Maarten A. Bouman

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.

Spatiotemporal Modulation Transfer in the Human Eye

The contrast sensitivity of the human eye for sinusoidal illuminance changes in space and time, obtained by means of traveling-wave stimuli, was measured as a function of spatial and temporal frequency for white light. The average retinal illuminance was varied between 0.85 and 850 trolands. The threshold modulation for perception of a moving grating is generally higher than that for detection of brightness changes, in space and/or time, that give rise to flicker phenomena. Flicker-fusion characteristics, as determined from the thresholds for the flicker phenomenon, are found to lose their band-pass-filter resemblance for spatial frequencies of more than 5 cycles per degree of visual angle. The thresholds at flicker fusion for spatial- and temporal-frequency combinations in which not both frequencies are very low, appear to be proportional to the inverse of the square root of mean retinal illuminance, in the investigated range. This suggests a photon-noise-dependent threshold mechanism which is operative in a wider illuminance range than that found with contrast-sensitivity measurements for periodic illuminance variations only in space or only in time.

Spatiotemporal Chromaticity Discrimination

The threshold visibility of uniformly moving colored gratings was investigated. The gratings were equiluminous sine-wave patterns, generated on a color-television display. The traveling waves were detected by the subject over a range of three log units of background illuminance, including various spatial- and temporal-frequency combinations. The experiments indicate that no resonance phenomena occur in the spatiotemporal color-discrimination system of the eye. This system probably functions as a low-pass filter. The color coding takes place in much narrower frequency bands than the brightness coding. A regular motion of the pattern never enhances the visibility of the color gratings. The temporal characteristics of the chromatic-discrimination system show very much resemblance to its spatial qualities. Our experiments show that the threshold chromatic contrast is proportional to the square root of the illuminance. This fundamental relationship can easily be understood from the statistical properties of the photons, absorbed in the differential receptor systems.

Perimetry of contrast detection thresholds of moving spatial sine wave patterns. I. The near peripheral visual field (eccentricity 0°–8°)

Contrast detection thresholds for moving spatial sine wave gratings were obtained, at the fovea, and at eccentricities of 1 degree, 2 degrees, 4 degrees, 6 degrees, and 8 degrees on the nasal horizontal meridan, for two subjects. The target field subtended 30 X 30 minutes of arc. The spatial frequency range extended from 2 cpd up to the spatial resolution limit, the temporal frequency range from 0.1 Hz up to the CFF. Mean retinal illuminance was 10 trolands. We find for these conditions: (i) Contrast detection thresholds are higher, the higher the spatial and/or temporal frequency of the stimulus. (ii) Acuity appears to be independent of the temporal frequency, the CFF appears to be independent of the spatial frequency. (iii) The higher the eccentricity, the higher the contrast detection threshold for any drifting sine wave pattern. The threshold doubles roughly any 2 degrees-3 degrees for spatial frequencies of 2-20 cpd, except that the visual field for a given fineness of grating is blind beyond a certain critical eccentricity. This critical eccentricity is a monotonically decreasing function of the spatial frequency of the grating. These measurements do not support the hypothesis that coarse patterns are preferentially detected at extrafoveal sites in the visual field.

Perimetry of contrast detection thresholds of moving spatial sine wave patterns. III. The target extent as a sensitivity controlling parameter.

Contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6 degrees, 21 degrees, and 50 degrees on the nasal horizontal meridian. The targets subtended from 30 X 30 minutes of arc up to 16 degrees X 16 degrees. We have found that the contrast detection thresholds depend critically on the extent of the target field. If this extent is large enough peripheral detection thresholds are on a par with those measured at the fovea, only the sensitivity range is shifted to lower spatial frequencies. We show that if the just resolvable distance at any eccentricity is taken as a yardstick, and field width and spatial frequency are scaled accordingly, then the spatio-temporal contrast detection thresholds become identical over the whole visual field. It is shown that a smaller area, measuring several just resolvable distances across, has to be stimulated before successive or simultaneous contrast detection is possible at all. Detection performance improves if the stimulated area is enlarged up to diameters of at least 10(2) just resolvable distances. The just resolvable distance correlates well with mean interganglion cell distance, and with the cortical magnification factor.

Transfer of spatial chromaticity-contrast at threshold in the human eye.

Color-discrimination data are compared with the predictions of a generalized fluctuation theory for visual threshold behavior. Our observations for the tritanopic component of vision at low luminances are in good agreement with the expectations from this theory. We measured just-noticeable differences of hue with equiluminous square-wave test objects, which were modulated only in chromaticity. A chromaticity-contrast sensitivity function was introduced for the description of these results, in analogy of the luminance-contrast sensitivity function. Observations were made for different spatial frequencies at four reference wavelengths and at several luminance levels. The results do not show an attenuation of the low frequencies such as appears in the luminance-threshold contrast modulation. We infer from this that spatial interactions are different in the chromaticness and brightness channels of the visual system. Furthermore a decrease of the luminance level causes an increase of the neural integrative interaction of the color signals. We divided the measured chromaticity-contrast sensitivity function into an optical and a nervous component. A calculation for the optical part is given.

The Two-Quanta Explanation of the Dependence of the Threshold Values and Visual Acuity on the Visual Angle and the Time of Observation

As shown by van der Velden, for the observation of a short and small light flash it is necessary that at least two quanta of light be effectively absorbed by the visual purple within a time τ (about 0.02 sec.) and within an area corresponding to a visual angle D (about 10′): the two-quanta hypothesis, by which the laws of Ricco, Piper, and Talbot were explained. In the present paper the theoretical foundation is recapitulated and further experiments are described.The extensive experimental results in the present paper are completely covered by the two-quanta hypothesis as far as regards the flash time t<3τ or the visual angle of the light spot d<2D.It is shown, that for the simultaneous occurrence of long flashes and large visual angles, considerable deviations from the theoretical curves derived from the two-quanta hypothesis occur.From these deviations we conclude that T seconds (about 3τ) after the absorption of light quanta the condition of the retina in the neighborhood of these absorptions (within about 3D) is such as to decrease the chance of observation of a subsequent pair of absorbed quanta.Measurements of the visual acuity are found to be in agreement with the two-quanta case.The experimental results of Hecht and Pirenne and the paper by De Vries are discussed, as is also the note of C. Peyrou and H. Piatier about experiments similar to those of van der Velden.

Perimetry of contrast detection thresholds of moving spatial sine wave patterns. II. The far peripheral visual field (eccentricity 0°–50°)

Contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6°, 12°, 21°, 32°, and 50° on the nasal horizontal meridian. The field subtended 4° × 4°. Spatial frequencies ranged from 0.25 cpd up to the resolution limit, temporal frequencies from 0.1 Hz up to the CFF. Mean retinal illuminance was 10 trolands. We find for these conditions: (i) For any eccentricity there exists a unique combination of spatial frequency and velocity for which the threshold is a minimum. (Extremes are 2 cpd and 2° s−1 at the fovea, and 0.5 cpd and 12° s−1 at an eccentricity of 50°. (ii) Acuity depends little on velocity, the CFF only little on spatial frequency. (iii) The higher the eccentricity, the higher the threshold for any drifting sine wave pattern. Except for this the qualitative threshold behavior as a function of spatial and temporal frequency is identical at the fovea and at eccentricities up to 50°. The thresholds double every 12° for spatial frequencies of 0.25–2 cpd. For a given spatial frequency the visual field is blind beyond a certain critical eccentricity. This critical eccentricity is a monotonically decreasing function of spatial frequency.

The Two-Quanta Hypothesis as a General Explanation for the Behavior of Threshold Values and Visual Acuity for the Several Receptors of the Human Eye

With the aid of the three methods for the determination of the number of absorbed quanta necessary for light perception described in previous papers, it is found from extensive threshold measurements with flashes for foveal and peripheral vision that a “red cone” in the periphery probably gives rise to a light impression when two quanta are absorbed in it within a time τ.For the foveal cone systems a light impression is caused for every wave-length by the absorption of two quanta within a time τ and within an angular distance of 2–4 minutes. The different kinds of receptors proved to be capable of reacting in mutual dependence on each other, and the conclusion is drawn that all receptors send a nerve impulse to the nerve connection when one quantum is absorbed.A light impression will occur when a second quantum is absorbed after the first absorption within τ sec. within a receptor within a distance D of the first receptor.Experiments on the visual acuity demonstrate that for all wave-lengths, for foveal as well as for peripheral vision, the dependence of the visual acuity on the intensity agrees with the two-quanta theory.

A mechanistic approach to threshold behavior of the visual system

A dynamic model based on electrophysiological findings is presented for information processing in the visual system. The visual system behaves as an optimal encoder both of information perturbed by Poisson noise at low luminances and of noise-distorted images at suprathreshold level. The basic elements of the model, are: (1) a first layer of square-root scalers mainly performing noise reduction, where each scaler consists of two leaky integrators and a comparator; (2) a layer containing a light detector consisting of one leaky integrator and a comparator, and an increment/decrement detector consisting of two leaky integrators and a comparator. The results of simulations of threshold behavior are given. The authors show that all generally known psychophysical facts can be described with this model. When spatial interaction between neighboring basic elements is introduced, the effects of these interactions spread over a large area, thus changing properties of the total network. So far, this extensive effect has only been proved with phenomenological models. Possible applications of this model in image processing are proposed.