## Equations for Sensation and Perception

Linear Interpolation for determining threshold:

Method of Constant Stimuli

 Threshold= (50%-Lower%)* (UpperVal-LowerVal) (Upper%-Lower%) +LowerVal

Forced-Choice Method

 Threshold= (75%-Lower%)* (UpperVal-LowerVal) (Upper%-Lower%) +LowerVal

Calculations Related to Measurements of Visual Intensity:

 Reflectance = Luminance   Illuminance

 Contrast Ratio= Luminance_Max  Luminance_Min

Calculation of Dioptric Power of a Lens:

 Diopters (D) = 1                       Focal Distance (m)

Weber's Law

 k = DI          I

Fechner's Law

S=klog(I)

Steven's Power Law
S=cIb

Reflectance

 Reflectance = Luminance   Illuminance

Contrast Ratio

 CR = Lmax _____________     Lmin

Conversion from Cycles/Screen to Cycles/Deg

• Step 1 Develop Conversion Ratio (CR):
• CR = (Known Cycles/deg)/(Known Cycles/Screen)
• e.g. for the demonstration in class: standard = 3 cycles/deg & setting 128 cycles/screen on my monitor
• CR = 3/128
• Step 2: Conversion
• Multiply your mean results by this value.
• You can only do those results from a given screen.  If you change monitors, you will need a new CR for the screen values from that monitor.

Calculating Perceived Distance

Relative Distance = (ViewingDistance*Disparity)/InterpupillaryDistance (all units should be mm)

Actual Distance = ViewingDistance-RelativeDistance

Size Constancy

Both of the following equations hold simultaneously:

Sr α 1/dp

Sp ~= k

Emmert's Law

Both of the following equations hold simultaneously:

Sr = k

Sp α dp

Calculation of decibels