Abstract

The response of the human visual system to an optical image is assumed to be linearly related to the logarithm of the spread function of the photographic system projected onto the retina combined with the spread function of the visual system. From psychophysical data derived from viewing (at different distances) a series of pictures generated with different spread functions, an estimate is obtained of the variance of the spread function of the visual system. The square root of this variance ranges from 3µ to 8µ, depending on the techniques used and on the training of the judges. Although the residual errors in this determination are small, they show systematic trends, indicating that definition depends on other factors than the composite variance.

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  1. R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).
  2. The term "sharpness" was used for this concept by them, but that term has since been reserved for a description of the appearance of a single edge.
  3. L. L. Thurstone, Am. J. Psychol. 38, 368 (1927).
  4. J. P. Guilford, Psychometric Methods (McGraw-Hill Book Company, Inc., New York, 1954), pp. 154–177.
  5. G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952); PSA Journal (Phot. Sci. Tech.) 19B, 55 (1953).
  6. J. H. Morrissey, J. Opt. Soc. Am. 45, 373 (1955).
  7. G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).
  8. G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).
  9. R. N. Wolfe and S. A. Tuccio, Phot. Sci. Eng. 4, 330 (1960).
  10. H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).
  11. E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).
  12. J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 51, 474 (1961) (abstract only).
  13. R. N. Wolfe, J. Opt. Soc. Am. 49, 1133 (1959).
  14. E. W. H. Selwyn, Phot. J. 88B, 6 (1948).
  15. O. Schade, RCA Review 9, 5 (1948); and later papers.
  16. R. L. Anderson and T. A. Bancroft, Statistical Theory in Research (McGraw-Hill Book Company, Inc., New York, 1952), p. 60.
  17. S. S. Stevens, Daedalus 88, 606 (1959); Am. Scientist 48, 226 (1960).
  18. Note added in proof. A note in the December, 1961, issue of the J. Opt. Soc. Am. 51, 1441, announced an agreement with the ICO Subcommittee for Image Assessment Problems to change "what is at present known under a variety of names, e.g., sine-wave responise, frequency response, contrast transfer, etc.," to "optical transfer function" when the complex function (i.e., including phase) is intended, as in Part I of this series. The agreement also provides the term "modulation transfer function" for use when phase is not pertinent. These nomenclature recommendations were adopted too late to be incorporated into this paper, but the new nomenclature will be used in future papers.
  19. R. L. Iamberts, J. Opt. Soc. Am. 49, 425 (1959).
  20. H. Gulliksen, Am. Scientist 47, 178 (1959).
  21. Only one observation of a single pair of pictures, say A and B, was made; the presentation of A on the left and B on the right was considered to be equivalent to the presentation of A on the right and B on the left.
  22. G. Young and A. S. Householder, Psychometrika 3, 19 (1938).
  23. S. J. Messick and R. P. Abelson, Psychometrika 21, 1 (1956).
  24. S. J. Messick, Ph.D. thesis, Princeton University, and Educational Testing Service, Princeton, New Jersey (1954).
  25. K. A. Brownlee, Slatislical Theory and Methodology in Science and Engineering (John Wiley & Sons, New York, 1960), pp. 303–306.
  26. "True" is here used to mean those values of b and σv which would be obtained if there were no random errors in the experiment.
  27. O. Schade, J. Opt. Soc. Am. 46, 721 (1956).
  28. E. Ludvigh, U. S. Naval School of Aviation Medicine and Kresge Eye Institute, Bureau of Medicine and Surgery, Project No. NM 001 075.01.04, 17 August, 1953.
  29. G. A. Fry, Blur of the Retinal Inage (Ohio State University Press, Columbus, Ohio, 1955).
  30. F. Flamant, Rev. optique 34, 433 (1955).
  31. K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

1961 (2)

E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 51, 474 (1961) (abstract only).

1960 (1)

R. N. Wolfe and S. A. Tuccio, Phot. Sci. Eng. 4, 330 (1960).

1959 (6)

G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).

R. N. Wolfe, J. Opt. Soc. Am. 49, 1133 (1959).

S. S. Stevens, Daedalus 88, 606 (1959); Am. Scientist 48, 226 (1960).

R. L. Iamberts, J. Opt. Soc. Am. 49, 425 (1959).

H. Gulliksen, Am. Scientist 47, 178 (1959).

K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

1958 (1)

H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).

1956 (2)

S. J. Messick and R. P. Abelson, Psychometrika 21, 1 (1956).

O. Schade, J. Opt. Soc. Am. 46, 721 (1956).

1955 (3)

F. Flamant, Rev. optique 34, 433 (1955).

J. H. Morrissey, J. Opt. Soc. Am. 45, 373 (1955).

G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).

1954 (1)

S. J. Messick, Ph.D. thesis, Princeton University, and Educational Testing Service, Princeton, New Jersey (1954).

1953 (1)

R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).

1952 (1)

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952); PSA Journal (Phot. Sci. Tech.) 19B, 55 (1953).

1948 (2)

E. W. H. Selwyn, Phot. J. 88B, 6 (1948).

O. Schade, RCA Review 9, 5 (1948); and later papers.

1938 (1)

G. Young and A. S. Householder, Psychometrika 3, 19 (1938).

1927 (1)

L. L. Thurstone, Am. J. Psychol. 38, 368 (1927).

Abelson, R. P.

S. J. Messick and R. P. Abelson, Psychometrika 21, 1 (1956).

Anderson, R. L.

R. L. Anderson and T. A. Bancroft, Statistical Theory in Research (McGraw-Hill Book Company, Inc., New York, 1952), p. 60.

Bancroft, T. A.

R. L. Anderson and T. A. Bancroft, Statistical Theory in Research (McGraw-Hill Book Company, Inc., New York, 1952), p. 60.

Brownlee, K. A.

K. A. Brownlee, Slatislical Theory and Methodology in Science and Engineering (John Wiley & Sons, New York, 1960), pp. 303–306.

DePalma, J. J.

E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 51, 474 (1961) (abstract only).

Eisen, F. C.

R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).

Flamant, F.

F. Flamant, Rev. optique 34, 433 (1955).

Fry, G. A.

G. A. Fry, Blur of the Retinal Inage (Ohio State University Press, Columbus, Ohio, 1955).

Guilford, J. P.

J. P. Guilford, Psychometric Methods (McGraw-Hill Book Company, Inc., New York, 1954), pp. 154–177.

Gulliksen, H.

H. Gulliksen, Am. Scientist 47, 178 (1959).

Higgins, G. C.

G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).

H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).

G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952); PSA Journal (Phot. Sci. Tech.) 19B, 55 (1953).

Householder, A. S.

G. Young and A. S. Householder, Psychometrika 3, 19 (1938).

Iamberts, R. L.

R. L. Iamberts, J. Opt. Soc. Am. 49, 425 (1959).

Jones, L. A.

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952); PSA Journal (Phot. Sci. Tech.) 19B, 55 (1953).

Lamberts, R. L.

G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).

Lowry, E. M.

E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 51, 474 (1961) (abstract only).

Ludvigh, E.

E. Ludvigh, U. S. Naval School of Aviation Medicine and Kresge Eye Institute, Bureau of Medicine and Surgery, Project No. NM 001 075.01.04, 17 August, 1953.

MacAdam, D. L.

H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).

Messick, S. J.

S. J. Messick and R. P. Abelson, Psychometrika 21, 1 (1956).

S. J. Messick, Ph.D. thesis, Princeton University, and Educational Testing Service, Princeton, New Jersey (1954).

Morrissey, J. H.

J. H. Morrissey, J. Opt. Soc. Am. 45, 373 (1955).

Schade, O.

O. Schade, J. Opt. Soc. Am. 46, 721 (1956).

O. Schade, RCA Review 9, 5 (1948); and later papers.

Selwyn, E. W. H.

E. W. H. Selwyn, Phot. J. 88B, 6 (1948).

Stevens, S. S.

S. S. Stevens, Daedalus 88, 606 (1959); Am. Scientist 48, 226 (1960).

Stultz, K. F.

K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

Thurstone, L. L.

L. L. Thurstone, Am. J. Psychol. 38, 368 (1927).

Tuccio, S. A.

R. N. Wolfe and S. A. Tuccio, Phot. Sci. Eng. 4, 330 (1960).

Wolfe, R. N.

R. N. Wolfe and S. A. Tuccio, Phot. Sci. Eng. 4, 330 (1960).

R. N. Wolfe, J. Opt. Soc. Am. 49, 1133 (1959).

G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).

G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).

R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).

Young, G.

G. Young and A. S. Householder, Psychometrika 3, 19 (1938).

Zweig, H. J.

K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).

Other (31)

R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).

The term "sharpness" was used for this concept by them, but that term has since been reserved for a description of the appearance of a single edge.

L. L. Thurstone, Am. J. Psychol. 38, 368 (1927).

J. P. Guilford, Psychometric Methods (McGraw-Hill Book Company, Inc., New York, 1954), pp. 154–177.

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952); PSA Journal (Phot. Sci. Tech.) 19B, 55 (1953).

J. H. Morrissey, J. Opt. Soc. Am. 45, 373 (1955).

G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).

G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).

R. N. Wolfe and S. A. Tuccio, Phot. Sci. Eng. 4, 330 (1960).

H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).

E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).

J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 51, 474 (1961) (abstract only).

R. N. Wolfe, J. Opt. Soc. Am. 49, 1133 (1959).

E. W. H. Selwyn, Phot. J. 88B, 6 (1948).

O. Schade, RCA Review 9, 5 (1948); and later papers.

R. L. Anderson and T. A. Bancroft, Statistical Theory in Research (McGraw-Hill Book Company, Inc., New York, 1952), p. 60.

S. S. Stevens, Daedalus 88, 606 (1959); Am. Scientist 48, 226 (1960).

Note added in proof. A note in the December, 1961, issue of the J. Opt. Soc. Am. 51, 1441, announced an agreement with the ICO Subcommittee for Image Assessment Problems to change "what is at present known under a variety of names, e.g., sine-wave responise, frequency response, contrast transfer, etc.," to "optical transfer function" when the complex function (i.e., including phase) is intended, as in Part I of this series. The agreement also provides the term "modulation transfer function" for use when phase is not pertinent. These nomenclature recommendations were adopted too late to be incorporated into this paper, but the new nomenclature will be used in future papers.

R. L. Iamberts, J. Opt. Soc. Am. 49, 425 (1959).

H. Gulliksen, Am. Scientist 47, 178 (1959).

Only one observation of a single pair of pictures, say A and B, was made; the presentation of A on the left and B on the right was considered to be equivalent to the presentation of A on the right and B on the left.

G. Young and A. S. Householder, Psychometrika 3, 19 (1938).

S. J. Messick and R. P. Abelson, Psychometrika 21, 1 (1956).

S. J. Messick, Ph.D. thesis, Princeton University, and Educational Testing Service, Princeton, New Jersey (1954).

K. A. Brownlee, Slatislical Theory and Methodology in Science and Engineering (John Wiley & Sons, New York, 1960), pp. 303–306.

"True" is here used to mean those values of b and σv which would be obtained if there were no random errors in the experiment.

O. Schade, J. Opt. Soc. Am. 46, 721 (1956).

E. Ludvigh, U. S. Naval School of Aviation Medicine and Kresge Eye Institute, Bureau of Medicine and Surgery, Project No. NM 001 075.01.04, 17 August, 1953.

G. A. Fry, Blur of the Retinal Inage (Ohio State University Press, Columbus, Ohio, 1955).

F. Flamant, Rev. optique 34, 433 (1955).

K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

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