>Psychtoolbox>PsychCal

weight=ContrastMatch(device,dimWeight,[foreColor],[backColor])

Displays two gratings. The bright grating alternates white and weight*white,
producing luminances LMax and LBright.
The dim grating alternates dimWeight*white and black, producing luminances
LDim and LMin.
When the grating contrasts match, LMax/LBright=LDim/LMin.
In a more compact notation, L1/Lb=Ld/L0. We set the weight wd that produces
Ld, and the observer adjusts the weight wb that produces Lb. They are related
by the gamma function, y=g(w), where y is the normalized luminance,
y=(L-L0)/(L1-L0). We know wb and wd, and we have access to the gamma function,
so we can compute yb and yd. Solving for L, we have
L=y*(L1-L0)+L0
Our relation at match can be rewritten as
L1*L0=Ld*Lb
0=Ld*Lb-L1*L0
=(yd*(L1-L0)+L0)*(yb*(L1-L0)+L0)-L1*L0
Let’s divide by L1^2, and define r=L0/L1.
=(yd*(1-r)+r)*(yb*(1-r)+r)-r
This is a quadratic equation in r
=(yd+(1-yd)*r)*(yb+(1-yb)*r)-r
=yd*yb+(yb*(1-yd)+yd*(1-yb)-1)*r+(1-yd)*(1-yb)*r^2
c=[(1-yd)*(1-yb) yb*(1-yd)+yd*(1-yb)-1 yd*yb]; % coefficients of quadratic polynomial
r=roots(c)
The answer, r, is the desired ratio of L0/L1.

5/28/96 dgp Wrote it.
5/28/96 dgp Updated to use new GetMouse, that flushes mouse events.
8/4/96 dhb Changed name to ContrastMatch.
8/16/97 dgp Changed “text” to “theText” to avoid conflict with TEXT function.
7/19/98 dgp Removed obsolete TIMER.
6/30/03 dgp Updated Screen OpenScreen to Screen OpenWindow.