Abstract

In order to develop a complete specification for the appraisal of the quality of a photographic system by the use of sine-wave response functions, the sine-wave response of the complete visual system must also be known. A method has been worked out for determining the above-mentioned response of the eye. Whenever the eye views a diffuse luminous boundary in which a sudden change of luminance gradient occurs, a bright line appears at the junction of the gradient and the higher luminance, and a dark line at the junction of the gradient and the lower luminance. This phenomenon is a purely subjective one, because physical measurements of the luminances involved show no luminance higher or lower than the two between which the gradient exists.

A visual slit photometer has been built with which the subjective intensity distribution may be evaluated directly. By application of Fourier analysis, the objective and subjective intensity distributions have been combined to yield the sine-wave response of the visual system.

© 1961 Optical Society of America

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References

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  1. F. Flamant, Rev. opt. 34, 433 (1954).
  2. D. DeMott, J. Opt. Soc. Am. 49, 571 (1959).
    [Crossref] [PubMed]
  3. K. F. Stultz and H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959).
    [Crossref]
  4. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref] [PubMed]
  5. E. W. H. Selwyn, Phot. J.,  B88, 6 (1948).
  6. K. J. Rosenbruch, Optik 16, 135 (1959).
  7. S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).
  8. E. Mach, The Analysis of Sensations (Jena, 1886), pp. 216-21.
  9. R. V. Shack, J. Research Natl. Bur. Standards 56, 246 (1956).
    [Crossref]
  10. E. Ingelstam, E. Djurle, and B. Sjögren, J. Opt. Soc. Am. 46, 707 (1956).
    [Crossref]
  11. P. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).
  12. A. Fiorentini, “Problems in contemporary optics” (Proc. Florence Meeting, September 10–15, 1954) (Ist. Naz. di Ottica, Firenze, 1956), p. 600.
  13. A. Fiorentini and G. Toraldo di Francia, Optica Acta 1, 192 (1955).
  14. E. Hartwig, Optik 15, 414 (1958).
  15. C. McCollough, J. Exptl. Psychol. 49, 141 (1955).
    [Crossref]
  16. A. Kühl, Physik. Z. 29, 1 (1928).
  17. The amplitude function |A#(ν)| is sometimes called the “modulus” and the phase function, the “argument.”
  18. R. L. Lamberts, J. Opt. Soc. Am. 49, 425 (1959).
    [Crossref]
  19. R. N. Wolfe, J. Opt. Soc. Am. 49, 1133(A) (1959); J. Opt. Soc. Am. 50, 1140(A) (1960).
  20. E. H. Linfoot, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref]
  21. P. Lindberg, Optica Acta 1, 80 (1954).
    [Crossref]
  22. P. M. Duffieux, L’Integral de Fourier et ses applications à l’optique (Soc. anon. Oberthur, Rennes, France, 1946).
  23. J. A. Eyer, J. Opt. Soc. Am. 48, 938 (1958); L. O. Hendeberg, Arkiv Fysik 16, 417 (1960).
    [Crossref]
  24. In N. Wiener, The Fourier Integral and Certain of its Applications (Dover Publications, New York, 1933).
  25. R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1953) p. 88.
  26. C. R. Wylie, Advanced Engineering Mathematics (McGraw-Hill Book Company, Inc., New York, 1951), pp. 138–139.

1959 (6)

D. DeMott, J. Opt. Soc. Am. 49, 571 (1959).
[Crossref] [PubMed]

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

K. J. Rosenbruch, Optik 16, 135 (1959).

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

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

R. N. Wolfe, J. Opt. Soc. Am. 49, 1133(A) (1959); J. Opt. Soc. Am. 50, 1140(A) (1960).

1958 (2)

1956 (4)

1955 (3)

P. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

A. Fiorentini and G. Toraldo di Francia, Optica Acta 1, 192 (1955).

C. McCollough, J. Exptl. Psychol. 49, 141 (1955).
[Crossref]

1954 (2)

F. Flamant, Rev. opt. 34, 433 (1954).

P. Lindberg, Optica Acta 1, 80 (1954).
[Crossref]

1948 (1)

E. W. H. Selwyn, Phot. J.,  B88, 6 (1948).

1928 (1)

A. Kühl, Physik. Z. 29, 1 (1928).

DeMott, D.

Ditchburn, R. W.

R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1953) p. 88.

Djurle, E.

Duffieux, P. M.

P. M. Duffieux, L’Integral de Fourier et ses applications à l’optique (Soc. anon. Oberthur, Rennes, France, 1946).

Eyer, J. A.

Fellgett, P. B.

P. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Fiorentini, A.

A. Fiorentini and G. Toraldo di Francia, Optica Acta 1, 192 (1955).

A. Fiorentini, “Problems in contemporary optics” (Proc. Florence Meeting, September 10–15, 1954) (Ist. Naz. di Ottica, Firenze, 1956), p. 600.

Flamant, F.

F. Flamant, Rev. opt. 34, 433 (1954).

Hartwig, E.

E. Hartwig, Optik 15, 414 (1958).

Ingelstam, E.

Kühl, A.

A. Kühl, Physik. Z. 29, 1 (1928).

Lamberts, R. L.

Lindberg, P.

P. Lindberg, Optica Acta 1, 80 (1954).
[Crossref]

Linfoot, E. H.

E. H. Linfoot, J. Opt. Soc. Am. 46, 721 (1956).
[Crossref]

P. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Mach, E.

E. Mach, The Analysis of Sensations (Jena, 1886), pp. 216-21.

McCollough, C.

C. McCollough, J. Exptl. Psychol. 49, 141 (1955).
[Crossref]

Ooue, S.

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

Rosenbruch, K. J.

K. J. Rosenbruch, Optik 16, 135 (1959).

Schade, O. H.

Selwyn, E. W. H.

E. W. H. Selwyn, Phot. J.,  B88, 6 (1948).

Shack, R. V.

R. V. Shack, J. Research Natl. Bur. Standards 56, 246 (1956).
[Crossref]

Sjögren, B.

Stultz, K. F.

Toraldo di Francia, G.

A. Fiorentini and G. Toraldo di Francia, Optica Acta 1, 192 (1955).

Wiener, N.

In N. Wiener, The Fourier Integral and Certain of its Applications (Dover Publications, New York, 1933).

Wolfe, R. N.

R. N. Wolfe, J. Opt. Soc. Am. 49, 1133(A) (1959); J. Opt. Soc. Am. 50, 1140(A) (1960).

Wylie, C. R.

C. R. Wylie, Advanced Engineering Mathematics (McGraw-Hill Book Company, Inc., New York, 1951), pp. 138–139.

Zweig, H. J.

J. Appl. Phys. (Japan) (1)

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

J. Exptl. Psychol. (1)

C. McCollough, J. Exptl. Psychol. 49, 141 (1955).
[Crossref]

J. Opt. Soc. Am. (8)

J. Research Natl. Bur. Standards (1)

R. V. Shack, J. Research Natl. Bur. Standards 56, 246 (1956).
[Crossref]

Optica Acta (2)

P. Lindberg, Optica Acta 1, 80 (1954).
[Crossref]

A. Fiorentini and G. Toraldo di Francia, Optica Acta 1, 192 (1955).

Optik (2)

E. Hartwig, Optik 15, 414 (1958).

K. J. Rosenbruch, Optik 16, 135 (1959).

Phil. Trans. Roy. Soc. London (1)

P. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Phot. J. (1)

E. W. H. Selwyn, Phot. J.,  B88, 6 (1948).

Physik. Z. (1)

A. Kühl, Physik. Z. 29, 1 (1928).

Rev. opt. (1)

F. Flamant, Rev. opt. 34, 433 (1954).

Other (7)

E. Mach, The Analysis of Sensations (Jena, 1886), pp. 216-21.

A. Fiorentini, “Problems in contemporary optics” (Proc. Florence Meeting, September 10–15, 1954) (Ist. Naz. di Ottica, Firenze, 1956), p. 600.

P. M. Duffieux, L’Integral de Fourier et ses applications à l’optique (Soc. anon. Oberthur, Rennes, France, 1946).

The amplitude function |A#(ν)| is sometimes called the “modulus” and the phase function, the “argument.”

In N. Wiener, The Fourier Integral and Certain of its Applications (Dover Publications, New York, 1933).

R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1953) p. 88.

C. R. Wylie, Advanced Engineering Mathematics (McGraw-Hill Book Company, Inc., New York, 1951), pp. 138–139.

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Figures (9)

Fig. 1
Fig. 1

Diagrammatic representation of the Mach phenomenon.

Fig. 2
Fig. 2

Schematic of visual slit photometer.

Fig. 3
Fig. 3

Luminance distribution for edge No. 11: solid line, objective distribution; open circles, subjective distribution.

Fig. 4
Fig. 4

Luminance distribution for edge No. 12: solid line, objective distribution; open circles, subjective distribution.

Fig. 5
Fig. 5

Luminance distribution for edge No. 16: solid line, objective distribution; open circles, subjective distribution.

Fig. 6
Fig. 6

Fourier transforms of subjective image distribution curves: curve 1, edge No. 11; curve 2, edge No. 12; curve 3, edge No. 16.

Fig. 7
Fig. 7

Fourier transforms of object distribution curves: curve 1, edge No. 11; curve 2, edge No. 12; curve 3, edge No. 16.

Fig. 8
Fig. 8

Sine-wave response of the complete visual system: squares, edge No. 11; open circles, edge No. 12; solid circles, edge No. 16.

Fig. 9
Fig. 9

Comparison of sine-wave response of complete visual system (from present study) with those calculated from other data for the optical system of the eye: open circles, present study; solid triangle, from DeMott’s spread function for an excised steer eye; solid circles, from Flamant’s spread function; open triangles, from Stultz and Zweig.

Equations (9)

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I ( x ) = A ( x x ) O ( x ) d x .
A # ( ν ) = | A # ( ν ) | e i θ ( ν ) = A ( x ) exp [ 2 π i ν x ] d x ,
A # c ( ν ) = | A # c ( ν ) | = A ( x ) cos 2 π ν x d x .
I ( x ) = A ( x x ) O ( x ) d x ,
I # ( ν ) = A # ( ν ) · O # ( ν ) ,
A # ( ν ) = I # ( ν ) O # ( ν ) = | I # ( ν ) | | O # ( ν ) | exp { i [ θ I ( ν ) θ O ( ν ) ] } .
I # ( ν ) = | I # ( ν ) | exp [ i θ I ( ν ) ] = I ( x ) exp [ 2 π i ν x ] d x ,
O # ( ν ) = | O # ( ν ) | exp [ i θ O ( ν ) ] = O ( x ) exp [ 2 π i ν x ] d x ;
ν = n / p .