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

 

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