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:
- Take DFT2 (Discrete fourier transform along rows and columns) of
given samples of
i_given(x, y)and let it be
u,v = 1:N
- Sample the frequency domain of the transfer function
fx = u/N,fy = v/N
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?