Fun 6 098 Digital and Computational Photography 6 882 Advanced Computational Photography http www ritsumei ac jp akitaoka motion e htm Focus and Depth of Field Fr do Durand Bill Freeman MIT EECS Focusing In practice it s a little more complex Move film sensor Thin lens formula D 1 1 1 D D f D Various lens elements can move inside the lens Here in blue f Source Canon red book Defocus Depth of field 1 Circle of confusion Depth of focus circle of confusion From Basic Photographic Materials and Processes Stroebel et al From Basic Photographic Materials and Processes Stroebel et al Size of permissible circle Depth of field Object space Assumption on print size viewing distance human vision Typically for 35mm film diameter 0 02mm Simplistic view double cone Only tells you about the value of one pixel Things are in fact a little more complicated to asses circles of confusion across the image We re missing the magnification factor proportional to 1 distance and focal length Film sensor resolution 8 photosites for high end SLR Best lenses are around 60 lp mm Diffraction limit sensor Point in focus lens Object with texture Depth of field more accurate view Depth of field more accurate view Backproject the image onto the plane in focus Backproject circle of confusion Depends on magnification factor Depth of field is slightly asymmetrical Backproject the image onto the plane in focus Backproject circle of confusion Depends on magnification factor f D f Conjugate of circle of confusion D CD f C Point in focus lens Depth of field lens 2 Deriving depth of field Deriving depth of field Circle of confusion C magnification m Simplification m f D Focusing distance D focal length f aperture N As usual similar triangles D D d1 f N f N CD f CD f d2 d1 Deriving depth of field d1 Deriving depth of field N2C2D2 term can often be neglected when DoF is small conjugate of circle of confusion is smaller than lens aperture D D f N f N CD f d2 d1 CD f d1 d2 Depth of field and aperture DoF aperture Linear proportional to f number Recall big f number N means small physical aperture http www juzaphoto com eng articles depth of field htm f N CD f d1 d2 f 2 8 f 32 3 SLR viewfinder aperture Depth of field and focusing distance By default an SLR always shows you the biggest aperture Brighter image Shallow depth of field help judge focus Depth of field preview button Stops down to the aperture you have chosen Darker image Larger depth of field Quadratic bad news for macro but careful our simplifications are not accurate for macro D f N CD f d2 d1 Double cone perspective Depth of field focusing distance Seems to say that relationship is linear But if you add the magnification factor it s actually quadratic Point in focus sensor lens From Photography London et al Hyperfocal distance Hyperfocal distance When CD f becomes bigger than f N focus at D f2 NC and sharp from D 2 till infinity Our other simplifications do not work anymore there the denominator term has to be taken into account in f N From Basic Photographic Materials and Processes Stroebel et al CD f d1 CD f d2 4 Depth of field and focal length Depth of field focal length Inverse quadratic the lens gets bigger the magnification is higher Recall that to get the same image size we can double the focal length and the distance Recall what happens to physical aperture size when we double the focal length for the same f number It is doubled D f N CD f d1 d2 24mm 50mm Depth of field focal length DoF Focal length Same image size same magnification same f number DoF Same depth of field http www juzaphoto com eng articles depth of fiel d htm Wide angle lens DoF 50mm f 4 8 Telephoto lens 2x f same aperture 200mm f 4 8 from 4 times farther See also http luminous landscape com tutorials dof2 shtml Important conclusion Important conclusion For a given image size and a given f number the depth of field in object space is the same Might be counter intuitive For a given image size and a given f number the depth of field in object space is the same The depth of acceptable sharpness is the same But background far far away looks more blurry Because it gets magnified more Plus usually you don t keep magnification constant Very useful for macro where DoF is critical You can change your working distance without affecting depth of field Now what happens to the background blur far far away 5 Effect of parameters Recap aperture focusing distance focal length From applied photographic optics DoF guides Is depth of field good or evil It depends little grasshopper Want huge DoF landscape photojournalists portrait with environment Shallow DoF portrait wildlife From The Manual of Photography Jacobson et al Michael Reichman Steve McCurry Crazy DoF images Is depth of field a blur By Matthias Zwicker The focus is between the two sticks Depth of field is NOT a convolution of the image The circle of confusion varies with depth There are interesting occlusion effects If you really want a convolution there is one but in 4D space more about this in ten days Sharp version Really wide aperture version From Macro Photography 6 Depth of field It s all about the size of the lens aperture Sensor size Point in focus sensor lens Object with texture lens sensor Point in focus Object with texture Equation Sensor size Smaller sensor smaller C smaller f But the effect of f is quadratic http www mediachance com dvdlab dof index htm The coolest depth of field solution The coolest depth of field solution http www mediachance com dvdlab dof index htm Use two optical systems http www mediachance com dvdlab dof index htm lens sensor Point in focus diffuser lens lens sensor Object with texture Point in focus diffuser lens Object with texture 7 Seeing beyond occlusion Seeing through occlusion Photo taken through zoo bars Telephoto at full aperture The bars are so blurry that they are invisible Synthetic aperture Confocal imaging Stanford Camera array Willburn et al http graphics stanford edu papers CameraArray Confocal microscopy invented by Minsky From Levoy s paper http graphics stanford edu papers confocal Why a bigger aperture Aperture To make things blurrier Depth of field To make things sharper Diffraction limit Sharpness aperture e g for the Canon 50mm f 1 4 http www slrgear com reviews showproduct php product 140 sort 2 cat 10 page 3 f 1 4 soft geometrical aberrations super shallow Dof Lots of light f 2 8 getting really sharp shallow depth of field f 5 6 best sharpness f 16 diffraction kicks in loses sharpness