Basic Principles of Imaging and Lenses

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• Basic Principles of Imaging and Lenses

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• Light

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Electromagnetic Radiation
Light
Photons
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These three are the same

• Light
• pure energy
• Electromagnetic Waves
• energy-carrying waves emitted by vibrating
  electrons
• Photons
• particles of light

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EM Radiation Travels as a Wave
c 3 x 108 m/s
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EM Radiation Carries Energy
Quantum mechanics tells us that for photons E
hf where E is energy and h is Plancks
constant. But f c/l Putting these
equations together, we see that E hc/l
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Electromagnetic Wave Velocity

• The speed of light is the same for all seven
  forms of light.
• It is 300,000,000 meters per second or 186,000
  miles per second.

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The Electromagnetic Spectrum

• Radio Waves - communication
• Microwaves - used to cook
• Infrared - heat waves
• Visible Light - detected by your eyes
• Ultraviolet - causes sunburns
• X-rays - penetrates tissue
• Gamma Rays - most energetic

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The Multi-Wavelength Sun
UV
Visible
X-Ray
Composite
Radio
Infrared
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EM Spectrum Relative Sizes
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• The Visible Spectrum
• Light waves extend in wavelength from about 400
  to 700 nanometers.

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Transparent Materials

• Transparent - the term applied to materials
  through which light can pass in straight lines.

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Opaque Materials

• Opaque - the term applied to materials that
  absorb light.

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• Are clouds transparent or opaque to visible
  light?
• Answer opaque
• Are clouds transparent or opaque to ultraviolet
  light?
• Answer almost transparent

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Special Things About a Light Wave
It does not need a medium through which to
travel It travels with its highest velocity in
a vacuum Its highest velocity is the speed of
light, c, equal to 300,000 km/sec The
frequency (or wavelength) of the wave
determines whether we call it radio, infrared,
visible, ultraviolet, X-ray or gamma-ray.
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A Brief History of Images
1544
Camera Obscura, Gemma Frisius, 1558
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Camera Obscura
"When images of illuminated objects ... penetrate
through a small hole into a very dark room ...
you will see on the opposite wall these objects
in their proper form and color, reduced in size
... in a reversed position, owing to the
intersection of the rays". Da Vinci
Slide credit David Jacobs
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Abu Ali Al-hasen Ibn Alhasen, mathematician, born
in Basra, d. 1038 Cairo, claimed he could control
the inundations of the Nile, for which caliph
Hakim ordered him to Cairo in 1015 or 1017.
Realizing his abilities as civil engineer were
less than his skill as a mathematician, he
feigned insanity to save his head. Until Hakim
died in 1021, Alhazen spent his time at the
library of Alexandria, writing on geometry,
optics, perspective and the camera obscura.
Translated into Latin in 1270 and printed as
Opticae Thesaurus Alhazani in 1572. MSS at Paris,
Oxford, Leyden. An additional MS at the Vatican
Library is annotated by Lorenzo Ghiberti of the
Florence Baptistry doors (1378 - 1455). Earlier
MSS may have existed, for Roger Bacon writes
about optics and the camera obscura before
1266. Alhazen is the first to show how an image
is formed on the eye, using the camera obscura as
an analog. Alhazen states (in the Latin
translation), and with respect to the camera
obscura, "Et nos non inventimus ita", we did not
invent this.
Source http//www.acmi.net.au/AIC/CAMERA_OBSCURA.
html
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A Brief History of Images
1558
1568
Lens Based Camera Obscura, 1568
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Jetty at Margate England, 1898.
http//brightbytes.com/cosite/collection2.html
(Jack and Beverly Wilgus)
Slide credit David Jacobs
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A Brief History of Images
1558
1568
1837
Still Life, Louis Jaques Mande Daguerre, 1837
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A Brief History of Images
1558
1568
1840?
Abraham Lincoln?
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A Brief History of Images
1558
1568
1837
Silicon Image Detector, 1970
1970
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A Brief History of Images
1558
1568
1837
1970
Digital Cameras
1995
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A Brief History of Images
1558
1568
1837
1970
Hasselblad HD2-39
1995
2006
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Pinhole Cameras

• Pinhole camera - box with a small hole in it
• Image is upside down, but not mirrored
  left-to-right
• Question Why does a mirror reverse left-to-right
  but not top-to-bottom?

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Pinhole and the Perspective Projection
Is an image being formed on the screen? YES!
But, not a clear one.
(x,y)
screen
scene
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Magnification
B
y
d
f
A
optical axis
z
Pinhole
A
x
d
planar scene
image plane
B
From perspective projection
Magnification
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Properties of Projection

• Points project to points
• Lines project to lines
• Planes project to the whole or half image
• Angles are not preserved
• Degenerate cases
• Line through focal point projects to a point.
• Plane through focal point projects to line

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Distant Objects are Smaller
Size is inversely proportional to distance.
Note that B and C labels should be switched.
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Parallel Lines Meet
Common to draw film plane in front of the focal
point. Moving the film plane merely scales the
image.
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Vanishing Points

• Each set of parallel lines meets at a different
  point
• The vanishing point for this direction
• Sets of parallel lines on the same plane lead to
  collinear vanishing points.
• The line is called the horizon for that plane

• Good ways to spot faked images
• scale and perspective dont work
• vanishing points behave badly
• supermarket tabloids are a great source.

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Problems with Pinholes

• Pinhole size (aperture) must be very small
  to obtain a clear image.
• However, as pinhole size is made smaller,
  less light is received by image plane.
• If pinhole is comparable to wavelength of
  incoming light, DIFFRACTION
• effects blur the image!
• Sharpest image is obtained when
• pinhole diameter
• Example If f 50mm,
• 600nm (red),
• d
  0.36mm

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The Reason for Lenses
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Image Formation using (Thin) Lenses

• Lenses are used to avoid problems with
  pinholes.
• Ideal Lens Same projection as pinhole but
  gathers more light!

o
i
P
P
f
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Focus and Defocus
aperture
aperture diameter
Blur Circle, b
d
Gaussian Law
Blur Circle Diameter
Depth of Field Range of object distances over
which image is sufficiently well focused, i.e.,
range for which blur circle is less than the
resolution of the imaging sensor.
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Problems with Lenses
Vignetting
Compound (Thick) Lens
B
principal planes
A
nodal points
thickness
more light from A than B !
Chromatic Abberation
Radial and Tangential Distortion
ideal
actual
ideal
actual
image plane
Lens has different refractive indices for
different wavelengths.
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Spherical Aberration
Spherical lenses are the only easy shape to
manufacture, but are not correct for perfect
focus.
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Two Lens System
object
final image
image plane
intermediate virtual image
lens 2
lens 1

• Rule Image formed by first lens is the object
  for the second lens.
• Main Rays Ray passing through focus emerges
  parallel to optical axis.
• Ray through optical center passes
  un-deviated.

• Magnification

Exercises What is the combined focal length of
the system? What is the combined focal
length if d 0?
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Lens systems

• A good camera lens may contain 15 elements and
  cost a many thousand dollars
• The best modern lenses may contain aspherical
  elements

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Insect Eye

• We make cameras that act similar to the human
  eye

Fly
Mosquito
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Human Eye

• The eye has an iris like a camera
• Focusing is done by changing shape of lens
• Retina contains cones (mostly used) and rods (for
  low light)
• The fovea is small region of high resolution
  containing mostly cones
• Optic nerve 1 million flexible fibers

http//www.cas.vanderbilt.edu/bsci111b/eye/human-e
ye.jpg
Slide credit David Jacobs
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Human Eye

• Rods
• Intensity only
• Essentially night vision and peripheral vision
  only
• Since we are trying to fool the center of field
  of view of human eye (under well lit conditions)
  we ignore rods

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Human Eye

• Cones
• Three types perceive different portions of the
  visible light spectrum

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Human Eye

• Because there are only 3 types of cones in human
  eyes, we only need 3 stimulus values to fool the
  human eye
• Note Chickens have 4 types of cones

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Human Eye vs. the Camera

• We make cameras that act similar to the human
  eye

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CCD Cameras
http//huizen.ddsw.nl/bewoners/maan/imaging/camera
/ccd1.gif
Slide credit David Jacobs