1. Lecture #13 Non simple eyes Mirrors and multifacets (compound) 3/7/13 (Not on midterm)

2. Homework • Do you want me to post the equations from 10-11 HW I have electronically? • Do folks mind having their HW posted?

3. Today • Mirrored eyes • Compound eyes • Apposition • Superposition • How well can they see? • What are they good for?

4. How many eye designs? Mirror Fig 1.9

5. Mirrors occur in eyes all the time • Tapetumlucidum– reflecting structure behind photoreceptors • Have light do a double pass through the retina by adding reflector at back

6. Tapetum – reflecting platelets • Usually high index platelets (guanine) in lower index matrix • Anchovy rod outer segments (ros) surrounded by reflecting layer Fig 6.13

7. Scallop: mirrors as optical elements 60-100 eyes - 1 mm

8. Scallop eye - closeup

9. Eye contains a lens sitting right on top of retina Fig 6.2b+c

10. Eye does form an image! Fig 6.3

11. Mirror will form an image object f=r/2 lens focal length Image of far off object forms at distance f which is half radius of curvature r=radius of curvature image

12. Mirascope – creating a real image

13. Light passes through retina 2x: 1st time unfocused, 2nd time focused Fig 6.4 Lens even has correction for spherical aberration

14. Fish also use mirrors

15. Spookfish, Dolichopteryx longipes Lives at 1000m Upward pointing tubular eyes Downward pointing mirror eyes

16. Two retina and two collecting elements: 1 lens and 1 mirror Looking up “diverticulum” eye with m = mirror Looking down

17. Mirror has slanted reflectors

18. Light is focussed by this diverticulum

19. Deep sea bioluminescence Bristlemouth Lanternfish anglerfish

20. Apposition Superposition How many eye designs? Fig 1.9

21. Two kinds of compound eyes Apposition Superposition Diurnal insects Nocturnal insects Deep sea crustaceans

22. The Compound Eye Photoreceptor Lens Aperture Focal Length

23. Modification 1

24. Modification 2

25. Modification 3

26. Modification 4

27. Apposition eyes • Each ommatidium points in different direction • Views different part of image Fig 7.3

28. Leeuwenhoek’s experiment - a hundred points of light • Viewed candle flame through the compound insect cornea • Each lens of compound cornea produced a focused inverted image • What does the insect see? Fig 8.2

29. Apposition eyes • Apposition • Light through each lens goes to all cells of rhabdom • Image is not resolved by 8 cells • Each lens views different part of image Fig 7.4

30. Resolution in terms of sampling frequency is same in compound and simple eyes • Sampling angle • ΔΦ= D / r = Δρ • D = receptor diameter • r = lens radius of curvature • Same as d/f in camera eye • Resolution = 1/ΔΦ = r/D Compound Simple Fig 7.1

31. Resolution is not too bad in compound eyes

32. Bee ommatidium UV B G

33. Bee’s eye view Human view Photo through UV transmitting lens Dr. Adrian Dyer, Monash Univ

34. Bee’s eye view Human view Photo through UV transmitting lens False color and lower resolution to account for ommatidium acceptance angle What bee’s brain might do to process image Dr. Adrian Dyer, Monash Univ

35. Pixelation

36. B-EYE view

37. Organismal diversity • Apposition - Diurnal insects • Bees, grasshoppers, water fleas, crabs • Neural superposition • True (two winged) flies

38. Dipterans - true two winged flies • Horse fly, picture wing, hoverfly • Use neural superposition

39. Apposition eyes • Apposition • Light through each lens equally detected by all 8 receptors • Neural superposition • 7 receptors in ommatidium are spaced further apart • “Resolve image” of different locations in space Fig 7.4

40. Neural superposition Some overlap in view of neighboring ommatidia Certain receptors view same part of space These then sum together so get more signal for same part of image Increase sensitivity for same resolution!

41. What strategies could insects use to collect light? • Focal length – curvature, thickness, index of refraction • Vertebrates change shape - ???? • Aperture – let in more light • Alter index across the lens

42. Different kinds of apposition lenses • Easiest way to make an image is with curved cornea • Get image about 4r behind lens Fig 7.5a

43. Different kinds of apposition lenses • For water bugs, normal cornea is useless • Use high index plus lower index • Correct spherical aberration? Fig 7.5b

44. Different kinds of apposition lenses • Limulus must function in water and on land • Has graded index lens Fig 7.5c

45. Different kinds of apposition lenses • Graded index lens with 15 um x 5 mm long light guide • Helps camouflage the eye • Phronima Fig 7.5d

46. Different kinds of apposition lenses Image forms inside crystalline cone Graded lens cylinder which makes light parallel and directs to rhabdom Fig 7.5e compare to 7.5a

47. Resolution actually determined by acceptance angle and diffraction • Ommatidia geometry determines resolution • Bee Δρ= 1.9° • But diffraction can degrade resolution set by geometry Fig 7.6

48. To improve bee resolution • For bee to have human resolution • v =1/ 2Δρ= 60 cycle / degree • Δρ = 0.00014 rad • To not be limited by diffraction: D = 2 mm • So r = D /Δρwhich is 13.8 m Fig 7.6

49. To improve bee resolution • If bees had human resolution, eye would have to be 27 m in diameter Fig 7.7

50. To improve bee resolution • If bees had human resolution, eye would have to be 27 m in diameter • If let resolution vary with angle then only 1 m diameter Fig 7.7