Abstract

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.

© 1955 Optical Society of America

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References

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  1. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).
    [CrossRef]
  2. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203 (1946).
    [CrossRef]
  3. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 37, 217 (1947).
    [CrossRef] [PubMed]
  4. These curves were shown in Fig. 21 of reference 3.
  5. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 41 (1951).
    [CrossRef]
  6. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 64 (1951).
    [CrossRef]
  7. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 192 (1951).
    [CrossRef]
  8. This symbol is being used for typographical reasons in place of SΔD as in the figures and as the authors would prefer to write it.
  9. L. A. Jones and N. Deisch, J. Franklin Inst. 190, 657 (1920).
    [CrossRef]

1951 (3)

1947 (1)

1946 (1)

1945 (1)

1920 (1)

L. A. Jones and N. Deisch, J. Franklin Inst. 190, 657 (1920).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Frequency distribution of density differences of a uniformly exposed sample as indicated by a microdensitometer under certain conditions. Solid curve, syzygetic density differences as defined in the text; broken curve, differences from mean measured at short, uniform intervals along the sample.

Fig. 2
Fig. 2

Frequency distribution of syzygetic density differences of a certain sample for scanning spots of various diameters as marked on the curves.

Fig. 3
Fig. 3

Logarithm of the mean syzygetic density differences of several materials as a function of effective density when the sample illuminance is constant and the critical scanning aperture is used. All the values of SΔD were used to compute the mean for each sample, and the diameter of the retinal cones was taken as 1.5 μ. Correlation coefficient, 0.941.

Fig. 4
Fig. 4

Logarithm of the mean syzygetic density differences as for Fig. 3 but with the cone diameter taken as 2.0 μ. Correlation coefficient, 0.914.

Fig. 5
Fig. 5

Frequency distribution of syzygetic density differences (for the critical scanning aperture) of three common amateur films varying in speed and graininess. For explanation of the cutoff, see text.

Fig. 6
Fig. 6

Logarithm of the mean syzygetic density differences as for Fig. 3 but computed on the basis of a 98 percent cutoff as defined in the text. Correlation coefficient, 0.990. This curve is taken as the threshold gradient sensitivity function of the human eye for graininess.

Fig. 7
Fig. 7

Comparison of subjective graininess measurements (solid curves) with values computed from granularity measurements made as described in text (broken curves) for three materials.

Tables (1)

Tables Icon

Table I Characteristics of the three negative materials whose curves of syzygetic density difference are shown in Fig. 5. The materials decrease in graininess and speed in the order A, B, C. Development was in Kodak Developer DK-50 at 68°F for the times tD given in minutes. The effective density is the density computed from the luminance of the screen of the visual graininess instrument when the magnification is below the blending magnification. The graininess H was computed from the blending magnification M and the critical value of ø in microns was then computed from Eq. (2). Each mean value of syzygetic density difference 〈SΔDAv was computed from a curve like those of Fig. 5 on the basis of a 98 percent cutoff as defined in the text.

Equations (2)

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H = 1000 / M .
cr = 2000 17.18 · 1.5 M = 175 M = 0.175 H .