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:
  

 
 

 
Calculation of Dioptric Power of a Lens:
 

 
 
Weber's Law

 

Fechner's Law

                                                S=klog(I)

Steven's Power Law
                                                S=cI^b

Reflectance

 

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:

S_r α 1/d_p 

S_p ~= k

Emmert's Law

Both of the following equations hold simultaneously:

S_r = k 

S_p α d_p

Calculation of decibels