# Fourier Transform for Blazed Fork Grating

I built blazed fork grating on Mathematica and the idea of using blazed fork grating instead of normal one is to eliminate the other diffracted order. So the blazed fork grating will let only the 1st order to go through (only +1 but not -1). However, I'm still not sure if what I built is correct. So I'm trying to do Fourier Transform for that grating to see if only the first order will get through. I tried to do the following but I don't think it's right.

So the data set I used to built the blazed fork grating is called enhblazefork

and this is the function I used to do Fourier Transform:

ListLinePlot[Abs[Fourier[enhblazefork]], PlotRange -> All] However I don't see how this FT helping because I don't see if only the 1st diffracted order is going through, any thoughts?

This is the Full code for building the blazed fork grating:

R[x_, y_] := Norm[{x, y}];
th[x_, y_] :=
Piecewise[{{2 \[Pi] - ArcCos[x/Norm[{x, y}]], y >= 0}, {ArcCos[x/Norm[{x, y}]], y < 0}}];
spiral[x_, y_] := l th[x, y];

sawtooth[s_] := SawtoothWave[{-1, 1}, s/(2 *[Pi])];

contrastfunction[gratin_, contrast_, npix_] := Module[{inmax, inmin},
inmax = Max[gratin];
inmin = Min[gratin];
scaledinitial = ((gratin - inmin) (npix - 1))/(inmax - inmin);
scaledcontrast = scaledinitial contrast;
shifted = scaledcontrast - 127 (contrast - 1);
shifted = Clip[shifted, {0, npix - 1}];
shifted];

nx = 1024;
ny = 768;
(*nx = 100;
ny = 100;*)

l = 4;
tilt = -200;
contrast = 3;
ampfork := Monitor[
Table[Re[E^(I (spiral[x, y] + tilt 2 \[Pi] x/2))], {x, -1, 1, (
1 - (-1))/(nx - 1)}, {y, -1, 1, (1 - (-1))/(ny - 1)}], N[x]];
blazefork :=
Monitor[Table[Re[sawtooth[spiral[x, y] +tilt 2 \[Pi] y/2]], {x, -1, 1, (1 - (-1))/(nx - 1)}, {y, -1, 1, (1 - (-1))/(ny - 1)}], N[x]];

• Are you looking for help interpreting the results, or with the model you built? Either way you're going to have to include some more code, or data. – N.J.Evans Jun 27 '16 at 20:23
• Just with doing FT for the data, I added the code for building the blazed fork grating. – Alaa Jun 27 '16 at 20:35