Retinal noise and absolute threshold

On the molecular origin of photoreceptor noise

Retinal photoreceptors are noisy. They generate discrete electrical events in the dark indistinguishable from those evoked by light and thereby limit visual sensitivity at low levels of illumination. The random spontaneous events are strongly temperature-dependent and have been attributed to thermal isomerizations of the vitamin A chromophore of rhodopsin, the light-sensitive molecule in photoreceptors. But thermal generation of dark events in both vertebrate and invertebrate photoreceptors requires activation energies in the range of 23 to 27 kcal mol-1, which are significantly less than the energy barrier of 45 kcal mol-1, for photoisomerization of the chromophore of native rhodopsin. We propose that photoreceptor noise results from the thermal isomerization of a relatively unstable form of rhodopsin, one in which the Schiff-base linkage between the chromophore and protein is unprotonated. This molecular mechanism is supported by both theoretical calculations of the properties of rhodopsin and experimental measurements of the properties of photoreceptor noise.

Temporal and spatial summation in the human rod visual system

1. Absolute and increment thresholds were measured in a retinal region 12 deg temporal from the fovea with 520 nm targets of varying size and duration. Measurements were made under rod-isolation conditions in two normal observers and in a typical, complete achromat observer who has no cone-mediated vision. The purpose of these experiments was to determine how the temporal and spatial summation of rod-mediated vision changes with light adaptation. 2. The absolute threshold and the rise in increment threshold with background intensity depend upon target size and duration, but the psychophysically estimated dark light of the eye (the hypothetical light assumed to be equivalent to photoreceptor noise) does not. 3. The rise in increment threshold for tiny (10 min of arc), brief (10 ms) targets approaches the de Vries-Rose square-root law, varying according to the quantal fluctuations of the background light. The slope of the rod increment threshold versus background intensity (TVI) curves in logarithmic co-ordinates is about 0.56 +/- 0.04 (when cones are not influencing rod field adaptation). For large (6 deg) and long (200 ms) targets, a maximum slope of about 0.77 +/- 0.03 is attained. 4. The steeper slopes of the rod-detected TVI curves for large, long targets implies some reduction in temporal or spatial summation. In fact, the change in summation area is much more critical: under conditions where only the rod system is active the TVI curve slope is independent of target duration, suggesting that temporal summation is practically independent of background intensity. 5. The rise in threshold also depends on the wavelength of the background field in the normal observer but not in the achromat, confirming reports that the field adaptation of the rods is not independent of the quantal absorptions in the cones. The cone influence is most conspicuous on long-wavelength backgrounds and is found for all target sizes and durations, but is greater for large and long targets than for the other conditions.

Retinal origins of the temperature effect on absolute visual sensitivity in frogs

1. The absolute sensitivity of vision was studied as a function of temperature in two species of frog (Rana temporaria, 9-21 degrees C, and Rana pipiens, 13-28 degrees C). 2. Log behavioural threshold (measured as the lowest light intensity by which frogs trying to escape from a dark box were able to direct their jumping) rose near-linearly with warming with a regression coefficient of 1.26 +/- 0.03 log units per 10 degrees C (Q10 = 18). Threshold retinal illumination corresponded to 0.011 photoisomerizations per rod per second (Rh* s-1) at 16.5 degrees C. 3. The effect of dim backgrounds on jumping thresholds suggested 'dark lights' of 0.011 Rh* s-1 at 16.5 degrees C and 0.080 Rh* s-1 at 23.5 degrees C, corresponding to Q10 = 17. 4. Response thresholds of retinal ganglion cells were extracellularly recorded in the isolated eyecup of R. temporaria. The thresholds of the most sensitive cells when stimulated with large-field steps of light were similar to the behavioural threshold and changed with temperature in a similar manner. 5. The decrease in ganglion cell 'step' sensitivity with warming consisted of a decrease in summation time (by a factor of 2-3 between 10 and 20 degrees C) and an increase in the threshold number of photoisomerizations (a decrease in 'flash' sensitivity, by a factor of 2-5 over the same interval). No effect of temperature changes on spatial summation was found. 6. Frequency-of-response functions of ganglion cells indicated an 11-fold increase in noise-equivalent dark light between 10 and 20 degrees C (mean values in four cells 0.009 vs. 0.10 Rh* s-1). 7. The temperature dependence of ganglion cell flash sensitivity could be strongly decreased with dim background illumination. 8. It is concluded that the desensitization of dark-adapted vision with rising temperature is a retinal effect composed of shortened summation time and lowered flash sensitivity (increased numbers of photons required for a threshold response) in ganglion cells. The desensitization bears no simple relation to the apparent retinal noise increase.

Noise and the absolute thresholds of cone and rod vision

Literature data on light detection by cone and rod vision at absolute threshold are analysed in order (1) to decide whether the threshold performance of dark-adapted cone vision can, like that of rod vision, be consistently explained as limited by noise from a "dark light"; (2) to obtain comparable estimates of the dark noise and dark light of (foveal) cones and (peripheral) rods. The dark noise was estimated by a maximum-likelihood procedure from frequency-of-seeing data and compared with the dark light derived from increment-threshold functions. In both cone and rod vision, the estimated dark noise coincides with Poisson fluctuations of the estimated dark light if 17% (best estimate) of lambda max-quanta incident at the cornea produce excitations. At that fraction of quanta exciting, dark lights are equivalent to 112 isomerisations per sec in each foveal cone and 0.011 isomerisations per sec in each rod. It is concluded that (1) the threshold performance of dark-adapted cone as well as rod vision can be consistently described as noise-limited, but not by postulating a multi-quantum coincidence requirement for single receptors; (2) the underlying intrinsic activity in both the cone and the rod system is light-like as regards correspondence between noise effect and background adaptation effect. One possibility is that this activity is largely composed of events identical to the single-photon response, originating in the visual pigment, in cones as well as in rods.

Quantal noise and decision rules in dynamic models of light adaptation

To evaluate some of the consequences of including probabilistic processes (e.g. quantal noise) in a computable model of light-adaptation dynamics, we considered the behavior of a general class of models. These models contain four stages: (1) early noise; (2) a deterministic filtering and gain-changing stage; (3) late noise; (4) a decision rule that is either an ideal (signal-known-exactly) detector or a peak-trough detector. With the ideal detector and without late noise, the observer's sensitivity as a function of mean luminance and temporal frequency is not affected by the filtering and gain-changing stage. Consequently, if the early noise is entirely quantal fluctuations, sensitivity will always be a square-root function of mean luminance and a uniform (flat) function of temporal frequency. This latter prediction is contradicted by all known data; either the ideal-detector is the wrong decision rule or sensitivity is almost always limited by sources of noise other than quantal fluctuations. With the peak-trough detector, however, with or without late noise, the observer's sensitivity as a function of temporal frequency does reflect the sensitivity of the low-level filtering and gain-changing stage. Late noise is needed, however, if the observer's sensitivity as a function of mean luminance is to go through both a square-root and a Weber region. Comparing these conclusions to similar work on the spatial frequency dimension highlights differences between the spatial and temporal frequency domains. Finally, on the basis of these analyses and evidence from the literature, we question whether quantal fluctuations limit visual sensitivity under any condition.

Scotopic visual efficiency: constraints by optics, receptor properties, and rod pooling

We studied the influence of optics, photoreceptor properties, and rod pooling on scotopic contrast sensitivity by comparing the performance of an ideal discriminator to that of human observers. Comparisons of human and ideal contrast sensitivities indicated that preretinal factors and summation area were not sufficient to explain the shape of the human CSF. Spatial pooling of rods was explored as a possible explanation of this discrepancy. Our highest efficiency, expressed in terms of a human/ideal contrast sensitivity ratio, was about 1:3 (0.33) for a contrast discrimination task.

Temporal filtering in retinal bipolar cells. Elements of an optimal computation?

Recent experiments indicate that the dark-adapted vertebrate visual system can count photons with a reliability limited by dark noise in the rod photoreceptors themselves. This suggests that subsequent layers of the retina, responsible for signal processing, add little if any excess noise and extract all the available information. Given the signal and noise characteristics of the photoreceptors, what is the structure of such an optimal processor? We show that optimal estimates of time-varying light intensity can be accomplished by a two-stage filter, and we suggest that the first stage should be identified with the filtering which occurs at the first anatomical stage in retinal signal processing, signal transfer from the rod photoreceptor to the bipolar cell. This leads to parameter-free predictions of the bipolar cell response, which are in excellent agreement with experiments comparing rod and bipolar cell dynamics in the same retina. As far as we know this is the first case in which the computationally significant dynamics of a neuron could be predicted rather than modeled.

The frequency of isomerization-like 'dark' events in rhodopsin and porphyropsin rods of the bull-frog retina

1. The dark current and responses to dim flashes were recorded with the suction pipette technique from single rods in pieces of bull-frog retina taken from either the dorsal porphyropsin or the ventral rhodopsin field. 2. The composition of visual pigment in the rods was determined by microspectrophotometry. Rods from the dorsal pieces contained 70-88% porphyropsin523 mixed with rhodopsin502. The ventral rods contained almost pure rhodopsin, any possible admixture of porphyropsin being below the level of detectability (less than 5%). 3. In most cells, the responses to dim flashes were well fitted by a four-stage linear filter model, with no systematic differences in the response kinetics of porphyropsin and rhodopsin rods. The amplitude of saturated responses varied between 8 and 55 pA and that of responses to single isomerizations between 0.4 and 3.5 pA. 4. In porphyropsin rods, discrete events similar to the response to one photoisomerization were clearly seen in complete darkness. The dark current amplitude histogram was fitted by a convolution of the probability densities for the Gaussian continuous noise component and the averaged dim-flash response waveform. This allows estimation of the frequency and amplitude of discrete events and the standard deviation of the continuous component. The mean frequency of discrete dark events thus obtained from six porphyropsin cells was 0.057 rod-1 s-1 at 18 degrees C. 5. In rhodopsin rods, the dark current amplitude histogram appeared completely symmetrical, indicating that the frequency of discrete events must be lower than 0.005 rod-1 s-1 (except in one rod where it was 0.006 events rod-1 s-1). Per molecule of rhodopsin, the events are then at least 5 times rarer than reported for toad rhodopsin rods at the same temperature. 6. The low rate of isomerization-like 'dark' events in bull-frog rhodopsin rods shows, firstly, that results cannot be generalized across species even for rhodopsins which appear spectrally identical. Secondly, it suggests that these events need not (in an evolutionary sense) constitute an irreducible noise factor which must set the ultimate limit to the sensitivity of dark-adapted vision. 7. The difference between porphyropsin and rhodopsin rods shows that, given (presumably) the same opsin, the pigment utilizing retinal2 and absorbing maximally at longer wavelengths produces more noise. The signal/noise ratio attained in the photoreceptor may be an important factor in the natural selection of visual pigments.

Weber and noise adaptation in the retina of the toad Bufo marinus

Responses to flashes and steps of light were recorded intracellularly from rods and horizontal cells, and extracellularly from ganglion cells, in toad eyecups which were either dark adapted or exposed to various levels of background light. The average background intensities needed to depress the dark-adapted flash sensitivity by half in the three cell types, determined under identical conditions, were 0.9 Rh*s-1 (rods), 0.8 Rh*s-1 (horizontal cells), and 0.17 Rh*s-1 (ganglion cells), where Rh* denotes one isomerization per rod. Thus, there is a range (approximately 0.7 log units) of weak backgrounds where the sensitivity (response amplitude/Rh*) of rods is not significantly affected, but where that of ganglion cells (1/threshold) is substantially reduced, which implies that the gain of the transmission from rods to the ganglion cell output is decreased. In this range, the ganglion cell threshold rises approximately as the square root of background intensity (i.e. in proportion to the quantal noise from the background), while the maintained rate of discharge stays constant. The threshold response of the cell will then signal light deviations (from a mean level) of constant statistical significance. We propose that this type of ganglion cell desensitization under dim backgrounds is due to a post-receptoral gain control driven by quantal fluctuations, and term it noise adaptation in contrast to the Weber adaptation (desensitization proportional to the mean background intensity) of rods, horizontal cells, and ganglion cells at higher background intensities.

Equivalent intrinsic blur in spatial vision

We used Gaussian blurred stimuli to explore the effect of blur on three tasks: (i) 2-line "resolution"; (ii) line detection; and (iii) spatial interval discrimination, in both central and peripheral vision. The results of our experiments can be summarized as follows. (i) 2-Line "resolution": thresholds for pairs of unblurred, low contrast, stimuli are approx. 0.5 min arc in the fovea. When the stimulus blur is small, it has little effect upon 2-line "resolution"; however, when the stimulus blur, sigma, exceeds 0.5 min, thresholds are degraded. We operationally define this transition point as the equivalent intrinsic blur or Bi. When the standard deviation of the stimulus blur, sigma, is greater than Bi, then the "resolution" threshold is approximately equal to sigma. Both the unblurred "resolution" threshold, and the equivalent intrinsic blur, Bi, vary with eccentricity in a manner consistent with the variation of cone separation within the central 10 deg. When the stimulus blur exceeds the equivalent intrinsic blur, "resolution" in the periphery is the same as in the fovea. (ii) Line detection: when the standard deviation of the stimulus blur, sigma, is less than Bi, then the line detection threshold is approximately inversely proportional to sigma (it is approximately TdBi/sigma) i.e. it obeys Ricco's law. When the standard deviation of the stimulus blur, sigma, is greater than Bi, then the "resolution" threshold is approximately equal to sigma and the detection threshold is approximately a fixed contrast (to be referred to as Td). According to (i) and (ii), the equivalent intrinsic blur, Bi, plays a dual role in determining both the "resolution" threshold and the detection threshold, Bi corresponds to the "Ricco's diameter" for spatial summation in a detection task, and it also corresponds to the "resolution" threshold for thin lines. This connection between detection and "resolution" is somewhat surprising. (iii) Spatial interval discrimination: thresholds are proportional to the separation of the lines (i.e. Weber's law). At the optimal separation, the thresholds represent a "hyperacuity" (i.e. they are smaller than the "resolution" threshold). For unblurred lines, the optimal separation is approximately 2-3 times the "resolution" limit at all eccentricities, so the optimal separation varies with eccentricity at the same rate as the equivalent intrinsic blur, Bi. However, the optimal spatial interval threshold falls off with eccentricity about 3-4 times more rapidly, consistent with the rate of decline of other position acuity tasks.(ABSTRACT TRUNCATED AT 400 WORDS)

Low retinal noise in animals with low body temperature allows high visual sensitivity

The weakest pulse of light a human can detect sends about 100 photons through the pupil and produces 10-20 rhodopsin isomerizations in a small retinal area. It has been postulated that we cannot see single photons because of a retinal noise arising from randomly occurring thermal isomerizations. Direct recordings have since demonstrated the existence of electrical 'dark' rod events indistinguishable from photoisomerization signals. Their mean rate of occurrence is roughly consistent with the 'dark light' in psychophysical threshold experiments, and their thermal parameters justify an identification with thermal isomerizations. In the retina of amphibians, a small proportion of sensitive ganglion cells have a performance-limiting noise that is low enough to be well accounted for by these events. Here we study the performance of dark-adapted toads and frogs and show that the performance limit of visually guided behaviour is also set by thermal isomerizations. As visual sensitivity limited by thermal events should rise when the temperature falls, poikilothermous vertebrates living at low temperatures should then reach light sensitivities unattainable by mammals and birds with optical factors equal. Comparison of different species at different temperatures shows a correlation between absolute threshold intensities and estimated thermal isomerization rates in the retina.

Ganglion cell performance at absolute threshold in toad retina: effects of dark events in rods

1. The performance of ganglion cells in detecting flashes of light near the absolute threshold was studied in an isolated eye-cup preparation of toad retina. Retinal ganglion cells, through which all visual information from the rods must flow to the brain, are in a key position for evaluating the still unproven hypothesis that the absolute light sensitivity is limited by rod noise (Barlow, 1956). 2. The dark-adapted threshold intensity for these cells, which were selected on the basis of their high sensitivity, averaged 0.029 Rh* flash-1 (range 0.008-0.062), where Rh* signifies one photoisomerization per rod. On average, 46 photoisomerizations were needed per receptive field per flash to evoke a threshold response (range 16-84). 3. In the threshold region, frequency of responses versus mean flash intensity was determined. Threshold performance could be described by theoretical frequency of response curves, allowing intrinsic noise to be estimated in terms of an equivalent rate of photoisomerization-like (dark) events. In two completely characterized cells the rate of dark events corresponded to 0.03 and 0.06 Rh*DS-1, where Rh*D signifies one dark event per rod. 4. Threshold elevations produced by dim backgrounds were studied. The results of these experiments are consistent with a dark event rate equivalent to 0.046 Rh*DS-1, or 0.037 Rh*DS-1 after correcting for a probable decrease in summation time. 5. The rate of actual dark events (0.028 Rh*DS-1, 20 degrees C) measured in Bufo rods (Baylor, Lamb & Yau, 1980) is close to the equivalent rates determined here. Thus, for the ganglion cells signalling the dimmest lights, the dark events in rods appear to be the most significant intrinsic retinal noise source limiting detection.

Adaptation-related changes in the spatial and temporal summation of frog retinal ganglion cells

The spatial and temporal summation of light by the receptive field centre of frog retinal ganglion cells were studied by extracellular recording in the eyecup preparation. The purpose was to quantify how summation changes with the state of light and dark adaptation and to clarify whether changes are due to the transition between rod and cone vision. Spatial summation was found to decrease by 30-50% as the cell was light-adapted to a threshold some 4 log units above the dark-adapted one. Temporal summation for threshold responses fell as the power -0.17 of the intensity of an adapting steady background. Neither change was bound to the rod-cone transition but occurred in the ranges of both receptor types; at equal sensitivities the summation of both receptor systems was matched.

The signal-to-noise characteristics of rod-cone interaction

1. The influence of rods on cone-mediated vision was assessed in eight human observers. To this end, increment threshold functions were obtained by determining thresholds of a cone-detected test flash (25 ms duration, 655 nm wave-length, 13' diameter) as a function of the illuminance of larger, 500 ms duration, rod-detected masking flashes. The type of photoreceptor influenced by each stimulus was carefully checked by means of a series of control procedures involving action spectra and selective rod adaptation.2. When the rod mask was 512 nm in wave-length, 40' in diameter, and less than one scotopic td in illuminance, increment threshold functions show that [Formula: see text], where I(Cth) is cone test threshold, I(R) is rod mask illuminance, and D is a dark noise term similar to that used by Barlow (1956). Further increases in I(R) have no additional influences on cone test threshold until threshold is influenced by the combined action of the mask on both rods and cones. If I(R) is expressed in terms of scotopic flux rather than illuminance, the functional relationship obtained with all rod masks </= 40' diameter and </= 580 nm wave-length is identical.3. Over the range of illuminance where a square-root relationship is obtained, probability of seeing functions show that a signal-to-noise mechanism limits the detectability of the cone test flash. These findings suggests a quantitative model in which cones produce a signal in a detector which is proportional to the illuminance of the cone test flash. Within a neural locus designated E (excitatory spatial summator), a response is produced which over at least a 40' diameter area, is proportional to the scotopic flux of the rod mask. E, however, feeds into a gain box, S, which saturates at illuminance levels at least 3 log(10) units less than usual estimates of rod saturation. Other than saturation, S behaves in a linear fashion.4. As diameter increases beyond 60', rod masks of equal scotopic illuminance have progressively less influence on cone test threshold; rod masks > 2 degrees have negligible influence on cone test threshold. We propose that I (inhibitory spatial summator), a neural locus which responds to scotopic flux provided over a very large area, attenuates the activity of E. The combined action of E and I is designated a rod channel. The response of cones and the rod channel summate at a detector. Within the detector, cone signals are distinguished from rod-related activity and intrinsic dark noise on the basis of signal-to-noise discriminations.5. The neural substrate for this rod channel most probably involves the combined action of several neurones which synapse within the inner plexiform layer of the retina. The relationship of this rod channel to other perceptual phenomena is discussed.

The precision of numerosity discrimination in arrays of random dots

The precision of making discriminations between the numbers of dots in a pair of irregular arrays was measured. The results fit the assumption that the observer adds intrinsic variance to whatever variance is present in the numbers displayed, the errors depending upon the sum of the two. We found no evidence for incomplete use of the sample of information presented, other than this observer variance. Its value increases as about the 0.75 power of the mean number of dots in a display, except for numbers up to about 20 where it changes much more rapidly. Decreased irregularity in the arrangement of the dots decreases observer variance, but it is little affected by large variations in average density of dots per unit area, and is also little changed by making the dots vary irregularly in brightness.

An analysis of voltage noise in rod bipolar cells of the dogfish retina

1. The power spectral density of voltage noise in depolarizing rod bipolar cells was analysed during darkness and steady illumination. 2. The variance of the voltage fluctuations increased nearly linearly with dim light but was suppressed by bright light. 3. The spectrum in darkness and during illumination could be resolved into two components. One component was attributed to random quantal events arising from spontaneous or light-induced isomerization of rhodopsin in the bipolar cell's rod pool. 4. The second component had a peaked spectrum and was attributed to synaptic noise. 5. A significant fraction of the noise variance in the dark arose from spontaneous thermal isomerization of rhodopsin, with a rate constant of 6 X 10(-12) s-1 or a half-life for rhodopsin of 3700 years at 17 degrees C. 6. The peak amplitude of the single-photon signal in the bipolar cell was about 200 microV, associated with a peak conductance increase of 200 pS. The spectral data suggest that there may be a random delay in the generation of these events. 7. It was concluded that the limitation to single-photon detection in the dark-adapted state may be the rate of spontaneous rhodopsin isomerization. Synaptic noise at the rod-bipolar cell level would not seriously degrade the signal-to-noise ratio.

Multiplication noise in the human visual system at threshold: 1. Quantum fluctuations and minimum detectable energy

We have carried out a series of frequency-of-seeing experiments similar to those performed by Hecht, Shlaer, and Pirenne [J. Gen. Physiol. 25, 819-840 (1942)], using an Ar+ laser operated at 514.5 nm as the source of light. In certain blocks of trials, our subjects were encouraged to report as seen those trials in which the stimulus might have been present. It was determined that sensitivity and reliability were traded against each other over a broad range: for our subjects, the detection of 147 photons at the cornea with 60% frequency of seeing entailed, on the average, a 1% false-positive rate (FPR), whereas the detection of 34 photons at the cornea with 60% frequency of seeing was accompanied by a 33% FPR. A new neural-counting model has been developed in the framework of signal-detection theory. It combines Poisson stimulus fluctuations with additive and multiplicative neural noise, both of which are known to be present in the visual system at threshold. The resulting probability-of-detection curves, derived from the Neyman Type-A counting distribution, are in good accord with our experimental frequency-of-seeing data for sensible values of the model parameters. We deduce that, on the average, our four subjects are able to detect a single photon at the retina with 60% frequency of seeing, at the expense of a 55% FPR. In Part 2 of this set of papers [P.R. Prucnal and M.C. Teich, Biol. Cybern. 43, 87-96 (1982)], we use the normalizing transform, together with probit analysis, to provide improved estimates of threshold parameters, whereas in Part 3 [M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, and W.J. McGill, submitted to Biol. Cybern.], we consider the effects of non-Poisson quantum fluctuations.

Multiplication noise in the human visual system at threshold. 3. The role of non-Poisson quantum fluctuations

Several kinds of light used in vision experiments produce photon statistics that are distinctly non-Poisson. Representative examples are light from a cathode-ray tube and an image-intensifier device. For the class of vision experiments in which the photon statistics play an important role, excess fluctuations produced by such light sources can alter the observed results and obscure the visual mechanisms being studied. They must therefore be accounted for in a proper way. We use the results of a Hecht-Shlaer-Pirenne type experiment, carried out with modulated Poisson light, to illustrate the point. Sensitivity and modulation depth, as well as sensitivity and reliability, are shown to be traded against each other. Finally, we demonstrate that number-state light, which is comprised of photons of an ideal kind, provides the ultimate tool for extracting information about the intrinsic noise distribution in the visual system at threshold. The state of the art in producing such light is discussed.

Multiplication noise in the human visual system at threshold: 2. Probit estimation of parameters

A mathematical technique is described that relates detection model parameters to stimulus magnitude and experimental probability of detection. The normalizing transform is used to make the response statistics approximately Gaussian. Conventional probit analysis is then applied. From measurements at M stimulus levels, a system of M equations is solved and estimates of M unknown parameters of the detection model are obtained. The technique is applied to a threshold vision model based on additive and multiplicative Poisson noise. Results are obtained for the parameter estimates for individual subjects, and for the standard deviation of the estimates, for various values of the stimulus energy and number of trials. A frequency-of-seeing experiment is performed using a point-source stimulus that randomly assumes 3 energy levels with 200 trials per level. With a central efficiency of 50%, the estimated ocular quantum efficiency for our four subjects lies between 12% and 23%, the average dark count at the retina lies between 8 and 36 counts, and the threshold count for our (low false-report rate) data lies between 11 and 32. The theoretical results reduce to those obtained by Barlow (J. Physiol. London 160, 155-168, 1962), in the absence of dark light and multiplication noise.

Spatial and temporal summation in the human dark-adapted retina

A coherent set of absolute-threshold data is presented for circular flashes with a diameter of 5-343 min of arc, a flash duration of 32-1000 msec, and at eccentricities between 7 and 50 deg in the temporal retina. A reduction in the flash interval from 4 to 1 sec causes a threshold elevation for eccentricities exceeding 15 deg for all other stimulus parameters. It is shown that local adaptation affects the measurements significantly, especially when long-lasting stimuli and large eccentricities exist. The results can be described with the help of a quanta-coincidence model if adaptational properties are included.

The Ferrier Lecture, 1980. Critical limiting factors in the design of the eye and visual cortex

The main factors limiting the performance of the peripheral parts of the visual system can be specified, and doing this clarifies the nature of the interpretive tasks that must be performed by the central parts of the system. It is argued that the critical factor that hinders development of better resolving power is the difficulty of confining light within the waveguide-like outer segment, and that for sensitivity this critical factor is the thermal decomposition of photosensitive pigments. Knowledge of these limits makes many surprising details of the eye intelligible. Understanding the difficulties posed by the narrow dynamic range of nerve fibres may give similar insight into the coding of the retinal image for transmission to the brain. Our level of understanding changes when we come to the visual cortex, for although we do not lack good anatomical and neurophysiological data, these do not make the principles of operation self-evident in the way that the structure of the eye immediately suggests that it is an image-forming device. The cortex converts the representation of the visual field that it receives into reliable knowledge of the world around us, and the trouble may be that we lack good models of how this can be done. A system that can respond to single quanta and resolve almost to the diffraction limit is unlikely to employ grossly inefficient methods for those higher functions upon which its whole utility depends, and so it is worth seeking out the limiting factors. The quality of human performance at certain higher perceptual tasks is high compared with the limit of reliable statistical inference; hence much of the sample of information available in a visual image must be effectively utilized. But there are strong limitations on the connectivity in the cortex, so that one is forced to consider how the relevant information can be collected together. Three stages of dealing with the visual image are proposed: the improvement of the cortical map in primary visual cortex by processes analogous to spatial and temporal interpolation ; the detection of linking features in this map; and the concentration of this information by non-topographical mapping in adjacent visual areas.

Photon-like signals following weak rhodopsin bleaches

The rod visual system in its dark-adapted state behaves as a near-ideal light detector. Psychophysical studies on the reliability of light detection in man, analysis of the dark noise in rod bipolar cells and observation of photon-like events in rods in the dark suggest that the visual pigment, rhodopsin, is very stable against spontaneous isomerization. When a light which bleaches a small fraction of the rhodopsin is extinguished, the visual threshold may be increased by several orders of magnitude. The eye is then 'light-adapted' and the process (or processes) by which the sensitivity returns constitutes dark adaptation. We report here that bleaching of a small fraction of the rhodopsin produces a prolonged increase in the noise observed in the dark in rod bipolar cells of the dogfish retina. The associated noise events are similar to those produced by the absorption of light quanta and presumably have their origin in the rods which transmit their signals to the bipolar cells. This increased noise after bleaching would decrease the reliability of detection of light quanta and contribute to the elevation of visual threshold.

Spontaneous quantal events induced in toad rods by pigment bleaching

Barlow proposed that absolute visual threshold is limited by photon-like noise events in the rod photoreceptors, and he later extended the idea to explain the elevation of threshold following bright bleaching lights in terms of increased noise in the photoreceptors. Rushton, on the other hand, has proposed that the threshold elevation during dark adaptation involves changes not within the photoreceptors themselves but rather in the gain of a subsequent 'pool'. I report here measurements of outer segment current in individual rod photoreceptors which demonstrate that spontaneous fluctuations occur at a greatly increased rate following bleaches of around 1%, and that these fluctuations have the form expected for random occurrences of the single photon events. This is consistent with Barlow's ideas but does not indicate whether a gain change subsequent to the receptors also occurs.

The single-photon signal in rod bipolar cells of the dogfish retina

1. Responses of depolarizing bipolar cells to dim light flashes were recorded with intracellular micro-electrodes in the dark-adapted retina of the dogfish, Scyliorhinus canicula. 2. Fluctuations in the responses were analysed by a method of matched filtering in order to improve the signal-to-noise ratio. 3. Both the mean and variance of the response amplitude increased linearly with light intensity for intensities not exceeding a mean of 1 photon absorbed per 50 rods. 4. On the assumption that the most significant source of the fluctuation is the quantal absorption of light by the rod outer segments, a single photoisomerization leads to a post-synaptic event of mean size 250 micronV. 5. The mean number of rods in the pool sending signals to a bipolar cell is estimated as 1600. Individual rod pools are 90-330 micrometer in diameter on the retinal surface. 6. It is estimated that the conductance of 1 divided by 400 of the total number of light-modulated ionic channels in the bipolar cell is increased by a single photon acting within its rod pool. 7. In the absence of a light stimulus, the residual noise in the output of a matched filter can be interpreted as due mainly to spontaneous isomerization of rhodopsin in the rods and behaves as the 'dark light' postulated to limit detection at absolute threshold.

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications

A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [IEEE Trans. Inf. Theory IT-25, (March, 1979)].

Electrophysiological measurement of the number of rhodopsin molecules in single Limulus photoreceptors

Two partly independent electrophysiological methods are described for measuring the number of rhodopsin molecules (R) in single ventral photoreceptors. Method 1 is based on measurements of the relative intensity required to elicit a quantal response and the relative intensity required to half-saturate the early receptor potential (ERP). Method 2 is based on measurements of the absolute intensity required to elicit a quantal response. Both methods give values of R approximately equal to 10(9). From these and other measurements, estimates are derived for the surface density of rhodopsin (8,000/micrometer2), the charge movement during the ERP per isomerized rhodopsin (20 X 10(-21) C), and the half-time for thermal isomerization of rhodopsin (36yr).

Light-evoked and spontaneous discrete waves in the ventral nerve photoreceptor of Limulus

Discrete waves, recorded from the ventral nerve photoreceptor, occur in the light and in the dark. Spontaneous waves, on the average, are smaller than light-evoked waves. This suggests that not all spontaneous waves can arise from spontaneous changes in the visual pigment molecule identical to changes induced by photon absorption. Spontaneous and light-evoked waves are statistically independent of each other. This is shown by determination of frequency of response as a function of pulse energy for short pulses and determination of the distribution of intervals between waves evoked by steady lights. The available data can be explained by two models. In the first each photon produces a time-dependent excitation that goes to zero the instant the wave occurs so that the number of effective absorptions from a short light pulse equals the number of waves produced by the light pulse. In the second the excitation produced by photon absorption is unaffected by the occurrence of the waves so that the number of waves produced from a short light pulse may be different from the number of effective absorptions. Present results do not allow a choice between the two models.

Single units and sensation: a neuron doctrine for perceptual psychology?

The problem discussed is the relationship between the firing of single neurons in sensory pathways and subjectively experienced sensations. The conclusions are formulated as the following five dogmas:

To understand nervous function one needs to look at interactions at a cellular level, rather than either a more macroscopic or microscopic level, because behaviour depends upon the organized pattern of these intercellular interactions. The sensory system is organized to achieve as complete a representation of the sensory stimulus as possible with the minimum number of active neurons. Trigger features of sensory neurons are matched to redundant patterns of stimulation by experience as well as by developmental processes. Perception corresponds to the activity of a small selection from the very numerous high-level neurons, each of which corresponds to a pattern of external events of the order of complexity of the events symbolized by a word. High impulse frequency in such neurons corresponds to high certainty that the trigger feature is present.

The development of the concepts leading up to these speculative dogmas, their experimental basis, and some of their limitations are discussed.

Perceptual indices of performance: the measurement of 'inspection time' and 'noise' in the visual system

Indices of human performance are less clear-cut than analogous measures in the physical sciences for several reasons. Variables which can alter performance include the noise upon which sensory signals are imposed, the bias shown by an observer towards one or another alternative, the use of an optional-stopping strategy for examining sensory input, and the accumulation of statistical information over time concerning the source of the input. The development of a theoretical appreciation of these variables is traced and, on this basis, a measure of the noise, which sets a limit to discriminative capacity, is suggested. The proposed index is simply the standard deviation of the best fitting normal ogive, calculated for the psychometric function obtained in a forced-choice discrimination task by the method of constant stimuli, the discriminanda being presented for 100 ms, in random order, and followed by appropriate backward masking. The index is thus closely related to traditional psychophysical measures, but is distinguished by the detailed specification of conditions under which it should be obtained. Analysis of data from previous experiments gives some indication of the order of magnitude that might be expected from a carefully controlled determination of the measure. In addition, three experiments were carried out to evaluate this suggestion, and to test its underlying rationale. In the first two, observers were required to discriminate, by pressing one of two keys, between two lines of markedly different length, exposed in random order for ten different durations. In the third, stimulus exposure was held constant, while ten different stimulus differences were presented in random order. Results from the first two experiments yielded estimates of minimum inspection time close to 100 ms, and were inconsistent with the view that observers can abandon an optional-stopping procedure of processing sensory information in favour of responding by a deadline. Measures of noise calculated in the third experiment were of the order expected on the proposed rationale, while response latencies were again inconsistent with the notion of deadline responding. Further analysis of the results of the three experiments suggests that measures of inspection time and noise, together with a third index related to the degree of caution exercised by an observer, appear to be stable and consistent descriptors of performance. The wider implications of the successful use of this kind of perceptual index of performance are discussed with reference to the measurement of visual acuity, as a means for detecting effects of environmental stress, and as a conceptual framework for the understanding of individual differences.