$2D$ Fourier Transform of squares

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I'm trying to take the 2D Fourier Transform of the below attached image, but I'm having trouble understanding how to do this.

I know that by definition, $\text{ rect }(x/A, y/A) = \{1 \text{ for } |x| < A/2, |y| < B/2, \text{ and } 0 \text{ otherwise}\}.$

The Fourier transform of a single rect is $\text{ sinc(x) = $\frac{sin \pi x}{\pi x}$}$ the sinc function. But from here I don't see how to take the Fourier transform of this partial field of rects.

Anyone have any ideas?

enter image description here