Separation of three-dimensional scattering effects in tilt-series Fourier ptychography.

We investigate a strategy for separating the influence of three-dimensional scattering effects in tilt-series reconstruction, a method for computationally increasing the resolution of a transmission microscope with an objective lens of small numerical aperture, as occurs in the transmission electron microscope (TEM). Recent work with visible light refers to the method as Fourier ptychography. To date, reconstruction methods presume that the object is thin enough so that the beam tilt induces only a shift of the diffraction pattern in the back focal plane. In fact, it is well known that the diffraction pattern changes as a function of beam tilt when the object is thick. In this paper, we use a simple visible light model to demonstrate a proof-of-principle of a new reconstruction algorithm that can cope with this difficulty and compare it with the aperture-scanning method. Although the experiment uses a model specimen with just two distinct layers separated along the optic axis, it should in principle be extendable to continuous objects.

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).