Image Formation: Optics and Imagers

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Image FormationOptics and Imagers
Real world
Optics
Sensor
Acknowledgment some figures by B. Curless, E.
Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwissen
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Optics

• Pinhole camera
• Lenses
• Focus, aperture, distortion

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Pinhole Camera

• Camera obscura known since antiquity

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Pinhole Camera

• Camera obscura known since antiquity
• First recording in 1826 onto a pewterplate (by
  Joseph Nicéphore Niepce)

Pinhole camera
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Pinhole Camera Limitations

• Aperture too big blurry image
• Aperture too small requires long exposure or
  high intensity
• Aperture much too small diffraction through
  pinhole ? blurry image

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Lenses

• Focus a bundle of rays from a scene point onto a
  single point on the imager
• Result can make aperture bigger

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Ideal Lenses

• Thin-lens approximation
• Gaussian lens law
• Real lenses and systems of lenses may be
  approximated by thin lenses if only paraxial rays
  (near the optical axis) are considered

1/do 1/di 1/f
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Camera Adjustments

• Iris?
• Changes aperture
• Focus?
• Changes di
• Zoom?
• Changes f and sometimes di

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Zoom Lenses Varifocal
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Zoom Lenses Parfocal
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Focus and Depth of Field

• For a given di, perfect focus at only one do
• In practice, OK for some range of depths
• Circle of confusion smaller than a pixel
• Better depth of field with smaller apertures
• Better approximation to pinhole camera

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Field of View

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

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Computing Field of View
1/do 1/di 1/f
tan ? /2 ½ xo / do
xo / do xi / di
? 2 tan-1 ½ xi (1/f?1/do)
? ? xi / f
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Aperture

• Controls amount of light
• Affects depth of field
• Affects distortion (since thin-lens approximation
  is better near center of lens)

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Aperture

• Aperture typically given as f-number(also
  f-stops or just stops)
• What is f /4?
• Aperture is ¼ the focal length

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Monochromatic Aberrations

• Real lenses do not follow thin lens approximation
  because surfaces are spherical (manufacturing
  constraints)
• Result thin-lens approximation only valid
  iffsin ? ? ?

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Monochromatic Aberrations

• Consider the next term in the Taylor series, i.e.
  sin ? ? ? - ?3/3!
• Third-order theory deviations from the ideal
  thin-lens approximations
• Called primary or Seidel aberrations

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Spherical Aberration

• Results in blurring of image, focus shifts when
  aperture is stopped down
• Can vary with the way lenses are oriented

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Coma

• Results in changes in magnification with aperture

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Coma
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Distortion

• Pincushion or barrel radial distortion
• Varies with placement of aperture

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Distortion

• Varies with placement of aperture

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Distortion

• Varies with placement of aperture

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Distortion

• Varies with placement of aperture

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First-Order Radial Distortion

• Goal mathematical formula for distortion
• If distortion is small, can be approximated by
  first-order formula
• Higher-order models possible

r r (1 ? r2) r ideal distance to center
of image r distorted distance to center of
image
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Correcting for Aberrations

• Compound lensesuse multiplelens elements
  tocancel outaberrations
• Lenses of differentmaterials
• 5-15 elements, more for extreme wide angle

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Catadioptrics

• Catadioptric systems use bothlenses and mirrors
• Motivations
• Systems using parabolic mirrors can be designed
  to not introduce these aberrations
• Easier to make very wide-angle systems with
  mirrors

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Wide-Angle Catadioptric System
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Other Limitations of Lenses

• Flare light reflecting(often multiple
  times)from glass-air interface
• Results in ghost images or haziness
• Worse in multi-lens systems
• Ameliorated by optical coatings (thin-film
  interference)

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Other Limitations of Lenses

• Optical vignetting less power per unit area
  transferred for light at an oblique angle
• Transferred power falls off as cos4 ?
• Result darkening of edges of image
• Mechanical vignetting due to apertures

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Sensors

• Film
• Vidicon
• CCD
• CMOS

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Vidicon

• Best-known in family of photoconductivevideo
  cameras
• Basically television in reverse

? ? ? ?
Scanning Electron Beam
Electron Gun
Lens System
Photoconductive Plate
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Digression Gamma

• Vidicon tube naturally has signal that
  varieswith light intensity according to a power
  lawSignal Eg, g ? 1/2.5
• CRT (televisions) naturally obey a power law with
  gamma ? 2.5
• Result standard for video signals hasa gamma of
  1/2.5

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MOS Capacitors

• MOS Metal Oxide Semiconductor

Gate (wire)
SiO2 (insulator)
p-type silicon
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MOS Capacitors

• Voltage applied to gate repels positive holes
  in the semiconductor

10V

Depletion region (electron bucket)
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MOS Capacitors

• Photon striking the material createselectron-hole
  pair

10V
Photon

?
?
?
?
?
?
?

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Charge Transfer

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

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Charge Transfer

• Various schemes (e.g. three-phase-clocking) for
  transferring a series of charges along a row of
  buckets

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CCD Architectures

• Linear arrays
• 2D arrays
• Full frame
• Frame transfer (FT)
• Interline transfer (IT)
• Frame interline transfer (FIT)

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Linear CCD

• Accumulate photons, then clock them out
• To prevent smear first move charge to opaque
  region, then clock it out

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Full-Frame CCD

• Other arrangements to minimize smear

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Frame Transfer CCD
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Interline Transfer CCD
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Frame Interline Transfer CCD
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CMOS Imagers

• Recently, can manufacture chips that combine
  photosensitive elements and processing elements
• Benefits
• Partial readout
• Signal processing
• Eliminate some supporting chips ? low cost

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Color

• 3-chip vs. 1-chip quality vs. cost

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Chromatic Aberration

• Due to dispersion in glass (focal length varies
  with the wavelength of light)
• Result color fringes near edges of image
• Correct by building lens systems with multiple
  kinds of glass

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Correcting Chromatic Aberration

• Simple way of partially correcting for residual
  chromatic aberration after the fact scale R,G,B
  channels independently

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Video

• Depending on the scene, pictures updatedat 1570
  Hz. perceived as continuous
• Most video cameras use a shutter, so they are
  capturing for only part of a frame
• Short shutter less light, have to open aperture
• Long shutter more light, but motion blur
• Television uses interlaced video

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Interlacing
These rows transmitted first
These rows transmitted 1/60 sec later
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Television

• US NTSC standard
• Fields are 1/60 sec.
• 2 fields 1 frame ? frames are 1/30 sec.
• Each frame has 525 scanlines, of which
  approximately 480 are visible
• No discrete pixels along scanlines, but if pixels
  were square, there would be about 640 visible

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Television

• NTSC standard
• Thus, an NTSC frame is about 640?480
• Color at lower resolution than intensity
• PAL standard
• Lower rate fields at 50 Hz. (frames at 25 Hz.)
• Higher resolution about 768?576