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 3 μ to 8 μ, 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.

© 1962 Optical Society of America

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References

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  1. R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 43, 914 (1953).
    [Crossref]
  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).
    [Crossref]
  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).
    [Crossref] [PubMed]
  7. G. C. Higgins and R. N. Wolfe, J. Opt. Soc. Am. 45, 121 (1955).
    [Crossref]
  8. G. C. Higgins, R. L. Lamberts, and R. N. Wolfe, Optica Acta 6, 272 (1959).
    [Crossref]
  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).
    [Crossref]
  11. E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).
    [Crossref] [PubMed]
  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 response, 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.
    [Crossref]
  19. R. L. Lamberts, 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.
    [Crossref]
  22. G. Young and A. S. Householder, Psychometrika 3, 19 (1938).
    [Crossref]
  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, Statistical 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.
    [Crossref] [PubMed]
  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, 17August, 1953.
  29. G. A. Fry, Blur of the Retinal Image (Ohio State University Press, Columbus, Ohio, 1955).
  30. F. Flamant, Rev. optique 34, 433 (1955).
    [Crossref]
  31. K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959)

1961 (3)

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).
[Crossref]

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

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

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

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

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

1958 (1)

1956 (2)

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

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

1955 (3)

1953 (1)

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).
[Crossref]

1927 (1)

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

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, Statistical 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).
[Crossref] [PubMed]

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

Eisen, F. C.

Flamant, F.

F. Flamant, Rev. optique 34, 433 (1955).
[Crossref]

Fry, G. A.

G. A. Fry, Blur of the Retinal Image (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).
[Crossref]

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

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

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).
[Crossref]

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).
[Crossref]

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

Lowry, E. M.

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

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

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, 17August, 1953.

MacAdam, D. L.

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.

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.

Thurstone, L. L.

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

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).
[Crossref]

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

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

Young, G.

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

Zweig, H. J.

Am. J. Psychol. (1)

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

Am. Scientist (1)

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

Daedalus (1)

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

J. Opt. Soc. Am. (11)

J. Soc. Motion Picture Television Engrs. (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).

Optica Acta (1)

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

Phot. J. (1)

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

Phot. Sci. Eng. (1)

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

Psychometrika (2)

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

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

RCA Review (1)

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

Rev. optique (1)

F. Flamant, Rev. optique 34, 433 (1955).
[Crossref]

Other (9)

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, 17August, 1953.

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

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

K. A. Brownlee, Statistical 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.
[Crossref] [PubMed]

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

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.
[Crossref]

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.

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

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Figures (12)

Fig. 1
Fig. 1

Diagram of apparatus for “photographing” a transparency so that the spread function is uniform over the entire picture. The transparency is wrapped around the right-hand end of the drum and the negative film around the left-hand end.

Fig. 2
Fig. 2

Test object used in the apparatus shown in Fig. 1. The upper part consists of patterns used for obtaining sine-wave response data and the lower of a pictorial scene.

Fig. 3
Fig. 3

Frequency-response curves for each of the nine focal settings. The separation between settings was 0.01 in.

Fig. 4
Fig. 4

Spread functions corresponding to the response curves of Fig. 3, with values of standard deviation σ indicated. Since the functions are bilaterally symmetrical, only one half of each is shown.

Fig. 5
Fig. 5

Standard deviation of spread function as a function of focal setting u.

Fig. 6
Fig. 6

Average response r ˆ of 50 observers as a function of focal setting u for the three indicated viewing distances by the paired-comparison method. The curves are quadratic functions fitted to the points and represent r ˆ 1 . The maxima are indicated by ticks.

Fig. 7
Fig. 7

Variation of focal setting u for maximum of subjective response r ˆ 1 with viewing distance D.

Fig. 8
Fig. 8

Illustration of method of triads. The perplexed simian is trying to decide whether the square or the circle is more nearly like the triangle. (From Gulliksen, by permission. © American Scientist.)

Fig. 9
Fig. 9

Average response r ˆ of 30 observers as a function of focal setting u for a viewing distance of 21 in. by the method of triads. U, untrained observers; T, trained observers.

Fig. 10
Fig. 10

Value of b as a function of σ V in Eq. (6) from (P) paired-comparison data for all viewing distances and (T) triad data for a 21-in. viewing distance. The significance of points A, A′, B, and C is explained in the text.

Fig. 11
Fig. 11

Average response r ˆ of 50 observers as a function of focal setting u for the three indicated viewing distances (in inches) by the paired-comparison method. The curves are functions that minimize the SSE and represent r ˜ . The maxima are indicated by ticks.

Fig. 12
Fig. 12

Subjective response for relatively short viewing distances as functions of response for relatively long distances. Circles, experimental points r ˆ , numbered according to the focal settings at which they were obtained; solid curves, values r ˆ 1 from best quadratic function for each viewing distance (Fig. 6); broken curves, values r ˜ from mathematical model (Fig. 11).

Tables (4)

Tables Icon

Table I Size of physical spread function in terms of standard deviation σ P on the photograph and for three viewing distances.

Tables Icon

Table II Subjective picture definition r ˆ as a function of the focal settings at which the photographs were made and the distances from which they were viewed. The method of paired comparisons was used for judging pictures.

Tables Icon

Table III Subjective picture definition r ˆ as a function of the focal settings at which the photographs were made for a viewing distance of 21 in. The method of triads was used for judging pictures.

Tables Icon

Table IV Summary of determinations of size of the human visual spread function. References are to footnotes in the text.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

f P V ( z ) = - + f P ( x ) f V ( z - x ) d x .
σ = [ - x 2 f ( x ) d x ] 1 2 .
σ P V 2 = σ P 2 + σ V 2 .
r = a + b log σ P V 2 ,
r = a + b log ( σ P 2 + σ V 2 ) .
r = a + b log { [ ( l / D ) σ P ] 2 + σ V 2 } .
Δ i j = r i - r j + e i j ,
α = 1 n r ˆ = 0
all pairs e i j 2 ,
r ˆ 1 = α + β u + γ u 2
r = f ( σ P , D ; a , b , σ V ) = f ,
r i = f i .
Δ i j = ( f i - f j ) + e i j
all pairs e i j 2
σ = Φ / ( 2 π ) 1 2 ,