Why not use Sensors without Optics ? ! • 1 Pinhole: Rays of light come straight The Art, Science and Algorithms from each point of an object ! of Photography ! – no distortion. ! – straight lines are still Lenses & Depth of Field (DOF) ! straight ! Optics I ! – infinite DOF ! CSCI 4900/6900 ! • Larger Pinhole ! Maria Hybinette ! – Fuzzy image, due to geometric blur ! !"#$%%&&&'#()*+*),#!-./*.'0(1%10%23/4)5*6789'!:;,< 1 ! 2 ! Larger Pinhole ! Smaller Pinhole ! • Diffraction limit, smaller apertures means more diffraction ! • Small hole does not create a bright dot but a diffused circular disk, called an Airy’s disc, surrounded by concentric circular rings ! • Geometric Blur ! !"#$%%!-#6(#!-./*.'#!-=).:('1.3'643%!A).6%#!-0#:%*/()##C'!:;,< 4 ! !"#$%%&&&'!36*)546,)'*0;%!36=>%#/5=#4?%@(0A6(=BCDE6,,;)5'#4?< 3 ! Pinhole Size Summary ! Replacing pinhole with a lens ! • Large pinhole gives geometric blur (2mm) ! • Optimal pinhole gives little light (0.35mm) ! – Maximum sharpness, aperture is proportional to its distance from the image plane. ! • Small pinhole gives diffraction blur (0.07mm) ! F6*!:<G<2)56.)5<HI#+*.<J:!<64'K<#CDL< 5 ! 6 !
Replacing pinhole with a lens ! Geometrical Optics ! • 1 Pinhole: Rays of light come • Parallel rays converge to a point located at straight from each point of an focal length f from lens ! object ! – no distortion, ! – straight lines are still straight ! • Rays going though center of lens are not – infinite DOF ! • Larger Pinhole fuzziness ! ! deviated – so points are shown at the same • Lens : Need to collect rays emanating from a ‘near’ point in the scene perspective ! through different pinholes, so that they so converge at a point at the sensor. ! 7 ! 8 ! Gauss’ ray tracing construction ! Same Lens: Changing Focus Distance ! • Focus distance (from f f camera to the object in scene). !! – To focus on objects at different focus distances, move the sensor relative to the lens. ! • Rays coming from points on a plane parallel to Scene Inside Camera the lens are focused on another plane parallel to the lens ! M)(*<N6O0-<CDPD< 9 ! 10 ! Depth of field ! Depth of field (Depth of focus*) ! • Range of distance of subject that is sharp ! • Range of distance of subject that is – Shallow / deep ! sharp ! – Short / long ! • Control parameters: ! – Small / large ! – Focal length ( f ) ! • Control parameters: ! – Camera to subject distance ( s ) ! – Focal length* ! – Aperture (f-number) ( a ) ! – Camera to subject distance ! – Format size (as related to circle of – Aperture (f-number) ! confusion, C ) ! – Format size (circle of confusion)” ! T<U0;6+;6.<H46#:!<0?<?0*3.K<(6?6(.< :0<:!6<?0*3.<):<:!6<.650(<)54<46#:!< DOF ! 2 aCs 2 0?<S6,4<(6?6(.<:0<:!6<?0*3.<):<:!6< .3AV6*:'< f 2 !"#$%%65'&/Q/#64/)'0(1%&/Q/%R6#:!70?7S6,4< !"#$%%65'&/Q/#64/)'0(1%&/Q/%R6#:!70?7S6,4< 11 ! 12 !
Focal Length ! Same focus distance: Focal Length ! • A measure on how • Tree is in focus at the lens focal length when it is strongly of how strongly a placed ‘infinitely’ away. ! lens focuses or converges • Weaker lenses (lower optical power) have longer focal light. ! lengths (assuming the lens is • Categories (35 mm built with one lens) ! M6).3(64<?(0;<0#+*),<*65:6(<0?< • To stay in focus needs to ,65.<0(<.-.:6;<0?<,65.6.<&!/,6< format) ! :!6<,65.</.<?0*3.64<:0</5S5/:-< move sensor further back ! • Stronger lenses – wider – Wide, short (<35mm) ! lenses bends light more M)15/S6.W<XIYW<RIX< Focal length is measured in – Normal (35mm-65mm) ! E/46<Z<,051<RIXW<&/46<?0O< ‘strongly’ ! millimeters and is directly [0(;),<Z<JJW<?0O<!3;)5<6-6< proportional to the magnification – Telephoto, long (>65mm) ! N051<Z<5)((0&<XIYW<.!0(:<RIX< of the images. ! !"#$%%65'&/Q/#64/)'0(1%&/Q/%X0*),7,651:!< 13 ! 14 ! Same focus distance: Focal Length ! FOV and Focal Length ! • Weaker lenses (lower • Wide Angle – decreases size, long DOF ! optical power) have • Telephone – magnified, narrow, short DOF ! longer focal lengths (assuming the lens is built with one lens) ! • To stay in focus needs to move sensor further back ! • If sensor size is FOV = 2 arctan( h / 2 f ) ! constant, the field of view becomes smaller ! !"#$%%65'&/Q/#64/)'0(1%&/Q/%X0*),7,651:!< 15 ! 16 ! Focal Length & DOF ! Focal Length & Field of View ! • Same distance same setting. ! • Wide Angle – decreases size, long DOF ! • Telephone – magnified, narrow, short DOF ! 500mm 1000mm FOV is measured diagonally on a 35mm full frame camera (24 x 36mm) ! N66<X(0.:W<CDD9W<H@!0:01()#!-K< 17 ! 18 !
Subject to Camera Distance & DOF ! Hyperfocal Distance ! • Larger distance the longer DOF ! • Point of focus everything from half that • Smaller, shorter DOF ! distance (a set distance) to infinity is in focus ! • Where the focus occurs with relation to the – Aperture size (f-stop) ! – Focal Length of lens ! hyper focal distance ! 19 ! 20 ! Changing focal length versus Summary: Hyper Focal Distance ! changing the view point ! • Largest possible DOF for a given f-number ! – Half the hyperfocal distance to infinite and and !"#$%%&&&'-03:3A6'*0;%&):*!\O]/OJPE^/--2.< beyond! ! • Moving back while changing focal length lets you keep objects at one depth the same size ! • In cinematography, this is called the dolly zoom, or “vertigo effect”, after Alfred Hitchock’s movie ! • http://www.kevinwilley.com/GIF ! 21 ! 22 ! Focal length on portraits ! Summary ! • Pinhole cameras compute correct linear • Standard portrait lens (85 mm) ! perspective ! – But too dark ! – Diffraction limited ! • Lenses gather more light ! – But only one plane of scene in focus ! – Focus by moving the sensor or lens ! • Focal length determines field of view ! – From wide angle to telephoto ! – Depends on sensor size (shortly) ! Wide Angle ! Normal ! Telephoto ! 23 ! 24 !
Changing focal length versus Changing the sensor size ! changing the view point ! • If the sensor is smaller, the field of view is smaller too ! • Smaller sensors E/46<)51,6W< either have fewer .:0(-<:6,,/51< • Changing the focal length let us move back from the pixels, or noisier subject, while maintaining the size of the image ! pixels (closer to • But moving back changes perspective relationships ! together) ! !"#$%%&&&'*);A(/416/5*0,03('*0;%:3:0(/),.%4/1/:),=*);6()=.65.0(=./_6'!:;< 25 ! 26 ! Slide Credits/Resources ! • Prof. Fredo Durand & Prof. Marc Levoy ! • Videos: http://snodart.com/tutorials.php ! • Depth of field, Focal Length: ! – http://en.wikipedia.org/wiki/Depth_of_field ! – http://www.cambridgeincolour.com/tutorials/depth-of-field.htm ! – http://en.wikipedia.org/wiki/Focal_length ! – http://www.kevinwilley.com/l3_topic02.htm ! • London, Stone, Upton “Photography” Book ! • Applets (next week): ! – http://www-graphics.stanford.edu/courses/cs178-10/applets/#lens ! – http://www-graphics.stanford.edu/courses/cs178-10/applets/zoom.html ! • Various: ! – http://www.stsite.com/camera/cam02.php ! – http://super.nova.org/DPR/LensPortrait/ ! – http://super.nova.org/DPR/ ! – http://www.cambridgeincolour.com/tutorials/camera-lenses.htm ! 27 !
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