Image Formation: Optics and Imagers Real world Optics

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Image Formation:
Optics and Imagers
Real world
Optics
Sensor
Acknowledgment: some figures by B. Curless, E. Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwisse
Optics
• Pinhole camera
• Lenses
• Focus, aperture, distortion
Pinhole Camera
• “Camera obscura” – known since antiquity
Image plane
Image
Pinhole
Object
Pinhole camera
Pinhole Camera
• “Camera obscura” – known since antiquity
Image plane
Image
Pinhole
Object
Pinhole camera
• First recording in 1826 onto a pewter
plate (by Joseph Nicéphore Niepce)
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
Lenses
• Focus a bundle of rays from a scene point
onto a single point on the imager
• Result: can make aperture bigger
Ideal Lenses
• Thin-lens approximation
• Gaussian lens law:
1/do + 1/di = 1/f
• Real lenses and systems of lenses may be
approximated by thin lenses if only
paraxial rays (near the optical axis) are
considered
Camera Adjustments
• Focus?
– Changes di
• Zoom?
– Changes f
• Iris?
– Changes aperture
Focus and Depth of Field
• For a given di, “perfect” focus at only one
do
• In practice, focus is 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
Field of View
• Q: What does field of view of camera
depend on?
– Focal length of lens
– Size of imager
– Object distance?
Computing Field of View
1/do + 1/di = 1/f
tan  /2 = ½ xo / do
xo

xi
xo / do = xi / di
 = 2 tan-1 ½ xi (1/f1/do)
do
di
Since typically do >> f,
  2 tan-1 ½ xi / f
  xi / f
Aperture
• Controls amount of light
• Affects depth of field
• Affects distortion (since thin-lens
approximation is better near center of lens)
Aperture
• Aperture typically given as “f-number”
(also “f-stops” or just “stops”)
• What is f /4?
– Aperture is ¼ the focal length
Monochromatic Aberrations
• Real lenses do not follow thin lens
approximation because surfaces are
spherical (manufacturing constraints)
• Result: thin-lens approximation only valid
iff sin   
Distortion
• Pincushion or barrel radial distortion
• Varies with placement of aperture
Distortion
• Varies with placement of aperture
Distortion
• Varies with placement of aperture
Distortion
• Varies with placement of aperture
First-Order Radial Distortion
• Goal: mathematical formula for distortion
• If distortion is small, can be approximated
by “first-order” formula:
r’ = r (1 +  r2)
r = ideal distance to center of image
r’ = distorted distance to center of image
• Why (1 +  r2) and not (1 +  r)?
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
Correcting for Aberrations
• High-quality
compound lenses
use multiple
lens elements to
“cancel out”
distortion and
aberration
• Often 5-10 elements, more for extreme wide
angle
Sensors
• Film
• Vidicon
• CCD
• CMOS
Vidicon
• Best-known in family of “photoconductive
video cameras”
• Basically television in reverse

++++
Scanning Electron Beam
Electron Gun
Lens System
Photoconductive Plate
MOS Capacitors
• MOS = Metal Oxide Semiconductor
Gate (wire)
SiO2 (insulator)
p-type silicon
MOS Capacitors
• Voltage applied to gate repels positive
“holes” in the semiconductor
+10V
++++++
Depletion region
(electron “bucket”)
MOS Capacitors
• Photon striking the material creates
electron-hole pair
+10V
Photon
++++++


+





Charge Transfer
• Can move charge from one bucket to
another by manipulating voltages
CCD Architectures
• Linear arrays
• 2D arrays
Linear CCD
• Accumulate photons, then clock them out
• To prevent smear: first move charge to
opaque region, then clock it out
Full-Frame CCD
• Other arrangements to minimize smear
CMOS Imagers
• Recently, can manufacture chips that
combine photosensitive elements and
processing elements
• Benefits:
– Partial readout
– Signal processing
– Eliminate some supporting chips  low cost
Color
• 3-chip vs. 1-chip: quality vs. cost
Video
• Depending on the scene, pictures updated
at 15–70 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
Interlacing
These rows
transmitted
first
These rows
transmitted
1/60 sec later
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
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
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