The Art, Science and Algorithms from each point of an object ! of - - PDF document

The Art, Science and Algorithms

• f Photography!

Lenses & Depth of Field (DOF)! Optics I! CSCI 4900/6900! Maria Hybinette!

1!

Why not use Sensors without Optics?!

• 1 Pinhole: Rays of

light come straight from each point of an

• bject !

– no distortion.! – straight lines are still straight! – infinite DOF!

• Larger Pinhole!

– Fuzzy image, due to geometric blur!

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Larger Pinhole!

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• Geometric Blur!

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 !

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Pinhole Size Summary!

• 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)!

5!

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Replacing pinhole with a lens!

6!

Replacing pinhole with a lens!

• 1 Pinhole: Rays of light come

straight from each point of an

• bject !

– no distortion, ! – straight lines are still straight! – infinite DOF!

• Larger Pinhole fuzziness!

7!

!

• Lens: Need to collect rays emanating from a ‘near’ point in the scene

through different pinholes, so that they so converge at a point at the sensor.!

Geometrical Optics!

• Parallel rays converge to a point located at

focal length f from lens!

• Rays going though center of lens are not

deviated – so points are shown at the same perspective!

8!

Gauss’ ray tracing construction!

• Rays coming from points on a plane parallel to

the lens are focused on another plane parallel to the lens!

9!

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Same Lens: Changing Focus Distance!

• Focus distance (from

camera to the object in scene). !!

– To focus on objects at different focus distances, move the sensor relative to the lens.!

10!

f f

Scene Inside Camera

Depth of field!

11!

• Range of distance of subject that is sharp!

– Shallow / deep ! – Short / long! – Small / large!

• Control parameters:!

– Focal length*! – Camera to subject distance! – Aperture (f-number)! – Format size (circle of confusion)”! !"#$%%65'&/Q/#64/)'0(1%&/Q/%R6#:!70?7S6,4<

Depth of field (Depth of focus*)!

12!

• Range of distance of subject that is

sharp!

• Control parameters:!

– Focal length (f)! – Camera to subject distance (s)! – Aperture (f-number) (a)! – Format size (as related to circle of confusion, C)!

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DOF ! 2aCs2 f 2

Focal Length!

13!

• A measure on how

strongly of how strongly a lens focuses or converges light.!

• Categories (35 mm

format)!

– Wide, short (<35mm)! – Normal (35mm-65mm)! – Telephoto, long (>65mm)!

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Same focus distance: Focal Length!

• Tree is in focus at the lens

focal length when it is placed ‘infinitely’ away.!

• Weaker lenses (lower optical

power) have longer focal lengths (assuming the lens is built with one lens)!

• To stay in focus needs to

move sensor further back!

• Stronger lenses – wider

lenses bends light more ‘strongly’!

14!

Focal length is measured in millimeters and is directly proportional to the magnification

• f the images.!

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Same focus distance: Focal Length!

• Weaker lenses (lower
• ptical power) have

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

constant, the field of view becomes smaller!

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FOV and Focal Length!

• Wide Angle – decreases size, long DOF!
• Telephone – magnified, narrow, short DOF!

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Focal Length & DOF!

• Same distance same setting.!
• Wide Angle – decreases size, long DOF!
• Telephone – magnified, narrow, short DOF!

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Focal Length & Field of View!

FOV is measured diagonally on a 35mm full frame camera (24 x 36mm)!

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500mm 1000mm

Subject to Camera Distance & DOF!

• Larger distance the longer DOF!
• Smaller, shorter DOF!
• Where the focus occurs with relation to the

hyper focal distance!

19!

Hyperfocal Distance!

• Point of focus everything from half that

distance (a set distance) to infinity is in focus!

– Aperture size (f-stop)! – Focal Length of lens!

20!

Summary: Hyper Focal Distance!

• Largest possible DOF for a given f-number!

– Half the hyperfocal distance to infinite and and beyond!!

21!

Changing focal length versus changing the view point!

• Moving back while changing focal length lets you keep
• bjects 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!

22!

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Focal length on portraits!

• Standard portrait lens (85 mm)!

23!

Wide Angle! Normal! Telephoto!

Summary!

• Pinhole cameras compute correct linear

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)!

24!

Changing focal length versus changing the view point!

• Changing the focal length let us move back from the

subject, while maintaining the size of the image!

• But moving back changes perspective relationships!

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Changing the sensor size!

• If the sensor is

smaller, the field of view is smaller too!

• Smaller sensors

either have fewer pixels, or noisier pixels (closer to together)!

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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!

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