Psychophysical Interface Thresholds (plume and landscape) Judgments of visual air quality Value assessment
Dec 21, 2015
Psychophysical Interface
Thresholds (plume and landscape) Judgments of visual air quality Value assessment
fxNNNN
N bmbm 2cos22
The mean square radiance associated with the above equation can be shown to equal
where m is the modulation contrast, m=(Nm-Nb)/(Nm+Nb), is the average image
radiance, and (1/2) is the mean square radiance fluctuation.
22222/1 NmNN
N22 Nm
Modulation Contrast (mean square radiance is the relative psychophysical variable)
More complicated one-dimensional images can be represented as weighted sums of light and dark bars of various frequencies and intensities. Mathematically,
where Nr(x) is the one dimensional image radiance
field at an observer image distance r, ao is the
average image radiance, , and an are the
weighting factors associated with various sinusoid frequencies n2πfo. The second term, , is
the modulation of average image radiance ao.
xfinn
onnor
oeaaxN 2
,
N
xfinn
onn
oea 2
,
Superposition Principle
Equivalent Contrast
The mean square radiance associated with the above equation yields
Comparison of two mean square radiance equations suggests that the second term in each of these equations can be set equal to each other to yield
and
222n
nor aaN
2222/1 nn
aNm
N
amC
nn
eq
22
Modulation Transfer Function
The effect of an increase in atmospheric aerosol concentration on a complex scene is
xnfin
nror
oeaTNTaxN 2
The modulation contrast of any sinusoid is then
ron NTaTam /
If the change in scene equivalent contrast is a result of addition or subtraction of atmospheric aerosol, initial and final contrast are related to each other by
where Mtf is the atmospheric modulation
transfer function given by
itff CMC
TaNM
ortf /1
1
Transfer of Equivalent Contrast
2222 iTif CkCCC
The quadratic detection model stated
mathematically:
Quadratic Detection Model
where
of aC /2
Thresholds vs Judgments of Visual Air Quality
Perceived Visual Air Quality (PVAQ) Visual Air Quality Index (VAQI) Scenic Beauty Estimate (SBE)
Value Assessment of Visual Air Quality
Willingness to pay Utility function (time and dollars) Importance value Visual air quality and behavior Etc.