D. H. Kelly

Motion and vision. II. Stabilized spatio-temporal threshold surface.

The stabilized contrast-sensitivity function measured at a constant retinal velocity is tuned to a particular spatial frequency, which is inversely related to the velocity chosen. The Fourier transforms of these constant-velocity passbands have the same form as retinal receptive fields of various sizes. At low velocities, in the range of the natural drift motions of the eye, the stabilized contrast-sensitivity function matches the normal, unstablized result. At higher velocities (corresponding to motions of objects in the environment), this curve maintains the same shape but shifts toward lower spatial frequencies. The constant-velocity passband is displaced across the spatio-temporal frequency domain in a manner that is almost symmetric about the constant-velocity plane at v = 2 deg/s. Interpolating these diagonal profiles by a suitable analytic expression, we construct the spatio-temporal threshold surface for stabilized vision, and display its properties in terms of the usual frequency parameters; e.g., at low spatial frequencies, the temporal response becomes nearly independent of spatial frequency, while at low temporal frequencies, the spatial response becomes independent of temporal frequency.

Spatiotemporal variation of chromatic and achromatic contrast thresholds

Moving the retinal image of a sinusoidal grating at a constant velocity (compensated for eye movements) provides controlled spatial and temporal frequencies at every point in the stimulus field. Using this controlled-velocity technique, we have measured the detection threshold for isoluminance, red/green gratings as a function of their spatial and temporal frequencies. The chromatic contrast-threshold surface obtained in this way is analogous to the achromatic contrast-threshold surface measured previously, but the results are quite different. For very low temporal frequencies (below 0.2 Hz), the chromatic sensitivity decreases steadily with decreasing temporal frequency. Below 0.01 Hz, chromatic patterns disappear completely even at maximum contrast (although achromatic or homochromatic patterns do not). In the region above 0.2 Hz, both achromatic and chromatic thresholds can be explained by the same receptive-field-like model. When the center and the surround components of this model are additively combined, they form the chromatic threshold surface; when the sign of either component is reversed, they form the achromatic one.

Motion and vision. I. Stabilized images of stationary gratings

To demonstrate that eye movements have profound effects on the sine-wave contrast threshold, the author uses a new method of stabilizing the retinal image, in which the Purkinje reflections from the eye move the stimulus pattern displayed on a CRT screen. Calibration of this compensatory motion is very critical; a gain error greater than 1% may produce significant destablization. Under optimum conditions, image stabilization elevates the subjects contrast threshold by a factor of about 20; it also produces after-images with resolution greater than 12 c/deg. These results compare favorably with those obtained by other methods.

Spatio-temporal frequency characteristics of color-vision mechanisms*

Spatio-temporal sine-wave response functions are inferred for the red-, green-, and blue-sensitive receptor mechanisms of the visual process, by selective chromatic-adaptation experiments and Weber-law calculations. The complete spatio-temporal threshold surface for each cone mechanisms is abbreviated to four critical profiles: two contrast-sensitivity curves measured at the temporal frequencies of minimum and maximum sensitivity, and two flicker-sensitivity curves measured at the spatial frequencies of minimum and maximum sensitivity. Throughout most of the spatio-temporal frequency domain, the green sensitivity is greatest, the red is less, and the blue is least of all. The curve shapes can be qualitatively explained in terms of antagonistic interactions in the early visual pathways.

Nonlinear visual responses to flickering sinusoidal gratings

Over a range of high temporal and low spatial frequencies, counterphase flickering gratings evoke the so-called frequency-doubling illusion, in which the apparent brightness of the grating varies at twice its real spatial frequency. The form of the nonlinearity that causes this second-harmonic distortion of the visual response was determined by a cancellation technique. The harmonic distortion can be measured as a function of amplitude (or contrast) by adding to the flickering grating a real, nonflickering, double-frequency component with the amplitude and phase required to cancel the illusory second harmonic. Harmonic distortion curves obtained in this way imply that the nonlinearity is of the form /s/p, where s is the stimulus pattern (without its dc component) and p is close to 0.6. If p = 1, or if the absolute value is not taken, this expression predicts distortion curves that differ significantly from the experimental results. Hence neither rectification nor compression alone is sufficient to account for the second-harmonic distortion; both are required.

Theory of Flicker and Transient Responses,* II. Counterphase Gratings

The model derived in the preceding paper is applied to new sine-wave flicker data, obtained with 7° circular, uniform-field and counterphase-grating targets, at four adaptation levels ranging from 1.67 to 1670 td. The data from all eight conditions are well fitted by varying two parameters associated with neural-inhibition processes; the major effect of changing the spatial pattern is on the number of neural units involved. But even when lateral inhibition is minimized, low-frequency feedback still dominates the transient responses of the model. These results can be interpreted in terms of spatial and temporal filtering in the outer and inner plexiform layers of the retina.

Flickering Patterns and Lateral Inhibition

The effects of spatial patterns on the sine-wave flicker sensitivity are explored with sharp and blurred edges, circular and rectilinear targets having various flickering and nonflickering areas, and gratings of various spatial frequencies with adjacent bars flickering in opposite phases. The results are consistent with pattern responses studied electro-physiologically by Spekreijse, Riggs, and others. Pattern effects (as opposed to area effects) are confined to frequencies below 10 Hz, and can be explained in terms of the temporal characteristics of lateral inhibition. Earlier differences between the flicker data of deLange and those of Kelly are resolved on this basis, and a response function is calculated for the cross-connecting filters of the inhibiting network.

Retinal inhomogeneity. I. Spatiotemporal contrast sensitivity

Spatiotemporal sine-wave contrast thresholds were measured at four retinal eccentricities: 0 degrees, 3 degrees, 6 degrees, and 12 degrees. Threshold functions of spatial frequency were determined for each eccentricity at two selected temporal frequencies, and functions of temporal frequency at two selected spatial frequencies. Fixation was controlled by stabilizing the retinal image. The stimulus patterns were circular cosine targets confined to annular zones, so that stimulation occurred in all meridians simultaneously. In spite of these unusual conditions, our results were in good agreement with unstabilized, single-meridian data from other laboratories. The spatial-frequency functions obtained at both high and low flicker rates scaled with eccentricity in the same way. For the bandpass functions obtained at 0.5 Hz, the reciprocal of the peak spatial frequency varied linearly with eccentricity. Measured with spatial patterns chosen in accord with this scaling relation, both sets of temporal-frequency functions were essentially independent of eccentricity. Threshold functions at constant velocity were also consistent with the same scaling relation.

Spatiotemporal characteristics of visual mechanisms: excitatory-inhibitory model

The stabilized spatiotemporal threshold response surface can be modeled as the linear difference between the threshold response surfaces of two mechanisms, each of which is simply the product of a spatial and temporal frequency response curve. With no free parameters, the resulting model is shown to be a good fit to available data.

Diffusion model of linear flicker responses.

Recent cascaded-integrator models do not fit the sine-wave flicker thresholds as well as we might wish, but neither does the Ferry–Porter law. In fact, the Ferry–Porter function is not physically realizable as a linear model. By modifying it to yield realizable responses like those of the cascaded integrator, we obtain a much simpler model, which appears to be a special case of the photochemical diffusion mechanism proposed by Ives and more recently by Veringa. This model is a good fit, not only to the flicker data, but also to human phase-shift measurements obtained by the phosphene method. We infer that receptor-cell properties probably control the high-frequency linear filtering of flicker waveforms.