Although Weber has given us the theory of JND for the perception of stimuli, which are the basis of the further researches in psychophysics, originally Gustav Fechner first studied the relationship between incoming physical stimuli and the responses to them.
Fechner, with a number of assumptions, generalised Weber’s findings which indicated a broader relationship between sensory and physical intensity. Fechner’s law stated that the strength of a sensation grows as the logarithm of stimulus intensity. The formula is
S = K log I
Where S is psychological (i.e. subjective)
I is stimulus intensity
K is constant
Fechner’s law makes good biological sense as our nervous system compress the huge range of sensation awareness into some manageable scope and this is what a logarithmic transformation does for us.