G. C. Higgins

Photographic Granularity and Graininess*III. Some Characteristics of the Visual System of Importance in the Evaluation of Graininess and Granularity

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.

Variation of Visual Acuity with Various Test-Object Orientations and Viewing Conditions*

Visual acuity was measured in terms of the reciprocal of the angle in minutes subtended by the individual lines in a parallel-line test object at the limit of perception of the lines when the observer was allowed to see the target for less than one millisecond. Visual acuity, measured with the lines passing either vertically or horizontally through the visual field, was found to be approximately 20 percent higher than when measured with the lines passing diagonally through the visual field at angles of 45 and 135 degrees with the horizontal. These results indicate that the variation in the visibility f a parallel-line test object as a function of its orientation is not produced by preferential directions for eye movements. The variation of visual acuity with test-object orientation was also measured as a function of pupil diameter and fixation point, but these data do not give any conclusive evidence as to the factors producing the variations.

Visual Acuity as Measured with Various Orientations of a Parallel-Line Test Object*

Visual acuity has been measured in terms of the reciprocal of the angle in minutes subtended by the individual lines in a parallel-line test object at the limit of perception of the lines. Both clear and opaque lines in this test object were of equal width. It was found that the limit of perception of the lines in such a test object depends upon the orientation of the lines. Visual acuity, measured with the lines passing diagonally through the visual field at an angle of 45 degrees to the horizontal, is between 10 and 20 percent lower than that measured with the parallel lines passing vertically or horizontally through the visual field.

On the Information-Detecting Capacity of Photographic Emulsions*

The concepts of quantum efficiency and detecting capacity of photographic emulsions are discussed with reference to the granularity, spread function, and characteristic curve of the emulsion. A measure of informational sensitivity is introduced which depends on these quantities and provides an objective measure of performance of emulsions when they are compared at their optimum working scales. In terms of this measure, as well as from a direct visual appraisal of picture quality, it appears that two emulsions, such as Kodak Tri-X Film and Kodak Panatomic-X Film, can have widely different sensitometric speeds but quite similar informational sensitivities.

Measurement and Analysis of the Distribution of Energy in Optical Images

It is pointed out that a theoretical relation exists between the distribution of energy in the image of an edge (edge trace) and the distribution in the image of a line (line spread-function). Experimental data are presented in support of this relation and the method of determining these distributions experimentally is outlined. It is also pointed out that, since the spot diagram of a lens represents the point spread-function, the line spread-function, needed for the foregoing procedure, can be found by mechanical summation of this diagram. An example is given to show that the edge trace of the finished lens can be thus predicted from the spot diagram.

Photographic Granularity and Graininess†,*II. The Effects of Variations in Instrumental and Analytical Techniques

Several proposals for measuring the granularity of developed silver images, in purely objective terms, have appeared in the literature. These can be classified into two general groups, namely: those which base the evaluation of granularity upon the variations in the transmittance of relatively small elements of the developed image and those which use variations in density. In this paper one method representing each of the two classes is examined in some detail, especially with respect to the dependence of the granularity value upon the size of the scanning aperture which is used in obtaining basic data on the variations in transmittance or density. The experimental results indicate clearly that values of granularity, determined on the basis of the assumption that the distribution of transmittance values is represented by the Gaussian equation, are not independent of the size of the scanning aperture. Moreover, the frequency of occurrence of transmittance variations departs markedly from the Gaussian law when relatively small scanning apertures are used. Values of granularity based upon the variations in density, assuming a Gaussian distribution of these variations, also depend upon the size of the scanning apertures used. While the frequency of occurrence of density variations corresponds approximately to the Gaussian law for some scanning aperture sizes, the departure from Gaussian distribution is very marked in the case of small scanning apertures. With the photographic materials used in this work, no scanning aperture size was found which gave granularity-versus-density functions similar in shape to the graininess-density function. Some alternative methods of analyzing the basic data are discussed briefly. None of these show promise of yielding a satisfactory solution of this problem which, in our opinion, demands that the granularity-density function derived from objective functions shall be identical in shape to that of the graininess function. Finally, some preliminary discussion of certain visual aspects of the general problem is given. It is assumed that some definite and unique relationship should exist between the size of the scanning aperture used in the objective evaluation of granularity and the effective size of the light-sensitive elements of the eye. Some semiquantitative data are presented which illustrate, in a general way at least, the distribution of illuminance on the retinal mosaic when the granular photographic image is viewed at the blending distance. These indicate that the number of visual field elements imaged on a single visual receptor (foveal cone) is small, usually of the order of 3 or 4, and seldom exceeding 8 or 10, even though the photographic materials used in this work varied over a wide range with respect to the coarseness of granular structure.

Frequency and Amplitude of Ocular Tremor

Data are presented on the magnitude and frequency of the involuntary eye motions (rapid motions superimposed on slow drifts) that take place during attempted fixation on a target. A record of these motions was obtained by directly photographing a blood vessel of the eye. Vertical and horizontal motions were recorded for both monocular and binocular fixation. The rapid motions were found to have an average frequency of 50 cps and an average amplitude of 1.2 minutes of arc. These data are in approximate agreement with previous data of Adler and Fliegelman and of Ratliff and Riggs. Simultaneous tracks of head and eye motions show that the rapid eye motions are independent of head motions.

The Relationship Between the Granularity and Graininess of Developed Photographic Materials

The objective quantity, “granularity,” which refers to the spatial variations in transmitting or reflecting characteristics of a developed photographic material, has been determined for a group of materials differing widely in sensitivity and grain size. These measurements were made by several different methods which have been proposed by various workers. The psychophysical quantity, “graininess,” which refers to the visual appearance of the granular structure in a developed photographic material, has been measured by the method proposed by Jones and Deisch. These measurements of graininess were made on the same samples as those which were used in the evaluation of granularity. None of the methods of measuring granularity give the same functional relation between granularity and the density of the silver image as that existing between graininess and density. However, by choosing arbitrarily a density level which is not the same for all of the objective methods, all these methods can be made to give granularity values which place the different photographic materials in approximately the same order as the graininess values, but for no method is the order exactly the same. Moreover, even when the order is the same, the granularity values are not proportional to the graininess values. These results indicate that the objective methods measure one or more, but not all, of the factors which determine graininess.

Experimental Study of rms Granularity as a Function of Scanning-Spot Size*

Experimental data on the constancy of Selwyn granularity, S=σ(D)·(2a)12, with variations in scanning-aperture diameter are presented. Selwyn granularity S is found to be essentially constant for a series of aperture diameters from 7.5 to 384 μ if the sample is clean and has no macroscopic variations in density. The effect of sample imperfections, such as density wedging, streaks, scratches, and dirt is discussed.

Methods for Engineering Photographic Systems

The treatment of a photograph as a communication channel is reviewed. The characteristics that are peculiar to photography, such as adjacency effects and the double function of the emulsion as light diffuser and transducer, are emphasized, and the diverse standpoints from which quality can be appraised are pointed out.