Science 113:292-293 (March 16, 1951)
Critical examination of existing monocular visual acuity data has allowed an estimate of the informational capacity of a human eye to be made in this paper. The problem, analogous to that of the ear (1), is simpler in that visual acuity is ordinarily measured in a way which allows a calculation of total numbers of yes-no decisions, i.e., the standard informational units of "bits" (binary digits) to be made directly.
The maximum acuity of the eye, measured as the inverse of the minimum angular distance necessary to resolve two objects under conditions of good illumination and central fixation is 60/degree (1' of arc is the acuity angle) for a person with "normal," or Snellen 20/20, vision. Consensus of data (2–5) indicates a variable, but higher, acuity figure for many eyes at high illuminations. We have somewhat arbitrarily taken 100/degree as the maximum acuity.
If the visual pattern be regarded as a fine mosaic of "acuity squares," which are either black or white, of an area corresponding to the square of the acuity angle, lasting for a time of the order of the fusion period, the informational capacity can be calculated. The tacit assumption is that the acuity square can be recognized as either present or absent, in a complex retinal pattern, thus furnishing one yes-no decision, or bit of information. With the Landolt ring method of measuring acuity, this is a defensible standpoint, since the discrimination of the presence or absence of the square that size in the pattern is the major task of the eye during the test.
This model, which is a discrete "cell" representation of changes on the retina with time and space, will require a number of bits/sec for specification equalling the total number of such squares/mosaic multiplied by the frequency of appearance of new mosaics. This paper utilizes critical estimates of the best available experimental data bearing on these two quantities.
The classical study of the peripheral dependence of visual acuity is that of Wertheim (6). A number of more recent, and better, studies have been made on acuity in the macular region (7–10). A critical composite of the recent data up to 4½° peripheral, and of the Wertheim data beyond this, is replotted in Fig. 1, as the function r A2 (r), where r is the peripheral angle of vision (degrees), and A (r) the acuity, in inverse degrees. Assuming A (r) to remain azimuthally constant, the total number of acuity squares is seen to be ò0¥prA2 (r) dr, or p times the area under the curve of Fig. 1.
Numerical integration of this curve, and multiplication by p gives a figure of 240,000 acuity squares/mosaic.
To find the maximum number of such mosaics perceptible in a second,
two data are used: (a) the observation that the eye will integrate signals
at high illumination and central fixation over a period of about 0.03 sec
(11), and (b) the measurement that the
decrease of the fusion frequency at a peripheral angle of 100 is about
1.8-fold (12). This is the center of density
of the acuity squares plotted in Fig. 1. These data
give
This figure is valid under conditions of high illumination. For light of lower intensities, both the acuity and the fusion frequency decrease substantially. The only data available on over-all change in retinal acuity with decreasing illumination are those of Mandlebaum and Sloan (8). Fig. 2 is a plot of these data after integrating over the whole retina to convert to informational units, and correcting for decrease in fusion frequency. It resembles an ordinary acuity-illumination curve, but the usual break between rod and cone vision levels is smoothed out by the spatial integration used.
The increase in informational capacity from color perception has been ignored. It would certainly not triple the capacity, and the increase is probably small compared to uncertainties in the data and methods of calculation.
Comparison with similar figures for the ear leads to interesting results. For "random" sound–i.e., sound evenly distributed in frequency and intensity through out the hearing region–a capacity of 8,000 bits/sec has been calculated for the ear (1). Intense sounds will give a 10,000 bit/sec capacity, a result more nearly comparing to the high-illumination calculations of the present paper. A 430-fold difference, informationally speaking, is seen to distinguish the maximal capacities of the two receptors.
A factor of about 30 in the relative capacities of eye and ear can be accounted for by the ratio of nerve fibers leading from these organs (13, 14), but a further difference is evident in the efficiency with which an individual nerve fiber transmits information. The order of 5 bits/sec, av, can be produced by the 900,000 fibers of the optic nerve, compared with a maximum of about 0.33 bits/sec from each of the 30,000 fibers of the auditory nerve. This is clearly due to the greater independence with which the optic nerve signals are produced, in contrast to the prevalence of cooperative signals in the auditory bundles. The phenomenon of masking is less apparent in signals from the eye, which may be said to encode its observations more efficiently.
