img=;

h=KroneckerProduct[IdentityMatrix[3],{1,1,1,1}];
v=Transpose@KroneckerProduct[{1,1,1},IdentityMatrix[4]];

f[i_,j_,k_]:=If[i-j==k,Sqrt@2,0]
d1=Table[Flatten@Table[f[i,j,k],{i,1,3},{j,1,4}],{k,2,-3,-1}]

g[i_,j_,k_]:=If[i+j==k,Sqrt@2,0]
d2=Table[Flatten@Table[g[i,j,k],{i,1,3},{j,1,4}],{k,2,7}];

A=Join[h,v,d1,d2];

preImg=Flatten@ImagePartition[#,{75,56}]&@ColorConvert[img,"Grayscale"]
laser[i_]:=Mean@Flatten@ImageData[i]
m=Flatten@ArrayReshape[#,{3,4}]&@Map[laser,preImg]

img

{height,width}=(Dimensions@ImageData@img)[[1;;2]];
s1=Join[Table[0,width*27],Table[1,width],Table[0,width*28+2*width*56]];

Flatten@ImageData@ColorConvert[img,"Grayscale"].s1