Abstract

The literature concerning the characteristics of the human visual system is reviewed, with special emphasis on the dioptrical and histological properties of the eye and its closely associated nerve structures which are most relevant to the perception of graininess. From the histological evidence and from the results of measurements on visual acuity reported in this paper and in the literature, the conclusion is drawn that the neural responses from relatively few cones situated around the center of the fovea centralis are determinants of the perception of graininess. When viewing a granular field, these cones are stimulated by a rapidly changing illuminance, since, even during attempted fixation on a point in the visual field, the eyeball is not absolutely stationary but is subject to a multidirectional vibratory motion of relatively small amplitudes and high frequencies, the physiological nystagmus. Microdensitometric traces on a group of developed photographic deposits were obtained which show the characteristics of the stimuli incident upon the retinal receptors which are supraliminal, liminal, and subliminal with respect to graininess perception. Since the magnitude of the neural response of about 80 percent of the foveal cones is determined largely by the temporal rate of change in the stimulus incident thereon, it appears that the most relevant characteristics of the stimuli mentioned in the previous sentence are the temporal gradients (that is, the time rate of change) of the stimuli. Merging distance measurements were made on several types of graininess patterns of known geometric design, and from these the spatial distributions of illuminance on the fovea corresponding to the graininess threshold were computed. The temporal illuminance gradients on the retinal receptors when these conventionalized patterns were viewed at the blending distance were also computed by employing the most probable values for the constants of the physiological nystagmic motion of the eye. From these computations it is apparent that the illuminance gradient required to evoke the perception of threshold graininess decreases as the average transmittance of the sample (and hence the average illuminance incident on the retina) decreases. Hence the sensitivity of a receptor to the time rate of change in the incident illuminance varies inversely with the average illuminance to which it is adapted. This functional relation is defined as the gradient sensitivity of a retinal receptor. In the measurement of graininess, either by the variable viewing distance or by the variable magnification techniques, the average illuminance incident on the retina (the adapting illuminance) decreases as the density of the developed silver deposit increases. Hence the gradient sensitivity of the receptors increases as the density of the silver deposit increases. At the same time the configuration of the pattern in the visual field, which is determined by the number, size, shape, and distribution of the developed grains and clumps thereof (and possibly the luminous transmittance of these visual field elements) changes as the density of the silver deposit increases from a low to a high value. These purely objective characteristics of the developed silver image determine that component of the total graininess which may be termed the structural component of graininess. These same structural aspects of the silver deposit also determine the granularity of the sample. Granularity may be measured in a large number of different ways, each leading to a unique numerical value. Each of these values can be defined in terms of the operations used in its determination. Since we are seeking a method of measuring granularity which will yield values which correlate either with the total graininess or with the structural component of graininess of a sample or a group of samples, it is evident that the desired operational definition of granularity must be in harmony with the modes of functioning of the visual system. From an analysis of these modes, it is concluded that the most promising procedure is to evaluate granularity in terms of the frequency of occurrence of the density or transmittance differences existing between a large number of pairs of surface elements of the sample, the two members of each pair of elements being of equal area and immediately adjacent to each other. Such density (or transmittance) differences are termed syzygetic density (or transmittance) differences, SΔD, or SΔT. These particular types of differences must not be confused with the density (or transmittance) differences, ΔD or ΔT, obtained by using the average transmittance, T¯, or the integrated density, ID, of the whole sample as a basis for computation. It is probable that not all of the SΔD or the SΔT values are relevant for the evaluation of granularity, but that those values less than some limit, x, and greater than another limit, y, should be discarded. Moreover, the size of the surface element used in the determination of SΔD or SΔT should be related in some definite manner to the size of the central foveal cones. The evidence indicates that the most probable relationship is that the surface elements of the sample should have a size very nearly equal to that of central retinal cones as projected by the dioptrical elements of the eye onto the sample when viewed at a distance such that the graininess is just perceptible. Since the photographic materials in which we are interested vary over a wide range with respect to the coarseness of their granular structures, it is extremely unlikely that the required values of SΔD or SΔT for the whole gamut of materials can be obtained by employing scanning apertures of fixed sizes in the microprojector used for their measurement. Hence an instrumental technique involving constant magnification with scanning apertures of variable size, or a variable magnification with scanning apertures of constant size, is indicated. The problem of establishing a graininess scale having uniform subjective intervals which involves the determination of just noticeable graininess differences is discussed. New instruments, now under construction, having characteristics in conformity with the requirements based upon conclusions reached by a study of the modes of functioning of the visual system are discussed briefly.

© 1947 Optical Society of America

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