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16.098 Digital and Computational Photography 6.882 Advanced Computational PhotographyFocus and Depth of FieldFrédo DurandBill FreemanMIT - EECSFun• http://www.ritsumei.ac.jp/~akitaoka/motion-e.htmFocusingfDD’1D’ D11f+=• Move film/sensor• Thin-lens formulaIn practice, it’s a little more complex• Various lens elements can move inside the lens– Here in blueSource: Canon red book. Defocus & Depth of field2Circle of confusionFrom Basic Photographic Materials and Processes, Stroebel et al. circle of confusionDepth of focusFrom Basic Photographic Materials and Processes, Stroebel et al. Size of permissible circle?• Assumption on print size, viewing distance, human vision– Typically for 35mm film: diameter = 0.02mm• Film/sensor resolution (8μ photosites for high-end SLR )• Best lenses are around 60 lp/mm• Diffraction limitDepth of field: Object spacelenssensorPoint in focusObject with texture• 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)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 asymmetricallensPoint in focusConjugate of circle of confusionDepth of fieldDepth of field: more accurate view• Backproject the image onto the plane in focus– Backproject circle of confusion– Depends on magnification factor ¼ f/DlensCD/fDC¼ f3Deriving depth of field• Circle of confusion C, magnification m• Simplification: m=f/D• Focusing distance D, focal length f, aperture N• As usual, similar trianglesCD/ff/NDd1d2Deriving depth of fieldCD/ff/ND-d1d1Deriving depth of fieldCD/ff/NDd1d2Deriving depth of fieldCD/ff/NDd1d2N2C2D2term can often be neglected when DoF is small (conjugate of circle of confusion is smaller than lens aperture)Depth of field and aperture• Linear: proportional to f number• Recall: big f number N means small physical apertureCD/ff/Nd1d2DoF & aperture• http://www.juzaphoto.com/eng/articles/depth_of_field.htmf/2.8 f/324SLR viewfinder & aperture• 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 fieldDepth of field and focusing distance• Quadratic (bad news for macro)(but careful, our simplifications are not accurate for macro)f/Nd1d2DCD/fDouble cone perspective• Seems to say that relationship is linear• But if you add the magnification factor, it's actually quadraticlenssensorPoint in focusDepth of field & focusing distanceFrom Photography, London et al. Hyperfocal distanceFrom Basic Photographic Materials and Processes, Stroebel et al. 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 CD/ff/Nd1d2CD/f5Depth of field and focal length• Inverse quadratic: the lens gets bigger, the magnification is higherCD/ff/NDd1d2Depth of field & focal length• 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 doubled24mm 50mm• Same image size (same magnification), same f number• Same depth of field!Depth of field & focal lengthWide-anglelensTelephotolens (2x f), same apertureDoFDoFDoF & Focal length• http://www.juzaphoto.com/eng/articles/depth_of_field.htm50mm f/4.8 200mm f/4.8(from 4 times farther)See also http://luminous-landscape.com/tutorials/dof2.shtmlImportant 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. • 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 faraway?Important conclusion• 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 blurryBecause it gets magnified more• Plus, usually, you don't keep magnification constant6RecapEffect of parametersFrom applied photographic opticsaperturefocusing distancefocal lengthDoF guidesFrom "The Manual of Photography" Jacobson et al Is depth of field good or evil?• It depends, little grasshopper• Want huge DoF: landscape, photojournalists, portrait with environment• Shallow DoF: portrait, wildlifeSteve McCurryMichael ReichmanCrazy DoF images• By Matthias Zwicker• The focus is between the two sticksSharp versionReally wide aperture versionIs depth of field a blur?• 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)From Macro Photography7Sensor sizeDepth of field• It’s all about the size of the lens aperturelenssensorPoint in focusObject with texturelenssensor Point in focusObject with textureEquation• Smaller sensor– smaller C– smaller f• But the effect of f is quadraticSensor size• http://www.mediachance.com/dvdlab/dof/index.htmThe coolest depth of field solution• http://www.mediachance.com/dvdlab/dof/index.htm• Use two optical systemslensdiffuserPoint in focusObject with texturelenssensorThe coolest depth of field solution• http://www.mediachance.com/dvdlab/dof/index.htmlensdiffuserPoint in focusObject with texturelenssensor8Seeing through occlusionSeeing beyond occlusion• Photo taken through zoo bars• Telephoto at full aperture• The bars are so blurry that they are invisibleSynthetic aperture• Stanford Camera array (Willburn et al.http://graphics.stanford.edu/papers/CameraArray/)Confocal imaging• Confocal microscopy (invented by Minsky)From Levoy'spaper http://graphics.stanford.edu/papers/confocal/ApertureWhy a bigger aperture• To make things blurrier– Depth of field• To make things sharper– Diffraction limitSharpness & aperture (e.g. for the Canon 50mm


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MIT 6 098 - Focus and Depth of Field

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