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pattern intensity

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									        Lecture outline - 9/12
• The information in light
• The computational problem of transduction
  – What problems does the grand eye designer
    have to solve?
• Evolution of biological eyes
• The human eye
• Focus
The information in light
     The physical nature of light
• Light behaves like a wave traveling through some
  medium.



• Light is composed of discrete photons
        The wave nature of light
• Light has wavelength
   – 390 - 440 nm (violet)
   – 440 - 500 nm (red)
   – 500 - 570 nm (green)
   – 570 - 590 nm (yellow)
   – 590 - 610 nm (orange)
   – 610 - 700 nm (red)
• Light is composed of photons with different wavelengths
   – Wavelength spectrum = proportion of photons at each
     wavelength
       How light travels through the
               environment
• Scattering
   – Sky appears blue because low wavelength light is scattered more
     by molecules in the atmosphere.
• Refraction
   – Sunsets are red because higher wavelengths of light are “bent”
     more when entering the atmosphere.
• Reflection / absorption
   – Moon is white because it reflects a broad spectrum of wavelengths
   – Deep water appears blue because water absorbs high wavelength
     light
           The Optic Array: pattern of light intensity arriving
at a point as a function of direction (q, W), time (t) and wavelength(l)
                              I = f(q, W, t, l)
Sensory transduction
        Sensory transduction
• Transduction - converting the information
  encoded in one form of energy to
  information encoded in another form of
  energy.
         Sensory transduction
• Transduction - converting the information
  encoded in one form of energy to
  information encoded in another form of
  energy.
• Sensory transduction
  – Converting a pattern of light energy to a
    pattern of neural responses.
           Sensory transduction
• Transduction - converting the information
  encoded in one form of energy to information
  encoded in another form of energy.
• Sensory transduction
   – Converting a pattern of light energy to a pattern of
     neural responses.
• Visual transducers
   – Capture light in an array of light receptors.
          Goals of eye design
• Form high spatial resolution image
  – Accurately represent light intensities coming
    from different directions.
     • E.g. minimize blur in a camera
• Maximize sensitivity
  – Trigger neural responses at very low light
    levels.
  – Particle nature of light places fundamental limit
    on sensitivity.
Biological eye design
Simple Eye Cup
(the planarium)
           Design Problem
• What is a problem with the simple eye cup
  as an imaging device?
• What simple changes could you make in the
  eye cup to make it a better imaging device?
Two ways to improve resolution
     of simple eye cup
Pin-hole camera
     Pin-hole camera




Advantage: High resolution image
      Pin-hole camera




Advantage: High resolution image

Disadvantage: Low sensitivity
Why low sensitivity?
             point 1     point 2




 Luminance
             point 1            point 2




                        Position on retina




Luminance




                       Position on retina
ommotidium
Mammalian solution - the simple eye
               Question
• What is one advantage of a compound eye
  over a simple eye?
Focus - the lens equation
                              1   1    1
            lens power =            
                              f   d o di
                                  1
   lens power (diopt ers) =
                              f (meters)
     Accommodation - bringing
         objects into focus
Focused on




        Focused on
                   Some numbers
• Refractive power of cornea
   – 43 diopters
• Refractive power of lens
   – 17 - 25 diopters
• Other eyes
   – Diving ducks - 80 diopter accommodation range
   – Anableps - two pairs of eyes with different focusing
     power
       Accommodation errors
         (focus problems)
• Myopia
  – Near-sightedness
• Emmetropia
  – Far-sightedness
        Accomodation errors
         (focus problems)
• Myopia
  – Near-sightedness
• Emmetropia
  – Far-sightedness
• Presbyopia
  – Hardening of lense with age (cannot
    accommodate to near objects)
        Depth of Field (DOF)
• DOF = range of depths at which objects are
  “reasonably” in focus
  – E.g., at which blur is less than some threshold
    limit.
• How can one increase one’s depth of field?
Transduction in the retina
 Sensitivity / resolution trade-off
• Increase sensitivity => decrease resolution
• Increase resolution => decrease sensitivity
 Sensitivity / resolution trade-off
• Increase sensitivity => decrease resolution
• Increase resolution => decrease sensitivity
• One example - changing pupil size

                       Increased spatial resolution
      Shrink pupil
                       Decreased sensitivity
          Other examples
• Wavelength
• Time
• Wavelength
           Duplicity Theory:
          Two receptor systems
• Cones
  – Encode wavelength information
  – High resolution image coding in fovea
  – Low sensitivity
• Rods
  – High sensitivity
  – Concentrated in periphery
  – Lower resolution coding in periphery
    Part 2 of solution to sensitivity /
           resolution trade-off
  • Foveal coding
     – One-to-one connections from cone receptors to bipolar cells and
        from bipolar cells to ganglion cells
  • Peripheral coding (neural pooling)
     – Many-to-one connections from receptors to bipolar cells


                         Fovea             Periphery
  Receptors

Bipolar cells
 General solution to sensitivity /
      resolution trade-off
• Place high resolution / low sensitivity
  system in fovea
• Place high sensitivity / low resolution
  system in periphery
• Use eye movements to obtain high
  resolution images of peripheral objects
           Problem:
High resolution coding of intensity
           information
                       Example
• Computer monitors typically use 8 bits to encode
  the intensity of each pixel.
   – 256 distinct light levels
• Old monitors only provided 4 bits per pixel.
   – 16 distinct light levels
• Number of light levels encoded = intensity
  resolution of the system.
• Human visual system can only distinguish ~ 200 -
  250 light levels.
        Code wide range of light intensities

• Range of light intensities receptors can encode

                  106 107 candelas / m2
• Dynamic range of receptors and of ganglion cells limits # of
  distinguishable light levels.
• Problem
    – How does system represent large range of intensities while
      maintaining high intensity resolution?
Some typical intensity values

                           candelas / m2
white paper in sunlight      - 10 4
Video screen                - 10 1  102
white paper in moonlight     - 10 2
white paper in starlight     - 10 4
Limited dynamic range of
      receptor cell
                          Solution
• Dynamic range of receptors (cones)
   – 10 - 1000 photons absorbed per 10 msec.
• Range of intensities in a typical scene
   – 10-6 - 10-4 cd / m2 in starlight
   – 102 - 104 cd / m2 in sunlight
   – 100:1 range of light intensities
• Only need to code 100:1 range of intensities within a scene
• Solution - Adaptation adjusts dynamic range of receptors to match
  range of intensities in a scene.
        # photons hitting       % photons    # photons
            receptor            absorbed     absorbed

Scene       10 - 1,000            100%       10 - 1,000
  1
        Increase Illumination   Adaptation


Scene     1,000 - 100,000         10%        10 - 1,000
  2
      Starlight     Moonlight     Indoor lighting         Sunlight

10   -6
             10-4   10-2     10          102        104         106


                            Window of visibility
                           Adapt to the dark
                    (e.g. % photons absorbed = .1)

      Starlight         Moonlight      Indoor lighting         Sunlight

10   -6
             10-4        10-2     10        102          104         106


           Window of visibility
                       Adapt to the bright
             (e.g. % photons absorbed = .000000001)

      Starlight     Moonlight    Indoor lighting         Sunlight

10   -6
             10-4    10-2   10        102          104         106


                                               Window of visibility
                    Adaptation
• After absorbing a photon, retinal molecule separates from
  opsin molecule (bleaching).
• Enzymes from pigment epithelium help regenerate
  photopigment
• % photons absorbed depends on % of bleached
  photopigment.
• Equilibrium point between bleaching and photopigment
  regeneration determines adaptation state of receptor.

								
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