Image Formation:Image Formation:Optics and ImagersOptics and Imagers

Real worldReal world OpticsOptics SensorSensor

Acknowledgment:Acknowledgment: some figures by B. Curless, E. Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwissen some figures by B. Curless, E. Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwissen

OpticsOptics

• Pinhole cameraPinhole camera

• LensesLenses

• Focus, aperture, distortionFocus, aperture, distortion

PinholePinholeObjectObject

Pinhole cameraPinhole camera

Pinhole CameraPinhole Camera

• ““Camera obscura” – known since Camera obscura” – known since antiquityantiquity

ImageImage

Image planeImage plane

Pinhole CameraPinhole Camera

• ““Camera obscura” – known since Camera obscura” – known since antiquityantiquity

• First recording in 1826 onto a pewterFirst recording in 1826 onto a pewterplate (by Joseph Nicéphore Niepce)plate (by Joseph Nicéphore Niepce)

PinholePinholeObjectObject

ImageImage

Pinhole cameraPinhole camera

Image planeImage plane

Pinhole Camera LimitationsPinhole Camera Limitations

• Aperture too big: blurry imageAperture too big: blurry image

• Aperture too small: requires long Aperture too small: requires long exposure or high intensityexposure or high intensity

• Aperture much too small: diffraction Aperture much too small: diffraction through pinhole through pinhole blurry image blurry image

LensesLenses

• Focus a bundle of rays from a scene Focus a bundle of rays from a scene point onto a single point on the point onto a single point on the imagerimager

• Result: can make aperture biggerResult: can make aperture bigger

Ideal LensesIdeal Lenses

• Thin-lens approximationThin-lens approximation

• Gaussian lens law:Gaussian lens law:

• Real lenses and systems of lenses Real lenses and systems of lenses may be approximated by thin lenses if may be approximated by thin lenses if only only paraxialparaxial rays (near the optical rays (near the optical axis) are consideredaxis) are considered

1/1/ddoo + 1/ + 1/ddii = 1/ = 1/ff

Camera AdjustmentsCamera Adjustments

• Focus?Focus?– Changes Changes ddii

• Zoom?Zoom?– Changes Changes ff

• Iris?Iris?– Changes apertureChanges aperture

Focus and Depth of FieldFocus and Depth of Field

• For a given For a given ddii, “perfect” focus at only , “perfect” focus at only

one one ddoo

• In practice, focus is OK for someIn practice, focus is OK for somerange of depthsrange of depths– Circle of confusionCircle of confusion smaller than a pixel smaller than a pixel

• Better depth of field with smaller Better depth of field with smaller aperturesapertures– Better approximation to pinhole cameraBetter approximation to pinhole camera

Field of ViewField of View

• Q: What does field of view of camera Q: What does field of view of camera depend on?depend on?– Focal length of lensFocal length of lens– Size of imagerSize of imager– Object distance?Object distance?

Computing Field of ViewComputing Field of View

xxoo

ddii

xxii

ddoo

1/1/ddoo + 1/ + 1/ddii = 1/ = 1/ff

xxo o / / ddoo = = xxi i / / ddii

= 2 tan= 2 tan-1-1 ½ ½ xxi i

(1/(1/ff1/1/ddoo))Since typically Since typically ddoo >> >> f,f,

2 tan2 tan-1-1 ½ ½ xxi i / / ff

tan tan /2 = ½ /2 = ½ xxo o // ddoo

xxi i / / ff

ApertureAperture

• Controls amount of lightControls amount of light

• Affects depth of fieldAffects depth of field

• Affects distortion (since thin-lens Affects distortion (since thin-lens approximation is better near center approximation is better near center of lens)of lens)

ApertureAperture

• Aperture typically given as “Aperture typically given as “ff--number”number”(also “(also “ff-stops” or just “stops”)-stops” or just “stops”)

• What is What is ff /4?/4?– Aperture is ¼ the focal lengthAperture is ¼ the focal length

Monochromatic AberrationsMonochromatic Aberrations

• Real lenses do not follow thin lens Real lenses do not follow thin lens approximation because surfaces are approximation because surfaces are spherical (manufacturing constraints)spherical (manufacturing constraints)

• Result: thin-lens approximation only Result: thin-lens approximation only valid iff sin valid iff sin

DistortionDistortion

• Pincushion or barrel Pincushion or barrel radial distortionradial distortion

• Varies with placement of apertureVaries with placement of aperture

• Varies with placement of apertureVaries with placement of aperture

DistortionDistortion

• Varies with placement of apertureVaries with placement of aperture

DistortionDistortion

• Varies with placement of apertureVaries with placement of aperture

DistortionDistortion

First-Order Radial DistortionFirst-Order Radial Distortion

• Goal: mathematical formula for Goal: mathematical formula for distortiondistortion

• If distortion is small, can be If distortion is small, can be approximated by “first-order” formula:approximated by “first-order” formula:

• Why (1 + Why (1 + rr22) and not (1 + ) and not (1 + rr)?)?

rr’ = ’ = rr (1 + (1 + rr22))rr = = ideal distance to center of imageideal distance to center of imagerr’ = ’ = distorted distance to center of imagedistorted distance to center of image

Chromatic AberrationChromatic Aberration

• Due to dispersion in glass (focal Due to dispersion in glass (focal length varies with the wavelength of length varies with the wavelength of light)light)

• Result: color fringes near edges of Result: color fringes near edges of imageimage

• Correct by building lens systems with Correct by building lens systems with multiple kinds of glassmultiple kinds of glass

Correcting for AberrationsCorrecting for Aberrations

• High-qualityHigh-qualitycompound lensescompound lensesuse multipleuse multiplelens elements tolens elements to“cancel out”“cancel out”distortion anddistortion andaberrationaberration

• Often 5-10 elements, more for extreme wide Often 5-10 elements, more for extreme wide angleangle

SensorsSensors

• FilmFilm

• VidiconVidicon

• CCDCCD

• CMOSCMOS

VidiconVidicon

• Best-known in family of Best-known in family of “photoconductive video cameras” “photoconductive video cameras”

• Basically television in reverseBasically television in reverse

Electron Gun

Photoconductive Plate

Lens System

+ + + +

Scanning Electron Beam

MOS CapacitorsMOS Capacitors

• MOS = Metal Oxide SemiconductorMOS = Metal Oxide Semiconductor

Gate (wire)Gate (wire)

SiOSiO22 (insulator) (insulator)

pp-type silicon-type silicon

MOS CapacitorsMOS Capacitors

• Voltage applied to gate repels Voltage applied to gate repels positive “holes” in the semiconductorpositive “holes” in the semiconductor

+10V+10V

Depletion regionDepletion region(electron “bucket”)(electron “bucket”)

+ + + + + ++ + + + + ++ + + + + ++ + + + + +

MOS CapacitorsMOS Capacitors

• Photon striking the material createsPhoton striking the material createselectron-hole pairelectron-hole pair

+10V+10V

+ + + + + ++ + + + + +

PhotonPhoton

++

Charge TransferCharge Transfer

• Can move charge from one bucket to Can move charge from one bucket to another by manipulating voltagesanother by manipulating voltages

CCD ArchitecturesCCD Architectures

• Linear arraysLinear arrays

• 2D arrays2D arrays

Linear CCDLinear CCD

• Accumulate photons, then clock them Accumulate photons, then clock them outout

• To prevent smear: first move charge To prevent smear: first move charge to opaque region, then clock it outto opaque region, then clock it out

Full-Frame CCDFull-Frame CCD

• Other arrangements to minimize smearOther arrangements to minimize smear

CMOS ImagersCMOS Imagers

• Recently, can manufacture chips that Recently, can manufacture chips that combine photosensitive elements combine photosensitive elements and processing elementsand processing elements

• Benefits:Benefits:– Partial readoutPartial readout– Signal processingSignal processing– Eliminate some supporting chips Eliminate some supporting chips low low

costcost

ColorColor

• 3-chip vs. 1-chip: quality vs. cost3-chip vs. 1-chip: quality vs. cost

VideoVideo

• Depending on the scene, pictures updatedDepending on the scene, pictures updatedat 15–70 Hz. perceived as “continuous”at 15–70 Hz. perceived as “continuous”

• Most video cameras use a shutter, so they Most video cameras use a shutter, so they are capturing for only part of a frameare capturing for only part of a frame– Short shutter: less light, have to open apertureShort shutter: less light, have to open aperture– Long shutter: more light, but motion blurLong shutter: more light, but motion blur

• Television uses Television uses interlacedinterlaced video video

InterlacingInterlacing

These rowsThese rowstransmittedtransmitted

firstfirstThese rowsThese rowstransmittedtransmitted

1/60 sec later1/60 sec later

TelevisionTelevision

• US: NTSC standardUS: NTSC standard– Fields are 1/60 sec.Fields are 1/60 sec.– 2 fields = 1 frame 2 fields = 1 frame frames are 1/30 frames are 1/30

sec.sec.– Each frame has 525 scanlines, of which Each frame has 525 scanlines, of which

approximately 480 are visibleapproximately 480 are visible– No discrete pixels along scanlines, but No discrete pixels along scanlines, but

if pixels were square, there would be if pixels were square, there would be about 640 visibleabout 640 visible

TelevisionTelevision

• NTSC standardNTSC standard– Thus, an NTSC frame is about 640Thus, an NTSC frame is about 640480480– Color at lower resolution than intensityColor at lower resolution than intensity

• PAL standardPAL standard– Lower rate: fields at 50 Hz. (frames at Lower rate: fields at 50 Hz. (frames at

25 Hz.)25 Hz.)– Higher resolution: about 768Higher resolution: about 768576576