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Basic Principles of Imaging and Lenses
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Light
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LightLightPhotonsPhotons
ElectromagneticElectromagneticRadiationRadiation
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These three are the same
Light
* pure energy
Electromagnetic Waves* energy-carrying aves emitted !y vi!rating electrons
Photons* particles of light
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E" #adiation Travels as a Wave
c $ % & '()ms
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E" #adiation +arries Energy
,uantum mechanics tells us that for photons E $ hf
here E is energy and h is Planc.s constant/
But f $ c
Putting these e0uations together1 e see that
E $ hc
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Electromagnetic Wave 2elocityElectromagnetic Wave 2elocity
The speed of light is the same for all seven forms of light/
It is %((1(((1((( meters per second or ')31((( miles per second/
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The Electromagnetic 4pectrumThe Electromagnetic 4pectrum
Radio Waves - communication
Microwaves - used to cook
Infrared - heat waves Visible Light - detected by your eyes
ltraviolet - causes sunburns
!-rays - "enetrates tissue
#amma Rays - most energetic
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The "ulti-Wavelength 4un
X-Ray UV Visible
Infrared #adioComposite
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E" 4pectrum #elative 4i5es
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The 2isi!le 4pectrumThe 2isi!le 4pectrum
Light aves e&tend in avelength from a!out 6(( to 7(( nanometers/
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Camera Obscura1 8emma 9risius1 '::)
':66A Brief History of Images
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http;/acmi/net/au
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Lens Based +amera >!scura1 ':3)
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':3)< Brief Gistory of Images
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http;!right!ytes/comcositecollectionH/html @ac and Beverly Wilgus
etty at "argate England1
')J)/
Slide credit: David Jacobs
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Still Life1 Louis a0ues "ande Kaguerre1 ')%7
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':3)< Brief Gistory of Images
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'::)
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':3)< Brief Gistory of Images
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4ilicon Image Ketector1 'J7(
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A Brief History of Images
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'::)
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A Brief History of Images
Kigital +ameras
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A Brief History of Images
Gassel!lad GKH-%J
H((3
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8eometric >ptics and Image 9ormation
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Pinhole +ameras
Pinhole camera - !o& ith a small hole in it Image is upside don1 !ut not mirrored left-to-right
QuestionWhy does a mirror reverse left-to-right !ut not top-to-!ottom
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Pinhole and the Perspective ProDection
(x,y)
screen scene
Is an image !eing formed
on the screen
ME4N But1 not a Oclear one/
image plane
effective focal length,fopticala&is
y
x
z
pinhole
),,( zyx=r
z
y
f
y
z
x
f
x==
'
'
'
'
zf
rr
=
'
'
)',','(' fyx=r
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Pro!lems ith Pinholes
Pinhole si5e @aperture must !e Overy small to o!tain a clear image/
Goever1 as pinhole si5e is made smaller1 less light is received !y image plane/
If pinhole is compara!le to avelength of incoming light1 KI99#A
effects !lur the imageN
4harpest image is o!tained hen;
pinhole diameter
E&le; If f = 50mm,
= 600nm@red1
d = 0.36mm
'2 fd =
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The #eason for Lenses
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Image 9ormation using @Thin Lenses
Lenses are used to avoid pro!lems ith pinholes/
Ideal Lens; 4ame proDection as pinhole !ut gathers more lightN
i o
foi
111=+8aussian Lens 9ormula;
f is the focal length of the lens Q determines the lens.s a!ility to !end @refract light
fdifferent from the effective focal length fdiscussed !eforeN
P
P
f
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9ocus and Kefocus
foi
111=+
!epth of "ield#ange of o!Dect distances over hich image is sufficiently ell focused1
i/e/1 range for hich blur circle is less than the resolution of the imaging sensor/
d
aperture
diameter
aperture
foi
1
'
1
'
1=+8aussian La;
Blur +ircle1b
)'()()'(
)'( oofo
f
fo
fii
=
Blur +ircle Kiameter ; )'('
iii
db =
i
'i
o
'o
P !l i h L
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Pro!lems ith Lenses
+ompound @Thic Lens 2ignetting
+hromatic
thicness
principal planes
nodal points
1L2L3L B
ptic nerve; ' million fle&i!lefi!ers
Slide credit: David Jacobs
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The Eye
The human eye is a cameraNQ Iris- colored annulus ith radial muscles
Q Pupil- the hole @aperture hose si5e is controlled !y the iris
Q What.s the Ofilm
photoreceptor cells @rods and cones in the retina
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Guman Eye vs/ the +amera
We mae cameras that act Osimilar to the human eye
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Image 9ormation
Kigital +amera
The Eye
9ilm
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Insect Eye
We mae cameras that act Osimilar to the human eye
9ly
"os0uito
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The #etina
Cross-section of eye
Ganglion cell layer
Bipolar cell layer
Receptor layer
Pigmentedepithelium
Ganglion axons
Cross section of retina
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#etina up-close
Light
T flh
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Stephen E. Palmer, 2002
Cones
cone-shapedless sensitiveoperate in high lightcolor vision
Two types of light-sensitive receptors
cone
rod
Rodsrod-shapedhighly sensitiveoperate at nightgray-scale vision
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#od +one sensitivity
The famous soc-matching pro!lem
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Guman Eye
#ods
Q Intensity only
Q Essentially night vision and peripheral vision only
Q 4ince e are trying to fool the center of field of vie of human
eye @under ell lit conditions e ignore rods
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Guman Eye
+ones
Q Three types perceive different portions of the visi!le light
spectrum
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Guman Eye
Because there are only % types of cones in human eyes1
e only need % stimulus values to fool the human eye
Q Aote; +hicens have 6 types of cones
Ditibti fRd dC
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Stephen E. Palmer, 2002
Distribution of Rods and Cones.
0
150,000
100,000
50,000
0 2040608020406080
Visual Angle (degrees from fovea)
Rods
Cones Cones
Rods
Fovea
Blind
Spot
#
R
eceptors/m
m
Aight 4y; hy are there more stars off-center
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Th Ph i fLiht
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The Physics of Light
.
#
Photons
D. Normal Daylight
Wavelength (nm.)
B. Gallium Phosphide Crystal
400 500 600 700
#
Photons
Wavelength (nm.)
A. Ruby Laser
400 500 600 700
400 500 600 700
#
Photons
C. Tungsten Lightbulb
400 500 600 700
#
Photons
Some examples of the spectra of light sources
Stephen E. Palmer, 2002
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"ore 4pectra
metamers
ThePhysicsofLight
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The Physics of Light
Some examples of the reflectance spectra of surfaces
Wavelength (nm)
%PhotonsReflecte
d
Red
400 700
Yellow
400 700
Blue
400 700
Purple
400 700
Stephen E. Palmer, 2002
ThePsychophysicalCorrespondence
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The Psychophysical Correspondence
There is no simple functional description for the perceivedcolor of all lights under all viewing conditions, but ...
A helpful constraint:
Consider only physical spectra with normal distributions
area
Wavelength (nm.)
# Photons
400 700500 600
mean
variance
Stephen E. Palmer, 2002
ThePsychophysicalCorrespondence
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The Psychophysical Correspondence
Mean Hue
yellowgreenblue
#
Photons
Wavelength
Stephen E. Palmer, 2002
ThePsychophysicalCorrespondence
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The Psychophysical Correspondence
Variance Saturation
Wavelength
high
medium
low
hi.
med.
low#
Photons
Stephen E. Palmer, 2002
ThePsychophysicalCorrespondence
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The Psychophysical Correspondence
Area Brightness
#
Photons
Wavelength
B. Area Lightness
bright
dark
Stephen E. Palmer, 2002
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Kigital camera
< digital camera replaces retina ith a sensor arrayQ Each cell in the array is light-sensitive diode that converts photons to electrons
Q To common types
+harge +oupled Kevice @++K +">4
Q http;electronics/hostuffors/comdigital-camera/htm
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++K +ameras
http;hui5en/dds/nl!eonersmaanimagingcameraccd'/gif
Slide credit: David Jacobs
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4ensor
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4ampling and ,uanti5ation
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Interlace vs/ progressive scan
http;/a&is/comproductsvideocameraprogressive=scan/htm
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Progressive scan
http;/a&is/comproductsvideocameraprogressive=scan/htm
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Interlace
http;/a&is/comproductsvideocameraprogressive=scan/htm
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+olor 4ensing in +amera @#8B
%-chip vs/ '-chip; 0uality vs/ cost
Why more green
http;/cooldihttp;/cooldictionary/comordsBayer-filter/iipediationary/comordsBayer-filter/iipedia
Why % colors
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Practical +olor 4ensing; Bayer 8rid
Estimate #8B
at R8. cels from
neigh!oring
values
http://www.cooldictionary.com/
words/Bayer-filter.wikipedia
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Image 9ormation
f(,!" = reflectance(,!" # illumination(,!"$eflectance in %0,&', illumination in %0,inf'
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White Balance
White World 8ray World assumptions
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Pro!lem; Kynamic #ange
1500
1
25,000
400,000
2,000,000,000
The real orld has
Gigh dynamic range
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pixel (312,284) = 42
Image
42 photos?
Is +amera a photometer
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Long E&posure
10-6 106
10-6 106
Real world
Pic!re
0 o 255
"ig# d$%amic ra%ge
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4hort E&posure
10-6 106
10-6 106
Real world
Pic!re
0 o 255
"ig# d$%amic ra%ge
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scenescene
radianceradiance
@Wsrm @Wsrm
sensorsensor
irradianceirradiancesensorsensor
e&posuree&posure
&e%&e% #!er#!er
HH
tt
analog
voltages
digital
values
pi&el
values
* +* Remappi%g
Image T a photometerN
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2arying E&posure
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What does the eye sees
The eye has a huge dynamic range