Skip to main content
Log in

On the psychophysical function

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Summary

Certain mathematical principles for the phenomenological description of data are introduced and applied to establish a new psychophysical function for the sensation of brightness. This function, which is the integral of the lognormal probability density function, has the psychophysical functions of Fechner and Stevens as limiting cases. The predictions of the new function are compared with experimental evidence on the discrimination of light intensity by the human eye, and an estimate of the total number of distinct steps of brightness discrimination is determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Dolby, J. L.: A quick method for choosing a transformation. Technometrics 5, 317–325 (1963).

    Google Scholar 

  2. Fechner, G. T.: Über ein wichtiges psychophysisches Grundgesetz und dessen Beziehung zur Schätzung der Sterngrößen. Abh. k. sächs. Ges. Wissensch., Math.-Phys. Kl. 4 (1858).

  3. Fisher, R. A.: Professor Karl Pearson and the method of moments. Ann. Eugenics (= Ann. Human Genetics) 7, 303 (1937).

    Google Scholar 

  4. Hecht, S.: The visual discrimination of intensity and the Weber-Fechner law. J. Gen. Physiology 7, 235–267 (1924).

    Google Scholar 

  5. Hecht, S.: A theory of visual intensity discrimination. J. Gen. Physiology 18, 767–789 (1935).

    Google Scholar 

  6. Koenig, A., Brodhun, E.: Experimentelle Untersuchungen über die psychophysische Fundamentalformel in bezug auf den Gesichtssinn. Sitzungsber. preuss. Akad. Wissensch. 1888, 917–931; Zweite Mitteilung. Sitzungsber. preuss. Akad. Wissensch. 1889, 641–644.

  7. Pearson, K.: Contributions to the mathematical theory of evolution, I — On the systematic fitting of curves to observations and measurements. Biometrika 2, 265 (1902).

    Google Scholar 

  8. Pirenne, M. H.: Luminal brightness increments, Vol. 2, Chap. 8 of The Eye (Hugh Davson, ed.) New York: Academic Press 1962.

    Google Scholar 

  9. Steinhardt, J.: Intensity discrimination in the human eye. I: The relation of Δ I/I to intensity. J. Gen. Physiology 20, 185–209 (1936).

    Google Scholar 

  10. Stevens, S. S.: To honor Fechner and repeal his law. Science 133, 80–86 (1961).

    Google Scholar 

  11. Stevens, S. S.: Neural events and the psychophysical law. Science 170, 1043–1050 (1970).

    Google Scholar 

  12. Stiles, W. S., Wyszecki, G.: Color Science. New York: J. Wiley 1967.

    Google Scholar 

  13. Tukey, J.: On the comparative anatomy of transformations. Ann. Math. Statistics 28, 602–632 (1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Resnikoff, H.L. On the psychophysical function. J. Math. Biology 2, 265–276 (1975). https://doi.org/10.1007/BF00277155

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00277155

Keywords

Navigation