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In signal and image processing theory, it is known that taking the Fourier transform of a zero-padded image gives the oversampled Fourier transform of the image. And that oversampling is a necessary condition for there to be a unique solution to the phase retrieval problem (i.e. the problem of recovering an image from the magnitude of its Fourier transform).

It appears that the same principle is in play in Coherent Diffraction Imaging, i.e. see Miao et al. (http://journals.iucr.org/d/issues/2000/10/00/ba0041/ba0041.pdf), which discusses the role of oversampling. Here it appears that the role of zero-padding is played by the 'empty space' around the specimen to be imaged.

However, it also appears that there is light passing through the empty space that will reach the detector. Thus, I don't understand how this can play the role of zero-padding.

I would be very grateful for any assistance in understanding this. Thank you very much.

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It is a fancy way of saying that when you are sampling a continuos function the sampling rate is to be at least the Nyquist rate by the Shannon Whittaker theorem.

The oversamplig is beyoung the Nyquist rate, which can also create issues.

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