BASIC VISUAL SCIENCE CORE Absolute and Increment Thresholds Ronald S. Harwerth Fall, 2016 1. Psychophysics of Vision 2. Light and Dark Adaptation Michael Kalloniatis and Charles Luu 1
The Neuron Doctrine for Perception The neural basis for behavior - there should be a correlation between psychophysically determined functions and neurophysiology. An early example - Hartline proposed that lateral inhibition, similar to that measured in a Limulus eye, could account for Mach bands. Mach Bands Mach Bands 2
Limulus Eyes The lateral eyes of Limulus (Horseshoe crab) are faceted. The visual receptors (ommatidia) are connected by lateral neurons. The lateral interactions between ommatidia are inhibitory. Limulus Eyes A: Limulus lateral eye. Dark spots in photograph are individual ommatidia. Width of eye 1 cm. B: Schematic drawing of an ommatidium in the lateral eye. l, lens; a, aperture; b, rhabdomere; r, retinular cell; p, pigment cell; e, eccentric cell; i, synaptic sites of self and lateral inhibition; x, site of spike generation. Diameter of ommatidium 250 μm. C: Functional diagram of optical and neural mechanisms operating in the lateral eye that transform visual scenes into patterns of optic nerve activity, or neural images. Passaglia, et al., J Neuro Physiol 1998;80:1800-1815. 3
Decrease in frequency (impulses per sec) Lateral Inhibition in Limulus Eyes Log intensity falling on inhibiting spot Distance between inhibiting and inhibited facets Lateral inhibition in the Limulus eye is directly proportional to the intensity of the inhibiting stimulus and inversely proportional to the distance of the inhibiting ommatidium. Lateral Inhibition and Mach Bands Based on the neurophysiology of the Limulus eye, the lateral inhibition from receptors to the left of the green spot will be greater than the inhibition from the receptors to the right. The lower figure shows recordings from an ommatidium as an edge moves across the eye with either, all other ommatida occluded (triangles) or illuminated (circles). 4
The Neuron Doctrine for Perception: Barlow s Dogma The activity of a single nerve cell and influences of other cells is a complete enough description for understanding the nervous system. The sensory system is organized to achieve as complete representation as possible with the minimum number of active neurons. The frequency of neural impulses codes certainty: a high impulse frequency corresponds to a high degree of certainty that the cause of the percept is present. Barlow, HB. Perception 1972;1:371 394. Definitions: Absolute and Increment Thresholds R 0 R 1 Response continuum R 2 I I S 0 S 1 Stimulus continuum S 2 Absolute threshold - the lowest energy level (S 0 ) that can be perceived (R 0 ). Increment threshold (differential threshold) - the lowest amount of energy which must be added to an existing stimulus intensity in order to see a change in the stimulus. Increment thresholds often follow the predictions of Weber s law ( I / I = K) or Fechner s law (R = K * log(s)). 5
Response magnitude Log threshold intensity Absolute and Increment Thresholds Background Test field Log background intensity Weber s Law I / I = K Log transformation log( I) = log(i) + log(k) Weber s law predicts a linear relationship between the log threshold intensity and log background intensity with a slope = 1 and y-intercept = K. Absolute and Increment Thresholds Background Test field Fechner s law R = K * log(s) Fechner s law predicts a linear relationship between the response magnitude and log background intensity with a slope = K and y- intercept = 0. Log background intensity 6
Absolute and Increment Thresholds I 0 I D I B The form of empirical data follows the form: I = (I B2 + I D2 ) 0.5 where I = increment threshold I B = background intensity I D = intrinsic noise Log background intensity The Classic Experiments of Hecht, Shlaer and Pirenne Experiments designed to determine the absolute minimum intensity of light needed for vision. The results provided important data to answer two basic questions. 1. Is there an absolute threshold for seeing? 2. What is the minimum number of neural impulses required for seeing? Hecht, Shlaer, & Pirenne, J Gen Physiol. 1942;25:819 840. 7
The Classic Experiments of Hecht, Shlaer and Pirenne 1. Is there an absolute threshold for seeing? The psychometric or frequency-of-seeing function is an ogive or Sshaped curve (black line), not a step function (green line) that would be predicted for a system with and absolute threshold. The shape of the function indicates that there is noise in the measurement. The Classic Experiments of Hecht, Shlaer and Pirenne 2. What is the minimum number of neural impulses required for seeing? Light has a quantum nature (E = h ). where: E = energy of a quantum h = Plank s constant = the frequency of light The number of quanta at threshold = the number of rhodopsin isomerizations = the number of neural impluses generated. 8
Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 1. The wavelength of the test stimulus (510 nm). There are three peaks in the absorption spectrum of rhodopsin. The action of light on rhodopsin causes a shift in the absorption peak in visible light (. peak). The absorption spectrum also represents the probability of absorption of a quantum of light. Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 1. The wavelength of the test stimulus (510 nm). After correction for pre-retinal light losses, the spectral sensitivity of the dark adapted eye matches the absorption spectrum of rhodopsin. The optimal wavelength - the highest probability for absorption of quanta - will be close to the peak absorption of rhodopsin at 505 nm. 9
Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 2. The retinal area for the test stimulus (20 deg, temporal retina). The density of cones and rods varies across the retina. The optimal stimulus location will be the eccentricity with the highest density of rod photoreceptors - about 20 deg, on temporal retinal to avoid the optic nerve head. Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 2. The retinal area for the test stimulus (20 deg, temporal retina). Diagram of fixation and test field. 10
Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 3. The state of adaptation (30-40 min of dark adaptation). Cone phase Final rod threshold Rod - cone break Rod phase The visual threshold decreases with time in the dark (dark adaptation). The absolute threshold cannot be measured until the time of the final rod threshold. Time in the dark (min) Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 3. The state of adaptation (30-40 min of dark adaptation). Time in the dark (min) The visual threshold decreases with time in the dark (dark adaptation). The time of the rod-cone break and the final rod threshold depend on the amount of light adaptation prior to dark adaptation. The final rod threshold will occur after 30-40 min of dark adaptation, even after intense rhodopsin bleaching. 11
Log threshold intensity Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 4. The duration of the stimulus (1 msec). (I * t) = k I = k t c -1 0 1 2 Log stimulus duration (msec) Bloch s law (I * t) = k for t < t c, I = k for t > t c, where I = threshold intensity t = time k = constant For stimulus duration of less than 80-100 mesc, threshold is determined by total energy (I * t). For stimulus duration greater than a critical duration (t c ), threshold is determined by stimulus intensity (I = k). Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 4. The duration of the stimulus (Bloch s law). Bloch s law (I * t) = k for t < t c, I = k for t > t c, where I = threshold intensity t = time k = constant Log time The plotted data show the product I * t as a function of t for central and peripheral stimuli, to illustrate the constant integration across the retina. 12
Log threshold intensity Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 5. The size of the stimulus (10 min diameter). (I * a) = k I = k a c -2-1 0 Log stimulus diameter (deg) Ricco s law (I * a) = k for a < a c, I = k for a > a c, where I = threshold intensity a = area k = constant The a c depends on the retinal eccentricity - at an eccentricity of 20 deg the reciprocity for area and intensity holds for stimulus diameters up to about 1 deg. For foveal vision, a c is about 5 min diameter. Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 5. The size of the stimulus (Ricco s law). Ricco s law (I * a) = k for a < a c, I = k for a > a c, where I = threshold intensity a = area k = constant Log radius The psychophysical thresholds as a function of the diameter of the stimuli for foveal and peripheral stimuli illustrate the differences in integration of central and peripheral retina. 13
Hecht, Shlaer and Pirenne The critical parameters for empirical measurements of absolute thresholds: 6. The psychophysical method for determining thresholds. 1. The method-of-adjustment - The subject adjusts the intensity of the stimulus to a just-seen (or not seen ) level. 2. The method-of-limits - Stimuli intensities are decreased (or increased) in discreet steps to determine the threshold. 3. The method-of-constant stimuli - Stimuli of fixed intensities are presented in random order to determine the frequency-of-seeing for each intensity level. Hecht, Shlaer and Pirenne The results: Method-of-limits measurements For the three observers, 54-148 quanta, at the cornea, were necessary for seeing. How many quanta were absorbed by rhodopsin? Approximate values for the major losses of light 1. The cornea reflects 4% of the light. 2. The crystalline lens absorbs 50% of light at 505 nm. 3. 80% of the light passes between the rod receptors. The threshold intensities represent 5-14 quanta absorbed by the photopigments. Conclusion - the threshold for seeing is determined by a small number of rods, each absorbing a single quantum, within a certain area and time. 14
Hecht, Shlaer and Pirenne The results: The absolute threshold 1. A single quantum is sufficient to activate a rod. At the 20 deg eccentricity, the 10 min diameter test stimulus covered approximately 500 rods, therefore, the probability of double hits for a single receptor is extremely small. 2. A single quantum is insufficient for seeing. A threshold of a single quantum is incompatible with Ricco s law or probability summation. At the retinal area of stimulation, Ricco s law predicts pooling of signals from over 17,000 rods. 3. If there is an absolute threshold for seeing, why is there a finite slope for psychometric functions? Hecht, Shlaer and Pirenne The results: Method-of-constant stimuli 1. Further evidence for an absolute threshold was derived by modeling their psychometric functions. n = 1 The Poission distribution p n = a n / e a n! The Poission probability distribution is a binomial distribution that is valid for a situation where there is a large number of possible events, but a very few actually occur. -1 0 1 Log average number of quanta per flash 15
Hecht, Shlaer and Pirenne The results: Method-of-constant stimuli 1. The family of Poission probability distributions represent templates to describe the psychometric function for each value of n. 2. The shape of the function will be constant, regardless of its location on the abscissa because of the logarithmic coordinate. Hecht, Shlaer and Pirenne The results: Method-of-constant stimuli 1. The templates for 5-7 quanta matched the psychometric functions for the three investigators. 2. The model is compatible with an absolute threshold. For example, Subject S.H. reported seen any time 6, or more, quanta were absorbed and never said seen if less than 6 quanta were absorbed. 16
Hecht, Shlaer and Pirenne The results: Method-of-constant stimuli 3. If the quantum efficiency is 1.0, then S.H. saw the light every time that 6 neural impulses were generated. 4. If there is an absolute threshold, then the noise in the threshold measure must arise from non-biological sources, probably the variability of the stimulus. Hecht, Shlaer and Pirenne Further considerations: Is there an absolute threshold? 1. The experiments did not consider criterion effects on threshold measurements. For the data shown, the subjects all used a very conservative criterion for saying seen because the false alarm rate for each psychometric function is zero. 17
Is there an absolute threshold? 1. In Sakitt s experiments ( Counting Every Quantum ), the subjects were trained to scale the apparent brightness of test stimuli seen at near threshold intensities. 2. She found that some subjects could reliably detect a single quantum and discriminate between intensity increments of one quantum - there was no absolute threshold. Sakitt, B. J Physiol. 1972;233:131-150 Is there an absolute threshold? 1. In more recent experiments, Teich, et al., investigated the effect of criterion on the absolute threshold. 2. They confirmed the results of HS&P if they instructed their subjects to use a strict criterion for reporting seen (< 5% false alarm rate). Teich, MC. et al., J Opt Soc Am. 1982;72:419-431 18
Is there an absolute threshold? 3. With a more lax response criterion, the subject s false alarm rates were elevated, but the psychometric functions still demonstrated a systematic relationship to the intensity of the stimulus. 4. An absolute threshold (60% correct) of 1 quantum is possible, if a false alarm rate of 55% is acceptable. Is there an absolute threshold for photopic vision? 1. The photopic system is most often studied under light adapted conditions because it is a high resolution, color system - not ordinarily operating in a quantum limited environment. 2. An absolute threshold with dark adaptation has been measured. Under optimal conditions (small, short, foveal test target), the absolute threshold is about 1000 quanta - statistically compatible with 5-7 quanta absorptions per cone, with pooling over about 40 cones. 19
Intensity Is there an absolute threshold for photopic vision? cones rods 1. The more recent analyses of the slopes of psychometric functions and spatial summation functions under dark and light adaptation have provided evidence against a multiple hit hypothesis. 2. The higher threshold for photopic vision may be caused by higher intrinsic noise in cones than rods. Donner, K. Vision Res. 1992;32:853-866 Brightness Discrimination (increment-threshold spectral sensitivity) Adaptation field Test field Methods: 1. White or chromatic adaptation field (background) to obtain static photopic state. 2. Threshold - the smallest perceptible light increment ( I of the monochromatic test field added to the adapting background (I). 3. Sensitivity = log (1 / threshold intensity). I I Distance 20
Log threshold intensity Increment threshold studies of visual function. (I t ) a I d (I b ) b The tvi relationship is I t = a (I b + I d ) b 1. The increment threshold as a function of background intensity is commonly known as a tvi (threshold-versusintensity) function. 2. The three independent variables of tvi functions are the absolute threshold (a) the intrinsic noise (I d ) the slope of the adaptation portion of the function (b) Increment threshold studies of visual function. 10 deg parafoveal function - 500 nm background 580 nm test Background field 500 nm Test field 580 nm Log background intensity 1. A common paradigm for increment thresholds is to determine the least perceptible amount of light that must be added to a stationary background as a function of the intensity of the background. Stiles, WS. Proc Nat Acad Sci USA., 1959;45:100-114. 21
Subjective methods of defining the cone fundamentals Background Intensity Stiles two-color, increment-threshold spectral sensitivity. Assumptions: 1. In any area of the retina there are several different photopigments, but the one with highest sensitivity will determine the visual threshold. 2. Photopigments that differ in their spectral locations will adapt at different rates for a given wavelength of the background. 3. Cone mechanisms can be identified by threshold-versus-intensity (TVI) functions. Stiles TVI functions With the correct choice of test field and background wavelengths, the color vision mechanisms can be isolated and their spectral sensitivities investigated. The example shows two independent color vision mechanisms, one more sensitive to the 480 nm test field at absolute threshold and which adapts more rapidly to the 540 nm background field. 22
Stiles TVI functions Measurements of TVI functions across wavelengths provides data to derive the spectra response function for each mechanism. Initially, Stiles called the functions cone photopigments, but later called them the pi mechanisms. Increment threshold studies of visual function - rod saturation. 9 deg parafoveal function - 580 nm background 500 nm test Background field 580 nm Test field 500 nm Log background intensity (scotopic trolands) 1. Aguilar & Stiles - Why do the rods stop contributing to vision at photopic adaptation levels? 2. The rod response saturates at about 100 scotopic trolands; cone responses do not saturate. Aguilar, M, & Stiles, WS. Acta Optica 1954;1:59-65 23
Log threshold of test field Increment threshold studies of visual function - Westheimer functions. 1. Westheimer functions - also called spatial interaction functions or perceptive fields - are psychophysical measures of the center (++) and surround (--) dimensions of retinal receptive fields. - - - + + - - - 2. The measurement involves the increment threshold for a small test field (~ 5 arcmin) on a background of variable size, but with a constant intensity. Westheimer, G. J Physiol. 1967;190:139 154 Increment threshold studies of visual function - Westheimer functions. 1. The first measurement, without a background, establishes the threshold of the receptive field without interacting stimuli. 1 Diameter of background (deg) 24
Log threshold of test field Log threshold of test field Increment threshold studies of visual function - Westheimer functions. 2. Subsequent measurements involve increment thresholds with a varying size background. When the background is smaller than the receptive field center, the increased noise causes an elevation of the increment threshold. 2 1 Diameter of background (deg) Increment threshold studies of visual function - Westheimer functions. 3. As measurements are made with larger backgrounds, as long as the background is smaller than the receptive field center, the elevation of the increment threshold is proportional to the size of the background field. 3 2 1 Diameter of background (deg) 25
Log threshold of test field Log threshold of test field Increment threshold studies of visual function - Westheimer functions. 4. The highest increment threshold will occur when the size of the background matches the size of the receptive field center. The portion of the Westheimer function showing increasing threshold as a function of increasing field size is called the desensitization limb. limb 3 2 1 4 Desensitization Size of receptive field center Diameter of background (deg) Increment threshold studies of visual function - Westheimer functions. 5. When the size of the background is larger than the receptive field center, the opponent activity of the surround reduces the noise induced by the center and, thus, results in a relatively lower threshold. 3 5 2 1 4 Diameter of background (deg) 26
Log threshold of test field Log threshold of test field Increment threshold studies of visual function - Westheimer functions. 6. The reduction in the increment threshold intensity continues with increasing field size, because the background stimulation of the surround is more effective in canceling the activity of the receptive field center. 3 5 2 1 4 6 Diameter of background (deg) Increment threshold studies of visual function - Westheimer functions. 7. When the size of the background matches the size of the surround of the receptive field, the field is maximally effective in canceling the activity of the center by the receptive field surround mechanism. 3 5 2 6 7 1 4 Diameter of background (deg) 27
Log threshold of test field Log threshold of test field Increment threshold studies of visual function - Westheimer functions. 8. Background sizes larger than the total size of the receptive field do not cause changes in the increment threshold intensity. The portion of the Westheimer function showing decreasing threshold as a function of increasing field size is called the sensitization limb. 3 5 2 1 4 Sensitization limb 6 7 8 Total size of receptive field Diameter of background (deg) Increment threshold studies of visual function - Westheimer functions. The final result is a psychophysical measurement of the center and surround sizes of the receptive field sizes at the retinal location of the measurement. - - - ++ - - - 3 5 2 1 4 center 6 7 8 center + surround Diameter of background (deg) 28
Increment threshold studies of visual function - Westheimer functions. Examples of Westheimer functions, under photopic conditions, as a function of retinal eccentricity. The sizes of the center and surround increase as a function of eccentricity, but a clear center-surround organization is apparent at all eccentricities. Increment threshold studies of visual function - Westheimer functions. Examples of Westheimer functions, under scotopic conditions, as a function of retinal eccentricity. The size of the receptive field center increases as a function of eccentricity, but under scotopic viewing the receptive fields do not exhibit clearly the center-surround properties of photopic functions. 29
The Neuron Doctrine for Perception There should be a correlation between psychophysically determined functions and neurophysiology. There are systematic relationships between stimulus parameters (size, duration, wavelength) that are based on physiological properties. The work of Hecht, Shlaer and Pirenne demonstrates the power of combining empirical data and modelling. Studies of Westheimer functions have demonstrated relationships between the structure of receptive fields and measures of vision function by increment thresholds. 30