Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design.

We reconsider the closed form solution of the ptychographic phase problem called the Wigner Distribution Deconvolution Method (WDDM), which has remained discarded for twenty years. Ptychographic reconstruction is nowadays always undertaken by iterative algorithms. WDDM gives rise to a 4 dimensional data cube of all the relative phases between points in the diffraction plane. Here we demonstrate a novel method to use all this information, instead of just the small subset used in the original 'stepping out' procedure developed in the 1990s, thus greatly suppressing noise. We further develop a method for designing an improved probe (illumination function) to further decrease noise effects during the deconvolution division. Combining these two with an iterative procedure for the deconvolution, which avoids the usual difficulty of a divide by a small number, we show in model calculations that WDDM competes well with the modern conventional iterative methods like ePIE (the extended Ptychographical Iterative Engine).