I'm trying to find a proper sampling grid size to avoid aliasing when modeling a point source model given by: \begin{align} pt(x, y) = \exp\left\{-j\frac{k}{2L}(x^2+y^2)\right\}\text{sinc}\left(\frac{x}{D_1}\right)\text{sinc}\left(\frac{y}{D_1}\right)\exp\left\{-\frac{x^2+y^2}{(4D_1)^2} \right\} \end{align} which is known as a Gaussian-sinc model.
I used the Wolfram Alpha to see if there is an analytic form of the Fourier spectrum of this function but there doesn't seem to exist. However, I think the sinc function term probably determines the bandwidth of the spectrum. We know that the spectrum of sinc function is a rectangle function:
\begin{align}
g(x,y) = \text{sinc}\left(\frac{x}{D_1}\right)\text{sinc}\left(\frac{y}{D_1}\right)
\leftrightarrow G(f_x,f_y)=D_1^2 \ \text{rect}(D_1 f_x) \text{rect}(D_1 f_y)
\end{align}
The bandwidth of $G(f_x,f_y)$ is $B = 1/(2D_1)$ along both x and y axis. Note that the bandwidth of the spectrum is defined as follows (from Voelz, Computational Fourier Optics, Chapter 2):
Thus, the sampling requirement of $pt(x,y)$ would be \begin{align} \delta<\frac{1}{2B}=D_1 \end{align} However, one paper using this point source model chooses $\delta=2D_1$ as the grid size. Any idea where I computed wrongly? Or, is this paper simply wrong?