Loyd A. Jones

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.

The Nature and Evaluation of the Sharpness of Photographic Images

The ability of a photographic material to produce pictures having good definition is commonly referred to as its sharpness, which is a subjective concept. The objective quantity 〈G 2 x 〉 Av . DS is shown to be a physical measurement which correlates with sharpness judgments. 〈G 2 x 〉 Av is the mean of the square of the density gradients, ×D/×x, across an abrupt boundary between a light and a dark area in the developed image and DS is the density difference between these areas. 〈G 2 x 〉 Av is evaluated only for those values greater than 0.005 in density per micron which represents the threshold gradient. It is shown that, contrary to the generally accepted belief, resolving power does not correlate well with sharpness judgments and in some cases is even misleading.

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.

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.

Photographic Granularity and Graininess. VIII.* A Method of Measuring Granularity in Terms of the Scanning Area Giving a Threshold Luminance Gradient†

It is shown that, when a photographic image of uniform density is viewed under such conditions that graininess is just perceptible, the average spatial luminance gradient on the cones of the eye is a function of the density of the sample alone if the illuminance on the sample is held constant. This function, which bears a logarithmic relation to net density and is independent of the nature of the photographic image, is herein termed the threshold gradient sensitivity function of the eye for graininess. Granularity is defined in terms of the diameter of the scanning aperture that will produce this threshold gradient on the cones of the eye for the density of the sample in question. It is shown that granularity as thus expressed can be multiplied by a constant factor to give the same numerical value of threshold graininess that would be obtained by measuring the sample visually under standard conditions.

The Control of Photographic Printing by Measured Characteristics of the Negative

A large amount of experimental data has been obtained to determine what portion of the D-log E curve of photographic paper is useful in making high quality prints. Psychophysical statistical methods were necessary in solving this problem. Special attention was given to selecting a procedure which would yield results of maximum practical significance. Prints were made from about 200 negatives using five different exposures on each of three contrast grades of paper for each negative. Most of the work was done with a normal, commercially available set of semi-matte surface papers having six different contrast grades. Additional work was done using glossy and matte surface papers. Every set of prints was judged by a number of observers to determine the best print. The location of the “first-choice” prints on their respective D-log E curves was then obtained from maximum and minimum density readings on the prints and on the negatives. The data for second-choice and third-choice prints were also obtained as a matter of general interest. It was found that the minimum or shadow density of a negative is a much more reliable guide for determining correct printing exposure than the maximum or highlight density. The integral or average density of the negative is nearly but not quite as satisfactory for this purpose as the minimum density. Of great interest is the fact that the useful maximum density of the printing paper was, on the average, considerably below the available maximum density, while the useful minimum density of the paper was usually very close to, and often equal to, zero density. The primary requirements, however, appear to be expressed by gradients rather than by densities. It was found that the limits of the useful portion of the D-log E curve of the positive material are determined very closely by fractional gradients of 0.1 Ḡ on the toe of the curve and 1.0 Ḡ on the shoulder of the curve, where Ḡ is the average gradient measured between these two limiting points. This conclusion has an important bearing on the establishment of a significant method for expressing the sensitometric characteristics of photographic papers. It leads to an evaluation of the effective printing speed and the useful exposure scale of the positive material. The proposal is made that speed be defined as 104/E, where E is the exposure corresponding to the limiting gradient on the shoulder of the curve. The useful log exposure scale of the paper is defined as the log exposure interval lying between the two limiting gradients. The application of these results to the making of prints by sensitometric control is discussed. In general, a negative should be printed so that its minimum density falls on the shoulder of the D-log E curve at the point where speed is measured. A method is given whereby the density scale of the negative can be used with reasonable success to determine the proper contrast grade of paper for making the print.

Photographic Granularity and Graininess. VI. Performance Characteristics of the Variable-Magnification Graininess Instrument*

Data obtained with the variable-magnification graininess instrument described in Part V of this series of communications are given showing the variation of graininess as a function of the luminance of the test field, the luminance of the various components of the observer’s field, the viewing distance, and the angular subtense of the test field. On the basis of these data, standard conditions for the various variables are established for the measurement of graininess. Graininess measurements in terms of blending magnification at a constant viewing distance are compared with graininess measurements in terms of blending distance at a constant magnification.

Photographic granularity and graininess. V. A variable-magnification instrument for measuring graininess

An instrument has been built to measure graininess in terms of the reciprocal of the blending magnification of an image of the sample as viewed by binocular vision from a constant distance. This instrument is essentially an autofocus variable-magnification projector which forms an image of constant size and of a luminance which is proportional to the transmittance of the sample. The image is formed on a rear-projection screen which is part of the front wall of a special observation room. The blending magnification may be determined either by permitting the observer to vary the magnification continuously until graininess is just perceptible, or by the experimenter varying the magnification discontinuously and presenting the enlarged image of the sample to the observer at ten predetermined magnifications and having the observer judge only whether or not graininess is perceptible at each magnification. With the latter method, the image at each of the predetermined magnifications is repeatedly presented to the observer in a random order and the frequency of perception of graininess at each magnification of the image is plotted as a function of magnification. From this psychometric function the blending magnification is determined as that magnification at which the observer has perceived graininess during 50 percent of the observations.

On the Relation between Time and Intensity in Photographic Exposure

Work has been continued on the failure of the photographic reciprocity law, E=It. The failure of this law using Panchromatic and Orthochromatic emulsions is somewhat greater than reported previously for high speed non-color sensitive emulsions. Slow Ordinary and Lantern emulsions show very great failure and also a marked change of gamma with intensity. In general, for fast plates the variation of density with intensity is small, optimal intensity is at a low value, and gamma is independent of intensity. For slow plates the density variation is great, optimal intensity high, and gamma drops at low intensities. As found by Kron, optimal intensity shifts to higher values with increasing development time.Kron’s usually accepted empirical law does not fit the observed data. An alternative form It=I0t02[(II0)α+(II0)−α]has been found to fit the observed data for fast plates over a range of 1:8,000,000 in intensity and to fit the data for slow plates at high intensities. For these emulsions the observed failure is greater than the calculated curve indicates at low intensities. This equation was suggested by Kron but it did not fit his observations. The observed data thus far indicate that the dependence of gamma on intensity follows as a result of changes in the effective grain size frequency function caused by a differential failure of the reciprocity law for grains of different sizes and sensitivities.

Photographic Granularity and Graininess. IV. Visual Acuity Thresholds; Dynamic versus Static Assumptions*

The distances at which a series of rectangular test objects are visible were determined experimentally. These test objects were black opaque rectangles having variable length-width ratios and were viewed against a trans-luminated background. Using these data, and an assumed nystagmic motion of the eyeball, the summated temporal illuminance gradients on the retina were computed. These values were found to be essentially constant, even though the length-width ratios of the test objects varied from 1 to 4050. Assuming a motionless eyeball, that is, perfect fixation, the summated values of ΔI were computed for the same observational conditions, ΔI being defined as the difference between the average illuminance incident on adjacent cones in the retinal mosaic. The values of summated ΔI are not constant. Since all of these test objects were just visible at the distance measured, they may be considered as being equal to each other with respect to their ability to excite a threshold neural response. It seems reasonable to conclude, therefore, that since the values of the summated temporal gradients are constant they are the most significant indices of the relative magnitudes of the neural responses. In our opinion these results lend considerable support to the assumption that the perception of inhomogeneities of luminance in the visual field is dependent directly upon the temporal illuminance gradients to which the retinal receptors are subjected by virtue of the movement of the image with respect to the retinal mosaic.