Abstract

Recent work by Jones and Higgins has led to an objective method for evaluating the granular structure of the developed photographic image by which materials of widely differing granularity can be ordered in correspondence with subjective graininess measurements. The present paper gives the theoretical calculations of statistical fluctuations of density and syzygetic density differences (<i>S</i>Δ<i>D</i>) for simplified density patterns when scanned with varied-size apertures. Average syzygetic density values, 〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub>, <i>versus</i> density curves are derived first for square, checkerboard density patterns and second for circular patterns containing uniform-size grains with random arrangement. By combining the experimental, threshold, visual, gradient sensitivity curve (〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub><i>versus</i> density for critical aperture), obtained by Jones and Higgins, with theoretical curves of 〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub><i>versus</i> density calculated here, it is shown how the graininess-density curve can be obtained.

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  1. L. A. Jones and N. Deisch, J. Franklin Inst. 190, 657 (1920).
  2. J. Eggert and A. Kuster, Kinotechnik 16, 127, 291, 308 (1934).
  3. A. Van Kreveld, Phot. J. 74, 590 (1934); J. Opt. Soc. Am. 26, 170 (1936); A. Van Kreveld and J. C. Schaffer, J. Opt. Soc. Am. 27, 100 (1937).
  4. A. Goetz and W. O. Gould, J. Soc. Motion Picture Engrs. 29, 510 (1937); Goetz, Gould, and Dember, ibid. 34, 279 (1940); A. Goetz and F. W. Brown, ibid. 39, 375 (1942).
  5. E. W. H. Selwyn, Phot. J. 75, 571 (1935); 79, 513 (1939).
  6. W. Raemer and E. W. H. Selwyn, Phot. J. 83, 17 (1943).
  7. E. W. H. Selwyn, Phot. J. 83, 227 (1943).
  8. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).
  9. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203 (1946).
  10. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 37, 217 (1947).
  11. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 38, 398 (1948).
  12. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 41 (1951).
  13. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 64 (1951).
  14. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 192 (1951).
  15. Jones, Higgins, and Stultz, "Photographic Granularity and Graininess. VIII. A Method of Measuring Granularity in Terms of the Scanning Area Giving a Threshold Luminance Gradient," J. Opt. Soc. Am. 45, 107 (1955).
  16. L. Silberstein and A. P. H. Trivelli, J. Opt. Soc. Am. 28, 441 (1938).

Deisch, N.

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

Eggert, J.

J. Eggert and A. Kuster, Kinotechnik 16, 127, 291, 308 (1934).

Goetz, A.

A. Goetz and W. O. Gould, J. Soc. Motion Picture Engrs. 29, 510 (1937); Goetz, Gould, and Dember, ibid. 34, 279 (1940); A. Goetz and F. W. Brown, ibid. 39, 375 (1942).

Gould, W. O.

A. Goetz and W. O. Gould, J. Soc. Motion Picture Engrs. 29, 510 (1937); Goetz, Gould, and Dember, ibid. 34, 279 (1940); A. Goetz and F. W. Brown, ibid. 39, 375 (1942).

A. Goetz and W. O. Gould, J. Soc. Motion Picture Engrs. 29, 510 (1937); Goetz, Gould, and Dember, ibid. 34, 279 (1940); A. Goetz and F. W. Brown, ibid. 39, 375 (1942).

Higgins, G. C.

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203 (1946).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 37, 217 (1947).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 38, 398 (1948).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 41 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 64 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 192 (1951).

Jones, L. A.

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 192 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 64 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 41 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 38, 398 (1948).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 37, 217 (1947).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203 (1946).

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

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).

Kuster, A.

J. Eggert and A. Kuster, Kinotechnik 16, 127, 291, 308 (1934).

Raemer, W.

W. Raemer and E. W. H. Selwyn, Phot. J. 83, 17 (1943).

Selwyn, E. W. H.

W. Raemer and E. W. H. Selwyn, Phot. J. 83, 17 (1943).

E. W. H. Selwyn, Phot. J. 83, 227 (1943).

E. W. H. Selwyn, Phot. J. 75, 571 (1935); 79, 513 (1939).

Silberstein, L.

L. Silberstein and A. P. H. Trivelli, J. Opt. Soc. Am. 28, 441 (1938).

Trivelli, A. P. H.

L. Silberstein and A. P. H. Trivelli, J. Opt. Soc. Am. 28, 441 (1938).

Van Kreveld, A.

A. Van Kreveld, Phot. J. 74, 590 (1934); J. Opt. Soc. Am. 26, 170 (1936); A. Van Kreveld and J. C. Schaffer, J. Opt. Soc. Am. 27, 100 (1937).

Other (16)

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

J. Eggert and A. Kuster, Kinotechnik 16, 127, 291, 308 (1934).

A. Van Kreveld, Phot. J. 74, 590 (1934); J. Opt. Soc. Am. 26, 170 (1936); A. Van Kreveld and J. C. Schaffer, J. Opt. Soc. Am. 27, 100 (1937).

A. Goetz and W. O. Gould, J. Soc. Motion Picture Engrs. 29, 510 (1937); Goetz, Gould, and Dember, ibid. 34, 279 (1940); A. Goetz and F. W. Brown, ibid. 39, 375 (1942).

E. W. H. Selwyn, Phot. J. 75, 571 (1935); 79, 513 (1939).

W. Raemer and E. W. H. Selwyn, Phot. J. 83, 17 (1943).

E. W. H. Selwyn, Phot. J. 83, 227 (1943).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203 (1946).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 37, 217 (1947).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 38, 398 (1948).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 41 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 64 (1951).

L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 41, 192 (1951).

Jones, Higgins, and Stultz, "Photographic Granularity and Graininess. VIII. A Method of Measuring Granularity in Terms of the Scanning Area Giving a Threshold Luminance Gradient," J. Opt. Soc. Am. 45, 107 (1955).

L. Silberstein and A. P. H. Trivelli, J. Opt. Soc. Am. 28, 441 (1938).

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