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1 How many photons are required to produce a visual sensation? Measurement of the Absolute Threshold" In a classic experiment, Hecht, Shlaer & Pirenne (1942) created the optimum conditions: -Used the best retinal location for rods -Used the best wavelength for rods -Subjects were completely dark adapted -All the light went through the pupil -The spot was very small -The flash of light was very brief The best retinal location" Stimulus location: 20 deg in temporal retina Where rods are most dense Best wavelength, complete adaptation" Wavelength of stimulus = 510 nm, near peak of scotopic spectral sensitivity function. Subjects were dark adapted, at least 40 min in complete darkness. All the light through the pupil: Maxwellian View " In Maxwellian View, all the light enters the eye through a small spot centered in the pupil. This removes the effect of pupil size in retinal illuminance, like viewing through a pinhole.
2 Use a Small Spot so all the photons get pooled " Photons ->" Rods ->" " " Ganglion Cells->" " Rod photoreceptors are pooled together in large numbers so that sensitivity is increased. However, this pooling has the effect of reducing spatial acuity. In this schematic example, a total of 10 quanta are pooled together, but the separation between the left and right spots would not be visible. Cones have less pooling, especially in central vision. The collection of light into pools is referred to as Spatial Summation " Scotopic system Higher sensitivity larger area). Poorer spatial resolution (visual acuity). Spatial Summation" More summation over space means better sensitivity to light, but worse acuity for image details Photopic system Less sensitive smaller area). Higher spatial resolution (can tell the two flashes are separated in space). Spatial Summation Area" 113 " 63 " 36 " 20 " 63 " 36 " 20 " 11 " 6 " Diameter in arc minutes Depends on retinal location: At the fovea: ~10 At 4 7 eccentricity: ~30 At 35 eccentricity: ~2 deg Depends on stimulus: Sparse S cones have bigger area than dense L cones. Rods have similar summation areas in the periphery, in between L cones and S cones in size. For example, at 20 eccentricity: ~1.5 Use a brief flash: Temporal Summation " The summation of photons over time is limited. For brief flashes, the photons are added together, but for longer flashes the signal decays or leaks even as new photons arrive. Slower decay (longer summation time) produces more sensitivity to light, but less ability to see fast changes. Faster decay produces less sensitivity to light, but better ability to see fast changes. Scotopic system High sensitivity longer period of time). Poorer temporal resolution. Integration time of about 100 msec Photopic system Lower sensitivity shorter period of time). Higher temporal resolution. Integration time of 40 msec or less.
3 Results of Hecht, Shlaer & Pirenne (1942) Frequency of Seeing Curves" Threshold defined as intensity that observers detected the flashes 60% of the time. As measured at the cornea, the average threshold was 90 quanta (range 54 to 148 quanta). How many quanta were actually absorbed by rods to reach threshold? " Estimate pre-retinal light losses: Reflection at cornea: ~3% lost. Pupil: no loss (Maxwellian view). Internal reflection, scattering, absorption through the aqueous, lens and vitreous: ~50% lost. Hence, about 48% of quanta actually arrived at the retina in the spot location. Estimate retinal light losses: About 80% of quanta arriving at the retina fail to enter rod or fail to be absorbed by photopigment. Only 20% are absorbed. Therefore for 100 quanta hitting the cornea, a subject will report seeing a flash 60% of time when about 9 or 10 quanta are absorbed by the photopigment. How many rods were activated by the 10 photons absorbed by the retina?" At 20 deg eccentricity, the 10 arc min test stimulus covered an area that contained about 300 rods. It is unlikely that two photons would be absorbed by the same rod when 10 photons hit 300 rods. Therefore: a single quantum can be sufficient to activate a rod, and a visual sensation can be produced by stimulating just 10 rods in the same pool.
4 Subject Variability" Quantal events are inherently random" Typical frequency-of-seeing curve for a dark-adapted subject. Why does the frequency of seeing increase gradually as a function of flash intensity? - Quantal fluctuations - Neural variability For a given light level, the number of photons actually captured varies from one trial to the next, following a Poisson statistical distribution. As the mean number of expected photons per flash increases, the frequency distribution becomes a Normal, or Gaussian distribution. Quantal Fluctuations" Sources of Neural Variability" Poisson distribution of a source that emits an average of 9 quanta per flash. Frequency-of-seeing curve for an ideal detector. Spontaneous isomerization (i.e., bleaching). Spontaneous neurotransmitter release at synapse. Other potential sources (e.g. blood pressure, temperature, subject s criterion, etc.) % of flashes that contain at least 6 quanta.
5 Use a Small Spot" If light is spread out too much, the brain cannot add the photons together efficiently. For small spots there is perfect spatial summation. This example for the fovea shows a summation area with diameter of about 10 arc minutes. In the periphery it is larger. Note for stimuli < 10 min of arc, threshold is constant. Ricco s Law of Spatial Summation: L * A = k L = stimulus luminance A = stimulus area k = constant Hecht et al. used a 10 min of arc spot, containing about 300 rods at 20 Ricco s Law of Spatial Summation" For small areas of retina, called the summation area or Ricco s Area, photon captures are summed together to produce a single neural response. Inside this area, it doesn t matter whether the photons all fall in one place or are spread around, they all get added together. Threshold for seeing a flash is determined by the total photons captured, as long as they all fall in the summation area. Ricco s Law: Luminance x Area = constant (k) (for small spots!) To reach threshold, you need the total luminous energy (L x A) to reach a constant value, k. When stimulus area doubles, you only need half the luminance to reach threshold. As stimulus area gets larger and larger, eventually it will exceed the summation area and the total energy required to reach threshold will start to rise. Use a Brief Stimulus Duration" If photons are spread out in time, the brain cannot add them together as efficiently. Photons that occur within a short period of time are added together in temporal summation. Hecht et al. used 1 msec Note for stimuli < 100 msec, threshold is constant. Bloch s Law of Temporal Summation: L * t = k L = stimulus luminance t = stimulus duration k = constant Bloch s Law of Temporal Summation" For small durations, called the integration time, photon captures are summed together to produce a single neural response. Inside this time window, it doesn t matter whether the photons all fall at once or are spread over time, they all get added together. Threshold for seeing a flash is determined by the total photons captured, as long as they all fall in the integration time. Bloch s Law: Luminance x Time = constant (k) (for short flashes!) To reach threshold, you need the total luminous energy (L x T) to reach a constant value, k. When stimulus duration doubles, you only need half the luminance to reach threshold. As stimulus duration gets longer and longer, eventually it will exceed the integration time and the total energy required to reach threshold will start to rise.
6 Temporal Summation" Temporal Summation IPI = Inter-pulse interval Dashed line indicates threshold for seeing a single pulse.
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