Abstract

Several theoretical models for the prediction of liminal contrast are studied. One model that employs the known excitation and inhibition spread functions of the eye accurately predicts, at 10 mL, thresholds for circular targets, sine waves, and rectangles, including the line as a special case. Semiempirically, this model is extended to include thresholds at low light levels.

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  1. A. Rose, J. Opt. Soc. Am. 38, 196 (1948).
  2. J. Johnson, private communication.
  3. H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).
  4. The asterisk is used to designate the convolution operation io(x,y,t)*ho(x,y,t)=∫dx′dy′dt′io(x′,y′,t′)ho[(x-x′),(y-y′),(t-t′)].
  5. J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966).
  6. M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).
  7. E. A. Trabka, J. Opt. Soc. Am. 59, 345 (1969).
  8. W. Feller, Probability Theory and its A pplications (Wiley, New York, 1950), p. 249.
  9. Another approach that gives a similar final result is that of M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908 (1947) in terms of multistage cells and omission of dark noise.
  10. The terminology "signal density" is arbitrary and possibly confusing. The signal is related to ∫ ∫ s2(x,y)dxdy, not ∫ ∫ s2(x,y)dxdy.
  11. A. van Meeteren and J. J. Vos, J. Opt. Soc. Am. 59, 1538 (1969).
  12. S. Hecht and E. U. Mintz, J. Gen. Physiol. 22, 593 (1939).
  13. O. Schade, Sr., J. Opt. Soc. Am. 46, 721 (1956).
  14. R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).
  15. G. A. Fry, in Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).
  16. M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).
  17. Because the glance time to is considerably greater than the response time of the eye, we approximate H(ω) to unity.
  18. D. E. Mitchell, R. D. Freeman, and G. Westheimer, J. Opt. Soc. Am. 57, 246 (1967).
  19. Ricco's law states that the threshold contrast is proportional to the inverse of the area of small targets.
  20. A. B. Kristofferson and H. R. Blackwell, private communication.
  21. E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).
  22. J. L. Brown, in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965), p. 39.
  23. F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).
  24. A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).
  25. P. Gaunt, Opt. Acta 15, 287 (1968).
  26. C. H. Graham, in Ref. 22, p. 68.
  27. S. Hecht, S. Ross, and C. G. Mueller, J. Opt. Soc. Am. 37, 500 (1947).
  28. J. L. Harris and S. Q. Duntley, in Performance of the Eye at Low Luminances, edited by M. A. Bouman and J. J. Vos (Excerpta Medica Foundation, Amsterdam and New York, 1966), p. 41.

Blackwell, H. R.

A. B. Kristofferson and H. R. Blackwell, private communication.

H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).

Bouman, M. A.

Another approach that gives a similar final result is that of M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908 (1947) in terms of multistage cells and omission of dark noise.

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).

Brown, J. L.

J. L. Brown, in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965), p. 39.

Campbell, F. W.

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

Davidson, M.

M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).

Duntley, S. Q.

J. L. Harris and S. Q. Duntley, in Performance of the Eye at Low Luminances, edited by M. A. Bouman and J. J. Vos (Excerpta Medica Foundation, Amsterdam and New York, 1966), p. 41.

Feller, W.

W. Feller, Probability Theory and its A pplications (Wiley, New York, 1950), p. 249.

Freeman, R. D.

D. E. Mitchell, R. D. Freeman, and G. Westheimer, J. Opt. Soc. Am. 57, 246 (1967).

Fry, G. A.

G. A. Fry, in Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).

Gaunt, P.

P. Gaunt, Opt. Acta 15, 287 (1968).

Graham, C. H.

C. H. Graham, in Ref. 22, p. 68.

Green, D. G.

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

Gubisch, R. W.

R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).

Harris, J. L.

J. L. Harris and S. Q. Duntley, in Performance of the Eye at Low Luminances, edited by M. A. Bouman and J. J. Vos (Excerpta Medica Foundation, Amsterdam and New York, 1966), p. 41.

Harris, Sr., J. L.

J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966).

Hecht, S.

S. Hecht, S. Ross, and C. G. Mueller, J. Opt. Soc. Am. 37, 500 (1947).

S. Hecht and E. U. Mintz, J. Gen. Physiol. 22, 593 (1939).

E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).

Hendley, C. D.

E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).

Hiwatashi, K.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).

Johnson, J.

J. Johnson, private communication.

Kristofferson, A. B.

A. B. Kristofferson and H. R. Blackwell, private communication.

Lamar, E. S.

E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).

Mintz, E. U.

S. Hecht and E. U. Mintz, J. Gen. Physiol. 22, 593 (1939).

Mitchell, D. E.

D. E. Mitchell, R. D. Freeman, and G. Westheimer, J. Opt. Soc. Am. 57, 246 (1967).

Mori, T.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).

Mueller, C. G.

S. Hecht, S. Ross, and C. G. Mueller, J. Opt. Soc. Am. 37, 500 (1947).

Nagata, S.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).

Rose, A.

A. Rose, J. Opt. Soc. Am. 38, 196 (1948).

Ross, S.

S. Hecht, S. Ross, and C. G. Mueller, J. Opt. Soc. Am. 37, 500 (1947).

Schade, Sr., O.

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

Shlaer, S.

E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).

Trabka, E. A.

E. A. Trabka, J. Opt. Soc. Am. 59, 345 (1969).

van der Velden, H. A.

Another approach that gives a similar final result is that of M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908 (1947) in terms of multistage cells and omission of dark noise.

van Meeteren, A.

A. van Meeteren and J. J. Vos, J. Opt. Soc. Am. 59, 1538 (1969).

Vos, J. J.

A. van Meeteren and J. J. Vos, J. Opt. Soc. Am. 59, 1538 (1969).

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).

Walraven, P. L.

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).

Watanabe, A.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).

Westheimer, G.

D. E. Mitchell, R. D. Freeman, and G. Westheimer, J. Opt. Soc. Am. 57, 246 (1967).

Other (28)

A. Rose, J. Opt. Soc. Am. 38, 196 (1948).

J. Johnson, private communication.

H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).

The asterisk is used to designate the convolution operation io(x,y,t)*ho(x,y,t)=∫dx′dy′dt′io(x′,y′,t′)ho[(x-x′),(y-y′),(t-t′)].

J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966).

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).

E. A. Trabka, J. Opt. Soc. Am. 59, 345 (1969).

W. Feller, Probability Theory and its A pplications (Wiley, New York, 1950), p. 249.

Another approach that gives a similar final result is that of M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908 (1947) in terms of multistage cells and omission of dark noise.

The terminology "signal density" is arbitrary and possibly confusing. The signal is related to ∫ ∫ s2(x,y)dxdy, not ∫ ∫ s2(x,y)dxdy.

A. van Meeteren and J. J. Vos, J. Opt. Soc. Am. 59, 1538 (1969).

S. Hecht and E. U. Mintz, J. Gen. Physiol. 22, 593 (1939).

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

R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).

G. A. Fry, in Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).

M. Davidson, J. Opt. Soc. Am. 58, 1300 (1968).

Because the glance time to is considerably greater than the response time of the eye, we approximate H(ω) to unity.

D. E. Mitchell, R. D. Freeman, and G. Westheimer, J. Opt. Soc. Am. 57, 246 (1967).

Ricco's law states that the threshold contrast is proportional to the inverse of the area of small targets.

A. B. Kristofferson and H. R. Blackwell, private communication.

E. S. Lamar, S. Hecht, S. Shlaer, and C. D. Hendley, S. Opt. Soc. Am. 37, 531 (1947); 38, 741 (1948).

J. L. Brown, in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965), p. 39.

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, Vision Res. 8, 1245 (1968).

P. Gaunt, Opt. Acta 15, 287 (1968).

C. H. Graham, in Ref. 22, p. 68.

S. Hecht, S. Ross, and C. G. Mueller, J. Opt. Soc. Am. 37, 500 (1947).

J. L. Harris and S. Q. Duntley, in Performance of the Eye at Low Luminances, edited by M. A. Bouman and J. J. Vos (Excerpta Medica Foundation, Amsterdam and New York, 1966), p. 41.

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