So take a 2D DFT for example: $$F(k,l)=\frac{1}{MN}\sum_{m=0}^{M-1}\sum_{n=0}^{N-1}{f(m,n)e^{-2\pi{i}(\frac{k}{M}m+\frac{l}{N}n)}}$$ Practically, this just means that we take a pre-set matrix of values that contains information on {$f(x_m,y_n)$} in spatial domain to compute the values of {$F(p_k,q_l)$} in frequency domain. If I know what my set of spatial coordinates {$(x_m,y_n)$} is, can I find out what my set of frequency coordinates {$(p_k,q_l)$} is?
For context, I am attempting to perform Fresnel diffraction given by: $$E(x,y,z)=\frac{e^{ikz}}{i\lambda{z}}e^{i\frac{\pi}{\lambda{z}}(x^2+y^2)}\mathcal{F}\{E(x^{'},y^{'},0)e^{i\frac{\pi}{\lambda{z}}(x^{'2}+y^{'2})}\}\\=h(x,y)\times{G(p,q)}$$ where $p=\frac{x}{\lambda{z}}$ and $q={\frac{y}{\lambda{z}}}$.
The problem here is that in order to ensure I get the correct $E(x,y,z)$, I should ensure that my $(x,y)$ matches the $(p,q)$ from the output matrix given by the DFT operation. However, I am uncertain where exactly the DFT result is defined on the frequency space. My original assumption is that it would be equivalent to the spatial coordinates in value, but I then realized that I don't have a proof for that.