Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

Locating atoms with higher precision: Two major problems that limit the resolution and interpretation of electron microscopy images are lens aberrations and multiple scattering. Chen et al. overcame these issues with ptychography, a technique that uses coherent scattering and multiple overlapping illumination spots to reconstruct an image from far-field diffraction patterns. This method works at a resolution that is limited, not by optics, but rather by the scattering strength of the sample, so it can work better with thicker samples. The authors achieved ultimate lateral resolution better than the thermal vibration of atoms in a PrScO ₃ sample and showed that it is theoretically possible to identify single dopant atoms. Science , abg2533, this issue p. 826

We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored.