## Predicting increment thresholds

Stiles' field sensitivities, his standard
t.v.i. template shape, and his Fechner fractions can be used
to predict how the increment thresholds for a 200 ms duration, 1-deg diameter flashed
target should depend on background intensity--for most target wavelengths (lambda) and
background wavelengths (*μ*).

Consider a graph in which log field radiance is plotted along the abscissa and log
increment threshold along the ordinate. The field sensitivities define the reciprocals of
the field radiances (in log quanta s^{-1}deg^{-2}) required to raise the
threhold of each "isolated" π-mechanism by one log
unit above its absolute threshold. Thus, for a particular field wavelength (*μ*) and a particular π mechanism, the value -log field sensitivity
fixes the horizontal position of the point on the t.v.i. template that is one log unit
above the absolute threshold (the threshold when there is no background). This point is
sometimes referred to as the field point.

The vertical position of the t.v.i. template can be estimated from the Fechner
fraction, which defines the ratio of the increment threshold to the field intensity at the
field point when the conditioning field has the same color as the test field (*μ* = *λ*). To calculate the vertical position
of the field point, find the field sensitivity of the π mechanism at the the target
wavelength (*λ*). The vertical position of the field point is then -log field
sensitivity +log (Fechner fraction).

The positions of the t.v.i. templates can be calculated in this way for all π mechanisms. At each field radiance, the π
mechanism(s) with the highest sensitivity is assumed to determine the subject's threshold.

This model is formalized in Section 7.4.2 of Wyszecki & Stiles (1982).

### References

Wyszecki, G., & Stiles, W. S. (1982). *Color Science: concepts and
methods, quantitative data and formulae*. (2nd ed.). New York: Wiley.