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.
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