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I heard once that the human eye has a logarithmic scale for luminance, e.g. to "feel" that a surface is three times as luminous compared to another, the former emits a light 8 times more powerful than the latter. Definitions are indeed vague as my memory doesn't serve me well.

Is this based on anything scientific?

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From Stevens & 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.

Fig. 1A from Stevens & Galanter (1957)

  • Stevens, S. S., & 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.
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  • $\begingroup$ actually if I'm not mistaken decibels are a logarithmic measure, so it's a power law over a logarithmic scale, right? $\endgroup$
    – Lorenzo Pistone
    Jan 16, 2014 at 22:32
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    $\begingroup$ No. decibels are indeed logarithmic, but note that the x-axis is "linear" in decibels, and the y-axis is logarithmic. So the relation between subjective estimate and luminance is linear in a log-log plot, i.e., a power-law. $\endgroup$
    – Ofri Raviv
    Jan 17, 2014 at 0:05
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This logarithmic increase in order to produce a just noticeable difference between stimuli of two different intensities is in fact a general property or the sensory system. It is known as (Weber-) Fechner's law:

Weber's law states that the just-noticeable difference between two stimuli is proportional to the magnitude of the stimuli. Gustav Theodor Fechner (1801–1887), a scholar of Weber, later used Weber's findings to construct a psychophysical scale in which he described the relationship between the physical magnitude of a stimulus and its (subjectively) perceived intensity. Fechner's law (better referred to as Fechner's scale) states that subjective sensation is proportional to the logarithm of the stimulus intensity.

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