Ferroelectric order in individual nanometre-scale crystals.

Ferroelectricity in finite-dimensional systems continues to arouse interest, motivated by predictions of vortex polarization states and the utility of ferroelectric nanomaterials in memory devices, actuators and other applications. Critical to these areas of research are the nanoscale polarization structure and scaling limit of ferroelectric order, which are determined here in individual nanocrystals comprising a single ferroelectric domain. Maps of ferroelectric structural distortions obtained from aberration-corrected transmission electron microscopy, combined with holographic polarization imaging, indicate the persistence of a linearly ordered and monodomain polarization state at nanometre dimensions.

Deterministic phase unwrapping in the presence of noise.

We present a new Fourier-based exact solution for deterministic phase unwrapping from experimental maps of wrapped phase in the presence of noise and phase vortices. This single-step approach has superior performance for images with high phase gradients or insufficient digital sampling approaching 2pi/pixel and therefore performs as a fast and practical solution for the phase-unwrapping problem for experimental applications in applied optics, physics, and medicine.