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Unformatted text preview: niversity of Texas Austin Friday, 6 September 2013 34 Courtesy of Max Snodderly, University of Texas Austin Friday, 6 September 2013 35 Courtesy of Max Snodderly, University of Texas Austin Friday, 6 September 2013 36 Courtesy of Max Snodderly, University of Texas Austin Friday, 6 September 2013 37 Courtesy of Max Snodderly, University of Texas Austin Friday, 6 September 2013 38 Friday, 6 September 2013 39 Friday, 6 September 2013 40 Foveal Mosaic Friday, 6 September 2013 41 Østerberg (1935) Receptor Density (receptors per mm2) Distribution of Rods and Cones 200000 from Table 3, Østerberg, 1935 Cones 150000 Rods 100000 50000 Nasal Retina 0 -100 -80 -60 -40 Temporal Retina -20 0 20 40 60 Retinal Locus in Degrees From Fovea Friday, 6 September 2013 42 Friday, 6 September 2013 43 Cone Receptors Friday, 6 September 2013 Rod Receptors 44 Friday, 6 September 2013 45 AN 1 deg nasal Friday, 6 September 2013 46 JW Nasal AN Nasal JW Temporal Monkey Nasal Friday, 6 September 2013 47 Friday, 6 September 2013 48 Friday, 6 September 2013 49 Friday, 6 September 2013 50 Friday, 6 September 2013 51 Principle of Univariance • A receptor can only signal the number of quanta (or the rate) absorbed. It can not signal the wavelength of the quanta. • All quanta, regardless of wavelength, cause the same voltage change when they are absorbed • 700 microvolts per quantum for rods • 25 microvolts per quantum for cones Friday, 6 September 2013 52 What Can We Do with Psychometric Functions? • Answer questions about sensory processes • What is the minimum amount of energy needed for “seeing?” • Hecht, Shlaer, & Pirenne (1942) Friday, 6 September 2013 53 Psychometric Function Simon S hlaer D ata 1.0 Probability of “yes” Probability of “yes” Selig H echt D ata 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 10 100 1000 10 Mean Number of Quanta at Cornea 100 1000 Mean Number of Quanta at Cornea 1.0 Probability of “yes” Probability of “yes” Maurice H enri P irenne D ata 1.0 0.8 0.6 0.4 0.2 0.0 0.6 0.4 0.2 0.0 10 100 1000 Mean Number of Quanta at Cornea Friday, 6 September 2013 0.8 10 100 1000 Mean Number of Quanta at Cornea 54 Poisson Probability Distribution −λ λe p( n : λ) = n! n λ > 0, n = 0,1, 2, 3… Mean = µ = λ Variance = σ = λ 2 Standard Deviation = σ = Friday, 6 September 2013 λ 55 Poisson Process Poisson Process (mean = 2.0) Number of Quanta per Flash 5 4 3 2 1 0 1 3 5 7 9 11 13 15 17 19 21 Trial Friday, 6 September 2013 56 Poisson Process (mean = 2.0) 8 Number of Quanta per Flash 500 Trials 7 6 5 4 3 2 1 0 0 100 200 300 400 500 Trial Friday, 6 September 2013 57 Observed Probabilities Poisson Process (mean = 2.0) 0.30 500 Trials 0.25 Probability 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 Number of Quanta per Flash Friday, 6 September 2013 58 Theoretical Poisson Distribution Poisson Distribution (mean = 2.0) 0.30 λn e− λ p( n : λ) = n! 0.25 Probability 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 Number of Quanta per Fl...
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