VIEWS: 0 PAGES: 56 POSTED ON: 12/4/2012
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 106 107 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.
Pages to are hidden for
"pattern intensity"Please download to view full document