Amplitude and Phase in 2D Fourier Transforms

In this Demonstration, we take the 2D Fourier transform of a 2D Gaussian, , with standard deviation :

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The middle and right panels plot the amplitude and phase of the transformed function, , respectively. The 2D Fourier transform of a real-valued function may result in a complex-valued function. The amplitude is determined by the contribution from a certain frequency component, while the phase carries additional information on the spatial distribution.