Abstract

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.

© 1946 Optical Society of America

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References

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  1. L. A. Jones and G. C. Higgins, “The relationship between the granularity and graininess of developed photographic materials,” J. Opt. Soc. Am. 35, 435 (1945).
    [Crossref]
  2. A. Goetz and W. O. Gould, “The objective quantitative determination of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 29, 510 (1937); A. Goetz, W. O. Gould, and A. Dember, “The objective measurement of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 34, 279 (1940).
  3. E. W. H. Selwyn, “Experiments on the nature of graininess,” Phot. J. 79, 513 (1939).
  4. L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).
  5. See reference 3, page 523.
  6. S. L. Polyak, The Retina (University of Chicago Press, Chicago, 1941).

1945 (1)

1939 (1)

E. W. H. Selwyn, “Experiments on the nature of graininess,” Phot. J. 79, 513 (1939).

1937 (2)

L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).

A. Goetz and W. O. Gould, “The objective quantitative determination of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 29, 510 (1937); A. Goetz, W. O. Gould, and A. Dember, “The objective measurement of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 34, 279 (1940).

Beacham, H. R.

L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).

Goetz, A.

A. Goetz and W. O. Gould, “The objective quantitative determination of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 29, 510 (1937); A. Goetz, W. O. Gould, and A. Dember, “The objective measurement of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 34, 279 (1940).

Gould, W. O.

A. Goetz and W. O. Gould, “The objective quantitative determination of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 29, 510 (1937); A. Goetz, W. O. Gould, and A. Dember, “The objective measurement of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 34, 279 (1940).

Higgins, G. C.

Jones, L. A.

L. A. Jones and G. C. Higgins, “The relationship between the granularity and graininess of developed photographic materials,” J. Opt. Soc. Am. 35, 435 (1945).
[Crossref]

L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).

Polyak, S. L.

S. L. Polyak, The Retina (University of Chicago Press, Chicago, 1941).

Russell, M. E.

L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).

Selwyn, E. W. H.

E. W. H. Selwyn, “Experiments on the nature of graininess,” Phot. J. 79, 513 (1939).

J. Opt. Soc. Am. (1)

J. Soc. Mot. Pict. Eng. (2)

A. Goetz and W. O. Gould, “The objective quantitative determination of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 29, 510 (1937); A. Goetz, W. O. Gould, and A. Dember, “The objective measurement of the graininess of photographic emulsions,” J. Soc. Mot. Pict. Eng. 34, 279 (1940).

L. A. Jones, M. E. Russell, and H. R. Beacham, “A developing machine for sensitometric work,” J. Soc. Mot. Pict. Eng. 28, 73 (1937).

Phot. J. (1)

E. W. H. Selwyn, “Experiments on the nature of graininess,” Phot. J. 79, 513 (1939).

Other (2)

See reference 3, page 523.

S. L. Polyak, The Retina (University of Chicago Press, Chicago, 1941).

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Figures (28)

Fig. 1
Fig. 1

Sample microphotometer record.

Fig. 2
Fig. 2

Hypothetical distribution functions. Curve A, Gaussian; B, symmetrical with finite limits; C, asymmetrical with finite limits.

Fig. 3
Fig. 3

Hypothetical data showing Fig. 2 plotted as cumulative frequency functions.

Fig. 4
Fig. 4

Cumulative frequency functions from Fig. 3 plotted on arithmetic probability paper.

Fig. 5
Fig. 5

Two configurations of equal area apertures compared to a hypothetical granular structure.

Fig. 6
Fig. 6

Microphotometer traces of a straight edge as made with various diameter scanning apertures. The points represent theoretical computed values.

Fig. 7
Fig. 7

Microphotometer traces made at different sample speeds: A, 0.17 mm/min.; B, 0.08 mm/min.

Fig. 8
Fig. 8

The variation of G G · a 1 2 with a 1 2. Sample A, Super-XX; B, Pan-X; C, FG Neg.

Fig. 9
Fig. 9

Cumulative frequency curves for Super-XX obtained with various diameter (μ) scanning apertures.

Fig. 10
Fig. 10

Cumulative frequency curves for Pan-X obtained with scanning apertures of various diameters.

Fig. 11
Fig. 11

Cumulative frequency curves for FG Neg. obtained with scanning apertures of various diameters.

Fig. 12
Fig. 12

Granularity, S, as a function of a 1 2. Each curve is for a different density on FG Neg.

Fig. 13
Fig. 13

Granularity, S, as a function of a 1 2. Each curve is for a different density on Super-XX.

Fig. 14
Fig. 14

Cumulative frequency curves for a single density on Super-XX obtained with scanning apertures of various diameters.

Fig. 15
Fig. 15

Cumulative frequency curves, for different densities on FG Neg., made with a scanning aperture of 39.9μ in diameter.

Fig. 16
Fig. 16

Variation of granularity, S, with density as measured with scanning apertures of various diameters. The curves in part A are for Super-XX and those in part B for FG Neg.

Fig. 17
Fig. 17

Cumulative frequency curves for a density of 0.42 on Tri-X, obtained with scanning apertures of various diameters.

Fig. 18
Fig. 18

Frequency distribution curves for a density of 0.42 on Tri-X, obtained with circular scanning apertures of various diameters.

Fig. 19
Fig. 19

Frequency distribution curves for a density of 0.42 on Tri-X, obtained with scanning apertures of various diameters.

Fig. 20
Fig. 20

Frequency distribution curves for a density of 0.42 on Tri-X, obtained with scanning apertures of various diameters.

Fig. 21
Fig. 21

Cumulative frequency curves for a density of 0.42 on Tri-X, obtained with scanning apertures of various diameters.

Fig. 22
Fig. 22

Cumulative frequency curves for a density of 0.42 on Tri-X, obtained with scanning apertures of various diameters.

Fig. 23
Fig. 23

The variation of granularity, S, with √a for a density of 0.42 on Tri-X.

Fig. 24
Fig. 24

Variation of Selwyn granularity (Curve A) and Goetz-Gould granularity (Curve B) with the diameter of the scanning aperture for the same sample of Super-XX (density = 0.42).

Fig. 25
Fig. 25

Frequency of occurrence of density differences as measured with a 10.7-μ-diameter scanning aperture on a sample of Tri-X having a density of 0.42

Fig. 26
Fig. 26

Photomicrographs representing the areas covered by scanning apertures of different diameters.

Fig. 27
Fig. 27

Composite photomicrographs representing the distribution of illuminance on the retinal mosaic when the sample is at the blending distance. (a) Tri-X, D = 0.45; (b) Super-XX, D = 0.43; (c) Pan-X, D = 0.45; (d) FG Neg., D = 0.44.

Fig. 28
Fig. 28

Composite photomicrographs representing the distribution of illuminance on the retinal mosaic (Super-XX, D = 0.43). The photomicrograph (a) is for a viewing distance 25 percent less than the blending distance; (c) is for the viewing distance 25 percent greater than the blending distance; and (b) is for a viewing distance equal to the blending distance.

Tables (7)

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Table I Photographic materials.

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Table II Goetz-Gould granularity versus size of scanning aperture.

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Table III Selwyn granularity versus size of scanning aperture. Fine Grain Panchromatic Duplicating Negative Film.

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Table IV Selwyn granularity versus size of scanning aperture. Aeromap Super-XX Film.

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Table V Effect on standard deviation of the non-Gaussian frequency distribution.

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Table VI Comparison of granularity measurements in terms of transmittance and density fluctuations. Super-XX, D = 0.43, ϕ = 39.9μ.

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Table VII Dimensional relationship between the retinal mosaic and the retinal image of a granular structure at the blending distance.

Equations (10)

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V K = average ( T a 1 T a 2 ) ,
G G = 1000 σ t g · 2 ,
S = σ d g ( 2 a ) 1 2 ,
Density = log 10 1 / transmittance .
y = A exp [ ( x x m ) 2 / 2 σ 2 ] ,
σ = [ ( x x m ) 2 / n ] 1 2 ,
y = 1 / ( σ ( 2 π ) 1 2 ) x exp [ ( x x m ) 2 / 2 σ 2 ] d x ,
D a D m = log 10 1 / T a log 10 1 / T m = log 10 T a / T m .
Δ D = log 10 [ 1 + ( T a T m ) / T m ] = log 10 ( 1 + Δ T / T m ) .
Δ D = 0.4343 [ Δ T / T m ( Δ T / T m ) 2 / 2 + ( Δ T / T m ) 3 3 ( Δ T / T m ) 4 4 ] .