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I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given the distance p and the electric field of another parallel plane.

Essentially I have to implement the following equation for light propagation given in the continuous time domain as a convolution.

i_required(x,y) = i_given(x,y)*hp(x,y)

Now, my doubt is when computing this using discrete Fourier transforms.

Note the Angular spectrum function is defined only in frequency domain Hp(fx,fy). For ease of explanation sampling of i_given(x, y) is done at 1 unit in each dimension.
The steps I am doing:

  1. Take DFT2 (Discrete fourier transform along rows and columns) of given samples of i_given(x, y) and let it be I(u, v) for u,v = 1:N
  2. Sample the frequency domain of the transfer function Hp(fx, fy) at fx = u/N,fy = v/N
  3. Multiply H(u,v)I(u,v)) and take the IDFT2

What is the consequence of sampling in frequency domain (Step 2)?
Will this cause aliasing in time-domain? Ways to mitigate effects if any?

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