De Vries-Rose Law Research Articles

Internal noise sources limiting contrast sensitivity

Contrast sensitivity varies substantially as a function of spatial frequency and luminance intensity. The variation as a function of luminance intensity is well known and characterized by three laws that can be attributed to the impact of three internal noise sources: early spontaneous neural activity limiting contrast sensitivity at low luminance intensities (i.e. early noise responsible for the linear law), probabilistic photon absorption at intermediate luminance intensities (i.e. photon noise responsible for de Vries-Rose law) and late spontaneous neural activity at high luminance intensities (i.e. late noise responsible for Weber’s law). The aim of this study was to characterize how the impact of these three internal noise sources vary with spatial frequency and determine which one is limiting contrast sensitivity as a function of luminance intensity and spatial frequency. To estimate the impact of the different internal noise sources, the current study used an external noise paradigm to factorize contrast sensitivity into equivalent input noise and calculation efficiency over a wide range of luminance intensities and spatial frequencies. The impact of early and late noise was found to drop linearly with spatial frequency, whereas the impact of photon noise rose with spatial frequency due to ocular factors.

Is the DeVries-Rose to Weber Transition Empirically Possible with Sine-Wave Gratings?

Visual functioning at various retinal illuminance levels is usually measured either by determining grating acuity as a function of light level or by determining how sensitivity to sine-wave gratings changes with retinal illuminance. The former line of research has shown that grating acuity follows a two-branch relationship with retinal illuminance, with the point of discontinuity occurring at the transition from scotopic to photopic vision. Results of the latter line of research have summarily been described as a transition from the DeVries-Rose law to Weber's law, according to which log sensitivity increases linearly with log illuminance with a slope of 0.5 over a range of low illuminances (the DeVries-Rose range) and then levels off and does not increase with further increases of illuminance (the Weber range). This paper aims at determining the compatibility of the results of these two lines of research. We consider empirical constraints from data bearing on the shape of the surface describing contrast sensitivity to sine-wave gratings as a function of spatial frequency and illuminance simultaneously, in order to determine whether they are consistent with a summary description in terms of DeVries-Rose and Weber's laws. Our analysis indicates that, with sine-wave gratings, the DeVries-Rose law can only hold empirically at low spatial frequencies.

Age-related increases in photopic increment thresholds are not due to an elevation in intrinsic noise

Threshold vs. intensity (tvi) functions were measured under conditions in which the slope of the rising branch approximated the deVries-Rose law in order to evaluate the contribution of intrinsic visual noise (dark light, Eigengrau) to age-related elevations in threshold under photopic conditions. Data were obtained from 48 observers (20-88 years) using a temporal 2AFC procedure. The stimulus was centered at 8° nasal retinal eccentricity and consisted of a 560 nm, 14.4' test flash (10 ms) concentric with a steady 500 nm (12.9°) adapting field (13 intensity levels ranging from 0-9 log quanta · sec(-1) · deg(-2)), which resulted in clear scotopic and photopic branches. Photopic thresholds increased linearly with age at a rate of 0.08 log unit per decade at the cornea. The mean slope of the rising portion of the tvi functions (in log-log coordinates) was 0.62, and not correlated with age. Dark light values increased with age, but not significantly. Dark light was a statistically significant predictor of individual differences in absolute photopic threshold, but it is not responsible for age-related increases in threshold under photopic conditions.

A new psychophysical method for determining the photopic spectral-luminosity function of the human eye.

Using an 8 mm pupil, 2AFC-method, and 2 x 2 deg2 grating at 2 c/deg we measured contrast sensitivity as a function of integrated radiance for a series of interference filters with peak wavelengths at 400-700 nm. Irrespective of the radiance level, contrast sensitivity was highest when wavelength was at and around 550 nm. It decreased towards longer and shorter wavelengths, reflecting the variation of the probability of quantal catch with light wavelength. When contrast sensitivity functions plotted in double logarithmic coordinates were shifted horizontally by multiplying the integrated radiances of each filter by an appropriate scaling factor, the functions superimposed onto a single curve. Contrast sensitivity at lower levels of relative radiance (R) increased in proportion to square root of R, obeying DeVries-Rose law, but at higher levels contrast sensitivity was constant, obeying Weber's law. Scaling factors plotted as a function of wavelength provided an estimate of V(lambda) quite similar to the standard 2 deg photopic spectral-luminosity function of CIE 1924.

Neural modulation transfer function of the human visual system at various eccentricities

We measured r.m.s. contrast sensitivity as a function of retinal illuminance at various spatial frequencies within 3–37 deg of eccentricity in the nasal visual field. In dim light contrast sensitivity increased in proportion to the square root of retinal illuminance obeying the De Vries-Rose law but in bright light contrast sensitivity was independent of luminance following Weber's law. Critical retinal illuminance ( I c ) marking the transition between the laws was found to be independent of grating area but proportional to the spatial frequency squared at all eccentricities, in agreement with the Van Nes-Bouman law of foveal vision. In addition, the proportionality constant was found to be independent of eccentricity and similar to that of the fovea. According to our contrast detection model of human vision the modulation transfer function ( P MTF ) of the neural visual pathways squared is directly proportional to the critical retinal illuminance. On this basis our result means that P MTF is similar, i.e. equal to spatial frequency across the visual field, thus attenuating low spatial frequencies relatively more than high spatial frequencies. Hence, up to the spatial cut-off frequency determined by the lowest neural sampling density of each retinal location the neural modulation transfer function is independent of visual location.

Spatiotemporal contrast sensitivity of early vision

Based on the spatial and temporal statistics of natural images, a theory is developed that specifies spatiotemporal filters that maximize the flow of information through noisy channels of limited dynamic range. Sensitivities resulting from these spatiotemporal filters are very similar to the human spatiotemporal contrast sensitivity, including the dependence on ambient light intensity. The theory predicts several psychophysical laws: Ferry-Porter's law, the de Vries-Rose law, Weber's law, Bloch's law, Ricco's law, and Piper's law.

What Does the Retina Know about Natural Scenes?

By examining the experimental data on the statistical properties of natural scenes together with (retinal) contrast sensitivity data, we arrive at a first principle, theoretical hypothesis for the purpose of retinal processing and its relationship to an animal's environment. We argue that the retinal goal is to transform the visual input as much as possible into a statistically independent basis as the first step in creating a redundancy reduced representation in the cortex, as suggested by Barlow. The extent of this whitening of the input is limited, however, by the need to suppress input noise. Our explicit theoretical solutions for the retinal filters also show a simple dependence on mean stimulus luminance: they predict an approximate Weber law at low spatial frequencies and a De Vries-Rose law at high frequencies. Assuming that the dominant source of noise is quantum, we generate a family of contrast sensitivity curves as a function of mean luminance. This family is compared to psychophysical data.

Psychophysical experiments on spatial summation at threshold level of the human peripheral retina

Experiments on spatial summation were done on the temporal retina between 4° and 40° eccentricity. The stimuli were circular discs between 7′ and 280′ of arc dia and 0.01 sec exposure at backgrounds from 0 to 10 −8 W/deg 2. The wavelength of the light was 510 nm for both background and test stimulus. The diameter of “Ricco's region” increases between 4° and 15° eccentricity and has an almost constant value of 100′ between 15° and 40°. For the smallest stimuli, deviations from Ricco's law were found. It appeared in increased thresholds between 15° and 40° eccentricity. We called this phenomenon the non-summation effect. The dependence of retinal sensitivity on eccentricity differs for different sizes of test stimulus and for absolute, scotopic and photopic background intensities. At photopic conditions increment thresholds are governed by Weber's law, the Weber fraction: increment intensity/background intensity ( Δ/LL) being dependent on retinal location and test stimulus size. For scotopic and mesopic adaptation levels at 7° eccentricity and small stimulus sizes the De Vries-Rose law: Δ/LL 0.50= constant holds. The transition from these power functions into Weber's law Δ/LL= c occurs all over the retina within the same narrow range of background intensities. Only the small stimuli that are subject to the non-summation effect also show a different behaviour in this respect.

Receiver operating characteristic analysis. Application to the study of quantum fluctuation effects in optic nerve of Rana pipiens.

Receiver operating characteristic (ROC) analysis of nerve messages is described. The hypothesis that quantum fluctuations provide the only limit to the ability of frog ganglion cells to signal luminance change information is examined using ROC analysis. In the context of ROC analysis, the quantum fluctuation hypothesis predicts (a) the detectability of a luminance change signal should rise proportionally to the size of the change, (b) detectability should decrease as the square root of background, an implication of which is the deVries-Rose law, and (c) ROC curves should exhibit a shape particular to underlying Poisson distributions. Each of these predictions is confirmed for the responses of dimming ganglion cells to brief luminance decrements at scotopic levels, but none could have been tested using classical nerve message analysis procedures.

Luminance-dependent changes in mesopic visual contrast sensitivity.

Spatial and temporal modulation transfer functions have been measured as a function of luminance at scotopic and mesopic levels. It is found that throughout the scotopic range the data can be accounted for by a two process visual system, with the processes having the following properties. Simple excitatory processThis mechanism summates over somewhat less than 1 square degree of visual angle and over about 200 msec of time. These properties do not change with luminance, but the over-all sensitivity of the mechanism follows the De Vries-Rose law. The temporal properties of this mechanism follows those of the scotopic b-wave. At high luminances, the temporal, but not spatial, properties of this mechanism break down in a manner which had not been studied.Low-frequency inhibitory processThis process is manifest as a decrease in sensitivity from that of the simple excitatory process. Its effect is observed only when both spatial and temporal frequency are low, suggesting that it has a larger (perhaps 3 x) summation area in both space and time. The inhibitory process is not observed below a certain threshold luminance, which is highly dependent upon the configuration of the stimulus. For a suitable stimulus, this threshold will be well into the scotopic luminance range.It is suggested that these two processes represent psychophysical correlates of the centre and surround of retinal receptive fields.

A model of a retinal sampling-unit based on fluctuation theory.

Synthesis of the well-known coincidence and fluctuation concepts for description of visual threshold in dependence of geometry and duration of test stimulus and of luminance and of color of a masking background was based on an arithmetic adaptation mechanism in the data processing action of the retina upon the incident quanta (Bouman, 1964; Bouman and Ampt, 1966). This mechanism is essentially a scaler with a scale factor depending on the present and past values of the input intensity and is for a constant input proportional and nearly equal to the square root of the average quanta input per unit time upon the scaler's retinal area. An increase of input makes the scale factor increase with a fixed number for every other pulse of the excess-output. This makes the successive K-values during light adaptation follow an arithmetic series. For dark-adaptation another adequate procedure is suggested. The neurophysiological relevance of the model is demonstrated by successful description of a number of experimental studies on spike-behavior notably by Hartline, Mueller, Ratliff and Kuffler, Fitzhugh and Barlow. As the model stems from psychophysical studies, relevance for visual threshold behavior is implicit in the paper. The De Vries-Rose law and Weber-Fechner law are proven to have unique positions in systems with one stage stochastical scaling mechanisms.

Spatial Modulation Transfer in the Human Eye

The contrast sensitivity of the human eye for sinusoidal illuminance changes was measured as a function of spatial frequency, for monochromatic light with wavelengths of 450, 525, and 650 nm. At each wavelength, data were obtained for a number of illuminance levels. All observations were taken at equal accommodation, and corrected for chromatic aberration. If the wavelength-dependent effects of diffraction on the modulation transfer are taken into account, no difference is found between the photopic contrast-sensitivity functions for red, green, or blue. For mean retinal illuminances B0 smaller than 300 td, threshold modulation M at a given frequency is found to increase in proportion to B0-12 (de Vries–Rose law). For B0 greater than 300 td M remains a constant fraction of it (Weber–Fechner law). After separation of the optical modulation transfer of the eye media from the measured psychophysical data, the remaining function can be considered as composed of a neural and a light-diffusion transfer function. The latter can be compared with the analytic transfer function of photographic film.

Fluctuation theory of luminance and chromaticity discrimination.

An attempt has been made to describe brightness and color discrimination in the framework of a fluctuation theory. The fluctuation theory states that a difference between two stimuli will be just noticeable if it exceeds, by some factor, the average of the fluctuations in the stimuli. If the statistical fluctuations in the number of quanta absorbed are considered as the determining factor, the de Vries–Rose law (ΔB/B~1/B^½) is unforcedly explained. The deflection from this law into Weber’s law (ΔB/B=const) becomes understood in the same framework, provided the statistics are applied on the neural coding rather than on the quantum incidence, considering a refractory period in the nervous transmission. Overfilling of the nervous channels, adaptation of the receptors and fluctuations in the refractory period are indicated as possible causes of the fall in contrast sensitivity at high levels of brightness. Adaptative effects like shrinking of the information-collecting time and area or changes in coincidence mechanisms with increasing luminance, may be reasons of deviations from the basic laws when large areas or exposure times are involved. The application of the fluctuation theory to chromaticity discrimination is elaborated for the case of tritanopia and illustrated for the general case of trichromasy. The agreement between theory and experiment is satisfactory.