Sensitivity of human eye to luminance
From Stevens &amp; Galanter (1957)


  Although an extensive investigation of the subjective scale of
  brightness is still in progress in this laboratory, enough has been
  learned to show that, for patches of white light viewed in a dark
  room, subjective brightness is a power function of luminance.
  Moreover, the exponent is of the order of one-third which is in
  reasonable agreement with results obtained by Hanes.





Stevens, S. S., &amp; Galanter, E. H. (1957). Ratio scales and category scales for a dozen perceptual continua. Journal of Experimental Psychology, 54(6), 377.


and the related study that is mentioned:


Hanes, R. M. (1949). The construction of subjective brightness scales from fractionation data: a validation. Journal of experimental psychology, 39(5), 719.