Applied prismatic and reflective optics

303 Pages·2010·53.43 MB·English

by  Dennis F Vanderwerf, Society of Photo-optical Instrumentation Engineers

Applied
Prismatic and
Refl ective Optics
Dennis F. Vanderwerf
Bellingham, Washington USA
LibraryofCongressCataloging-in-PublicationData
Vanderwerf,Dennis.
Appliedprismaticandreflectiveoptics/DennisVanderwerf.
p.cm.–(Pressmonograph;200)
Includesbibliographicalreferencesandindex.
ISBN978-0-8194-8332-4
1.Lenses–Designandconstruction–Mathematics.2.Mirrors–Designand
construction–Mathematics.3.Prisms–Designandconstruction–Mathematics.4.
Fermat’stheorem.5.Refraction.6.Reflection(Optics)I.Title.
QC385.2.D47V362010
681(cid:48).423–dc22
2010021193
Publishedby
SPIE
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Bellingham,Washington98227-0010USA
Phone:[phone]
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Email:[email protected]
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Copyright(cid:13)c 2010SocietyofPhoto-OpticalInstrumentationEngineers
Allrightsreserved.Nopartofthispublicationmaybereproducedordistributedin
anyformorbyanymeanswithoutwrittenpermissionofthepublisher.
The content of this book reflects the work and thought of the author(s). Every
effort has been made to publish reliable and accurate information herein, but the
publisherisnotresponsibleforthevalidityoftheinformationorforanyoutcomes
resultingfromreliancethereon.
PrintedintheUnitedStatesofAmerica.
Aboutthecover:TheimageonthecovershowslinearFresnelsolarconcentration
at work. The solar concentrator powers an air-conditioning system at South West
Gas Corporation’s facilities in Phoenix, Arizona. The system was designed by
HelioDynamics(photographcourtesyofLeeLangan).
Contents
Preface...............................................................................................................xiii
Chapter1 IntroductionandBackground........................................................ 1
1.1 Snell’sLawofRefraction.............................................................................. 1
1.2 OpticalDielectricMaterials......................................................................... 2
1.3 FresnelReflectionataDielectricSurface................................................ 4
1.4 ExternalReflectionatanOpticalSurface................................................ 5
1.5 InternalReflectionatanOpticalSurface................................................. 6
1.6 ReflectionPhaseShiftsataPlanarInterface.......................................... 7
1.7 AntireflectionandReflectionCoatings..................................................... 9
1.8 Effective f/#ofaConvergingLightBeam............................................. 9
1.9 RefractionandTranslationofSkewRaysatPlanarSurfaces........... 10
1.10 ConvergentBeamthroughaTiltedPlate................................................. 13
1.11 ReflectionandTranslationofSkewRaysatPlanarSurfaces............ 17
1.12 ReflectionMatrix............................................................................................. 18
1.13 OrientationofViewedImagesthroughPrisms...................................... 18
1.14 IntersectionCoordinateMatrix................................................................... 19
1.15 Three-MirrorBeam-DisplacingPrism...................................................... 21
1.16 RefractionMatrix............................................................................................. 24
1.17 Four-MirrorBeam-DisplacingPrism........................................................ 25
1.18 90-degBeam-DeviatingPrism..................................................................... 28
References....................................................................................................................... 32
Chapter2 GeneralPrismsandReflectors...................................................... 33
2.1 EquilateralPrism.............................................................................................. 33
2.2 AbbeDispersingPrism.................................................................................. 35
2.3 Pellin–BrocaDispersingPrism................................................................... 36
2.4 PentaPrism......................................................................................................... 38
2.5 Right-AnglePrism........................................................................................... 39
2.6 PorroPrism......................................................................................................... 40
2.7 DovePrism......................................................................................................... 42
2.8 BrewsterLaser-DispersingPrism............................................................... 44
2.9 LittrowPrism..................................................................................................... 46
v
vi Contents
2.10 SchmidtPrism................................................................................................... 49
2.11 PechanPrism..................................................................................................... 53
2.12 Schmidt–PechanPrism................................................................................... 54
2.13 Cube-CornerRetroreflector.......................................................................... 56
References....................................................................................................................... 60
Chapter3 PolarizationPropertiesofPrismsandReflectors......................... 61
3.1 PrismsProducingPolarizedLight.............................................................. 61
3.1.1 Uniaxialdouble-refractingcrystals........................................... 61
3.1.2 Nicolpolarizingprism................................................................... 61
3.1.3 Glan–Foucaultpolarizingprism................................................. 63
3.1.4 Glan–Thompsonpolarizingprism............................................. 64
3.1.5 Glan–Taylorpolarizingprism...................................................... 64
3.1.6 Beam-displacingpolarizingprism............................................. 65
3.1.7 Wollastonpolarizingprism.......................................................... 66
3.1.8 Nomarskipolarizingprism........................................................... 67
3.1.9 Rochonpolarizingprism............................................................... 67
3.1.10 MacNeillepolarizingbeamsplittercube.................................. 68
3.1.11 Birefringentmultilayerreflectivepolarizingfilm................. 70
3.1.12 Polarizing beamsplitter elements using birefringent
polarizingfilm................................................................................... 71
3.1.13 Wire-gridpolarizingbeamsplitter.............................................. 72
3.1.14 Polarizing beamsplitter using frustrated total internal
reflection............................................................................................. 73
3.1.15 Polarizing beamsplitter prism with common polariza-
tionoutput.......................................................................................... 74
3.2 PrismsControllingthePolarizationofLight.......................................... 75
3.2.1 Fresnelrhombretarders................................................................. 75
3.2.2 Total-internal-reflectingcube-cornerretarders...................... 78
3.2.3 Phase-coated total-internal-reflecting right-angle prism
retarders............................................................................................... 80
3.3 PolarizationPreservationinPrismsandReflectors.............................. 82
3.3.1 Polarization-preservingtotal-internal-reflectingprism....... 82
3.3.2 Polarization-preservingtwo-piecereflectiveaxicon............ 87
3.3.3 Polarization-preserving total-internal-reflecting cube-
cornerprism....................................................................................... 89
3.3.4 Stokesparameters............................................................................ 89
3.3.5 Depolarizingcube-cornerprism................................................. 90
3.4 Plane of Polarization Rotation Using Total-Internal-Reflecting
PrismsandReflectors..................................................................................... 92
3.4.1 90-deg polarization-rotating prism with coaxial beam
output................................................................................................... 92
3.4.2 90-deg polarization-rotating prism with retroreflected
beamoutput....................................................................................... 92
Contents vii
3.4.3 90-deg polarization-rotating prism with orthogonal
beamoutput....................................................................................... 92
3.4.4 Double Fresnel rhomb polarization rotator with
collinearbeamoutput..................................................................... 93
3.4.5 Four-mirror 90-deg polarization rotator with collinear
beamoutput....................................................................................... 94
References....................................................................................................................... 95
Chapter4 SpecializedPrismTypes................................................................ 97
4.1 DispersingPrism.............................................................................................. 97
4.1.1 Refractingdirect-visionprism..................................................... 97
4.1.2 Reflectivedispersingprismswithcollinearoutput.............. 98
4.1.3 Direct-visionprismswithwavelengthtuning........................ 99
4.1.4 Total-internal-reflectingdispersingprism............................... 99
4.1.5 Multiprismnegativedispersion................................................... 101
4.2 RefractingAchromaticCompoundPrism................................................ 101
4.3 AnamorphicPrismsforBeamCompressionandExpansion............ 103
4.3.1 Beamexpanderwithorthogonaloutput................................... 104
4.3.2 Beamcompressorwithcoaxialoutput..................................... 105
4.3.3 Beamexpanderwithcollinearoutput....................................... 106
4.3.4 Wedgeprismbeamcompressor/expander............................... 107
4.3.5 Anamorphicprismpairwithcoaxialoutput........................... 108
4.3.6 Multiprismdispersivecompressorsandexpanders.............. 109
4.4 AchromaticAnamorphicPrism................................................................... 111
4.4.1 Air-spacedprismpairwithcoaxialoutput.............................. 111
4.4.2 Compoundprismswithorthogonaloutput.............................. 113
4.4.3 Refracting/total-internal-reflecting prism pair with or-
thogonaloutput................................................................................. 113
4.5 AMisalignment-TolerantBeam-SplittingPrism................................... 116
4.6 AxiconPrism..................................................................................................... 116
4.7 AVariablePhase-ShiftingPrism................................................................ 116
References....................................................................................................................... 119
Chapter5 PrismandMirrorSystemDesign,Analysis,andFabrication.......121
5.1 PrismDesignandAnalysis........................................................................... 121
5.1.1 Sectionalelementapproachforprismdesign........................ 122
5.1.2 Right-angleprismsections........................................................... 124
5.1.3 Experientialdesignofmultiplereflectors............................... 124
5.1.4 Matrixmethodsfordesignandanalysis.................................. 125
5.1.5 Evolutionaryprismdesignusingageneticalgorithm......... 126
5.1.6 Athree-mirrortabletoplecternprojector................................. 127
5.1.7 Prismaberrations............................................................................. 128
viii Contents
5.2 PrismQualitySpecifications........................................................................ 130
5.2.1 Surfacequalityandflatnessspecifications.............................. 130
5.2.2 Opticalmaterialproperties........................................................... 130
5.2.3 Specifyingangularaccuracies..................................................... 131
5.2.4 TolerancingaDoveprism............................................................. 131
5.2.5 Techniquesforprismanglemeasurement............................... 131
5.3 SurveyofFabricationMethods................................................................... 135
5.3.1 Groundandpolishedglassprism............................................... 135
5.3.2 Fabrication of a Penta prism by measurement of the
angulardeviationerror................................................................... 135
5.3.3 Molded,pressed,andfire-polishedprisms.............................. 137
5.3.4 Fabricationoflargeprisms........................................................... 137
5.4 Someprism-mountingmethods.................................................................. 137
References....................................................................................................................... 138
Chapter6 ASelectionofPrismApplications.................................................141
6.1 LaserScanning.................................................................................................. 141
6.1.1 Reflectivescanningprism............................................................. 141
6.1.2 Refractiveprism-beamscanningandsteering....................... 141
6.1.2.1 Single-wedgeprism....................................................... 141
6.1.2.2 Wedgeprismpairs.......................................................... 143
6.1.2.3 LADARguidancesystemusingprismpairs.......... 145
6.1.2.4 Rotatingsquare-platelinearscanner........................ 146
6.2 InterferometryandSpectroscopy................................................................ 149
6.2.1 Laserinterferometerwithprismpolarizationrotator.......... 149
6.2.2 PolarizationinterferometerusingaWollastonprism.......... 149
6.2.3 Multipassopticalcellforlaserinterferometer....................... 150
6.2.4 Nomarskipolarized-lightinterferometer................................. 151
6.2.5 Aplanaticprismspectrograph...................................................... 152
6.3 PrismaticOpticalDevices............................................................................. 153
6.3.1 Prismswitchforfiber-opticconnections................................. 153
6.3.2 Lasergyroreadouts......................................................................... 153
6.3.3 Reflectingwedgeprismforopticalreader.............................. 155
6.3.4 Total-internal-reflectingtouchswitchusingaDoveprism 157
6.3.5 Inspectiondeviceforwindowsurfaces.................................... 158
6.4 Viewing,Display,andIlluminationSystems.......................................... 159
6.4.1 Direct-viewsystemforamicrodisplay..................................... 159
6.4.2 Binocularsurgicalloupewithflarereduction........................ 160
6.4.3 Inversionprismforrangefinders................................................ 161
6.4.4 Prismtransformingtransmittedintensityprofile.................. 161
References....................................................................................................................... 163
Contents ix
Chapter7 ProjectionDisplays........................................................................165
7.1 Color-SeparatingandColor-CombiningPrisms.................................... 165
7.1.1 Three-channelPhilipsRGBseparatingprism........................ 165
7.1.2 PhilipsprismsinreflectiveLCDprojectiondisplays.......... 166
7.1.3 Crosseddichroicx-cubeprismsforprojectiondisplays..... 168
7.1.4 Prismsfordigitallightprocessingprojection........................ 170
7.1.5 Othertypesofcolor-separatingprismsforprojectors......... 173
7.2 PolarizingBeamsplittersforProjectionDisplays................................. 175
7.2.1 MacNeillepolarizingbeamsplitters........................................... 175
7.2.2 Cartesianpolarizingbeamsplitters............................................. 176
7.2.3 Wire-gridpolarizingbeamsplittersinprojectiondisplays. 177
7.3 IlluminatorsforProjectionDisplays.......................................................... 179
7.3.1 Hollowtunnelintegrators.............................................................. 179
7.3.2 Solidlightpipes................................................................................ 180
7.3.3 Effectoflight-pipecrosssectiononuniformity.................... 180
7.3.4 Solidmicroprismaticlighthomogenizer.................................. 181
7.3.5 Tapered-tunnelilluminatorforprojectiondisplays.............. 183
References....................................................................................................................... 184
Chapter8 MicroprismaticArrays....................................................................187
8.1 RoofPrismLinearArray............................................................................... 187
8.2 SquarePrismaticHollowLightGuide...................................................... 195
8.3 CircularPrismaticHollowLightGuide.................................................... 197
8.4 LuminairewithContouredPrismaticExtractor..................................... 199
8.5 EllipticalLightGuidewithDirectionalOutput..................................... 199
8.6 PrismaticBacklightingDevices.................................................................. 202
8.7 BrightnessEnhancementforLiquidCrystalDisplays........................ 209
8.8 PolarizingPrismaticSheet............................................................................ 216
8.9 PrismaticReflectivePolarizerFilm........................................................... 217
8.10 LCDBacklightsProducingPolarizedLight........................................... 217
8.11 PrismaticArrayBeamsplittersandCombiners...................................... 222
8.12 PolarizationConvertersUsingPrismaticArrays................................... 226
8.13 Cube-CornerArrays........................................................................................ 228
8.14 DovePrismArrays.......................................................................................... 231
References....................................................................................................................... 234
Somecommercialnonsequentialray-tracingprograms:.................................. 235
Chapter9 FresnelLenses...............................................................................237
9.1 BasicRefractiveFresnelLensDesign...................................................... 237
9.1.1 Designexample:Fresnellenscollimator/searchlight.......... 240
9.2 High-TransmissionFresnelLensDoublet............................................... 242
9.3 ReflectiveFresnelLenses.............................................................................. 245
9.3.1 First-surfacereflectordesignparameters................................. 245
9.3.2 Second-surfacereflectordesignparameters........................... 247
x Contents
9.4 RefractivePlanarCircularFresnelLensSolarApplications............. 248
9.4.1 Multilenssolarfurnace.................................................................. 248
9.4.2 Multilens-arraysolarsimulator................................................... 248
9.5 RefractiveMeniscusFresnelLenses.......................................................... 248
9.6 ReflectivePlanarLinear-FocusSolarConcentrators........................... 250
9.6.1 Tiltedlinear-focusreflectivesolarconcentrator.................... 250
9.6.2 Linear-focus concentrator using a linear Fresnel lens
andacrossedlineartotal-internal-reflectingarray............... 250
9.6.3 Planarreflectivespot-focusconcentratorusingorthogo-
nalrefractiveandreflectivelinearFresnellenses................. 253
9.7 CurvedLinearFresnelLensSolarConcentrators................................. 255
9.8 FlexibleFresnelLensSolarConcentrators.............................................. 260
9.8.1 Sectionalplanarsolarconcentrators.......................................... 260
9.8.2 Inflatablecurvedsolarconcentrators........................................ 260
9.9 FresnelLensesUsingTotalInternalReflection..................................... 261
9.9.1 Low-profileoverheadprojector................................................... 262
9.9.2 CurvedcatadioptricFresnellenses............................................ 262
9.9.3 Photovoltaic solar concentrator using total internal
reflection............................................................................................. 264
9.10 FresnelLensesforRear-ProjectionScreens........................................... 264
9.11 FresnelLensManufacture............................................................................. 265
9.12 AchromaticFresnelLenses........................................................................... 265
9.12.1 Combinationofhigh-andlow-dispersionmaterials............ 267
9.12.2 AchromaticcatadioptricFresnellenses................................... 267
9.12.3 Dispersion-compensatedachromaticFresnellens................ 271
9.12.4 Design example: achromatic dual-grooved Fresnel lens
foroverheadprojector.................................................................... 273
9.12.5 AchromaticzoneplateusingaFresnellens........................... 274
9.13 DiffractionandCoherenceEffectsinFresnelLenses.......................... 276
9.13.1 DiffractioncompensationinaFresnellensreflector........... 276
9.13.2 Phase-optimizedFresnellens...................................................... 277
9.13.3 Phase-optimizedFresnellensforuseinanIRintrusion
detector................................................................................................ 278
9.14 DesignofaFresnelLensIlluminatorUsingGeneticAlgorithms... 278
References....................................................................................................................... 281
Afterword...........................................................................................................285
Index...................................................................................................................287
Preface
Thistextdealsprimarilywiththeopticsofrefractingandreflectingplanarsurfaces
in the form of prismatic refracting and reflecting components, and the design,
analysis,andapplicationsofthesecomponents.Opticalprismsconsistofmultiple
planar surfaces, constructed to a specified geometry and formed from optical
glass or plastic. The surfaces may have thin-film coatings that contribute to their
functionality. Optical prismatic elements can be classified into two general types:
those that are used in imaging systems, such as binoculars or projectors, and
those used in nonimaging systems, such as spectrometers, illuminators, and solar
concentrators.Inadditiontowell-knownprismsystems,newapplicationsofprisms
arebeingintroducedinthefieldsofelectro-optics,metrology,prismaticfilmsand
arrays,projectiondisplays,andothers.
Chapter 1 introduces and reviews the optical concepts that are useful for
the topics developed in the succeeding chapters. In Chapter 2, some better-
knownprismtypesarediscussed,alongwiththeessentialray-traceequationsthat
define their specific properties. This includes both single and compound prisms,
along with cube-corner retroreflectors. Birefringent prisms and polarizing beam-
splitting prisms that produce polarized light are discussed in Chapter 3, including
prisms that affect the polarization state of light, such as polarization-preserving
prisms and prisms that rotate the plane of polarization. Prisms with collinear and
coaxial dispersion properties, achromatic multiprisms, and anamorphic designs
for beam expansion and compression are examined in Chapter 4. In Chapter 5,
several methods of prism design are reviewed, including some of the more recent
methodologies. This chapter also covers prism fabrication, tolerancing, choice
of optical material, and some mounting methods. Specific uses of prisms in
optical systems, such as scanning, beam steering, spectroscopy, interferometry,
light coupling and switching, and viewing and illumination are presented in
Chapter 6. Chapter 7 covers the use of prisms as dichroic color beamsplitters and
combiners, polarizers, and light-beam homogenizers and integrators in projection
displays.Microprismarraysareveryusefulforlightguides,luminaires,brightness-
enhancement sheets, backlight displays, and sheet polarizers. These applications
are detailed in Chapter 8. Last, Chapter 9 covers Fresnel lens optics and the use
of both refractive and reflective lenses in illumination, solar concentration, and
direct-viewdisplays.Severaldesignmethodsforproducingachromaticandphase-
correctedFresnellensesarealsopresented.
References and examples are drawn from specialized texts, journal articles,
conference proceedings, trade publications, and patent literature. I wish to
acknowledge the editorial assistance of Gwen Weerts of SPIE Press for her
suggestionsandcontributionsduringthecompositionofthisbook.
DennisF.Vanderwerf
Austin,Texas
xi