The Fourier transform \( \mathcal{F}\{f(x, y)\} \) is given by the integral:
\[
\mathcal{F}\{f(x, y)\} = \int \int f(x, y) e^{-i (k_x x + k_y y)} \, dx \, dy
\]
where \( (k_x, k_y) \) are the frequency variables corresponding to the spatial variables \( (x, y) \).
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