time required for light to travel betwee two poits. OPL = I a homogeeous medium: b a OPL = d ( s) ds Wavefrots are surfaces of costat OPL from the source poit. Rays idicate the directio of eergy propagatio ad are ormal to the wavefrot surfaces. I a perfect optical system or a first-order optical system, all wavefrots are spherical or plaar. Fermat s priciple: The path take by a light ray i goig from poit a to poit b through ay set of media is the oe that reders its OPL equal, i the first approximatio, to other paths closely adjacet to the actual path. The OPL of the actual ray is either a extremum (a miimum or a maximum) with respect to the OPL of adjacet paths or equal to the OPL of adjacet paths. I a medium of uiform idex, light rays are straight lies. I a first-order or paraxial imagig system, all of the light rays coectig a source poit to its image have equal OPLs.

14 4 Geometrical Optics Sell s law of refractio: Refractio ad Reflectio 1 siθ 1 = 2 siθ 2 The icidet ray, the refracted ray ad the surface ormal are coplaar. Whe propagatig through a series of parallel iterfaces, the quatity siθ is coserved. Law of reflectio: θ 1 = θ 2 The icidet ray, the reflected ray ad the surface ormal are coplaar. Reflectio equals refractio with 2 = 1. Total iteral reflectio TIR occurs whe the agle of icidece of a ray propagatig from a higher idex medium to a lower idex medium exceeds the critical agle. siθ C = At the critical agle, the agle of refractio θ 2 equals 90 The reflectace ρ of a iterface betwee 1 ad 2 is give by the Fresel reflectio coefficiets. At ormal icidece with o absorptio, ρ 2 = θ C Critical agles for 2 = 1.0

15 Fudametals of Geometrical Optics 5 Optical Spaces Ay optical surface creates two optical spaces: a object space ad a image space. Each optical space exteds from to + ad has a associated idex of refractio. There are real ad virtual segmets of each optical space. Rays ca be traced from optical space to optical space. Withi ay optical space, a ray is straight ad exteds from to + with real ad virtual segmets. Rays from adjoiig spaces meet at the commo optical surface. A real object is to the left of the surface; a virtual object is to the right of the surface. A real image is to the right of the surface; a virtual image is to the left of the surface. I a optical space with a egative idex (light propagates from right to left), left ad right are reversed i these descriptios of real ad virtual. If a system has N optical surfaces, there are N + 1 optical spaces. A sigle object or image exists i each space. The real segmet of a optical space is the volume betwee the surfaces defiig etry ad exit ito that space. It is also commo to combie multiple optical surfaces ito a sigle elemet ad oly cosider the object ad image spaces of the elemet; the itermediate spaces withi the elemet are igored. I a multi-elemet system, the use of real ad virtual may become less obvious. For example, the real image formed by Surface 1 becomes virtual due to the presece of Surface 2, ad this image serves as the virtual object for Surface 2. I a similar maer, the virtual image produced by Surface 3 ca be cosidered to be a real object for Surface 4.

16 6 Geometrical Optics Gaussia Optics Gaussia optics treats imagig as a mappig from object space ito image space. It is a special case of a colliear trasformatio applied to rotatioally symmetric systems, ad it maps poits to poits, lies to lies ad plaes to plaes. The correspodig object ad image elemets are called cojugate elemets. Plaes perpedicular to the axis i oe space are mapped to plaes perpedicular to the axis i the other space. Lies parallel to the axis i oe space map to cojugate lies i the other space that either itersect the axis at a commo poit (focal system), or are also parallel to the axis (afocal system). The trasverse magificatio or lateral magificatio is the ratio of the image poit height from the axis h to the cojugate object poit height h: m h ---- h The cardial poits ad plaes completely describe the focal mappig. They are defied by specific magificatios: F Frot focal poit/plae m = F Rear focal poit/plae m = 0 P Frot pricipal plae m = 1 P Rear pricipal plae m = 1 The frot ad rear focal legths ( f F ad f R ) are defied as the directed distaces from the frot ad rear pricipal plaes to the respective focal poits.

17 Fudametals of Geometrical Optics 7 Refractive ad Reflective Surfaces The radius of curvature R of a surface is defied to be the distace from its vertex to its ceter of curvature CC. The frot ad rear pricipal plaes (P ad P ) of a optical surface are coicidet ad located at the surface vertex V. Power of a optical surface: Curvature: φ ( )C ( ) 1 = = C = --- R R The effective (or equivalet) focal legth (EFL or f E ) is defied as f = f 1 E -- φ The effective i EFL is actually uecessary; this quatity is the focal legth f. The frot ad rear focal legths are related to the EFL: f F = -- = f φ E f R = --- = f φ E f f F E = --- = f R ---- f R ---- f F = --- A reflective surface is a special case with = : φ = 2C = R R 1 f F = f R = -- = f φ E = --- = C

18 8 Geometrical Optics Newtoia Equatios For a focal imagig system, a object plae locatio is related to its cojugate image plae locatio through the trasverse magificatio associated with those plaes. The Newtoia equatios characterize this Gaussia mappig whe the axial locatios of the cojugate object ad image plaes are measured relative to the respective focal poits. By defiitio, the frot ad rear focal legths cotiue to be measured relative to the pricipal plaes. The Newtoia equatios result from the aalysis of similar triagles. z f = F m z = mf R zz = f F f R z f -- = E m z = mf E z z = f E 2 The frot ad rear focal poits map to ifiity ( m = ad 0 ). The two pricipal plaes are cojugate to each other ( m = 1 ). The cardial poits, ad the associated focal legths ad power, completely specify the mappig from object space ito image space for a focal system. Gaussia imagery aims to reduce ay focal imagig system, regardless of the umber of surfaces, to a sigle, uique set of cardial poits. The EFL of a system is determied from its frot or rear focal legth i the same maer used for a sigle surface: f E f F f = = ---- R f = f 1 E -- φ

19 Fudametals of Geometrical Optics 9 Gaussia Equatios The Gaussia equatios describe the focal mappig whe the respective pricipal plaes are the refereces for measurig the locatios of the cojugate object ad image plaes. z = f ( 1 m) F m z = ( 1 m)f R z -- = ( f 1 m) E m z --- = ( 1 m)f E m z --- z f z = F m = f R z f R z f F = 1 z --- z = -- z f E Whe the Newtoia ad Gaussia equatios are expressed i terms of the EFL or power (f E or φ), all of the axial distaces appear as a ratio of the physical distace to the idex of refractio i the same optical space. This ratio is called a reduced distace ad is usually deoted by a Greek letter, for example τ represets the reduced distace associated with the thickess t: t τ = -- The EFL is the reduced focal legth: it equals the reduced rear focal legth or mius the reduced frot focal legth. A ray agle multiplied by the refractive idex of its optical space is called a optical agle: ω = u

20 10 Geometrical Optics Logitudial Magificatio The logitudial magificatio relates the distaces betwee pairs of cojugate plaes. z = z 2 z 1 z = z 2 z 1 h m 1 h 1 = m 2 2 = z z h 1 f R = m1 m 2 f F These equatios are valid for widely separated plaes. As the plae separatio approaches zero, the local logitudial magificatio m is obtaied. m --- m 2 = Sice m varies with positio, m is a fuctio of z ad z. h 2 z = z m m 1 2 z = z m2 The use of reduced distaces ad optical agles allows a system to be represeted as a air-equivalet system with thi leses. Cosider the example of a refractig surface ad its thi les equivalet. Both have the same power φ.