Abstract

The psychometric function for the detection of a foveal luminance increment was studied in human observers. The signal to be detected was a modulation of a 1300 cd/m<sup>2</sup> 6′ circular red target. For an ideal photodetector, the theory of signal detectability predicts that <i>d</i>′, the index of detectability, should rise linearly with the luminance, <i>E</i>, of the luminance increment unless the observer has some uncertainty concerning the parameters of the signal to be detected. Uncertainty is expressed by the parameter <i>M</i> that indicates the number of orthogonal signals possible. If <i>M</i> is greater than 1.0, (<i>d</i>′)<sup>2</sup> = In{1-1/<i>M</i> +(1/<i>M</i>) exp(<i>E</i><sup>2</sup>/<i>N</i><sup>2</sup>)} where <i>N</i><sup>2</sup> is the variance of the noise that obscures the signal. In addition, the theory predicts that the slope of the receiver operating characteristic (ROC curve) should decrease with increasing <i>M</i>. In one experiment, in which <i>E</i> was varied, a nonlinear psychometric function and an ROC curve of relatively low slope were found. In another experiment that included a pulsed background (pedestal) whether or not the signal was presented, the predicted linear <i>M</i> = 1 psychometric function was found. Finally, the ROC slope that was measured in rating experiments increased when the pedestal was used. Presumably, the pedestal provides the signal-parameter information that the observer could not remember. We conclude that the human observer acts like an ideal photodetector that has imperfect memory concerning the signal to be detected.

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  1. S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).
  2. B. Sakitt, J. Physiol. 223, 131 (1972).
  3. W. P. Tanner, Jr. and J. A. Swets, Psychol. Rev. 61, 401 (1954).
  4. W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).
  5. J. Nachmias and E. C. Kocher, J. Opt. Soc. Am. 60, 382 (1970).
  6. D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  7. B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).
  8. W. P. Tanner, Jr., Ann. N. Y. Acad. Sci. 89, 752 (1961).
  9. W. P. Tanner, Jr. and R. Clark Jones, in Visual Research Problems, edited by A. Morris and E. P. Horne, Armed Forces NRC Committee on Vision (NAS-NRC Publication No. 712, Washington, D. C., 1960).
  10. L. W. Nolte and D. Jaarsma, J. Acoust. Soc. Am. 41, 497 (1967).
  11. T. G. Birdsall, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 67-08 217).
  12. T. E. Cohn, Am. J. Opt. 49, 1028 (1972).
  13. W. Volk, Applied Statistics for Engineers (McGraw-Hill, New York, 1969).
  14. S. Siegel, Nonparametric Statistics (McGraw-Hill, New York, 1956).
  15. T. E. Cohn, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 70-21 630).
  16. The label "ideal" must be qualified. We infer ideal performance from the linearity of the psychometric function, not from the value of its slope. The measured slope may be smaller than that achievable.
  17. R. FitzHugh, J. Gen. Physiol. 40, 925 (1957).
  18. W. P. Tanner, Jr., D. Main, and T. E. Cohn, in Current Developments in Optics and Vision, edited by W. Benson and M. Whitcomb, (NAS-NRC, Washington, D. C., 1968).
  19. T. E. Cohn and D. Lasley, Abstracts of 1974 A.R.V.O. Meeting (1974).

1974 (1)

T. E. Cohn and D. Lasley, Abstracts of 1974 A.R.V.O. Meeting (1974).

1972 (2)

B. Sakitt, J. Physiol. 223, 131 (1972).

T. E. Cohn, Am. J. Opt. 49, 1028 (1972).

1970 (1)

J. Nachmias and E. C. Kocher, J. Opt. Soc. Am. 60, 382 (1970).

1968 (1)

B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).

1967 (1)

L. W. Nolte and D. Jaarsma, J. Acoust. Soc. Am. 41, 497 (1967).

1966 (2)

T. G. Birdsall, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 67-08 217).

T. E. Cohn, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 70-21 630).

1961 (1)

W. P. Tanner, Jr., Ann. N. Y. Acad. Sci. 89, 752 (1961).

1957 (1)

R. FitzHugh, J. Gen. Physiol. 40, 925 (1957).

1954 (2)

W. P. Tanner, Jr. and J. A. Swets, Psychol. Rev. 61, 401 (1954).

W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).

1942 (1)

S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Birdsall, T. G.

T. G. Birdsall, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 67-08 217).

W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).

Cohn, T. E.

T. E. Cohn and D. Lasley, Abstracts of 1974 A.R.V.O. Meeting (1974).

T. E. Cohn, Am. J. Opt. 49, 1028 (1972).

T. E. Cohn, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 70-21 630).

W. P. Tanner, Jr., D. Main, and T. E. Cohn, in Current Developments in Optics and Vision, edited by W. Benson and M. Whitcomb, (NAS-NRC, Washington, D. C., 1968).

FitzHugh, R.

R. FitzHugh, J. Gen. Physiol. 40, 925 (1957).

Fox, W. C.

W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).

Green, D. M.

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Hecht, S.

S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Jaarsma, D.

L. W. Nolte and D. Jaarsma, J. Acoust. Soc. Am. 41, 497 (1967).

Jones, R. Clark

W. P. Tanner, Jr. and R. Clark Jones, in Visual Research Problems, edited by A. Morris and E. P. Horne, Armed Forces NRC Committee on Vision (NAS-NRC Publication No. 712, Washington, D. C., 1960).

Kocher, E. C.

J. Nachmias and E. C. Kocher, J. Opt. Soc. Am. 60, 382 (1970).

Lasley, D.

T. E. Cohn and D. Lasley, Abstracts of 1974 A.R.V.O. Meeting (1974).

Leshowitz, B.

B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).

Main, D.

W. P. Tanner, Jr., D. Main, and T. E. Cohn, in Current Developments in Optics and Vision, edited by W. Benson and M. Whitcomb, (NAS-NRC, Washington, D. C., 1968).

Nachmias, J.

J. Nachmias and E. C. Kocher, J. Opt. Soc. Am. 60, 382 (1970).

Nolte, L. W.

L. W. Nolte and D. Jaarsma, J. Acoust. Soc. Am. 41, 497 (1967).

Peterson, W. W.

W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).

Pirenne, M. H.

S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Raab, D. H.

B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).

Sakitt, B.

B. Sakitt, J. Physiol. 223, 131 (1972).

Shlaer, S.

S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Siegel, S.

S. Siegel, Nonparametric Statistics (McGraw-Hill, New York, 1956).

Swets, J. A.

W. P. Tanner, Jr. and J. A. Swets, Psychol. Rev. 61, 401 (1954).

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Tanner, Jr., W. P.

W. P. Tanner, Jr., Ann. N. Y. Acad. Sci. 89, 752 (1961).

W. P. Tanner, Jr. and J. A. Swets, Psychol. Rev. 61, 401 (1954).

W. P. Tanner, Jr. and R. Clark Jones, in Visual Research Problems, edited by A. Morris and E. P. Horne, Armed Forces NRC Committee on Vision (NAS-NRC Publication No. 712, Washington, D. C., 1960).

W. P. Tanner, Jr., D. Main, and T. E. Cohn, in Current Developments in Optics and Vision, edited by W. Benson and M. Whitcomb, (NAS-NRC, Washington, D. C., 1968).

Taub, H. B.

B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).

Volk, W.

W. Volk, Applied Statistics for Engineers (McGraw-Hill, New York, 1969).

Other (19)

S. Hecht, S. Shlaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

B. Sakitt, J. Physiol. 223, 131 (1972).

W. P. Tanner, Jr. and J. A. Swets, Psychol. Rev. 61, 401 (1954).

W. W. Peterson, T. G. Birdsall, and W. C. Fox, IRE Trans. Inform. Theory 4, 171 (1954).

J. Nachmias and E. C. Kocher, J. Opt. Soc. Am. 60, 382 (1970).

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

B. Leshowitz, H. B. Taub, and D. H. Raab, Percept. Psychophys. 4, 207 (1968).

W. P. Tanner, Jr., Ann. N. Y. Acad. Sci. 89, 752 (1961).

W. P. Tanner, Jr. and R. Clark Jones, in Visual Research Problems, edited by A. Morris and E. P. Horne, Armed Forces NRC Committee on Vision (NAS-NRC Publication No. 712, Washington, D. C., 1960).

L. W. Nolte and D. Jaarsma, J. Acoust. Soc. Am. 41, 497 (1967).

T. G. Birdsall, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 67-08 217).

T. E. Cohn, Am. J. Opt. 49, 1028 (1972).

W. Volk, Applied Statistics for Engineers (McGraw-Hill, New York, 1969).

S. Siegel, Nonparametric Statistics (McGraw-Hill, New York, 1956).

T. E. Cohn, Thesis (University of Michigan, 1966) (Univ. Microfilms, Ann Arbor, Mich., Order No. 70-21 630).

The label "ideal" must be qualified. We infer ideal performance from the linearity of the psychometric function, not from the value of its slope. The measured slope may be smaller than that achievable.

R. FitzHugh, J. Gen. Physiol. 40, 925 (1957).

W. P. Tanner, Jr., D. Main, and T. E. Cohn, in Current Developments in Optics and Vision, edited by W. Benson and M. Whitcomb, (NAS-NRC, Washington, D. C., 1968).

T. E. Cohn and D. Lasley, Abstracts of 1974 A.R.V.O. Meeting (1974).

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