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Lecture outline - 9/12

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.

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Lecture outline - 9/12

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  1. 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

  2. The information in light

  3. The physical nature of light • Light behaves like a wave traveling through some medium. • Light is composed of discrete photons

  4. 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

  5. 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

  6. 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)

  7. Sensory transduction

  8. Sensory transduction • Transduction - converting the information encoded in one form of energy to information encoded in another form of energy.

  9. 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.

  10. 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.

  11. 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.

  12. Biological eye design

  13. Simple Eye Cup (the planarium)

  14. 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?

  15. Two ways to improve resolution of simple eye cup

  16. Pin-hole camera

  17. Pin-hole camera Advantage: High resolution image

  18. Pin-hole camera Advantage: High resolution image Disadvantage: Low sensitivity

  19. Why low sensitivity?

  20. ommotidium

  21. Mammalian solution - the simple eye

  22. Question • What is one advantage of a compound eye over a simple eye?

  23. Focus - the lens equation

  24. Accommodation - bringing objects into focus Focused on Focused on

  25. 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

  26. Accommodation errors(focus problems) • Myopia • Near-sightedness • Emmetropia • Far-sightedness

  27. Accomodation errors(focus problems) • Myopia • Near-sightedness • Emmetropia • Far-sightedness • Presbyopia • Hardening of lense with age (cannot accommodate to near objects)

  28. 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?

  29. Transduction in the retina

  30. Sensitivity / resolution trade-off • Increase sensitivity => decrease resolution • Increase resolution => decrease sensitivity

  31. Sensitivity / resolution trade-off • Increase sensitivity => decrease resolution • Increase resolution => decrease sensitivity • One example - changing pupil size Increased spatial resolution Shrink pupil Decreased sensitivity

  32. Other examples • Wavelength • Time • Wavelength

  33. 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

  34. 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 Periphery Fovea Receptors Bipolar cells

  35. 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

  36. Problem: High resolution coding of intensity information

  37. 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.

  38. Code wide range of light intensities • Range of light intensities receptors can encode • 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?

  39. Some typical intensity values

  40. Limited dynamic range of receptor cell

  41. 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.

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