Lecture #8

1. Lecture #8 Sensitivity Land + Nilsson ch3 end 2/19/13

2. Topics for today • Challenges for high resolution • Contrast • Diffraction • Low light levels • Sensitivity

3. Vertebrate spatial frequencies: best case scenarios

4. Resolution problem #1) What if there is less contrast? • Contrast • If Imin= 0 then contrast is maximum = 100% White vs black

5. Contrast

6. Contrast

11. T

12. T

13. T

14. Problem #2) What if there is diffraction • Diffraction causes angular spreading • Width of central interference peak is w = λ / D D w

15. Diffraction Resolution is limited - can’t resolve anything smaller than this angle D w

16. Detectable grating frequency • Max frequency that can be detected depends on diffraction • vco is max cut-off frequency • w is width of diffraction peak (radians) • λis wavelength D is aperture

17. Detectable grating frequency - Humans • Max frequency that can be detected depends on diffraction • λis wavelength 500 nm D is pupil aperture2 mm w = 500 x 10-9 m / 2 x 10-3 m = 0.00025 rad vco = 4000 cycles / rad

18. Contrast Diffraction in optical systems blurs images • This decreases contrast • This makes gratings even harder to detect Imax Imin Lp/mm = line pairs/mm http://www.microscopyu.com/tutorials/java/mtf/spatialvariation/index.html

19. Diffraction decreases contrast and contrast ratio • Contrast of image decreases compared to contrast of object = contrast ratio • More loss of contrast with higher frequency grating • Spatial freq is normalized to diffraction limited cutoff, vCO Land and Nilsson fig 3.3

20. Fall off due to blurring by lens and diffraction from pupil Diffraction limit, vCO Contrast sensitivity function Lo contrast Contrast sensitivity Hi contrast Frequency

21. Diffraction decreases contrast and contrast ratio • Contrast of image decreases compared to contrast of object = contrast ratio • More loss of contrast with higher frequency grating • Spatial freq is normalized to diffraction limited cutoff, w=D/λ Land and Nilsson fig 3.3

22. Fall off due to blurring by lens and diffraction from pupil Diffraction limit, vCO Contrast sensitivity function On low frequency side size of neurons matter Contrast sensitivity Hi contrast Frequency

23. Contrast sensitivity decreases with age

24. Contrast sensitivity test

25. Contrast sensitivity test

26. Problem #3) Low light levels limit detection • Random arrival of photons at each receptor • Very low light levels cause image to be less certain

27. Seeing object - high light levels Black object on bright background Land & Nilsson fig 3.8

28. Seeing object - low light levels Black object on dim background Land & Nilsson fig 3.8

29. Seeing object at low light level Very few photons At light detection threshold Photoreceptor detecting light Land & Nilsson fig 3.8

30. Seeing object at low light level 10x more light - more receptors detect photons Land & Nilsson fig 3.8

31. Seeing object at low light level 10x 100x 1000x Land & Nilsson fig 3.8

32. Photon counting • At low light levels, rod will “count” the number of photons, n • Photon arrival is a poissonprocess • Uncertainty in photon arriving goes as √n • Fewer photons means more uncertainty • n √n • 100 10 • 10 3.3 • 1 1

33. Photon counting • Uncertainty in photons arriving • √n is 1 standard deviation • = 66% of variation • 2 √n is 2 standard deviations • = 95% of variation • So if 9 photons arrive on average in 1 s, for any particular second 9 ± 6 photons will arrive with 95% confidence

34. Contrast detection • The bright / dark stripe of a grating falls across two receptors • Contrast Imaxis intensity of brighter stripe Imin is intensity of darker stripe ΔI is difference between these two Average intensity, I = 1/2 (Imax + Imin)

35. Contrast detection • To detect stripes as being different, average number of photons must be greater than uncertainty in photon number • 95% confidence • So contrast in terms of photon number is

36. Contrast detection • To detect stripes as being different, average number of photons must be greater than uncertainty in photon number • 95% confidence • So contrast in terms of photon number is Detectable contrast

37. How many photons are needed? • To detect contrast, C Contrast is between 0 and 1. n will be greater than 1

38. How many photons are needed to detect contrast? • # photons needed n >1/C2

39. How many photons are needed to detect contrast? • # photons needed n >1/C2 Takes rod 0.1s to detect light so rate = # photons / 0.1s

40. How many photons are needed to detect contrast? • # photons needed n >1/C2 Only detect 30% of photons that arrive at eye so need 3x more

41. How many photons are out there? Bright sun is 1020 photons / m2 sr s But a photoreceptor is only 5 μm2 Collection angle is 0.0003 sr Land&Nilsson Table 2.1

42. Measuring incident light (lecture 3) • Irradiance • Light flux on a surface - from all directions • Photons /s m2 • Radiance • Light flux on a surface: from a particular direction and angle • Photons /s m2sr Radiance Irradiance

43. Light arriving at one photoreceptor - Bright sun

44. How many photons arrive at one photoreceptor

45. How many photons are needed to detect contrast?

46. How many photons are needed to detect contrast? • Can only detect high contrast in bright sun

47. Some caveats • In dark, rods gang together so you get a larger area of light collection to increase photon #s and so ability to detect contrast • To maximize ability to resolve fine detail requires high light levels • Gets worse with age

48. Eye sensitivity • Sensitivity tells how well photoreceptors detect light • Sensitivity = # photons (n) caught per receptor for standard radiance

49. D What impacts eye sensitivity?

50. Eye sensitivity Fig 3.11 • Eye sensitivity • S = n/R = # photons / radiance (W/m2 sr s) (photons m2 sr ) D = diameter of pupil Δρ = receptor acceptance angle Pabs = probability photon is absorbed