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 Difference threshold (separated stimuli) Increment threshold stimuli (edges of stimuli touch each other)

4. Fig. 1.2

5. Theory and Practice Theory:

6. Fig. 2.7 From Dr. Kraft’s course – Hecht, Shlaer & Pirenne Photon emission follows a Poisson distribution 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 If present the flash with a mean of 8 photons many times and a flash with a mean of 9 photons presented many times, there will be many times that the 9 photon flash will have more photons than the 8 photon flash

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.,  L = 0.95 SD)

12. Moreover, as L increases, the minimum threshold  L 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. As a result, 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

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

21. Both the deVries-Rose and Weber’s laws fail to account for thresholds at high light intensities 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

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

26. 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

27. 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 smaller the threshold  L, the smaller is the value of the Weber fraction for a given background L, (only the numerator changes) and the more sensitive the visual system is to differences in light intensity.

29. Fig. 1.2

30. The “dinner plate” example: Plate with luminance of 0.0102 footlamberts. Background is 0.01 footlamberts  L is thus 0.0102– 0.01 = 0.0002.  L/L = 0.0002/0.01 = 0.02 (plate is 2% more intense) From Figure 3-4, can learn that this is not visible.

31. .

32. 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

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. Sensitivity = 1/threshold

35. #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

36. Fig. 3.5 This is the basis for visual field tests

38. 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…

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

40. 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.

41. 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

42. 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

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

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