Lecture outline - 9/12

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?

23. ommotidium

25. Mammalian solution - the simple eye

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

28. Focus - the lens equation

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

30. 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

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

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

34. 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?

35. Transduction in the retina

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

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

40. Other examples • Wavelength • Time • Wavelength

41. 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

43. 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

44. 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

45. Problem: High resolution coding of intensity information

46. 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.

47. 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?

48. Some typical intensity values

49. Limited dynamic range of receptor cell

50. 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.