1. Intensity discrimination is the process of distinguishing one stimulus intensity from another Intensity Discrimination

2. Two types: Difference thresholds – the two stimuli are physically separate Increment thresholds – the two stimuli are immediately adjacent or superimposed

3. Fig. 1.1 Increment Difference

4. Fig. 1.2 Task: find the threshold ΔL

5. Theory and Practice of Increment Thresholds Theory:

6. Fig. 2.7 To distinguish a flash with a mean of 8 from a flash with a mean of 9 quanta is impossible! The distributions overlap almost completely

7. Mean of 8, vs. mean of 9 Just based on the number of photons in the two distributions, there is too much overlap for it to be possible to detect 9 vs. 8

8. Mean of 8, vs. mean of 12

9. Mean of 8, vs. mean of 16

10. Mean of 8, vs. mean of 20

11. In a Poisson distribution, the variance is equal to the mean. The standard deviation (SD) is the square root of the mean. In a two-alternative forced-choice task, to reach threshold (75% correct), L T must differ from L by 0.95 SD. (e.g., threshold  L = 0.95 SD) Mean of 8 photons, SD = √8 = 2.8 0.95 x 2.8 = 2.7 Can just detect 11 photon flash as different from 8 at threshold

12. Moreover, as L increases, the minimum  L needed to reach threshold also increases with the because the variance in a Poisson distribution equals the mean, so the SD changes with the square root of the mean

13. An “ideal” observer would follow the

14. Theory and Practice In practice: at low background intensities, human observers behave as an ideal detector (follow the deVries-Rose Law)

15. Fig. 3.1 deVries-Rose Law holds Line = DeVries-Rose law prediction Circles = data

17. Weber’s Law

18. Fig. 3.1 Weber’s Law holds

19. You always can determine the Weber fraction, even when Weber’s Law does not hold

20. Weber’s Law holds Weber’s Law does NOT hold (  L/ L rises as L decreases) Fig. 3.2 The x-axis is the same as in Fig. 3.1 but now the y-axis is the Weber fraction

21. Both the deVries-Rose and Weber’s laws fail to account The increment threshold data of a rod monochromat (circles) plotted along with the theoretical lower limit (deVries-Rose, dotted line) and the predictions of Weber’s Law (solid line). Luminance values are in cd/m 2. (Redrawn from Hess et al. (1990) Fig. 3.3 for thresholds at high light intensities

22. More practical issues: How changes in other stimulus dimensions affect the Weber fraction

23. Fig. 3.4 #1 Stimulus size: the Weber fraction is lower (smaller) for larger test stimuli

24. Log Background Intensity, L (cd/m 2 ) -7-6-5-4-3-20123 Log Weber Fraction,  L/L -3 -2 0 1 2 121' 4' Test Field Diameter More practical issues: Is a target visible under certain conditions? Is a spot with a particular luminance, relative to background, visible? It depends on its size. This is the target’s Weber fraction. It is NOT a threshold If the target is 121’, it is visible If 4’, it is not visible

25. Need to distinguish between the Weber fraction of a target vs. the threshold of a viewer. For a subject or patient viewing a target, if the subject’s Weber fraction is below a line, then the subject’s threshold is better (smaller). If the Weber fraction of a target is below the line, the target is NOT visible to someone whose threshold is on the line.

28. The “dinner plate” example: 121’ plate with luminance (L T ) of 0.0102 footlamberts. Background is 0.01 footlamberts The Weber fraction for the plate is:  L/L  L is (L T – L) = 0.0102 – 0.01 = 0.0002 L is 0.01 Target’s Weber fraction -  L/L = 0.0002/0.01 = 0.02 (plate is 2% more intense than the background) Plot this on Fig. 3.4 – Is this going to be visible? Need to compare actual plate Weber fraction with human Weber fraction.

29. . Target ΔL/L is less than the human threshold for a 121’ stimulus, so target is not visible.

30. Log Background Intensity, L (cd/m 2 ) -7-6-5-4-3-20123 Log Weber Fraction,  L/L -3 -2 0 1 2 121' 4' Test Field Diameter More practical issues: Is a target visible under certain conditions? Is a spot with a particular luminance, relative to background, visible? It depends on its size. Plate’s Weber fraction Threshold Weber fraction for 121’ objects

31. On Figure 3-4, can see that this is not visible. The target’s Weber fraction is less than an average person’s threshold Note: in lab, when you plot the value of YOUR threshold ΔL/L and it is below the 121’ line, that means YOU can have a lower threshold than that group of people.

32. More practical issues: How changes in other stimulus dimensions affect the Weber fraction

33. #2 Short-duration flashes are harder to see (are less discriminable) than long-duration flashes That is, the threshold  L increases as flash duration becomes shorter. Continuing: How changes in other stimulus dimensions affect the Weber fraction

34. #3 Threshold  L varies with eccentricity from the fovea At low luminance levels, threshold is lowest (sensitivity is highest) about 15-20 degrees from fovea and the fovea is “blind” At high luminance levels, threshold is lowest at the fovea Continuing: How changes in other stimulus dimensions affect the Weber fraction

35. Sensitivity = 1/threshold

36. Fig. 3.5 Note: threshold axis is “upside down”

39. Sensory Magnitude Scales Revisited Using the “just noticeable difference” (jnd) to create a scale for sensory magnitude vs. stimulus magnitude L + threshold  L = L T L T is one jnd more intense than L. L T + threshold  L = L T2 L T2 is one jnd more intense than L T And so on…

40. Stimulus Luminance, L (cd/m 2 ) 050100150200 Sensory Magnitude 0 2 4 6 8 10 12 L

41. Stimulus Luminance, L (cd/m 2 ) 050100150200 Sensory Magnitude 0 2 4 6 8 10 12 LTLT L L + threshold  L = L T L T is one “just noticeable difference” (jnd) more intense than L.

42. Stimulus Luminance, L (cd/m 2 ) 050100150200 Sensory Magnitude 0 2 4 6 8 10 12 L T + threshold  L = L T2 L T2 is one jnd more intense than L T and 2 jnd’s larger than L LTLT L L T2

43. Stimulus Luminance, L (cd/m 2 ) 050100150200 Sensory Magnitude 0 2 4 6 8 10 12 When Weber’s Law holds, the threshold  Ls keep getting larger, so 1 jnd is a larger increase in stimulus luminance LTLT L L T2 L Tn L Tn+1

44. Stimulus Luminance, L (cd/m 2 ) 050100150200 Sensory Magnitude 0 2 4 6 8 10 12 Fechner's Law: Log(L) Fechner’s Law

46. Comparing Fechner’s Law with Stevens’ Power Law Stevens’ Power Law resembles Fechner’s Law when the exponent is <1 Fig. 3.6

50. Fig. 3.7

51. Measuring the Visual Field: Perimetry

52. Automated Visual Field testers use multiple staircases with unequal down and up steps to “home in” on threshold very quickly A classic example of psychophysical measurement procedures

53. Fig. 3.6

54. The three main stimulus dimensions that are varied in visual perimetry are Stimulus size Stimulus intensity Retinal locus

55. Fig. 3.8

56. Fig. 3.7

58. Perimetry is used to detect visual field loss caused by glaucoma

60. A “Glaring” Deficiency Glare is ambient light that interferes with increment or difference threshold detections Due to the effects of scattered light

61. Scattered light Due to particles in the optical media If small relative to the wavelength of light, the amount of scatter is inversely proportional to the 10 4 of the wavelength (Rayleigh scattering) The sky is blue because of Rayleigh scattering

62. Scattered light Due to particles in the optical media If large relative to the wavelength of light, the amount of scatter independent of the wavelength (Mie scattering) I think cataracts give Mie scattering

63. L v = K (E o /  0  ) Eq. 3.4 where L v = veiling luminance, K is a constant, E o = illuminance of the glare source, and  0 = the angle between the glare source and the fixated target. The Stiles Holladay formula The amount of glare (L v ) goes down as the angle of the glare source goes up