You have two sets of (x,y) coordinates that represent the beam paths. Now if they two sets shared the same x coordinates, finding the difference in the paths would be as simple as subtracting corresponding y points
ydiff = y2-y1;
But if the x coordinates for the two data sets are different, you cant just do that because, for example, you can't subtract the y value for x = 1.5 cm from the other beams value that might be at 1.7 cm.
So you have to take one data set and estimate what its values would be if it had the same x values as the other. That's what the interp1 does
Vq = interp1(X,V,Xq)
X and V are the arrays containing the coordinates of one beam, Xq is an array containing the x coordinates of the OTHER beam, and Vq is the interpolated Y values that line up with the first x coords that you can use to find the difference.
say you have two data sets 1 and 2 with coordinates in arrays X1 Y1 and X2 Y2. If X1 is not identical to X2, then to find the difference...
X1 = [1 3 5 7 9];
Y1 = [10 14 18 22 26];
X2 = [2 4 6 8 10];
Y2 = [14 20 26 32 38];
Yint = interp1(X1, Y1, X2);
difference = Y2-Yint;
plot( X1,Y1,'-o', X2,Y2,'-o', X2,difference,'-o');
