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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)

    '::)

    ':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

    '::)

    ')%7

    ':3)< Brief Gistory of Images

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    '::)

    ')6(

    ':3)< Brief Gistory of Images

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    4ilicon Image Ketector1 'J7(

    '::)

    ')%7

    ':3)

    'J7(

    A Brief History of Images

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    '::)

    ')%7

    ':3)

    'J7(

    'JJ:

    A Brief History of Images

    Kigital +ameras

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    '::)

    ')%7

    ':3)

    'J7(

    'JJ:

    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&ample; 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