Camera SimulationTopicsPowerPoint PresentationRefractionParaxial ApproximationIncident RayRefracted RayDerivationSlide 9Ray CoordinatesGauss’ FormulaVergenceLens-makers FormulaConjugate PointsGauss’ Ray Tracing ConstructionRay Tracing: Finite ApertureReal LensDouble GaussRay Tracing Through LensesThick LensesSlide 21Field of ViewSlide 23Slide 24Perspective TransformationSlide 26Depth of FieldCircle of ConfusionDepth of Focus [Image Space]Slide 30Slide 31Depth of Field [Object Space]Hyperfocal DistanceDepth of Field ScaleFactors Affecting DOFResolving PowerSlide 37Image IrradianceSlide 39Slide 40Slide 41Relative Aperture or F-StopCamera ExposureAperture vs ShutterHigh Dynamic RangeSimulated PhotographSlide 47University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellCamera SimulationReferencesPhotography, B. London and J. UptonOptics in Photography, R. KingslakeThe Camera, The Negative, The Print, A. AdamsEffect CauseField of view Film size, stops and pupilsDepth of field Aperture, focal lengthMotion blur ShutterExposure Film speed, aperture, shutterUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellTopicsRay tracing lensesFocusField of viewDepth of focus / depth of fieldExposureLensesUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellRefractionI′Isin sinn I n I′ ′=Snell’s LawNnn′University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellParaxial Approximation0e ≈Rays deviate only slightly from the axisUz€ sin(U) ≈ U = utan(U) ≈ U = ucos(U) ≈1University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellIncident RayIUφ−φ= −I UAngles: ccw is positive; cw is negativeThe sum of the interior angles is equal to the exterior angle.University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellRefracted Ray−′U′Iφ= −′ ′I Uφ− = + −′ ′( ) ( )I Uφ−University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellDerivationParaxial approximationφ φ= − ⇒ = −I U i uφ φ= − ⇒ = −′ ′ ′ ′I U i uUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellDerivationParaxial approximationSnell’s Law= ⇒ =′ ′ ′ ′sin sinn I n I n i niφ φ= − ⇒ = −I U i uφ φ= − ⇒ = −′ ′ ′ ′I U i uφ φ− = −′ ′( ) ( )n u n uUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellRay Coordinates−zz′Ruφ− =hRφ−−′u=−huz− =′′huzhUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellGauss’ FormulaParaxial approximation to Snell’s LawRay coordinatesThin lens equationφ φ− = −′ ′( ) ( )n u n u( ) ( )( )h h h hn nz R z Rn n n nz z R′− = −′′ ′−= +′φ =−hR=−′′huz=−huzHolds for any height, any ray!University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellVergenceVergenceThin lens equationSurface Power equation⎡ ⎤≡ ≈ =⎢ ⎥⎣ ⎦1n nV dioptersr z mV V P′= +<0V=0V>0V≡ −′1( )P n nRDiverging ConvergingUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellLens-makers Formula⎛ ⎞= − − =′⎜ ⎟⎝ ⎠1 21 1 1( )P n nR R fConvergingDivergingRefractive PowerUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellConjugate Points1 1 1z z f= +′University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellGauss’ Ray Tracing ConstructionParallel RayFocal RayChief RayObjectImageUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellRay Tracing: Finite ApertureFocal Plane Back PlaneAperture PlaneUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellReal LensCutaway section of a Vivitar Series 1 90mm f/2.5 lensCover photo, Kingslake, Optics in PhotographyUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellDouble Gauss Radius (mm) Thick (mm) ndV-no aperture58.950 7.520 1.670 47.1 50.4169.660 0.240 50.438.550 8.050 1.670 47.1 46.081.540 6.550 1.699 30.1 46.025.500 11.410 36.09.000 34.2-28.990 2.360 1.603 38.0 34.081.540 12.130 1.658 57.3 40.0-40.770 0.380 40.0874.130 6.440 1.717 48.0 40.0-79.460 72.228 40.0Data from W. Smith, Modern Lens Design, p 312University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellRay Tracing Through LensesFrom Kolb, Mitchell and Hanrahan (1995)200 mm telephoto50 mm double-gauss35 mm wide-angle16 mm fisheyeUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellThick LensesRefraction occurs at the principal planesEquivalent LensField of ViewUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellField of ViewFrom London and UptonUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellField of ViewFrom London and UptonUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellField of ViewField of viewTypes of lensesNormal 26ºFilm diagonal focal lengthWide-angle 75-90ºNarrow-angle 10ºRedrawn from Kingslake, Optics in Photographytan2fov filmsizef=University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellPerspective TransformationThin lens equationRepresent transformation as a 4x4 matrix= + ⇒ =′+′⇒ =′+⇒ =′+1 1 1 fzzz z f z ffxxz ffyyz fDepth of FieldUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellDepth of FieldFrom London and UptonUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellCircle of Confusiond′ac d s za z z′ ′ ′−= =′ ′s′szz′cCircle of confusion proportional to the size of the apertureFocal PlaneBack PlaneUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don FussellDepth of Focus [Image Space]Depth of focus Equal circles of confusionTwo planes: near and far−′ ′ ′= =′ ′f ff fd s zca z zcafzsnzc′s′fz′nz′fd−′ ′
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