Highest frequency component in 2D Fourier transform
Note that the terms $e^{j\omega_in_i}$ in the formula of the Fourier transform are $2\pi$-periodic. Consequently, the Fourier transform $H(\omega_1,\omega_2)$ is also periodic in both dimensions with period $2\pi$. If we choose $\omega=0$ as the center of our fundamental interval (as shown in the figure), the fundamental interval extends from $-\pi$ to $\pi$. The frequency $\omega=\pi$ is referred to as the Nyquist frequency, and it corresponds to the maximum possible frequency of a discrete signal.