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Ptychography

    Ptychography is a name given to a technique invented by Hoppe (Hoppe W. (1969) Acta Cryst A25 495-501) that aims to solve the diffraction-pattern phase problem by interfering adjacent Bragg reflections coherently and thus determining their relative phase In the original formulation Hoppe envisaged that such interference could be effected by placing a very narrow aperture in the plane of the specimen so that each reciprocal-lattice point would be spread out and thus overlap with one another The name ptychography from the Greek 7rrv~ which means fold derives from this optical configuration; each reciprocal-lattice point isconvoluted with some function and thus made to interfere with its neighbours In fact measuring only the intensities of interfering adjacent diffracted beams still leads to an ambiguity of two possible complex conjugates for each underlying complex diffraction amplitude and so in its original formulation ptychography is equivalent to the well known theorem that for a finite specimen (that is one delineated by a narrow aperture sometimes known as a 'finite support') the onedimensional phase problem is soluble to within an ambiguity of 2 N, where N is the number of Fourier components that make up the specimen (Rodenburg 1989) However such ambiguities may be resolved by changing the phase profile or position of the illuminating beam in some way (Hoppe 1969) The fact that we must measure not only the intensities of the diffracted beams but also the intensities lying midway between the beams where the convoluted Bragg beams interfere is similarly an alternative statement of the Nyquist sampling theorem for components of diffracted intensity which in general have twice the frequency (in reciprocal space) of their underlying complex amplitudes
    cited fromT Plamann and J. M. Rodenburg Electron Ptychography II. Theory of Three-Dimensional Propagation Effects Acta Cryst (1998) A54 61-73 doi:101107/S0108767397010507