<p>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 <a href="http://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law" rel="nofollow">(Weber-) Fechner's law</a>:</p>

<blockquote>
  <p>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. <strong>Fechner's law (better referred to
  as Fechner's scale) states that subjective sensation is proportional
  to the logarithm of the stimulus intensity</strong>.</p>
</blockquote>

CC BY-SA 3.0
2014-01-16T21:45:56.027Z
2014-01-16T21:45:56.027Z
Ana
<p>From Stevens &amp; Galanter (1957)</p>

<blockquote>
  <p>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, <strong>subjective brightness is a power function of luminance</strong>.
  Moreover, <strong>the exponent is of the order of one-third</strong> which is in
  reasonable agreement with results obtained by Hanes.</p>
</blockquote>

<p><img src="https://i.sstatic.net/L3PrH.png" alt="Fig. 1A from Stevens &amp; Galanter (1957)"></p>

<ul>
<li>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.</li>
</ul>

<p>and the related study that is mentioned:</p>

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

CC BY-SA 3.0
2014-01-16T22:32:45.843Z
actually if I'm not mistaken decibels are a logarithmic measure, so it's a power law over a logarithmic scale, right?
Lorenzo Pistone
CC BY-SA 3.0
2014-01-17T00:05:28.227Z
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.
Ofri Raviv
CC BY-SA 3.0
2014-01-16T13:59:44.873Z
2014-01-16T13:59:44.873Z
Ofri Raviv
<p>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.</p>

<p>Is this based on anything scientific?</p>

<neuroscience><vision><color>
Sensitivity of human eye to luminance
Lorenzo Pistone
# Sensitivity of human eye to luminance

(Asked by: username_0 on 2014-01-16)

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?

**Tags:** neuroscience, vision, color


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## 2 answers

### Answer by username_2 on 2014-01-16. Score: 6 | Accepted answer

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)](https://i.sstatic.net/L3PrH.png)

* 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.

> **Comments:**
> **username_0**: actually if I'm not mistaken decibels are a logarithmic measure, so it's a power law over a logarithmic scale, right?  
> **username_2**: 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.  

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### Answer by username_1 on 2014-01-16. Score: 2

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](http://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_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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