Comparisons of the published data on the density D of receptive fields of retinal ganglion cells and on the cortical magnification factor M indicated that M2 is directly proportional to D in primates. Therefore, the human M can be estimated for the principal meridians of the visual field from the density-distribution of retinal ganglion cells and from the density of the centralmost cones. Using the previously published empirical data, we estimated the values of the human M and express the values in four simple equations that can be used for finding the value of M for any location of the visual field. The monocular values of M are not radially symmetric. These analytically expressed values of M make it possible to predict contrast sensitivity and resolution for any location of the visual field. We measured contrast sensitivity functions at 25 different locations and found that the functions could be made similar by scaling the retinal dimensions of test gratings by the inverse values of M. Visual acuity and resolution could be predicted accurately for all retinal locations by means of a single constant multiplier of the estimated M. The results indicate that the functional and structural properties of the visual system are very closely and similarly related across the whole retina. Visual acuity, e.g., bears the same optimal relation to the density of sampling executed by retinal ganglion cells at all locations of the visual fields.

This study shows that photopic contrast sensitivity and resolution can be predicted by means of simple functions derived by using the cortical magnification factor M as a scale factor of mapping from the visual field into the striate cortex. We measured the minimum contrast required for discriminating the direction of movement or orientation of sinusoidal gratings, or for detecting them in central and peripheral vision. No qualitative differences were found between central and peripheral vision, and almost all quantitative differences observed could be removed by means of a size compensation derived from M. The results indicated specifically that (1) visual patterns can be made equally visible if they are scaled so that their calculated cortical representations become equivalent; (2) contrast sensitivity follows the same power function of the cortical area stimulated by a grating at any eccentricity; (3) area and squared spatial frequency are reciprocally related as determinants of contrast sensitivity; and (4) acuity and resolution are directly proportional to M, and the minimum angle of resolution is directly proportional to M-1. The power law of spatial summation expressed in (2) and (3) suggests the existence of a central integrator that pools the activity of cortical neurons. This summation mechanism makes the number of potentially activated visual cells the most important determinant of visibility and contrast sensitivity. The functional homogeneity of image processing across the visual field observed here agrees with the assumed anatomical and physiological uniformity of the visual cortex.

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We recorded whole-scalp magnetoencephalographic (MEG) responses to black-and-white checkerboards to study whether the human cortical responses are quantitatively similar to stimulation of the lower and upper visual field at small, 0-6 degrees, eccentricities. All stimuli evoked strong occipital responses peaking at 50-100 ms (mean 75 ms). The activation was modeled with a single equivalent current dipole in the contralateral occipital cortex, close to the calcarine fissure, agreeing with an activation of the V1/V2 cortex. The dipole was, on average, twice as strong to lower than to upper field stimuli. Responses to hemifield stimuli that extended to both lower and upper fields resembled the responses to lower field stimuli in source current direction and strength. These results agree with psychophysical data, which indicate lower visual field advantage in complex visual processing. Parieto-occipital responses in the putative V6 complex were similar to lower and upper field stimuli.

In a generalized form, the cortical magnification theory of peripheral vision predicts that the thresholds of any visual stimuli are similar across the whole visual field if the cortical stimulus representations calculated by means of the cortical magnification factor are similar independently of eccentricity. Failures of the theory in spatial vision were analyzed, and the theory was tested with five visual acuity tasks and two hyperacuity tasks. Almost all increases in thresholds with eccentricity were explained by the theory in five of these tasks, which included the two-dot vernier hyperacuity test, the measurement of visual acuities with gratings, the Snellen E test, and two acuity tests that required either separation between dots or discrimination between two mirror-symmetric forms. The two-dot vernier thresholds could be explained as a special case of orientation discrimination, and orientation discrimination at different eccentricities was in agreement with the cortical magnification theory. The increase of thresholds in peripheral vision was larger than predicted by the theory in the Landolt visual acuity and bisection hyperacuity tests, possibly because of retinal undersampling.