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UT CS 395T - Camera Simulation

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Camera SimulationTopicsSlide 3RefractionParaxial 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 IrradianceRelative Aperture or F-StopCamera ExposureAperture vs ShutterHigh Dynamic RangeSimulated PhotographSlide 44CS348B Lecture 7 Pat Hanrahan, 2005Camera Simulation Effect Cause Field of view Film size,stops and pupils Depth of field Aperture, focal length Motion blur Shutter Exposure Film speed,aperture, shutterReferencesPhotography, B. London and J. UptonOptics in Photography, R. KingslakeThe Camera, The Negative, The Print, A. AdamsCS348B Lecture 7 Pat Hanrahan, 2005TopicsRay tracing lensesFocusField of viewDepth of focus / depth of fieldExposureLensesCS348B Lecture 7 Pat Hanrahan, 2005RefractionI�Isin sinn I n I� �=Snell’s LawNnn�CS348B Lecture 7 Pat Hanrahan, 2005Paraxial Approximation0e ��sinU u�tanU uRays deviate only slightly from the axisUzCS348B Lecture 7 Pat Hanrahan, 2005Incident RayIUf-f= -I UAngles: ccw is positive; cw is negativeThe sum of the interior angles is equal to the exterior angle.CS348B Lecture 7 Pat Hanrahan, 2005Refracted Ray-�U�If= -� �I Uf- = + -� �( ) ( )I Uf-CS348B Lecture 7 Pat Hanrahan, 2005DerivationParaxial approximationf= - � = -I U i uf= - � = -� � � �I U i uCS348B Lecture 7 Pat Hanrahan, 2005DerivationParaxial approximationSnell’s Law= � =� � ��sin sinn I n I n i nif= - � = -I U i uf= - � = -� � � �I U i uf- = -��( ) ( )n u n uCS348B Lecture 7 Pat Hanrahan, 2005Ray Coordinates- zz�Ruf- =hRf--�u=-huz- =��huzhCS348B Lecture 7 Pat Hanrahan, 2005Gauss’ FormulaParaxial approximation to Snell’s LawRay coordinatesThin lens equationf- = -��( ) ( )n u n u( ) ( )( )h h h hn nz R z Rn n n nz z R�- = -�� �-= +�f =-hR=-��huz=-huzHolds for any height, any ray!CS348B Lecture 7 Pat Hanrahan, 2005VergenceVergenceThin lens equationSurface Power equation� �� � =� �� �1n nV dioptersr z mV V P�= +<0V =0V >0V� -�1( )P n nRDiverging ConvergingCS348B Lecture 7 Pat Hanrahan, 2005Lens-makers Formula� �= - - =�� �� �1 21 1 1( )P n nR R fConvergingDivergingRefractive PowerCS348B Lecture 7 Pat Hanrahan, 2005Conjugate PointsTo focus: move lens relative to backplaneHorizontal rays converge on focal point in the focal plane1 1 1z z f= +�CS348B Lecture 7 Pat Hanrahan, 2005Gauss’ Ray Tracing ConstructionParallel RayFocal RayChief RayObjectImageCS348B Lecture 7 Pat Hanrahan, 2005Ray Tracing: Finite ApertureFocal Plane Back PlaneAperture PlaneCS348B Lecture 7 Pat Hanrahan, 2005Real LensCutaway section of a Vivitar Series 1 90mm f/2.5 lensCover photo, Kingslake, Optics in PhotographyCS348B Lecture 7 Pat Hanrahan, 2005Double 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 312CS348B Lecture 7 Pat Hanrahan, 2005Ray Tracing Through LensesFrom Kolb, Mitchell and Hanrahan (1995)200 mm telephoto50 mm double-gauss35 mm wide-angle16 mm fisheyeCS348B Lecture 7 Pat Hanrahan, 2005Thick LensesRefraction occurs at the principal planesEquivalent LensField of ViewCS348B Lecture 7 Pat Hanrahan, 2005Field of ViewFrom London and UptonCS348B Lecture 7 Pat Hanrahan, 2005Field of ViewFrom London and UptonCS348B Lecture 7 Pat Hanrahan, 2005Field of ViewField of viewTypes of lensesNormal 26ºFilm diagonal  focal lengthWide-angle 75-90ºNarrow-angle 10ºRedrawn from Kingslake, Optics in Photographytan2fov filmsizef=CS348B Lecture 7 Pat Hanrahan, 2005Perspective TransformationThin lens equationRepresent transformation as a 4x4 matrix= + � =�+�� =�+� =�+1 1 1 fzzz z f z ffxxz ffyyz fDepth of FieldCS348B Lecture 7 Pat Hanrahan, 2005Depth of FieldFrom London and UptonCS348B Lecture 7 Pat Hanrahan, 2005Circle of Confusiond�ac d s za z z� � �-= =� �s�szz�cCircle of confusion proportional to the size of the apertureFocal PlaneBack PlaneCS348B Lecture 7 Pat Hanrahan, 2005Depth of Focus [Image Space]Depth of focus  Equal circles of confusionTwo planes: near and far-� � �= =� �ffd s zca z zcafzsnzc�s�fz�nz�fd-� � �= =� �n nn nd z sca z z�ndCS348B Lecture 7 Pat Hanrahan, 2005Depth of Focus [Image Space]Depth of focus  Equal circles of confusion-� � �� �= = � = +� �� �� � � �1 11ff fd s zc ca z z z s acafzsnzc�s�fz�nz�fd-� � �� �= = � = -� �� �� � � �1 11n nn n nd z sc ca z z z s a�ndCS348B Lecture 7 Pat Hanrahan, 2005Depth of Focus [Image Space]Depth of focus  Equal circles of confusion� �= +� �� �� �1 11fcz s ac�s�fz�nz� �= -� �� �� �1 11ncz s a+ =� � �1 1 12f nz z s- =� � �1 1 2 1f ncz z a sCS348B Lecture 7 Pat Hanrahan, 2005Depth of Field [Object Space]Depth of field  Equal circles of confusion+ =1 1 12n fz z s� �- = - �� �� �1 1 2 1 1 2 1n fc cz z a f s a f= +�1 1 1fz z f= +�1 1 1n nz z fcfznzc= +�1 1 1s s fCS348B Lecture 7 Pat Hanrahan, 2005Hyperfocal Distancecfznzc- = = �21 1 2 1 12 2n fc cNz z a f HWhen� � = =�,2n fHs H z zH is the hyperfocal distance+ =1 1 12n fz z saNf�CS348B Lecture 7 Pat Hanrahan, 2005Depth of Field ScaleCS348B Lecture 7 Pat Hanrahan, 2005Factors Affecting DOFFrom http://www.kodak.com/global/en/consumer/pictureTaking/cameraCare/cameCar6.shtml=21 cNH fCS348B Lecture 7 Pat Hanrahan, 2005Resolving PowerDiffraction limit35mm film (Leica standard)CCD/CMOS pixel aperture[ ]l m= = � �1.22 1.22 64 .500 m=0.040 mmfca=0.025mmc=0.0116 mm (Nikon D1)cExposureCS348B Lecture 7 Pat Hanrahan, 2005Image Irradiancef22cos sin4aE L d L Lfpq w p qW� �= = =� �� ��aCS348B Lecture 7 Pat Hanrahan, 2005Relative Aperture or F-StopF-Number and


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UT CS 395T - Camera Simulation

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