Constructing a repeating array for a binary blazed diffraction grating

How can I build an array given the requirements below? The purpose of this is to construct a binary blazed diffraction grating

for an array NxM of A(i,j):

- for A(1,1), A(1,2), A(1,3) = 1 and A(1,4), A(1,5), A(1,6) = 0, repeat these 6 characters for A(1,M-5), A(1,M-4), A(1,M-3) = 1 and A(1,M-2), A(1,M-1), A(1,M) = 0.

- for A(2,1), A(2,2) = 1 and A(2,3), A(2,4), A(2,5), A(2,6) = 0, repeat these 6 characters for A(2,M-5), A(2,M-4) = 1 and A(2,M-3) A(2,M-2), A(2,M-1), A(2,M) = 0.

- for A(3,1) = 1 and A(3,2), A(3,3), A(3,4), A(3,5), A(3,6) = 0, repeat these 6 characters for A(3,M-5) = 1 and A(2,M-4), A(3,M-3), A(3,M-2), A(3,M-1), A(3,M) = 0

- Repeat the above 3 steps for N rows

i.e for a 12x12 array

    A = [1 1 1 0 0 0 1 1 1 0 0 0;
         1 1 0 0 0 0 1 1 0 0 0 0;
         1 0 0 0 0 0 1 0 0 0 0 0;
         1 1 1 0 0 0 1 1 1 0 0 0;
         1 1 0 0 0 0 1 1 0 0 0 0;
         1 0 0 0 0 0 1 0 0 0 0 0;
         1 1 1 0 0 0 1 1 1 0 0 0;
         1 1 0 0 0 0 1 1 0 0 0 0;
         1 0 0 0 0 0 1 0 0 0 0 0;
         1 1 1 0 0 0 1 1 1 0 0 0;
         1 1 0 0 0 0 1 1 0 0 0 0;
         1 0 0 0 0 0 1 0 0 0 0 0]

Answer 1

[Star Strider]

Use the repmat function:

Element = [1 1 1 0 0 0;
           1 1 0 0 0 0;
           1 0 0 0 0 0];

A = repmat(Element, 4, 2)

This takes the ‘Element’ array and duplicates it to create 4 copies vertically and 2 copies horizontally.

[Patrick Bevington]

Can you think of a way to do the same thing using loops? Initially this code will be sufficient but for my final use I will be wanting to execute the same effect but on a non symmetrically repeating units (the 'lines' constructed by the values of 1 will curve).

Thank you

[Star Strider]

My pleasure.

You could do it with loops easily enough, the easiest way being to vertically concatenate the ‘Element’ matrix with itself in the first loop, then duplicate it by horizontally concatenating the result of the first loop with itself, in the second loop.

I hesitate to write example code at this point because I don’t understand ‘(the 'lines' constructed by the values of 1 will curve)’. Can you give an example?

[Patrick Bevington]

Sorry I can see that my question was not clear, I meant can you think of a way to construct the repeating ' Element' matrix using loops?

The application of this is to make a saw toothed diffraction pattern, easy enough with a linear grating (example here, not yet sawtoothed: https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTsn5XzQAXdjDq6RffoF2yZOH_BEGAkZNqz2yEnwIzljOn1J8OV ), however I would like to do this for a forked grating (example here: https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTPyhsftJxNmhnfT2XG248q_sK0Q_kve_KLl9haWQoyqTZBLFPg ). I can provide code for creating either pattern if you think this would be helpful.

Thank you for your continued assistance.

[Star Strider]

This is much less efficient than using repmat, producing the same result:

RowRepeat = 4;
ColRepeat = 2;
Grating = [];
for k1 = 1:RowRepeat
    Grating = [Grating; Element];
end
for k1 = 1:ColRepeat-1
    Grating = [Grating Grating(:,1:size(Element,2))];
end
Grating                                                 % View Result

The code would be helpful because I have no idea what you’re doing.

If you already have the code for what you want to do, why not just use it?